"l HESIS

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A METHOD FOR PREDICTION OF SEATED SPINAL
CURVATURES

presented by

SAMUEL THOMAS LEITKAM

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A METHOD FOR PREDICTION OF SEATED SPINAL CURVATURES
By

Samuel Thomas Leitkam

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Engineering Mechanics

2010

ABSTRACT
A METHOD OF PREDICTION OF SEATED SPINAL CURVATURES
By
Samuel Thomas Leitkam

The purpose of this research was to determine if lumbar curvature could be
quantified by using only measurements made on the anterior portion of the body. To do
this, 31 subjects were tested in four static seated positions as well as dynamic seated
postures using a motion capture system. Anterior measurements were used to quantify
the relative positions of the ribcage and pelvis in a measure called “openness angle”.
Posterior measurements of the lumbar curvature were quantified in a measure called
“lumbar angle”. The relationship between the openness angle and the lumbar angle was
evaluated using a linear model and a second-order polynomial model for both the static
positions and the dynamic postures.

The relationship between the openness angle and the lumbar angle is fit well by
both the linear model and the polynomial model in both the static and dynamic cases.
Predictions of static lumbar angles of a population developed from linear and polynomial
models from a separate population were found to be statistically indistinguishable from
the actual lumbar angles. Subject specific predictions of static lumbar angles were also
found to be indistinguishable from actual lumbar angles when the subjects’ dynamic
models were used for prediction.

These results show reliable predictions of lumbar curvature are possible in static
postures by using openness angle in conjunction with a previously determined first or

second order calibration model.

This thesis is dedicated to my family in every form it takes.

iii

ACKNOWLEDGEMENTS

I’d like to acknowledge the many people who made this possible. First and
foremost, I’d like to thank the subjects who volunteered their time and without whom
there would be only be theory. I’d also like to thank my advisor, Dr. Tamara Reid Bush,
for giving me the opportunity, balancing the perfect amount of patience and pressure, and
for all of the guidance and advice along the way.

In addition, I’d like to thank my family, friends, and best friend for their infinite
support and keeping me attached to reality. I’d like to thank my committee members, Dr.
Joseph Vorro and Dr. Neil Wright, for lending me their time and advice so that this thesis
could evolve into a far more complete, polished and precise piece of work than it was
when I first thought I was done. Lastly, I’d like to thank Brad Rutledge, Katie
Friederichs, Trevor Deland, and everyone else in the Biomechanical Design and Research

Lab for all of their help. Thank you all.

iv

TABLE OF CONTENTS

INTRODUCTION ............................................................................................................... 1
LITERATURE REVIEW .................................................................................................... 4
Technology ..................................................................................................................... 4
Standing vs. Seated ........................................................................................................ 7
METHODS .......................................................................................................................... 9
Data Collection .............................................................................................................. 9
Subject pool ................................................................................................................. 9
Anatomical measures ................................................................................................ 10
Markers and motion tracking .................................................................................... 11

Test conditions ........................................................................................................... 1 5
Static positions .......................................................................................................... 15
Continuous motion .................................................................................................... 17
Analysis ........................................................................................................................ 19
Hip joint center .......................................................................................................... l9
Lumbar angle ............................................................................................................ 22
Statistical Analysis Methods ....................................................................................... 25
Distinct static positions ............................................................................................. 25
Anthropometric correlation to openness/lumbar angle slope ................................... 26
Predictive capacity .................................................................................................... 27
RESULTS .......................................................................................................................... 31
Openness and Lumbar Angles ................................................................................... 31
Distinct Static Positions .............................................................................................. 33
Relationship between Openness and Lumbar Angles .............................................. 34
Static .......................................................................................................................... 34
Dynamic .................................................................................................................... 42
Anthropometric Correlation to Openness/Lumbar Angle Slope ............................ 53
Predictive Capacity ..................................................................................................... 54
Static data predicting static positions for test population ......................................... 54
Dynamic data predicting dynamic positions for the test population ........................ 56
Static data predicting dynamic positions for the test population .............................. 59
Dynamic data predicting static positions for the test population ............................. 62
Static data predicting dynamic positions within a subject ........................................ 65
Dynamic data predicting static positions within a subject ....................................... 66
DISCUSSION AND CONCLUSIONS ............................................................................. 67
Openness and Lumbar Angles ................................................................................... 67
Distinct Static Positions .............................................................................................. 69
Observations between openness and lumbar angles ................................................ 7O
Static .......................................................................................................................... 7O

Dynamic .................................................................................................................... 72

Anthropometric Measures Related to Slope ............................................................. 73
Predictive Capacity ..................................................................................................... 73
Static data predicting static positions for the test population ................................... 74
Dynamic data predicting dynamic positions for the test population ........................ 74
Static data predicting dynamic positions for the test population .............................. 75
Dynamic data predicting static positions for the test population ............................. 75
Static data predicting dynamic positions within a subject ........................................ 76
Dynamic data predicting static positions within a subject ....................................... 77
APPENDIX ....................................................................................................................... 84
Al. Subject Questionnaire ......................................................................................... 84
A2. Individual Subject Measurements ..................................................................... 86
A3. Calibration Measurements ................................................................................. 87
A4. Lumbar radius calculation ................................................................................. 88
A5. Dynamic Openness and Lumbar Angles (deg) ................................................. 92
BIBLIOGRAPHY ........................................................................................................... l 17

vi

LIST OF TABLES

Table 1. Height, weight, and age of the subjects ................................................................. 9
Table 2. Height, weight, and age of the subjects as divided by gender .............................. 9
Table 3. Subject seated dimensions and pelvic dimensions (all values in cm) ................. 11
Table 4. Static openness angles for each subject at each posture ..................................... 31
Table 5. Static lumbar angles for each subject at each posture ......................................... 32

Table 6. Dynamic maximum, minimum, and range values for openness and lumbar

angles ................................................................................................................................. 33
Table 7. Probabilities that each pair of positions is the statistically the same as determined
by a paired t-test ................................................................................................................ 33
Table 8. Slope, linear r2 and polynomial r2 values for each subject as determined by best

fit line ................................................................................................................................ 41
Table 9. Summary table of slope, intercept and r2 for 15 dynamic subjects ..................... 47

Table 10. Pearson Product Moment Correlation Coefficients for Slope vs. each
anthropometric measure .................................................................................................... 53

Table l 1. Paired t-test values comparing predicted dynamic lumbar angles vs. actual
lumbar angles for a prediction model based off the same subject’s static data ................ 65

Table 12. Paired t-test values comparing predicted static lumbar angles vs. actual static
lumbar angles for a subject prediction model based off of the same subject’s dynamic
data .................................................................................................................................... 66

Table 13. Prediction methods summary table ................................................................... 78

vii

LIST OF FIGURES

Figure 1. Motion capture data collection configuration with global coordinate system
and origin shown ............................................................................................................... 12

Figure 2. Retroreflective markers applied to the posterior at C7, T12, MidPSIS while
standing erect with additional markers spaced approximately 3cm apart between C7
and MidPSIS ..................................................................................................................... 13

Figure 3. Retroreflective markers applied to the subject’s anterior and lateral sides ....... 14

Figure 4. Basic posture assumed by the subject with head over pelvis, feet flat on
floor, and gaze forward ..................................................................................................... 15

Figure 5. Static postures assumed by the subjects. Clockwise from top left: Maximum

Lumbar Lordosis, Maximum Lumbar Kyphosis, “Straight and Tall”, “Comfortable” ..... 17
Figure 6. Diagram of the “openness” angle as calculated fi'om the positions of HJC,
ASIS, Stemum marker and C7 .......................................................................................... 22
Figure 7. Calculation diagram for circumradius and lumbar angle ................................... 24
Figure 8. Diagram of the lumbar angle as calculated from the positions of T12, LU,

and Mid-PSIS .................................................................................................................... 25
Figure 9 (a-ee). Openness Angle vs. Lumbar Angle for each individual subject using
static postures with included linear and second order polynomial best fits ...................... 34
Figure 10 (a,b). a) Linear best fit plots for subjects 1-15 .................................................. 40

Figure. 11 (a-o). Openness Angle vs. Lumbar Angle for each individual subject using
static postures with included linear and second order polynomial best fits ...................... 42

Figure 12 (a-o). Dynamic and Static data plotted as Openness vs. Lumbar Angle for
each subject with sufficient dynamic data ......................................................................... 48

Figure 13. Graphical representation of linear predictive model developed from the
static openness and lumbar angle data of subjects SOl-Sl6 ............................................. 54

Figure 14. Predicted static lumbar angle values compared to actual static lumbar

angle values for linear static model applied to the openness angles of subjects 817-
S31 ..................................................................................................................................... 55

viii

Figure 15. Graphical representation of polynomial predictive model developed from
the static openness and lumbar angle data of subjects SOl-Sl6 ....................................... 55

Figure 16. Predicted static lumbar angle values compared to actual static lumbar

angle values for polynomial static model applied to the openness angles of subjects
S 1 7-831 ............................................................................................................................. 56

Figure 17. Graphical representation of linear predictive model developed from the
first eight subjects in the dynamic data group ................................................................... 57

Figure 18. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for linear dynamic model applied to the openness angles of the
last seven subjects in the dynamic data group ................................................................... 57

Figure 19. Graphical representation of polynomial predictive model developed fi'om
the first eight subjects in the dynamic data group ............................................................. 58

Figure 20. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for polynomial dynamic model applied to the openness angles of
the last seven subjects in the dynamic data group ............................................................. 59

Figure 21. Graphical representation of linear population predictive model developed
from all of the static openness and lumbar angle data ...................................................... 60

Figure 22. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for linear static population model applied to the openness angles
of the entire dynamic data group ....................................................................................... 60

Figure 23. Graphical representation of polynomial population predictive model
developed from all of the static openness and lumbar angle data ..................................... 61

Figure 24. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for polynomial static population model applied to the openness
angles of the entire dynamic data group ............................................................................ 62

Figure 25. Graphical representation of linear population predictive model developed
from all of the dynamic openness and lumbar angle data ................................................. 62

Figure 26. Predicted static lumbar angle values compared to actual static lumbar
angle values for linear dynamic population model applied to the openness angles of
the entire static data group ................................................................................................ 63

Figure 27. Graphical representation of polynomial population predictive model
developed from all of the dynamic openness and lumbar angle data ................................ 64

ix

Figure 28. Predicted static lumbarangle values compared to actual static lumbar
angle values for polynomial dynamic population model applied to the openness
angles of the entire static data group ................................................................................. 65

Figure 29. Diagram for radius calculation ....................................................................... 88

ASIS

C7

Qt

name

HJ C

IVD

LBP

LU

MidPSIS

MRI

—.

P

PD

LIST OF SYMBOLS AND ABBREVIATIONS

distance between MidPSIS and T12 lumbar markers
Anterior Superior Iliac Spine

distance between MidPSIS and LU lumbar markers
distance between T12 and LU lumbar markers

seventh cervical vertebra

global position vector of marker “name”

Hip Joint Center

Intervertebral Disc

local pelvis depth vector
local pelvis depth unit vector
local pelvis height vector
local pelvis height unit vector
local pelvis width vector

local pelvis width unit vector

Lower Back Pain

most eccentric lumbar marker

Midpoint between the right and lefi PSIS
Magnetic Resonance Imaging

Pelvis vector

Pelvic Depth

xi

PH
PSIS

PW

Qname

T12

"It

name

Pelvic Height
Posterior Superior Iliac Spine

Pelvic Width
translated and rotated global position vector of marker “name”

radius of calculated lumbar semicircle

Ribcage vector

twelfth thoracic vertebra

translated global position vector of marker “name”

lumbar angle

YZ-plane rotation angle

openness angle

xii

INTRODUCTION

Lower back pain (LBP) is a widespread and costly problem that results in
significant compensation claims and lost time at work. Several studies have shown that
the problem is prevalent in across different populations around the world and across
many different types of industry including, but not limited to, helicopter pilots, tractor
drivers, bus drivers, factory workers, commercial travelers, dental hygienists and steel
industry workers [1, 2].

This high prevalence of LBP can become costly for society [3]. A large part of
this cost comes from workers compensation claims alone [4]. However, it is not limited
to just the compensation cost. In Great Britain, in 1998, 1632 million pounds were spent
covering medical care associated with LBP including physiotherapists, hospital costs,
medication, community care, and radiology [5]. In the US, the figures are even more
staggering: The National Institute for Occupational Safety and Health (N IOSH)
estimates that low back pain costs American industry $14 billion dollars annually [6].

This back pain can be linked to seating [3, 7, 8]. It has been shown that people
who had jobs that required durations of static postures, such as being in a static seated
position, were more likely to develop back pain [9]. Researchers have tested many
hypotheses for the cause of lower back pain, ranging from reduced blood flow in the
region and reduced exercising of the intervertebral discs (IVD) to increased pressure and
forces in the ND and forces in the zygapophysial joints [10]. While the results are often
inconsistent, the constant through the research is that extended periods of static posture

are unhealthy for the lower back.

However, static postures are not the only option while seated. It has been shown
that a dynamic posture can be good for the body. Research has shown that a dynamic
posture can decrease vertebral disc degeneration over time [8]. Similarly, it has also been
shown that rotational body dynamics can have a positive influence the subject’s LBP
[l 1]. It is presumed that this is due to the increase in movement of the fluid into and out
of the avascular IVDs. Other research has shown that this increased activity should occur
in moderation as LBP occurs from not only low levels of back activity but also high
levels of back activity [2, 12].

Knowing this, it then becomes important to assess measures to prevent LBP by
ways of promoting healthier, dynamic postures. It has been suggested that dynamic
chairs offer potential advantage over simple static chairs [7]. Whereas simple chairs
support one static posture, dynamic chairs offer the possibility of supporting a wide range
of postures with a single chair. However, to confirm this, researchers need to understand
how the spinal curvature changes as people move through a full range of spinal
articulations. Once researchers understand this motion pattern, engineers can begin to
design for dynamic motions of a seat that will accommodate a range of anthropometry.

The problem then becomes measuring the human in a dynamic seat without
changing the human/seat interface. Understanding of the human/seat interface is crucial
to gaining a full knowledge of healthy and unhealthy seating. Of specific importance is
understanding and quantifying the change in spinal curvature with different seated
positions. Currently, there is no scientifically accepted research that addresses a means to
predict posterior human spinal curvatures over a comfortable range of motion while the

human’s back is obscured by a seatback.

Therefore, the purpose of this research was to determine if a relationship exists
between physical structures of the body that can be measured with anterior markers and

sagittal plane lumbar curvature. To address this, four distinct goals were formed:

1. A relationship exists between anterior body measurements and posterior
curvatures, determined through four unique seated static postures.

2. A relationship exists between anterior body measurements and posterior
curvatures, determined through a dynamic range of seated motion.

3. The relationship between the anterior measurements and posterior lumbar
curvatures identified in the static postures holds true for the dynamic range of motion in
the same seated environment.

4. The relationship between the anterior measurements and posterior lumbar
curvatures identified in the dynamic range of motion holds true for the static postures in

the same seated environment.

LITERATURE REVIEW

A vast amount of research has been conducted on the human spine. The spine has
been studied in many cases as site of discomfort or failing health [13-16], ergonomics
[17, 18], the study of balance [19], gait analyses [20], predictive modeling [19, 21-23],
and spinal stability [19, 21]. Back and spine research employs many different methods to
accomplish these quantifications including radio graphs, magnetic resonance imaging
(MRI), inclinometers, and three—dimensional (3D) motion capture amongst others [17, 24,
25]. While there are many ways to investigate the spine, each has its own associated

benefits and drawbacks.

Technology

The use of radiographs, which have been used as far back as 1957 [26], is the
most prevalent method used in spinal research. It is still widely used today as a method
to determine the position of each vertebra, particularly in a sagittal plane [13, 27-29].
Radiographs are sometimes preferred because of the precision of measurement of
positions of the vertebrae in living human subjects. However, the drawbacks are that the
positions must be taken statically, and it requires the subject be exposed to radiation.

MRI’s are also commonly used to determine the relative positions and
orientations of the vertebrae. MRI’s have the added benefit being able to reconstruct 3D
images so any plane, sagittal or otherwise can be viewed. This too, has been used by
several studies [30-32]. However, in large part this too has the drawback of only being

able to produce static images. There are MRI machines capable of capturing dynamic

data of a vertically supported subject, but they are expensive and not widely available.
In addition, the space inside most MRI machines is limited, restricting the range of
motion and positions that can be measured.

Another common source of spinal measurement data comes from the use of an
inclinometer. Several studies use this, primarily as a means to quantify the sacral angle
[33, 34]. This has the benefit of being a quick, non-invasive measure that can be
performed on live subjects. However, it has been shown by Bierrna et a1. [3 5] that these
measurements do not concur with radiographic data. They showed that the mean
difference between sacral inclination angle as measured by inclinometer and a radiograph
was 23.12 degrees with a standard deviation of 8.56 degrees. In addition, inclinometer
measurements must be taken statically, and require access to the subject’s back by the
researcher.

Three dimensional (3 D) motion capture is another data collection method that
presents its own set of benefits and drawbacks. By using cameras that track spherical
shaped markers attached to the subject, this method presents the opportunity to collect
continuous positional data that is non-invasive, making it the choice of several spinal
researchers [14, 19, 36-38]. Criticisms of this method arise because the markers must be
applied to the skin over the spinous processes of the vertebrae and are therefore subject to
shifting of the skin over the bony landmark. This problem is common to all motion
capture data collection.

However, several studies have shown that the relative movement between the
markers placed on the skin and the position the spinous process through ranges of

movement is minimal on the spine [30, 39]. Using sets of markers attached to both the

skin and the vertebrae at the level of T12, Stinton et a1. [40] showed that the maximum
difference in measured rotation angles between the skin and bone markers was 1.4
degrees, while the average was 0.4 degrees. This was over a range of flexion motion of
14.4 degrees.

Additionally, Morl and Blickhan [30] used MRI with markers affixed over the L3
and L4 vertebrae to show that there is a strong linear relationship (O.9l6<r<0.993,
p<0.000l) between the position of the spinous process and corresponding marker through
several seated postures.

Although 3D motion capture has many benefits, if one is interested in studying
spinal articulation in a seated position, the motion system presents a unique challenge. In
order for a marker to be tracked, there must be a clear line of sight between it and the
cameras. In a seated enviromnent, a seatback creates an obstruction that occludes the
view of markers on a subject’s back therefore making the markers immeasurable.
Therefore, in order to directly measure the subject’s back in a seated environment with
this method the seat must either not have a back, or have a back that has been specifically
designed for the lab environment. Because these direct methods cannot be effectively
and consistently applied to understanding the interface between a subject’s back and
seatback of many different commercially available chairs, this research seeks to develop
a method to infer the measurements of the back by establishing a correlation to anterior

measurements that can easily be obtained with 3D motion capture.

Standing vs. Seated

A majority of the literature discusses measuring and quantifying spinal curvature
in a standing position. For example, in a standing position, several studies have been
conducted to establish a normative database of lumbar spine ranges of motion [33, 41].
Guangyan Li and Peter Buckle composed an overview paper of many of the posture-
based techniques used prior to 1999 [34] including pen-and-paper based methods, video-
taping computer based observational methods and direct methods such as goniometers
and inclinometers.

However, while many have investigated standing postures there are only a limited
few studies that actually address seated spinal curvatures. Of particular note there were
studies by Black [36], Walsh [3 8], and Dunne [17]. This group of researchers studied the
various effects of spinal curvatures and the ways in which to quantify it.

The research by Black et al. [36] used 4 distinct seated positions to determine the
effect of posture on the cervical spine. They showed that lumbar posture could be
correlated to the movements of the cervical spine. While Black’s particular research
focused on the cervical region of the spine, it provided a precedent for techniques to be
used in the current study. This research established the ability to correlate positions of
the lumbar spine to positions elsewhere in the body.

Walsh et al. [3 8] performed research in 2006 that employed motion capture data
of the thoracic and lumbar spine to develop a single variable threshold model of the
spine. This model was used to determine posture based on overall flexion of the spine.
They found that the best indicator of total posture was the vector from the fourth lumbar

vertebra to the seventh cervical vertebra. This method was then used by Dunne et a1. [17]

in 2007 to verify a wearable method of posture monitoring. In relation to the current
study, this showed that a single variable model can be used to determine a relationship
about the spine. The current research seeks to expand upon the findings of Black, Walsh
and Dunne to determine a relationship as it not only relates to posture, but to the
curvature of the lumbar region of the human back.

Several other works, though not necessarily concerning specifically to seated
spinal curvature, also had a distinct influence on the experimental design of the current
research discussed here.

Janik et a1. [29] showed that the lumbar spine can be well fit by an ellipse. To
accomplish this, they used digitized standing radiographs of 50 healthy individuals. By
measuring the positions of the superior and inferior posterior margins of the bodies of the
lumbar vertebrae, they were able to fit approximately 85 degrees of an ellipse to the
lumbar spine, from the inferior margin of twelfih thoracic vertebra to the superior margin
of first sacral vertebra. The accuracy produced was a least squared error of 1.2 mm per
point along the path. The methods produced by this group were slightly modified for use
in the current research.

When modeling the lumbar spine, researchers have considered the ribcage to act
as a rigid body [19, 22]. The assumptions made are that the movements of the thoracic
vertebrae are minimal when compared to the movements of the lumbar vertebrae and
have little influence on the movement of the lumbar spine. These assumptions were also

adopted by the current study.

METHODS

Data Collection
Subject pool

Participants for this study were young healthy adults free of back pain or spinal
injuries. Following the subject’s written consent (lRB# 06-764), a questionnaire (Al)
was administered verbally to the subjects to assure each was healthy and lacking obvious
physical ailments that would preclude them from the study. A total of 31 subjects, 16
female and 15 male, were tested with an average age of 23.4 years (1.9 years) . The
average height and weight of the subjects was 1.68m (0.11m) and 663 N (151 N)
respectively. Table 1 and Table 2 show the ranges and distributions for these data. A
table with these data for each subject can be found in the appendix (A2).

Table 1. Height, weight, and age of the subjects

Height (cm) Weight (N) Age (years)
Total Total Total
Min 150 400 20
Max 185 1000 27
Average 168 663 23.4
SD 10.8 151 1.9
Table 2. Height, weight, and age of the subjects as divided by gender
Height (cm) Weight (N) Age (years)
Female Male Female Male Female Male
Min 1 50 1 65 400 609 20 20
Max 175 185 814 1000 26 27
Average 160 177 562 771 23.1 23 .7
SD 7.8 5.3 101 118 1.9 1.9

Anatomical measures

A variety of additional anthropometric measures were taken including seated
height, seated buttocks width, pelvic width, pelvic height, and pelvic depth. These
measures were used to quantify the physical characteristics of each of the subjects and the
subject pool in general. The method for collection of each of these measurements is
described below.

0 The seated height was taken with the subjects sitting on a stool with their
backs against a wall. The seated height was then measured as the distance
from the top of the seat pan to the top of their head.

0 The seated buttocks width was measured using anthropometers at the widest
part of the hips while the subject was seated.

o Pelvic width was measured as the lateral distance between the subject’s left
and right anterior superior iliac spines (ASIS) in a standing position.

0 Pelvic depth was measured as the anterior to posterior distance between the
subject’s right A818 and right posterior superior iliac spine (PSIS) in a
standing position.

0 Pelvic height was measured as the inferior to superior distance between the
subject’s pubic symphysis and his/her right ASIS in a standing position.

A summary of these data can be seen in Table 3 while subject specific data can be

found in the appendix (A2).

10

Table 3. Subject seated dimensions and pelvic dimensions (all values in cm)

Seated
Seated Buttocks Pelvic Pelvic Pelvic
Height Width Width Height Depth
Min 29 30.5 20 5.5 11.5
Max 37 46 28 12.5 19.5
Average 33.9 37.4 23.3 8.4 15.1
SD 2.00 3.19 1.91 1.78 1.93

Markers and motion tracking

After all anthropometric measurements were gathered, retroreflective motion
tracking markers were applied to each subject so that 3D motion data could be captured
during the testing process. The motion system used was a 6 camera Qualisys Motion
Tracking System (Gothenburg, Sweden) with marker sizes of 13mm and 19mm in
diameter. The 13mm markers were used on the subject’s back to allow for the highest
possible density of markers to be distinguished given the limitations of the system. The
19mm markers were used on the subject’s anterior to reduce the possibility that the
markers could be obscured by clothing or excess skin. All data were captured at 30 Hz.

A global Cartesian coordinate system was established within the testing space as
defined by the motion tracking software. The origin of the system was chosen during
calibration of the system to be the left posterior corner of the stool’s seat. The orientation
of the coordinate system was arranged such that the X-axis was oriented horizontally
from subject left to subject right; the Y-axis was oriented horizontally from posterior to
anterior; and the Z-axis was vertical from inferior to superior. The coordinate system
was the same for all subjects. A calibration of the system was performed each day prior

to data collection.

11

The accuracy of the system and configuration seen in Figure l was evaluated in
both length and angular measurements. The same camera configuration used for all data
collection was used to capture several premade marker arrays with known lengths and
angles. It was tested on two different days with a new calibration each day to ensure
repeatability. The greatest standard deviation in a known length was 1.64 mm. The
greatest standard deviation in angle for a 5 second motion file of the known angles was

0.38 degree. All of these data are located in the appendix (A3).

 

Figure 1. Motion capture data collection configuration with global coordinate
system and origin shown

The 13mm markers were attached along the subject’s back over specific
anatomical positions. The most superior back marker was placed over the spinous
process of the seventh cervical vertebra (C7). Then the spinous processes of the thoracic

vertebrae were palpated down to the twelfih thoracic vertebra (T12) and a marker was

12

placed over that bony landmark. Next, a marker was placed between the right and left
PSIS’s (MidPSIS). Once that was completed, additional markers were placed between
C7 and T12 and also between T12 and MidPSIS such that the markers were even spaced
approximately 3 cm apart. This was chosen as the spacing that would allow the most
data to be gathered by the system without exceeding the system’s capability to
distinguish between separate markers. It should be noted that these intermediate markers
were not placed on the back over any distinct spinous processes, but rather to give the
highest allowable linear density for data collection. These markers were used to monitor

the motion of the back and can be seen in Figure 2.

l

'I’I:__,

OII'CCOOo-....

MidPSIS "

. .r
..

 

Figure 2. Retroreflective markers applied to the posterior at C7, T12, MidPSIS
while standing erect with additional markers spaced approximately 3cm apart
between C7 and MidPSIS

To monitor the movement of the ribcage and pelvis, markers were also applied to
the anterior side of the subject. A three-marker pod was placed over the subject’s
sternum with the most superior portion of the pod being affixed just inferior to the stemal
notch. A fourth marker was also placed just superior to the sternal notch. Additionally,
markers were affixed over the subject’s left and right ASIS, over the lateral epicondyles

of each femur, and on each thigh. These can be seen in Figure 3.

 

Figure 3. Retroreflective markers applied to the subject’s anterior and lateral sides

The markers on the subject’s ASIS’s, MidPSIS, and knees were used to calculate

the position and orientation of the pelvis throughout the various test conditions.

Test conditions

To quantify a full range of seated spinal articulations for each subject,
measurements were taken in several different ways. Data were collected in two test
conditions:

1) Four static positions, and

2) Dynamic ranges of motion

Both conditions are described in detail below, but for all testing, subjects were
asked to sit with their feet flat on the floor, shoulder width apart, having their head above

their pelvis with a forward gaze, and arms at their sides, as seen in Figure 4.

 

Figure 4. Basic posture assumed by the subject with head over pelvis, feet flat on
floor, and gaze forward
Static positions
The goal of the four static postures was to determine the full range of motion for
each individual while in the seated position. Two extreme and two intermediate postures

were used to obtain this full range data,

The extreme postures were taken as:
1) Maximum Lumbar Lordosis (Max. Lord.): a maximally lordotic self-selected
position.
2) Maximum Lumbar Kyphosis (Max. Kyph.): a maximally kyphotic self-selected
position.
The intermediate postures were taken as:
3) Comfortable (Comfort): a self-selected position that the subject assumed when
asked to “sit comfortably”
4) Straight and Tall (S&T): A self-selected position that the subject assumed when
asked to “sit straight and tall”.
The purpose of the two intermediate postures was to obtain two measurement positions
that were located between the two extreme postures. All four postures can be seen below

in Figure 5 and were taken as the average of three seconds of data while the subject

maintained each position.

16

 

Figure 5. Static postures assumed by the subjects. Clockwise from top left:
Maximum Lumbar Lordosis, Maximum Lumbar Kyphosis, “Straight and Tall”,
“Comfortable”
Continuous motion
The continuous motion files were collected to show the complete continuous
trajectory of movement ranging from maximum kyphosis to maximum lordosis. These
data were captured while the subject moved from a comfortable position to a lordotic
position, to a kyphotic position, and back again to the comfortable position. The subject

was verbally queued throughout the motions to ensure a full cycle was completed within

the data collection timeframe and the subject was able to pause at the extreme positions.
The total duration of data capture for each continuous motion file was 20 seconds to
ensure a full cycle through the motions was possible. The only data that were used for
analysis were the data that occurred during the verbal instruction.

Once all of the positions and motions had been collected, the data were processed
in the motion capture software. Each marker was identified and labeled, tracked
throughout its trajectory, and exported to a spreadsheet in the form of the global XY Z
coordinates.

For the continuous capture dynamic motion data, only subjects with the most
complete motion files were used. Due to the unforeseen occlusion of some key markers,
most notably the A818 markers, some motion trajectories were not completely tracked
through the entire motion. This meant that for some subjects the necessary calculations
for analysis could not be made at all points in time. Therefore, the inclusion criteria for
the dynamic files were that at least 75% of the trajectory was tracked and the end-ranges
of motion were clearly distinguished, as noted by the pauses at the extreme postures.

These criteria left only 15 of the original 31 subjects in the dynamic data pool.

18

Analysis

Hip joint center

The first calculation was of each of the subject’s hip joint centers (HJ C). The
111 C locations were calculated by both the Seidel method [42] and then, secondly, by the
method developed by Bush and Gutowski [43]. In practice, a reference file would be
taken with posterior markers and the Seidel Method would be used to compute the HI C.
Then, using these data and the relationships formed between the calculated H] C, knee
marker and ASIS marker, the posterior markers could be removed and the Bush Method
would be used while the subject was seated in a chair. This is important because one of
the end goals of this research was to be able to predict posterior motions without having
any posterior markers measured.

For these calculations, anatomical directional vectors were developed on the
subject’s pelvis, such that the width vector was oriented from the subject’s left ASIS to
the right ASIS, the depth vector was oriented from the MidPSIS to the midpoint between
the subject’s left and right ASIS, and the height vector was oriented 90 degrees from both
the width and depth vectors in a superior direction. The vector notation for these

calculations can be seen in equation set 1.

EW = GRASIS - GLASIS
L0 = (GLASIS + GRASIS ) / 2 - GMidPSIS
ZH = ZW XZD (1)

LWunit = j-Z—WI

19

The H] C was then calculated as a position relative to the subject’s corresponding
ASIS using the local pelvis vectors and the subject’s pelvic measurements. According to
Seidel [42] the position of the H] C in relation to the ASIS is 14% of the subject’s pelvic
width in the medial direction, 34% of the subject’s pelvic depth in the posterior direction
and 79% of the subject’s pelvic height in the inferior direction.

For the right HJC, this meant starting at the position of the right ASIS, the right
H] C was 14% of the subject’s pelvic width in the negative X direction, 34% of the
subject’s pelvic depth in the negative Y direction and 79% of the subject’s pelvic height

in the negative Z direction. This calculation can be seen in equation set 2

PW = Pelvic Width
PD = Pelvic Depth
PH = Pelvic Height (2)

GRHJC = GRASIS - PW * 0.14 * iWuni, — PD * 0.34 * [:Dum-t — PH * 0.79 * rim,”

For the left HJ C, this meant starting at the position of the left ASIS, the left HJ C
was 14% of the subject’s pelvic width in the direction of the width vector, 34% of the
subject’s pelvic depth in the negative direction of the depth vector and 79% of the
subject’s pelvic height in the negative direction of the height vector. This calculation can

be seen in equation 3.

GLHJC = GLASIS + P W * 0-14 * iWum'z - PD * 0-34 * iDunit - PH * 0-79 * iHum'z (3)

20

Then, by Bush and Gutowski’s method, it was again calculated without the
MidPSIS marker by using the known length from the respective ASIS to the HI C and

from the lateral condyle marker to the HI C, as both distances should be constant.

Openness angle

Once the H] C were determined, it was possible to calculate the “openness” angle
(0). This was the measure used to quantify the relative orientations of the pelvis and the
ribcage. To calculate this angle, all data were viewed in the YZ (sagittal) plane to
eliminate any medial/lateral dependence or skewing. Once this was established, two

vectors were computed, one through the pelvis and one through the thorax. The pelvis

vector (P) was calculated originating at the average of the right and left H] C and passing

through the average of the right and left ASIS, seen in equation 4.

 

(4)

13 = [GLASIS + GRASIS ]_[GLHJC + 5mm J
2 2

The ribcage vector ( R ) was then created originating at the sternum pod and

passing through the C7 marker, seen in equation 5.

R = GC 7 — GMidSternum (5)

The angle created by these two vectors, seen in equation 6, was then calculated as

the “openness”. A diagram how this angle was calculated can be seen below in Figure 6.

21

s‘1 P ' R (6)

 

 

Z

 

 

 

 

Figure 6. Diagram of the “openness” angle as calculated from the positions of HJC,
ASIS, Stemum marker and C7
The openness angle was chosen because it can be calculated using markers that
are primarily on the anterior side of the subject and can all be obtained while a subject is
in a chair with a back. The C7 marker is on the posterior side of the subject, but most

seatbacks do not extend that high, so it is still a viable marker in seating research.

Lumbar angle
The second angle to be calculated was an angle on the posterior side of the
subject. This angle, referred to as the lumbar angle, was meant to capture the contour of

the lower back at the same time the “openness” angle was quantifying the relative

22

orientations of the ribcage and pelvis. It was calculated by taking the positions of the
markers at T12 and MidPSIS and the most eccentric marker between them (LU) and then
using those points to create a 3 point arc.

LU was calculated by first translating the positions of all markers uniformly so
that the MidPSIS marker was at the origin and each marker was renamed Tname. Next,
all marker positions were rotated uniformly in the sagittal plane such that T12 was
positioned vertically over the MidPSIS and the markers were renamed Qname by the

calculations seen in equation set 7. Then the LU marker was chosen to be the marker

between MidPSIS and T12 that had the largest magnitude y-value.

Tname : Gname ' GMidPSIS

_. A

Rotation Angle = ¢ = tan-1 TT12 ° J
T T12 ° k

_. QnameX 1 O O TnameX (7)
Qname = QnameY = 0 cos ¢ " Sin ¢ TnameY
QnameZ 0 Sin ¢ cos ¢ TnameZ

Once LU was defined, it was possible to calculate a circumradius of a circle that
would contain all 3 points (MidPSIS, T12, LU) as seen in Figure 7. This was calculated
using the known distances between the three points in the sagittal plane, seen in equation
8, and using the algebraic equations 9 and 10

GMidPSIS - GTizl = a
GMidPSIS - GLU I = b (8)

 

GT12-GLU|=C

23

r: a*b*c (9)
J(a+b+c)(-a+b+c)(a—b+c)(a+b—c)

 

 

a
a=2*sin-l[-/2—] (10)
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Figure 7. Calculation diagram for circumradius and lumbar angle
Once this radius was determined (derivation found in Appendix A4) it was
possible to calculate the angle of the whole circle that the 3 points formed. The equation
defining this relationship can also be seen above. A diagram for the lumbar angle (a) is

shown in Figure 8. In the case of a kyphotic lumbar position, where the LU marker was

posterior to the line between the T12 marker and the MidPSIS marker, the lumbar angle

was considered to be negative.

24

 

 

 

 

 

Figure 8. Diagram of the lumbar angle as calculated from the positions of T12, LU,
and Mid-PSIS
Statistical Analysis Methods
Distinct static positions
Before the relationship between the static measurements was evaluated, it was

necessary to confirm that each of the four postures were different from one another. This
analysis was conducted for both of the major measurements: openness angle and lumbar
angle. Upon the suggestion of a statistician, successive positions were tested using a
paired t-test, for both openness and lumbar angles. The null hypothesis was that position

A and position B were not statistically different.

25

Relationship between openness and lumbar angles

Given openness and lumbar angles that were distinct across each of the static
positions, the next step of analysis was to determine if a relationship existed between the
two angles across all the positions. This was performed on the static and dynamic data
with two separate models, a linear model and a second order polynomial model.

For the linear model, it was hypothesized that this was a linear relationship and

therefore the measure chosen to test this was a linear r2 correlation. Specifically, it was

hypothesized that with openness as the independent variable and lumbar angle as the

dependent variable, a model of the form a=m0+b could be developed and the r2 value
would tell how well the data fit that model. In this case, a is the lumbar angle, 0 is the
openness angle and “m” and “b” are the coefficients forming the relationship.

For the polynomial model, a second hypothesis was that the relationship between

the openness and lumbar angles followed a relationship of the form a=U02+V0+W,
where again, a was the lumbar angle and 0 was the openness angle and “U”, “V”, and

“W” were the coefficients forming the relationship. This was calculated as a best fit

polynomial and evaluated again with an r2 correlation.

These models were applied to both the static and dynamic data.

Anthropometric correlation to openness/lumbar angle slope

Once the linear relationship between openness angle and lumbar angle was
established, it was necessary to determine if any anthropometric measures had any
influence on the relationship. This was tested by using a Pearson product moment

correlation test. For the static sample size of 31 subjects at a significance level of 0.05,

26

the critical value of the correlation was 0.355. For the dynamic sample size of 15
subjects, at a significance level of 0.05, the critical value of correlation was 0.514. These
critical values were found by first finding critical t-values for confidence and prediction
intervals associated with the degrees of freedom and levels of significance required in
each set of data. Then the t-values were converted to r, by way of equation 11 for a test
of linear association in a bivariate normal population, where N is the number of subjects
[44]. Any values larger than the critical values are considered to be statistically

significant.

t:————- (11)

Predictive capacity
In order to test the predictive capacity of the relationships between the openness

angle and the lumbar angle, predictive models had to be developed from one group and
tested on another group. This lead to six total predictive combinations that were tested:

1. Static data predicting static positions for a test population

2. Dynamic data predicting dynamic positions for a test population

3. Static data predicting dynamic positions for a test population

4. Dynamic data predicting static positions for a test population

5. Static data predicting dynamic positions within a subject

6. Dynamic data predicting static positions within a subject

27

Static data predicting static positions for a test population
For the static to static predictive capacity measurement, the total static data set
was split into two groups. The first group consisted of the first 16 subjects and the

second group consisted of the last 15 subjects. From the all of the data points in the first

group, linear and second order predictive models of the form a=m0+b and a=U02+V0+W
were formed. These models were then applied to all of the openness values in the second
group, creating a linear and second order “predicted lumbar angle” for each openness
datum in the second group. Finally, paired t-tests were performed to test the actual
lumbar angles vs. the predicted lumbar angles to determine if the predicted lumbar angles

were statistically different from the actual lumbar angles.

Dynamic data predicting dynamic positions for a test population
A similar procedure was executed for all of the dynamic data. The subject pool
was split into two groups. The first group consisted of the first eight subjects with
sufficient dynamic data, and the second group consisted of the last seven subjects with
sufficient dynamic data. All of the data from the first group were used to produce a linear

prediction model of the form a=m0+b and a second order polynomial model of the form

a=U02+V0+W. These models were then applied to the second group’s openness angle
values to produce a “predicted lumbar angle” for each openness angle in the second
group for each model. The predicted lumbar angles were then compared to the actual
lumbar angles across each openness angle in the second group’s data using paired t-tests
to determine if the predicted lumbar angles were statistically different from the actual

lumbar angles.

28

Static data predicting dynamic positions for a test population
For these models, all of the static data and all of the complete dynamic data were

utilized. The static data from all subjects were used to form linear and second order

predictive models of the form a=m0+b and u=U02+V0+W. These two models were then
applied to all of the openness values in all of the complete dynamic subjects, creating a
linear and second order “predicted lumbar angle” for each openness datum in the
dynamic data group. Then, paired t-tests were performed to test if the actual lumbar
angles were statistically different than the predicted lumbar angles.

Note that these models were different than the models developed for the “static to
static” prediction because all of the subjects (S01-S3 1) were used instead of just the first

half (SOl-S l 6) to build the models.

Dynamic data predicting static positions for a test population
For these models, all of the static data and all of the complete dynamic data were

utilized. The dynamic data from all subjects with complete data sets were used to form a

linear and a second order predictive model of the forms a=m0+b and a=U02+V0+W.
These models were then applied to all of the openness values for all of the static data,
creating a linear and second order “predicted lumbar angle” for each openness datum in
the static data group. Paired t-tests were performed to test if the actual lumbar angles
were statistically different than the predicted lumbar angles.

Note that these models were different than the models developed for the “dynamic

to dynamic” predictions because all of the dynamic subjects were used to build these

29

models instead of just the first half of the dynamic subjects for the “dynamic to dynamic”

models.

Static data predicting dynamic positions within a subject
A similar approach was taken to determine if, within a subject, the static data
could be used to predict the same subject’s dynamic pattern of movement. To test this, a
linear model, of the form 0t=m0+b, was fit to the static data of each subject. These
models were then used to predict each dynamic lumbar angle using the same subject’s
dynamic openness angles. The predicted lumbar angles were compared to the actual

lumbar angles by utilizing a paired t-test, for each subject.

Dynamic data predicting static positions within a subject
Additionally, the ability to predict the static positions of a subject based on a
model developed from the dynamic data from that same subject was tested. Linear
models, of the form a=m0+b, were developed for each subject based off of their own
dynamic data. Then, each model was applied to the same subject’s openness angles for
each of the static positions, creating predicted static lumbar angles. The predicted static
lumbar angles were then compared to the actual static lumbar angles for each subject

using a paired t-test.

30

RESULTS

Openness and Lumbar Angles

The calculated openness angles for each subject in each static position are given

 

in Table 4.
Table 4. Static openness angles for each subject at each posture
Openness Angle, 0 (deg)
Maximum “Straight Maximum
Subject Lordotic and Tall” “Comfort” Kyphotic Total Range
S01 93.5 91.5 72.4 63.0 30.5
802 97.3 80.0 63.6 46.4 50.9
S03 133.8 119.5 107.5 89.9 43.9
S04 99.8 96.9 74.1 63.1 36.7
805 129.5 126.6 82.8 72.2 57.3
S06 98.0 78.4 56.1 40.6 57.3
S07 82.3 81.0 55.0 43.9 38.4
808 104.5 99.7 95.7 76.2 28.2
809 131.7 100.1 79.6 46.1 85.6
s10 129.4 115.7 90.8 78.2 51.3
811 126.8 107.0 94.4 78.5 48.2
812 111.6 99.3 84.6 67.2 44.4
813 125.2 94.6 78.0 64.6 60.7
814 155.2 127.6 112.1 80.5 74.7
815 88.3 75.9 61.1 22.1 66.2
816 105.1 87.1 74.2 52.5 52.6
817 129.3 119.3 101.6 78.8 50.5
818 100.3 91.0 80.4 66.8 33.5
819 99.1 92.3 78.0 70.4 28.7
820 122.7 107.3 75.7 54.0 68.8
821 113.7 103.7 83.6 46.6 67.1
822 120.8 111.7 92.5 69.4 51.4
823 122.0 97.9 80.6 59.1 62.9
824 118.9 93.5 77.5 50.0 68.9
825 104.1 92.7 74.1 38.1 66.0
826 119.3 105.2 82.7 59.8 59.5
827 129.4 111.0 74.2 52.2 77.2
828 104.2 79.4 63.4 42.7 61.6
829 124.4 102.5 92.1 72.4 52.0
S30 116.7 105.6 75.5 71.7 44.9
S31 92.0 91.4 79.1 67.3 24.7
AVG I 13.8 99.5 80.4 60.8 53.0
SD. 16.4 13.8 13.6 15.4 15.4

 

31

The calculated lumbar angles for each subject in each static position can be seen
below in Table 5. Note that in both the openness angles and lumbar angles, the trend
from lowest to highest in terms of the positions, is maximum kyphotic, comfortable,
“straight and tall”, and maximum lordotic.

Table 5. Static lumbar angles for each subject at each posture

 

Lumbar Angle, (1 (deg)
Maximum “Straight Maximum
Subject Lordotic and Tall” “Comfort” Kyphotic Total Range
S01 -5.2 -6.7 -9.2 -11.0 5.8
S02 21.9 -10.7 -17.8 -18.9 40.8
803 29.4 12.1 14.6 -12.8 42.3
804 34.4 19.0 6.9 -5.9 40.3
SOS 49.4 55.5 -16.1 -21.1 76.6
806 6.8 -11.7 -13.5 -17.5 24.3
S07 20.8 19.6 -4.3 -14.0 34.8
S08 34.8 11.0 8.8 -14.9 49.7
S09 49.6 9.7 -7.6 -17.3 66.9
810 62.9 34.9 -1.4 -14.6 77.4
811 15.5 22.6 7.5 -2.1 24.8
812 34.4 12.9 10.8 -9.1 43.5
813 17.6 -10.2 -13.2 -19.0 36.6
814 41.3 31.6 25.7 -21.3 62.6
SIS -19.4 2.8 -12.8 -27.0 29.8
816 8.0 -5.4 -17.1 -24.3 32.3
817 61.0 25.3 22.3 -6.7 67.7
818 -15.7 -4.4 -7.7 -11.9 11.3
819 3.8 3.2 -5.7 -8.8 12.5
820 -9.6 4.4 -10.0 -17.2 21.6
821 35.4 17.9 9.3 -20.4 55.8
S22 32.1 17.8 -10.1 -12.8 44.9
823 79.6 38.8 12.0 -8.8 88.4
S24 16.1 13.4 3.1 -16.4 32.5
825 61.4 36.4 13.3 -21.2 82.6
826 58.4 18.7 -6.5 -13.4 71.8
827 42.1 13.7 -20.8 -31.1 73.3
828 -8.5 -5.0 -22.9 -30.7 25.7
829 9.9 -5.4 -8.3 -9.3 19.2
S30 25.9 25.2 -11.6 -18.3 44.2
S31 -4.3 5.8 -11.3 -18.3 24.2
AVG 25.5 12.7 -3.0 -16.0 44.0
SD. 25.6 16.5 12.9 6.9 22.8

 

32

Table 6 shows the maximum, minimum and range values for the openness and
lumbar angles as calculated from the dynamic range of motion data.

Table 6. Dynamic maximum, minimum, and range values for openness and lumbar

 

angles
Openness Angle, 0 (deg) Lumbar Angle, 0. (deg)
Subject Max Min Range Max Min Range
S01 101.5 76.5 25.0 8.5 -6.2 14.7
S04 91.3 59.8 31.5 27.2 -7.9 35.1
808 102.5 56.3 46.2 33.5 -l7.9 51.4
810 124.5 74.2 50.3 51.3 7.2 44.0
811 119.1 67.9 51.2 34.6 0.9 33.7
812 109.6 63.3 46.3 43.3 4.4 38.9
S13 109.5 61.8 47.7 5.9 -20.9 26.8
817 127.1 80.4 46.7 50.7 8.6 42.1
818 92.2 57.1 35.1 -5.5 -l9.3 13.8
819 86.9 67.2 19.8 4.5 -9.2 13.7
821 118.8 51.1 67.7 67.9 -42.4 110.4
823 125.7 52.2 73.4 81.5 -25.6 107.0
826 122.9 61.4 61.5 35.7 -16.0 51.6
828 107.7 36.5 71.2 21.9 -34.5 56.4
S30 115.3 64.0 51.2 28.8 -l7.8 46.6
AVG 110.3 62.0 48.3 32.6 -l3.l 45.7
SD. 13.2 11.0 15.9 24.1 14.9 29.0

 

Distinct Static Positions
The probabilities, as determined by the paired t-test, that each set of positions are
the same are seen below in Table 7.

Table 7. Probabilities that each pair of positions is the statistically the same as
determined by a paired t-test

Test Condition Openness Angle Lumbar Angle
Max. Lord. vs. S&T <0.0001 0.0003
S&T vs. Comfort <0.0001 <0.0001
Comfort vs. Max. Kyph. <0.0001 <0.0001
Max. Lord. vs. Comfort <0.0001 <0.0001
S&T vs. Max. Kyph. <0.0001 <0.0001
Max. Lord. vs. Max. Kyph. <0.0001 <0.0001

33

Relationship between Openness and Lumbar Angles

Static

A graph for each subject’s static data can be seen in Figure 9 (a-ee). Also

included in the graphs are the linear and polynomial models with their associated r2
values. The linear best fit approximations are shown as gray lines, while the second

order polynomials are the black curves.

 

 

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34

 

 

  

 
   

 

 

 

 

 

 

 

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35

 

 

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. Poly.: r2=0.600 1 1 2
1 ED 40
1 1 a
1,__...1c_1__1--_!,1m7.. J 1 1 “E 0
1 1 =3
2". 120 160 1 ' -1 -20
1 -40
Openness Angle (deg) 1 ,
(0)
Figure 9 (cont.)

36

$12

Linear: r2 = 0.918
1 Poly.: r2 = 0.923

..

 

1

40

80

Openness Angle (deg)

120 160

 

S14

Openness Angle (deg)

Linear: :2 = 0.866
Poly.: r2 = 0.992

  

 

816

(n) _

Linear: r2 = 0.958

1 Poly.: r2 = 0.990

1 44+ 1 . g
40 120 160

Openness Angle (deg)

(P)

1
1

_J

1

$17 818
A 80 A 80 1
g“ 60 1Linearzr2=0.865 . 1 g” 60 1_Linear:r2=0.018
I: 1 Poly.: r2=0.884 1 E Poly.: r2=0.778 -
E0 40 ~ 1 ED 0 1
20 1 i 20 1
g 0 v » «fl 11 g 0 1 —<1 ‘ *-*1 1—41—"1 7’1 1 3
5 1 . 1 S A .
._: -20 1 40 80 120 160 1 1 ._1 -20 1 40 80 120 160 1
-40 1 1 1 -40 *
Openness Angle (deg) - Openness Angle (deg) 1
L (‘1) L L L (r) L L
$19 1 820
g” 60 Linearzr2=0.967 1,; .g 60 LLinearzr2=O.384 1
B“ 1Poly.: r2=0.975 1 o Poly.: r2=0.717 1
’31) 1 1 3b 40 1
g 20 , 1 ‘2 20 1
g 0 » + 171," N g 0 19% 1 1
_1 -20 1 40 80 120 160 1 1 -‘ -20 40 80 120 160 1
1 1
-40 ' 1 -40 1 1
. 1 1
Openness Angle (deg) 1 1 Openness Angle (deg) 1
_ _ ____(_??__LL . L __ _ (”LL—
321 1 522
A 80 1 1 A 80
go 60 Linearzr2=0.969 1 go 60 1Linearzr2=0.857
E 40 1Poly.: r2=0.971 1 1 E 40 1Poly.: r2=0.994
w - 1 1°" .
g 20 E 20 5
$2 1 s 1
g 0 1~ 1 E 0 1~1 +a+w1 +«+~1 1
.4 -20 1 '4 -20 1 40 120 160
-40 1- ‘ —40 1
Openness Angle (deg) 1 1 Openness Angle (deg) 1
(u) (v)
Figure 9 (cont.)

  

 

 

 

 

 

 

37

$23 ? $24 ;

  
   

 

    

 

5’3" 60 ’Linearzr2=0.984 .g 60 ;Linear:r2=o.898 ;
‘5 Poly.:r2=o.999 ,2 ; Poly.: r2=0.993
“Eb 40 l - in 40 g
5 20 - i :a 20 'r
g l l a
x g 0 l * l w .' g 0 -
...1 -20 40 80 120 160 -‘ -20 l
-40 ~ l -40 I
Openness Angle (deg) Openness Angle (deg)
f (W) __ ,, f * (X)___ A
$25 , 826 ‘
A 80 r a 80 l
; Q” 60 lLinear:12=O.97 . g 60 .Linear:r2=0.852
i T; Poly.r2=0.996 i I; Poly.: r2=o.992 l
5 S 20 :a 20 - '
g 0: e T ‘HEO‘ l +
‘ _1 -20 120 160 A -20 . 40 120 160
-40 l ~ -40 l ’
Openness Angle (deg) ‘ Openness Angle (deg)
i (y) if f i W _ _ (z) _ #
$27 . 828 i
‘ ’53 80 r' ‘ ’55 80 :
.g 60 LLinear:r2=O.965 ; g 60 (Linearzr2=o.745
\ :0: 3 P 1.: r2=1.000 i .2 'P01 .: r2=0.854
' in 4o 0" l E0 40 r y l
_ a 20 i» I a 20 4 ‘
7 .D 1 '0 ‘
i; 0* - g 0’ f e —-»
' —‘ -20 L 160 4 -20 . 40//‘no 160
-40 l -40 -
Openness Angle (deg) ‘ Openness Angle (deg)
(aa) (bb)

Figure 9 (cont.)

38

Lumbar Angle (deg)

Lumbar Angle (deg)
O‘\
o

.b
O

0
-20

N
O

329 1 l

00
O

-40 1

Figure 10 (a,b) shows the linear approximations for all of the subjects. In this

l Linear: r2 = 0.961

S30

(Poly; :2 = 0.999

1

T : A80
Linear: r2 = 0.807 ‘ a“
l ‘ , 360
L Poly.: r2=0.999 ‘ L o
r E040
38 20
i i ‘ ‘ ' ‘ "*— ‘ E O
, | 3 .
» 4 2 . ._1 .
l 0 8010160!_20i
" -40 .,
Openness Angle (deg)
(CC)
S31
. Lineartr2=0.814
, Poly.: r2=0.819
i (ee)
I, ‘ ;
l 40 120 160
Openness Angle (deg)
Figure 9 (cont.)

case, the data have been split into two graphs for ease of viewing.

39

160

t t—4 - 4r-
40 120
Openness Angle (deg)
(dd)

 

Lumbar Angle (deg)

Lumbar Angle (deg)

Subjects 1-15

 

Openness Angle (deg)

(11)

Subjects 16—31

 

Openness Angle (deg)

(b)
Figure 10 (a,b). :1) Linear best fit plots for subjects 1-15

h) Linear best fit plots for subjects 16-31

40

A summary table displaying the linear slopes and r2 values for the linear and

polynomial model for each subject in the static positions can be seen below in Table 8.

Note that the average linear r2 value is 0.829, the average polynomial r2 value is 0.935,

and all of the slope values are positive except for one subject.

Table 8. Slope, linear r2 and polynomial r2 values for each subject as determined by

 

41

best fit line
Subject Linear Slope Linear r2 Polynomial r2
801 0.171 0.964 0.964
802 0.767 0.760 0.985
803 0.888 0.887 0.906
804 0.919 0.903 0.904
SOS 1.380 0.981 0.985
806 0.386 0.808 0.943
807 0.909 1 .000 1.000
808 1.532 0.872 0.962
809 0.782 0.904 1.000
810 1.503 0.988 1.000
811 0.404 0.598 0.870
812 0.891 0.918 0.923
813 0.599 0.926 0.987
814 0.830 0.866 0.992
815 0.246 0.311 0.599
816 0.625 0.957 0.990
817 1.163 0.865 0.884
818 -0.046 0.018 0.778
819 0.473 0.967 0.975
820 0.181 0.384 0.717
821 0.775 0.969 0.971
822 0.888 0.857 0.994
S23 1.421 0.984 0.999
824 0.484 0.897 0.993
825 1.199 0.971 0.996
826 1.149 0.852 0.992
827 0.941 0.965 1.000
828 0.402 0.745 0.854
829 0.371 0.807 0.999
830 1 .040 0.962 1 .000
831 0.795 0.814 0.819
AVG 0.776 0.829 0.935
S.D. 0.409 0.221 0.096

Dynamic

Graphs for the dynamic data can be seen in Figure 11 (a-o). Also included in the

graphs are the graphical representations of the linear and polynomial models with their

associated r2 values. The linear best fit approximations are shown as gray lines, while

the second order polynomials are the black curves. Note that in some cases, such as

Figure 11 (a), due to the similarities in linear and polynomial models, it appears only the

polynomial black curve is visible. Figure 11 (c) provides a good example of a subject

where the linear and polynomial models do not overlap.

 

I 301
’53
‘ v 90
l 3 Linearzr2=0.930
D
'3'!) Poly.: r2=0.953
E 40 l
l g
‘ 5-10 ' AM ‘
4 b 50 100
j -60 l
Openness Angle (deg)
_ _ _ _______L_S*)____ _ _
l 304

\O
O

Linear: r2 = 0.960
Poly.: r2 = 0.960

Lumbar Angle (deg)
.h
O

C.»
O
l Mfi! ‘ ‘1"—

til
0
p—A
O
O

Openness Angle (deg)
(b)

[__

l
A

1

l

l

 

Figure 11 (a-o). Openness Angle vs. Lumbar Angle for each individual subject using static V
postures with included linear and second order polynomial best fits

42

Linear: r2 = 0.951 I
l Poly.: r2 = 0.983 1

 

Lumbar Angle (deg)
A
o

 

50 100 150:
-60
Openness Angle (deg) j
(C)
N‘ 310 l

\O
O

Lumbar Angle (deg)
.b-
o
t
‘.

Linear: r2 = 0.871
Poly.: r2 = 0.897

 

 

 

 

-10 L 88888 f l
7 50 100 150'
-60 l j
l Openness Angle (deg) :
(d)
. 811
l l.
l 90 Linear: r2 = 0.333 j

; Poly.: r2=0.500 ;

 

Lumbar Angle (deg)
J:
O

-10 l v.
50 100 150!
-60 ‘
Openness Angle (deg)
(C)
(cont.)

43

r
l

 

3;“ 90 l
2: Linear: r2 = 0.945
'80 . =
Ii 40 Poly.. r2 0.953 .
33 l
r-9 . i J 1
$-10 ~
.4 50 100
-60
Openness Angle (deg)
(f)
313

\O
O

1‘ Linear: r2 = 0.952
Poly.: r2 = 0.958

Lumbar Angle (deg)
A
O

-10 i _ —— _fi'fl ”"i
50 100
l
-60 ‘
Openness Angle (deg)
(g)
817
g” 90 ’ Linearzr2=0.958
E“ Poly.: r2=0.961
ED 40 E ”M
g L 7”. LL21- __
g -10 '
___] 50 100
l
-60 ‘
Openness Angle (deg)
(1!)
(cont.)

44

1 S18

\0
O

1
Linear: r2 = 0.506 ‘
l Poly.: 12 = 0.572 1

l

Lumbar Angle (deg)
A
C

 

 

 

w l l
l 50 ' 100 150
l
‘ -60 l
Openness Angle (deg) h
(i)
j 519 l
33390 f Linear:r2=0.553 ‘
3r: ‘ Poly.: 13:0.599 l
w 40 l
l 5 j
l
E, 10 . ‘ 'W’TL ‘ fl ‘
l E ‘ 50 100 150}
I i
, -60 l
j Openness Angle (deg)
(j)
L LLL ., +L l
l 321

Linear: r2 = 0.957
1 Poly.: r2 = 0.966

  

Lumbar Angle (deg)
A
O

 

l _10 I :
l 150:
l -601 l
L - 59993892816399). L L- L

(k)

(cont.)

Lumbar Angle (deg) Lumbar Angle (deg)

Lumbar Angle (deg)

 
 
 

 

 

 

 

 

 

 

90 - 1
Linear: r2 = 0.947
1
40 Poly.: r2=0.957 l
l
-10 r i T T ~ A ,
100 150)
l
-60 l
Openness Angle (deg) j
(I)
826 l
, l
90 l Linearzr2=0.947 3
Poly.: r2=0.953 l
40 l l
’ l
-10 (i l
‘ 1501
-60 ‘ 5
Openness Angle (deg) _J
(m)
828
Linear: r2 = 0.918 ‘
Poly.: r2=0.972 l
40
-10 m r r e . — é ~ 1
f. 100 150k
-60 l
Openness Angle (deg)
(11)
(cont.)

 

 

79:“ 90 ,1
'8 Linear: r2 = 0.889
'2 P 1 . r2: 0 947
in 40 o y.. .
:3 o . o ’ j
.o ;__ _ _ -_.- _ ___
g '10 L 000 I
'-l 50 100 150‘.

-60 l

Openness Angle (deg)
(0)
(cont.)

A summary table displaying the linear slopes and r2 values for the linear and

polynomial model for each subject in the dynamic positions can be seen below in Table

9. Note that the average linear r2 value is 0.841, the average polynomial 1‘2 value is

0.875, and that all of the slope values are positive except for one subject.

Table 9. Summary table of slope, intercept and r2 for 15 dynamic subjects

 

47

Subject Linear Slope Linear r2 Polynomial r2
801 0.435 0.930 0.953
804 0.93 1 0.960 0.960
808 1.042 0.951 0.983
S10 0.619 0.869 0.896
811 0.265 0.330 0.496
812 0.608 0.944 0.952
813 0.483 0.952 0.958
817 0.740 0.958 0.961
818 -0.149 0.507 0.573
819 0.293 0.554 0.600
821 1.380 0.957 0.966
823 1.009 0.947 0.957
826 0.770 0.947 0.954
828 0.561 0.919 0.972
S30 0.784 0.889 0.946

AVG 0.651 0.841 0.875
S.D. 0.372 0.202 0.167

A graph of the dynamic and static data for each subject with full data sets is
shown in Figure 12 (a-o). In this case, the linear and polynomial best fit models have

been lefl off the graphs for visual clarity of the data.

-e - _ r- e- w e 2..-“,

 

 

 

 

S01
’53 90 ~ 1
% 1
‘ 52 1 ° Dynarnic
: g 10 L fl"¢_ L I Staticfijl
- i I _
1 3 50 100 150 ‘
-60 j: ‘
Openness (deg)
. e L L __(1)_ L L.
304 b
g» 90 L .
'3 .
. 2 l l
1 DD 40 {—7— “‘ I:
l g I : ° Dynamie‘
‘ .8 . 2 A- hf/ L [I $13th 1
'10 >7 1‘
E | 50 100 150 l
l -60 ]
Openness (deg)
(b)

Figure 12 (a-o). Dynamic and Static data plotted as Openness vs. Lumbar Angle for
each subject with sufficient dynamic data

48

\O
O

Lumbar Angle (deg)
A
o

' * . Dynamici

L, L. L_ .éL‘LT'LL L __1 [I Static :3
A I‘mnag—‘i

50 100 :

 

-10 i
150
-60
Openness (deg)
_ (S) L L L
810
’63 90 w i
Q) l
.3 .
.2 ' i
w 40 9 ”I: ;~ * L.
é refs?!" i'Dynamw.
.8 1 - ‘34—” —»~4 fLSLthLiLCn
E -10 l I -
3 ‘ 50 100 150 l
-60 5
Openness (deg) j
L (d) — __ _...
SI] 1

l
‘l l l :

Lumbar Angle (deg)
A
o

. L, L . M L- ngtatic
-10 ' i ‘A’
i 50 100 150 l
-60
Openness (deg)
(C)

Figure 12 (cont.)

49

\O
O

Lumbar Angle (deg)
~-'--- A
o o

-60

\O
O

I
—l
O
T--.
l

Lumbar Angle (deg)
A
o

615
o

 

Lumbar Angle (deg)
A
o

 

 

 

mi." 1 ° Dynamic
LflLLl LLL LL LL J l»l%ic ‘4'
I
50 100 150 ‘
Openness (deg)
LL L (0 LL L L L
$13
I Dynamic
.1 ._ __ LLLLLLLML L '_Sta_ti§:
50 i 100 150 ‘
Openness (deg) l
_ (g) f~f ,, M f __
S17
- l
. 'a TD‘fll
’f’ I ‘ ynamu;
L _L L L L I Static l
I W h_ r
50 100 150 7
Openness (deg)
(11)
Figure 12 (cont.)

50

I
l

90'

40.

-10 '

Lumbar Angle (deg)

-60

Lumbar Angle (deg)
A
O

Lumbar Angle (deg)
A
O

150

Openness (deg)
(i)
S 1 9

IF I u
50 100 150
Openness (deg)

(i) __

$21

 

15” 100 150
Openness (deg)

00
Figure 12 (cont.)

51

 

; ° Dynamicl
|
L: _StaLtis

Lumbar Angle (deg)

-60 ‘

Lumbar Angle (deg)

Lumbar Angle (deg)
A
O

90 »
40 ~

-10 3

90‘
40-

-10 C

00’ . . .I. .;°'
. ’l o /.
AffifL.
s I
° 1 00
Openness (deg)
ELL
$26
00 ,0 ~°..%
0 ~ I

Openness (deg)
£9
828

A

L .L _ ”204‘“.
“dart" 100

Openness (deg)

(11)
Figure 12 (cont.)

52

150

150

1'3w9

I6%&@
1 ! Static l

. Dynamic
1

l

o Dynamic,

1.'_ 5&an .

Lumbar Angle (deg)
A
0

(LL. _LL
1 Mai' “Dy"a‘m‘;
l L LLL .L..L-.a°“°LL_L l gIStatic j
T -10 1 d.» “i _
' 50 100 150 j

l

-60
Openness (deg)
(0)

Figure 12 (cont.)

Anthropometric Correlation to Openness/Lumbar Angle Slope

Table 10 shows the correlation coefficients between the anthropometric measures
and the slope of the relationship between openness and lumbar angles. Note that only
seated height and pelvic depth in the dynamic model have correlation values with an

absolute value higher than the critical value.

Table 10. Pearson Product Moment Correlation Coefficients for Slope vs. each
anthropometric measure
Openness/Lumbar Slope Pearson Product Moment Correlation Coefficient

 

 

vs. Static Dynamic
Critical 0.355 0.514
Height -0.010 0.374
Weight -0.055 0.240
Age -0. 140 -0.226
Seated Height 0.195 0.628
Seated Buttocks Width 0.168 0.458
Pelvic Width 0.315 0.273
Pelvic Height -0.075 0.330
Pelvic Depth 0.060 0.601

53

Predictive Capacity

Static data predicting static positions for test population

The linear model developed from the first 16 subjects (801-816) was a=0.6870-
56.1, where a is the lumbar angle and 0 is the openness angle. This model was developed
by finding the best fit regression line for all of the static data for the first half of the

subjects, as described previously, and can be seen graphically in Figure 13.

 

 

 

Static Predictive Model Development from
Subjects 801-816
A 80 ,—
§ 60 1 a = 0.687 e - 56.1 .0
E 40 L
Cc!) .
< 20 t
g 0 L 4
g -20 200
A l
-40 r
-60 :
Openness Angle (deg)

 

 

 

Figure 13. Graphical representation of linear predictive model developed from the
static openness and lumbar angle data of subjects 801-816

Figure 14 shows both the actual data from the second group of subjects (S 1 7-
S31), and the predicted values for the same openness angles that were determined by

applying the model developed by the first group of subjects.

54

 

Openness Angles vs. Actual and Predicted Lumbar
Angles for Subjects S17-S31

 

100 7
§ 80 ~ °
3
2 60 * ° 0 9 .
g 40 ~ .0 . . 10Actual
h. -,L .0? . . ‘
é 2: 50 .~{:0 0. _ L'flEqLL‘fieq
IL _ L.-- L , LLL _.
3 “‘3 ° 150

-20 ~ :1’. .e§

Openness Angle (deg)

 

 

 

Figure 14. Predicted static lumbar angle values compared to actual static lumbar
angle values for linear static model applied to openness angles of subjects Sl7-S3l

Comparing the lumbar angles predicted from the linear model and actual lumbar

angles seen in Figure 14 with a paired t-test, the p-value was found to be 0.969.

The second order polynomial model developed from the first group, seen in

Figure 15, was found to be a=0.00302+0.0630-30.6, where a is the hunbar angle and 0 is

the openness angle.

 

  

 

Static Predictive Model Development from
Subjects 801-816
80
a a = 0.003 92 + 0.063 e - 30.6
8 60 H e
I? ‘ "
a 40 ~ 0
c .
E 20 »
S .
9 0 r 7* rs
-' -20 L 150 200
-40 r
Openness Angle (deg)

 

 

Figure 15. Graphical representation of polynomial predictive model developed

from the static openness and lumbar angle data of subjects 801-816

55

When this polynomial model, derived from the first group of subjects, was
applied to the second group, the predicted values seen in Figure 16 were found. Also
shown in Figure 16 are the actual values of lumbar angles for each corresponding
openness angle.

The p-value for a paired t-test comparison between the polynomial predicted

static lumbar angles and the actual lumbar angles for subjects 817-831 was found to be

 

 

 

 

 

0.827.
Openness Angles vs. Actual and Predicted Lumbar
Angles for Subjects 817-831
100 :-
§ 80 f ’
B ,
2 60 I“ ° 0 ° I
g 40 L .. . : ’oActual
s. O .
g 20 [ 50 .., . ° ., Reggie;
E 0 v _. W O .QI. 1.
3 ‘ S $ 0
'20 H ‘I’ .W . 150
O O
-40 ‘
Openness Angle (deg)

 

 

Figure 16. Predicted static lumbar angle values compared to actual static lumbar
angle values for polynomial static model applied to the openness angles of subjects
Sl7-S31

Dynamic data predicting dynamic positions for the test population
The linear model developed from the first set of subjects ($01, 804, 808, 810,

SI l, 812, 813, 817) was a=0.7540-57.2, where a is the lumbar angle and 0 is the

openness angle. This can be seen graphically in Figure 17.

56

 

Linear Dynamic Predictive Model Development

from First Subject Group
60 s

l

a = 0.754 9 - 57.2

  

A
O

 

Lumbar Angle (deg)
N
O 0
L

150

lb
o
‘

4's
0

Openness Angle (deg)

 

 

 

Figure 17. Graphical representation of linear predictive model developed from the
first eight subjects in the dynamic data group

Figure 18 shows both the actual data from the second group of dynamic subjects
($18, 819, S21, $23, $26, 828, S30), and the predicted values for the same openness

angles that were determined by applying the model developed by the first group of

dynamic subjects.

 

Openness Angles vs. Actual and Predicted Lumbar

Angles for Second Dynamic Subject Group
100 I

80 I
60 L
40

 

7 . Actual
I - Predicted

 

 

Lumbar Angle (deg)

150

 

 

Openness Angle (deg)

 

 

Figure 18. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for linear dynamic model applied to the openness angles of the
last seven subjects in the dynamic data group

57

Comparing the lumbar angles predicted from the dynamic linear model and actual
dynamic lumbar angles seen in Figure 18 with a paired t-test, the p-value was found to be
less than 0.0001.

The second order polynomial model developed from the first group, seen in
Figure 19, was found to be a=0.00202+0.340-39.0, where a is the lumbar angle and 0 is

the openness angle.

 

Polynomial Dynamic Predictive Model
Development from First Subject Group

0)
O

a = 0.002 92 + 0.34 6 - 39.0

  

A
O

 

Lumbar Angle (deg)
10
O O
.1.

rb
o

-40 ~-

 

Openness Angle (deg)

 

 

Figure 19. Graphical representation of polynomial predictive model developed
from the first eight subjects in the dynamic data group

When this polynomial model, derived fiom the first group of dynamic subjects,
was applied to the second group of dynamic subjects, the predicted values seen in Figure
20 were found. Also shown in Figure 20, are the actual values of lumbar angles for each

corresponding openness angle.

58

 

100

§ 80

E 60

a)

a 40

C

<

2;; 0

3 -20
-40
-60

 

N
O

F
l-

 

 

 

Openness Angles vs. Actual and Predicted Lumbar

Angles for Second Dynamic Subject Group

[__' _

. Actual
- Predicted

 

 

 

 

 

Openness Angle (deg)

 

Figure 20. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for polynomial dynamic model applied to the openness angles

of the last seven subjects in the dynamic data group

The p-value for a paired t-test comparison between the polynomial predicted

dynamic lumbar angles and the actual lumbar angles for the second group of dynamic

subjects was found to be 0.002.

Static data predicting dynamic positions for the test population

The linear model developed fi'om the entire static population was a=0.7230-59.3,
where a is the lumbar angle and 0 is the openness angle. Notice because this was the

entire population, as compared to only a subset of the test population, this linear model is

slightly different than the static model presented in the “Static predicting Static

population” This model was developed by finding the best fit regression line for all of

the static data and can be seen graphically in Figure 21.

59

 

 

Linear Static Predictive Model Development

100
a = 0.723 0 - 59.3

200

I 3‘ Lumbar Angle (deg)

 

 

Qpenness Ang'LeEEQ) L

__4

Figure 21. Graphical representation of linear population predictive model
developed from all of the static openness and lumbar angle data
Figure 22 shows both the actual data fiom the dynamic group of subjects and the
predicted values for the same openness angles that were determined by applying the

model developed by the static group of subjects.

 

Openness Angles vs. Actual and Predicted Lumbar
Angles for Dynamic Subject Group
100

80 r
60

5 . Rena ’
e- Predicted l

 

 

U Lumbar Angle (deg)

 

' -60 L l
L _ LL Ppenne§s 2195(‘E9LL !

Figure 22. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for linear static population model applied to the openness
angles of the entire dynamic data group

60

Comparing the lumbar angles predicted from the linear model and actual lumbar
angles seen in Figure 22 with a paired t-test, the p-value was found to be less than 0.0001.

The second order polynomial model developed from the static subjects, seen in
Figure 23, was found to be a=0.00402+0.0710-32.8, where o. is the lumbar angle and 0 is

the openness angle.

Polynomial Static Predictive Model Development

100 L a = 0.004 02+ 0.071 0 - 32.8 I

 

lilo?) 80 l
E l
‘2 60 r l
c) r
.5 4° 1" l
l a 20 l l
I .0
‘5 ° ’ *7 7 *' l
-20 l 200 I
-40 l ‘
Lg __ I I Openne§s Angle (deg) _______j

 

Figure 23. Graphical representation of polynomial population predictive model
developed from all of the static openness and lumbar angle data
When this polynomial model was applied to the dynamic openness angles, the
predicted values seen in Figure 24 were found. Also shown in Figure 24 are the actual
values of lumbar angles for each corresponding openness angle.
The p-value for a paired t-test comparison between the polynomial predicted
static lumbar angles and the actual lumbar angles for the dynamic data was found to be

less than 0.0001.

61

 

a ___—n- _— ._-_ .7 __LL L.____L_.L_ ___—__L___—._ _._ _—. L_..__l

l’ " l
l Openness Angles vs. Actual and Predicted Lumbar ‘

Angles for Dynamic Subject Group I
100 ~ 1

80 l I
60 l I

a‘“!

 

oActual
I - Predicted l'

Lumbar Angle (deg)

 

I Openn_e_ss Angle (deg) __ I

Figure 24. Predicted dynamic lumbar angle values compared to actual dynamic
lumbar angle values for polynomial static population model applied to the openness
angles of the entire dynamic data group

 

Dynamic data predicting static positions for the test population
The linear model developed from the dynamic population was a=0.8400-63.6,
where a is the lumbar angle and 0 is the openness angle. This model was developed by

finding the best fit regression line for all of the dynamic data and can be seen graphically

 

   

 

in Figure 25.
I Linear Dynamic Predictive Model Development I
l
100 I I
l 8’ 30 I I
I 3 60 : a:0.846-63.6 -
2 I
g) 40 i I
l < 20 L
I g 0 l - - _y i l
l -40 r
I -60 L

Openness Angle (deg)

Figure 25. Graphical representation of linear populationpredictive model
developed from all of the dynamic openness and lumbar angle data

 

62

Figure 26 shows both the actual data from the static population and the predicted
values for the same openness angles that were determined by applying the model

developed by the dynamic population.

Openness Angles vs. Actual and Predicted Lumbar
Angles for Static Population

 

l
l o Actual II
”a I - Predicted IE

 

Lumbar Angle (deg)

 

l
_40. . I
I

9890”?S$LAL”9'L9 (99L _ _

 

Figure 26. Predicted static lumbar angle values compared to actual static lumbar
angle values for linear dynamic population model applied to the openness angles of
the entire static data group

Comparing the lumbar angles predicted from the linear model and actual lumbar
angles seen in Figure 26 with a paired t-test, the p-value was found to be less than 0.0001.

The second order polynomial model developed from the dynamic population,
seen in Figure 27, was found to be a=0.00702-0.4210-12.8, where u is the lumbar angle

and 0 is the openness angle.

63

Polynomial Dynamic Predictive Model Development

 

l 100

’6: 80 .

fi 60 I 0:0.00702-0.4216-12.8 ”1:35"

a: l - . °

IE: 40 l- '

I C l

'E 20 r

g 0 I 7 _I ”I

3 -20 I- 150 l
-40
-60

LopenrlzsLsAnglalgegiL L

Figure 27 . Graphical representation of polynomial population predictive model
developed from all of the dynamic openness and lumbar angle data

When this polynomial model, derived fi'om the dynamic population, was applied
to the static population, the predicted values seen in Figure 28 were found. Also shown
in Figure 28 are the actual values of lumbar angles for each corresponding openness
angle.

The p-value for a paired t-test comparison between the polynomial predicted
lumbar angles and the actual lumbar angles for the static population was found to be less

than 0.0001.

64

Openness Angles vs. Actual and Predicted Lumbar
Angles Static Population

 

l g 100 ‘r -
E 80 I ° N
2 60 l. . . - r—e- A «f
I? 40 . / . l'ACtua'
h I o . I - .
2 20 ‘. 0 ° L L FLrechLtgd s
5 0 : ‘7
-20 I I: 150 200
-40 I
I 2931969135026 09% L

 

Figure 28. Predicted static lumbar angle values compared to actual static lumbar
angle values for polynomial dynamic population model applied to the openness
angles of the entire static data group
Static data predicting dynamic positions within a subject
The p-values associated with comparing actual dynamic lumbar angle and

predicted dynamic lumbar angle from the linear and polynomial models derived from
each subject’s static data using a paired t-test can be seen in Table 11.

Table 11. Paired t-test values comparing predicted dynamic lumbar angles vs.

actual lumbar angles for a prediction model based off the same subject’s static data
Paired T-Test Probability

Linear Polynomial

S01 <0.0001 <0.0001
804 <0.0001 <0.0001
$08 <0.0001 <0.0001
810 <0.0001 <0.0001
SI 1 <0.0001 <0.0001
812 <0.0001 <0.0001
Sl3 <0.0001 <0.0001
Sl7 <0.0001 <0.0001
$18 <0.0001 0.132

819 <0.0001 <0.0001
821 <0.0001 <0.0001
$23 <0.0001 <0.0001
826 0.13 5 0.164

828 <0.0001 <0.0001
S30 <0.0001 <0.0001

65

Note that the only instances where the p-value is above 0.0001 are in the linear

and polynomial models for subject S26 and the polynomial model for subject S18.

Dynamic data predicting static positions within a subject

The p-values associated with comparing actual static lumbar angles and predicted
static lumbar angles from the linear and polynomial models derived from each subject’s
dynamic data using a paired t-test can be seen in Table 12.

Table 12. Paired t-test values comparing predicted static lumbar angles vs. actual
static lumbar angles for a subject prediction model based off of the same subject’s

0.01.

dynamic data

Paired T-Test Probability

Linear Polynomial
801 0.096 0.002
S04 0.410 0.405
808 0.126 0.055
810 0.294 0.246
S11 0.466 0.592
812 0.073 0.072
813 0.856 0.519
S17 0.561 0.540
S18 0.21 1 0.174
S19 0.894 0.215
S21 0.282 0.345
823 0.290 0.392
S26 0.632 0.672
S28 0.069 0.377
S30 0.494 0.465

Note that only subject S01 in the polynomial model shows a p-value less than

66

DISCUSSION AND CONCLUSIONS

A methodology was developed to quantify and measure the curvature of the
lumbar spine during seated postural changes. Additionally, the relationships between
lumbar curvature changes and changes in the relative rotations of the ribcage and pelvis
were evaluated. These lumbar curvature and openness measurements were made in static
and dynamic postures, and the relationships between them were evaluated using both
linear and second-order polynomial models. These data and models were then evaluated
statistically to determine significance and predictive capacity. The goal was to establish a
reliable methodology that could be used to predict lumbar curvature of an individual
while his/her back was obscured by a seatback for use in seat validation research and seat

design.

Openness and Lumbar Angles

Table 4 shows the static openness angles for each subject in each position along
with the total range of motion for each subject. From these data it was observed that the
openness angles varied with each position. In general, the trend was for the largest
openness angle to occur in the maximum lordotic posture, while the smallest openness
angle occurred at a maximum kyphotic posture. Physically, this matched intuition,
because in a lordotic posture, the top of thorax rotated in the posterior direction while the
pelvis rotated in the opposite direction. Given the vector directions applied in defining
the openness angle, this resulted in a larger angle. The opposite was also true; for a

kyphotic posture the top of the thorax rotated forward, while the top of the pelvis rotated

67

rearward. This brought the thorax and pelvis vectors closer to parallel with each other,
meaning the openness angle was smaller.

The total ranges of motion as measured by the openness angle were also noted.
All of the subjects were able to produce a minimum range of 24 degrees between their
maximum lordotic and maximum kyphotic positions. The average range of motion as
measured by the openness angle was 53 degrees. This means that the ranges of openness
angles well above the error for the system (0.38 degree) and provided adequately large
range within which a relationship could be determined.

Examination of the static lumbar angles seen in Table 5 yielded similar results to
the observations found with openness angles. The trend for the lumbar angles was for
the largest angle to occur at the maximum lordotic posture, while the smallest angle
occurred at the maximum kyphotic posture. This too made intuitive sense as the largest
lumbar angles would occur when the most eccentric lumbar marker was the farthest
anterior. As defined, this was positive. Movement through a “straight back” alignment
of the markers produced a very small angle, and when the most eccentric marker was
posterior, as was the case in kyphotic postures, the angle was negative.

In terms of total ranges of motion, as measured by the static lumbar angles, the
average range of motion was 41 degrees, while the smallest range of motion was 5.8
degrees. While not as large as the ranges for the openness angle, these values were still
above the thresholds of the error of the system, and supplied a sufficient range to evaluate
any relationships that existed between openness and lumbar angles.

Table 6 shows the range values for the dynamic motions. As measured by the

openness angle, the average dynamic range of motion was fi'om 62 degrees to 110

68

degrees for a total range of 48 degrees. These values covered a similar range as the static
data seen in Table 4 (61 degrees to 114 degrees, total range of 53 degrees). Similarly, the
dynamic lumbar angles ranged from -1 3 degrees to 33 degrees for a total range of 46
degrees, which covered a similar range as the static lumbar angle range seen in Table 5
(-16 degrees to 25 degrees, total range of 41degrees). These similarities showed that the

static postures were encompassing the same range of data as the dynamic motion data.

Distinct Static Positions

The data in Table 7 show low paired t-test scores (p<0.001) when each position
was compared to every other position as measured by both the openness angle and the
lumbar angle. This meant that both measures, openness and lumbar angle, independently
distinguished the four different postures, ranging from lordosis to kyphosis, in a seated
position.

This information was the basis on which all subsequent data was founded and was
therefore important to note. Had the positions been indistinguishable from one another
using the given measures, then comparisons between these positions would not have been
appropriate. However, since the openness angle distinguished postures based on anterior
markers and the lumbar angle distinguished postures as measured at the lumbar spine, it
was reasonable to pursue establishing a relationship between the two measures across

positions.

69

Observations between openness and lumbar angles

Static
From the data presented in Figure l and summarized in Table 8, it was seen that

plotting lumbar angle vs. openness angle for the static positions produced a relationship
that was well approximated by both a linear relationship (average r2=0.829) and a
second-order polynomial relationship (average r2=0.935).

Upon further inspection, it was seen that the disparity between the two average r2

values was mainly attributed to a few subjects. The majority of the subjects displayed
approximately the same r2 value for both the linear fit and the polynomial fit, but subjects
S11, S15, S18, and S20 all had linear r2 values at least 0.25 less than the corresponding

polynomial r2 values. This apparent jump in fit values was explained by the relatively
low number of data points in the static models. Mathematically, two points are required
to quantify a line, three points can quantify a second-order polynomial, and four points
can be fit to a third-order polynomial. When this is understood in how well a best fit line
is approximating the data, it becomes much easier to have a second-order polynomial
closely fit 3 points and have a small error on the fourth, than it is to have a linear model
very closely fit all four points. This can also be inferred visually by observing the
individual plots. Additionally, by viewing Figure 9(a—ee), it was seen that in most cases,
the polynomial fit did not differ drastically when compared to the linear fit.

It should also be noted from Table 8, and visually from Figure 10, the general
trend of the static position slopes of the best fit lines was positive. This meant that as the

openness angle grew larger, i.e. moving from maximum kyphotic to maximum lordotic,

70

the lumbar angle also grew larger. Physically, this correlated to a situation where the top
of the ribcage tilted rearward with respect to the pelvis and the lumbar spine
accommodated this motion by moving from a kyphotic to lordotic posture.

The y-intercepts of the models had no discemable physical meaning. This was
ascertained by investigating how the choices of the orientations of the ribcage and pelvis
vectors that form the openness angle affected the overall openness/lumbar relationship.
The ribcage and pelvis vectors were chosen because they simply rode along with each
“rigid” body. It would have also been possible to choose any two other sagittal vectors
that rode with the ribcage and pelvis. For example, the ribcage vector could have been
chosen in the opposite direction, originating at the C7 marker and passing through the
sternum. The only changes that would have occurred in the data would have been a 180
degrees shift in the openness angle and a Shift in the intercept of the linear model. The
slope would have remained the same because it would still be calculated as the change in
lumbar angle over the change in openness angle. Once this was established it was
possible to see that one is not limited to using only the vectors chosen in this study, but
any sagittal vectors that ride with the ribcage and pelvis.

This observation also could become useful in practice, in that the ribcage vector
could be chosen such that all of the required markers were on the anterior region of the
subject. In the current configuration, the C7 marker was used because of the ease of
consistent placement on the subject, but it also had potential drawbacks. For instance,
with subjects who had long hair, the hair had a tendency to fall down over the C7 marker
which obscured it from the cameras, leading to inconsistent data collection. In future

studies this marker placement could also be obscured in practice if a chair had an

71

exceptionally tall seatback. While these situations are preventable with hair ties and
smaller chairs, it could be beneficial for ease of data collection to move the entire ribcage
vector to markers on the sternum of the subject, with the only change in results being an

offset in the openness angles.

Dynamic

The same trends that were visible in the static data existed for the dynamic data.

As seen in Figure 11 (a-o) and Table 9, the average r2 values from the dynamic
measurements were 0.841 for the linear model and 0.875 for the second-order model.

This again meant that both models fit the data well. However, for the dynamic data a

smaller difference between the linear and polynomial 9 fits was measured. As can be
seen in Figure 11 (a-o) this can be attributed to the fact that the two models nearly
overlapped each other for most subjects. Thus, the conclusion was drawn that the added
complexity of the second order model was not necessary and a simpler linear model
would have sufficed.

Also similar to the static posture data, all of the linear slopes were positive but
one. The same subject, S18, showed the only negative slope. Though it appeared out of
the norm for the rest of the data collected, it was consistent across the two different types
of testing. This showed a consistency in measurement that indicated that the
openness/lumbar angle models being produced could have been subject specific.

On a per subject basis, Figure 12 (a-o) shows the static and dynamic data. From
this, it was possible to see that in most cases, the static and dynamic data for each subject

overlaid each other. While the ranges did not always match up precisely, it was possible

72

to see that a slope drawn for the static data would be similar to a slope drawn for the
dynamic data. Further discussion of this visual observation is provided in the upcoming

“Predictive Capacity” section.

Anthropometric Measures Related to Slope

The data in Table 10 showed low values for the Pearson Product Moment
Correlation Coefficient. This meant that the anthropometric measures had low
correlation with the relationship between the openness angles and lumbar angles. For a
significance level of 0.05, the anthropometric measures did not produce a correlation
coefficient that was of a critical level for the static data. In the dynamic data, only seated
height and pelvic depth had correlation coefficients that reached the critical level at a
significance of 0.05. This meant that seated height and pelvic depth could have an
influence on the dynamic slope, but it was still not a strong possibility. At a significance
level of 0.01, the critical value for 15 subjects was 0.641 [44] which no correlation values
reached. This independence of correlation with the anthropometric measures meant that

the linear relationship could be determined solely from the openness and lumbar angles.

Predictive Capacity

The similarities between the static posture data and dynamic data, without any
dependence on anthropometric data, lead to testing of the predictive capability of each
group. First, four cases for the entire test population will be discussed, followed by two

cases of individual subject data.

73

Static data predicting static positions for the test population

The high p-value associated with the comparison between the predicted values
and the actual values for the static positions indicated that the two groups were not
statistically different. That meant that the first group produced a model that when applied
to the second group produced results that were statistically indistinguishable fi'om the
actual values. This meant that given a group of sample individuals, a singular linear
model could be developed that could predict lumbar angles of a separate population
based solely off of measured openness angles.

This demonstrated that the approach of measuring the relative motion between the
thorax and pelvis was a viable method for predicting lumbar curvature. This approach
then has the potential to be used in a seating research environment where only openness
angles are calculated to infer the lumbar curvature of the seated individual in static
postures. It should be noted, though, that was on a population basis, and required that a

population of subjects had been sampled, not just a single subject.

Dynamic data predicting dynamic positions for the test population

The dynamic to dynamic predictive modeling did not show the same results. The
low p-value obtained through the paired t-test for this test condition indicated that the
model and test pool were not from the same group. This meant that the dynamically
determined linear models did not produce a total model that would predict with any
certainty known lumbar angles given the openness angles of the second group. It is

possible that this was because of the high number data points available. Thus a linear fit

74

would not have been able to quantify the dispersion of the points, due to variation. It is
also possible that each subject had a specific profile that was not well captured by a total

linear model.

Static data predicting dynamic positions for the test population

The low p-values (p<0.0001) indicated that the actual lumbar angles and lumbar
angles predicted from the static population model for the dynamic movements were
statistically different. This meant that a model developed from a population of subjects
in static postures should not be used to infer a population of dynamic lumbar angle

movements.

Dynamic data predicting static positions for the test population

The low p-values (p<0.0001) indicated that the actual lumbar angles and lumbar
angles predicted fiom the dynamic population model for the static positions were
statistically different. Just as one should not predict a dynamic population from a static
population, this shows that a dynamic population model should be not be used to infer
static lumbar angles for a population.

For both the dynamic to static population prediction modeling and the static to
dynamic population prediction modeling, it was expected that the significance in
prediction power was lost when such a large and varied population was sampled. While
almost all of the subjects displayed a positive trend in their individual relationship
between openness angle and lumbar angle, the distinct nature of each of those

relationships was lost when viewed as a total population. The result, as seen in Figure

75

21-F i gure 28, was a broad collection of data points less focused around a single
trajectory. This, in turn, could have been a factor that diminished the predictive capacity

of each of the models.

Static data predicting dynamic positions within a subject

The data in Table 11, drawn from subject by subject linear and polynomial static
to dynamic prediction models, showed p-values that indicated that the predicted values of
lumbar angle in a dynamic environment based off of a subject’s static model were
statistically different from the actual lumbar angle values. Therefore, this method of
prediction of the lumbar angle was not consistent enough to be used reliably.

This was in contrast to what was previously observed in Figure 12 (a-o). Though
the static and dynamic data appeared to produce similar models, statistically, this
direction of prediction was insufficient. This could have come from any of several
reasons.

The mismatch could have been due to differences in the forces required to
produce static postures as opposed to dynamic movement. Basic dynamics show that
forces on an object in motion are different from the forces on the same object in static
equilibrium. In the human body, this takes on an even greater meaning as those forces
have to be generated by many different groups of muscles and interactions between many
rigid bodies. The muscles used and distribution of forces in the static postures could have
been very different from those used in the dynamic motions, which would explain the

different openness and lumbar angles.

76

Another explanation could be that the statistical method for determining the value
of the prediction was too strict. In the current models, the lumbar angle predictions laid
on distinct trajectories. This amplified every difference between the predicted and actual
values. For this reason, it is suggested that in future research broader prediction models
be explored.

The discrepancies between the prediction models and actual data could have also
been a result of people not moving through one specific trajectory when moving from
lordotic to kyphotic positions and vice versa. As seen most prominently in Figure 12 for
subjects 811 and S23 the dynamic trajectory appeared to form a loop. This implied that
there were multiple lumbar angles for each openness angle. A single linear or
polynomial model was not sufficient to capture that phenomenon.

Additionally, it would have been advantageous to have multiple sets of static and
dynamic data for each subject. These could have been used to determine repeatability
and test prediction models developed from one dynamic data set and applied to another

dynamic data set from the same individual.

Dynamic data predicting static positions within a subject

The p-values associated with dynamic data predicting the static data within
subject tell can be seen in Table 12. The only predicted values that were statistically
different than the actual static lumbar angle values with a p-value less than 0.01 were the
polynomial model values for subject S01. All other predicted values were not deemed to
be statistically different. In practice, this means that a model based off of a dynamic

“calibration” taken while the subject was seated in a backless chair could be used to

77

predict static lumbar angles for the same subject. With this established, it is possible to
pursue such applications as predicting lumbar angles while a subject is seated in a chair
with a back. Then the lumbar angles of static postures of maximum lordotic, maximum
kyphotic, “straight and tall”, and “comfortable” could be compared to similar measures in

seatbacks to determine how well a chair fits each user.

A summary of the prediction methods can be seen in Table 13. It should be noted
that the static to static population prediction model and the dynamic to static within
subject prediction model produced statistically indistinguishable predicted lumbar angles
when compared to the actual lumbar angles.

Table 13. Prediction methods summary table

Statistically p-value
' nM d l S' uif' L' ear Pol omial
. . a y ,.. .. , W .l. . .5

         
  

 

 
   
 

      
 
   

 

     

Individua
Population
Individual
P l '

 

  
    

 

       

3.; ‘
Static to Dynamic Population Yes <0.0001 <0.0001
Individual Yes see Table 12

 

 

Summary of findings

From this research the primary findings of the work are stated as follows:

0 Four distinct static postures can be identified by means of openness angle and the
lumbar angle.
0 The ranges of motion for the static postures covered the same ranges of motion as

the dynamic motions as measured by both the openness and lumbar angles.

78

o In both static postures and dynamic motions, the relationships between openness
angle and lumbar angle were positive.

0 In both static postures and dynamic motions, the relationships between openness
angle and lumbar angle were well defined by both linear and second-order
polynomial models.

0 It was possible to predict the relationship between openness and lumbar angles for
a group of subjects in static seated postures based upon a model developed from a
similar group of subjects seated in the same static seated postures.

0 It was possible to predict the relationship between openness and lumbar angles
experienced in static seated postures for a single subject based upon a linear or

polynomial model determined from the same subject’s dynamic motion.

In a broader sense, these results lead to two overarching outcomes. The first was
that a methodology was successfully developed to quantify seated lumbar curvatures
using a 3D motion capture system. The lumbar curvatures were then successfully related
to visible boney landmarks on the anterior portion of the body. This is valuable because
the curvature quantification can be used to inform seat designs with lumbar supports that
can match lumbar curvatures of seated occupants. The data collected from this
methodology also showed that it was feasible to predict postural change of individuals by
monitoring the positions of the pelvis and ribcage. This is valuable in the area of seating
evaluation where it is necessary to know the curvature of the lumbar region of the back

while it is obscured from direct measurement.

79

Relation to published research

These findings fill a void in the research of seated human movement and dynamic
lumbar movement. Based upon a review of the literature, studies reporting seated lumbar
postural change and its quantification are limited. Several researchers [33, 14, 19, 37]
have addressed changes in the lordotic curvature while standing; however these
measurements used landmarks on the posterior portion of the body. The approaches
presented by Ng et a1. [33], Choi et a1. [14], and Lee and Wong [37] would not be
possible in the seated position while the occupant’s back was obscured by a seatback.
Thus, the methodology and associated data from the research reported in this thesis
represent a new basis for the quantification of the contour of the lumbar region of the
back and its relationship to the relative angular displacement between the ribcage and
pelvis.

The novel nature of this research means that comparisons to other methods were
difficult. Methods in previous research relied upon the precise tracking of each vertebra
by means of radiographs, such as those presented by Frobin et al. [27], Harrison et a1.
[28], and Janik et al. [29], or by means of MRI’s such as those presented by Hedman and
Fernie [31], and Karadirnas et al. [32] while the method developed for this thesis relied
on measuring the surface contour of the lumbar region as a whole. The reason for this
was that a lumbar support, which is an integral part of the seat design, will not directly
support each vertebra, but rather would provide support to the entire region during
postural changes. Therefore, it was not necessary to know the exact position of each

vertebra, but rather the changes in contour of the entire lumbar region. This emphasis on

80

developing a practical method for the'seated position limited the comparisons to previous
research.

The need to quantify curvatures dynamically as people changed spinal curvature
also meant that the use of radiographs or MRI’s was not possible. Consequently,
comparisons between the static results of the previous work by Frobin et al., Harrison et
al., Janik et al., Hedman and Femie, and Karadimas et al. and the results presented in this
thesis were not appropriate. The method developed as part of this thesis provides a
unique means to measure the lumbar contour, as a whole, dynamically, for designing and
validating modern seating.

However, in terms of ranges of back motions, although not identical to this
thesis’s research, the data from Walsh et al. provides a means for comparison. Walsh et
al. quantified the movement of the angle formed by external markers located near the L4,
T7 and C7 vertebrae. Walsh et al. found the range of motion to be approximately 10-35
degrees across their sample of 10 subjects. From the research for this thesis, the range of
static openness was from 24.7-85.6 degrees and the range of static lumbar angles was
5.8-88.4 degrees. The larger ranges in the current study can be attributed to the extreme
kyphotic and lordotic cases that were included in this study but not in Walsh’s work. In
addition, both Walsh and the work reported here found the range of motion to be subject
specific (i.e. some individuals achieved the full range of motion while others achieved
only a subset of that range). In a broad sense, all three measures can be considered as

measures of the movement of the human back and their similarity is positive.

81

Low Back Pain, Chair Design and Dynamic Postural Change

The importance of a well designed seat is directly related to Low Back Pain
(LBP). LBP is costly to society monetarily, as well as in lost work time, impaired work
efficiency, and diminished quality of life. The costs come from worker’s compensation
claims, hospital costs, medication, community care and more [4,5]. The National
Institute for Occupational Safety and Health estimated that LBP costs $14 billion to
American industry annually [6].

LBP comes from the extremes of back activity: either high back activity or low
back activity. Low back activity comes from prolonged static postures. Particular to this
research, LBP has been linked to extended periods of static seating [9]. This static
seating occurs in automobile seating, office seating, and wheelchairs, amongst others.

To reduce LBP from prolonged static postures, dynamic postures should be
encouraged. It has been shown that dynamic postures can decrease intervertebral disc
degeneration over time [8]. It has also been shown that chairs that support dynamic
postures are more likely to induce back movement throughout the day [7]. The question
then becomes, “How do we design chairs that support dynamic postures?”

In terms of application to seatback design, the ranges of, and relationship between
the dynamic openness angles and lumbar angles developed in this research can be used to
design chairs that will support a wide range of positions. For most people, the openness
angle varies linearly between the maximum lordotic and maximum kyphotic curvatures
meaning that the lumbar region of a chair can be designed such that the trajectory of the

support curvature is linear between two maximums. Furthermore, the kinematic

82

orientation of the ribcage and pelvis could be used as the inputs that control the contour
of the lumbar support. Then, instead of statically calibrating a Chair’s lumbar support for
a single posture, a chair could be dynamically calibrated to the proper amount of lumbar
support change for a given amount of ribcage and pelvis movement.

These findings can also be used to evaluate commercially available chairs and
seats (e. g. car, trucks, busses, trains, airplanes; wheelchairs) for how well the motion of
the seatback matches the motion of the occupants which then can be related to the
support provided by the chair. Objective evaluations can serve the purpose of
distinguishing chairs from one another in terms of promoting dynamic postures and
confirming claims made by manufacturers regarding seat back movement. Chairs that do
not support a wide range of postures for an array of anthropometries can be objectively
identified.

To summarize, the methods and knowledge of dynamic human lumbar contours
developed from this research will support informed design and evaluation of chairs in a
broad range of applications, from office and automotive seating to design of seating for

the disabled, and thus have potential for tremendous societal impact.

83

APPENDIX

Al. Subject Questionnaire

 

Lifestyle Questionnaire

Please be as thorough and accurate as possible when answering the following questions.
If anything is unclear, please ask the test administrator for clarification on the day of
testing.

l.What is your current age? yrs. height ft. in. ,
weight lbs. Male Female (circle one)

 

2. Are you currently under medical care? Yes , No

Explain:

 

3. Have you been injured recently in the hand/wrist/ elbow/arm or back region?
Yes No

 

How long ago?

 

Is it a reoccurring pain/injury? If so, how often?

 

Are you under current treatment for this condition? Yes No
Has this condition impaired your daily activities? Yes No

Explain:

 

4. Have you experienced any back or neck pain today? Yes___,No _

Do you know the cause?

5. Are you currently taking any pain medications?
Yes No
If so, which medication(s)

 

 

 

What are the medications

for?

84

A1 (cont.).

 

6. Are you right or left handed?

7. What is your occupation?

 

8. Daily, how many hours would you say you are seated at a computer?

 

9. During the time you work at a computer, please estimate the % of time you:

_ use the keyboard

--------- use a mouse or similar device

--------- j ust studying the screen

(Percentages should add up to 100)) Example: 40% keyboard, 30% mouse, 30% screen)

10. Do you know what type of office chair you currently have?

 

11. Do you use your armrests when you mouse? Yes No if so, describe

 

12. Are you pregnant? Yes No _

(If the subject is pregnant, she may be excused from the testing.)

85

A2. Individual Subject Measurements

Seated

Seated B. Pelvic Pelvic Pelvic

Height Weight Age Height Width Width Height Depth
Subject (in.) (lb) (y.o.) Sex Hand (in.) (cm) (cm) (cm) (cm)
801 173 810 24 85.1 39.5 23.0 7.0 15.5
802 180 867 25 91.4 34.5 23.0 10.0 12.5
803 163 534 26 83.8 35.0 20.0 7.5 12.5
804 160 534 22 86.4 38.5 24.0 7.0 15.5
SOS 161 494 22 87.6 30.5 25.5 5.5 12.0
806 165 663 22 86.4 35.0 22.5 12.5 14.0
807 175 636 20 91.4 34.0 25.0 12.0 14.5
808 168 569 20 85.1 35.5 28.0 10.5 13.5
809 175 703 23 88.9 38.5 25.5 10.0 17.0
810 152 494 23 81.3 38.0 25.0 7.0 13.5
811 150 400 23 73.7 33.5 21.0 6.5 11.5
812 159 543 23 82.6 38.5 24.5 6.0 15.5
813 170 605 24 86.4 35.5 22.5 7.5 15.0
814 163 814 26 86.4 46.0 26.0 6.0 19.5
SIS 171 609 20 86.4 34.0 22.5 10.5 15.5
816 174 721 23 86.4 39.0 23.5 7.5 18.0
817 156 609 20 82.6 36.0 21.5 6.5 16.0
818 150 489 24 74.9 34.0 22.5 7.5 12.5
819 150 485 24 73.7 34.5 21.0 8.0 12.5
820 184 867 25 94.0 38.0 21.5 7.5 15.5
821 163 552 23 86.4 37.0 22.5 8.5 15.5
822 185 899 25 91.4 41.0 25.5 9.5 17.0
S23 169 676 26 87.6 41.5 22.0 8.0 16.5
824 154 494 21 81.3 38.5 21.0 8.5 15.0
825 177 689 23 86.4 38.0 22.5 10.0 15.5
S26 177 836 25 91.4 39.5 20.5 7.5 16.5
827 173 623 24 87.6 38.0 21.5 7.0 16.0
828 183 712 24 91.4 35.5 25.5 10.0 14.0
829 177 867 27 88.9 38.5 24.5 8.0 18.0
S30 179 1001 24 91.4 44.0 24.5 10.0 17.0
S31 179 770 25 88.9 38.5 24.0 10.0 15.5

ZZZZZZmeZmme-nzz'nrnrnmmmmZva-nrnz:
t-‘FUFUt-‘FUt-‘PUFUWFUFUFUFUFUFUFUWWFUFUWFUFUWFUFUFUFUW71W

 

Min 150 400 20 73.7 30.5 20.0 5.5 11.5
Max 185 1001 27 94.0 46.0 28.0 12.5 19.5
Average 168 663 23.4 86.0 37 .4 23.3 8.4 15.1
SD 10.8 151 1.89 5.09 3.19 1.91 1.78 1.93

86

A3. Calibration Measurements
Calibration measurements were made on two separate days to ensure accuracy of
motion tracking system. The first table shows length measurements of 3 different wands

with tracking markers on the each end. They are named by the measurement made by

hand.
lndlvldual Tracking (mm) 3 Wands at Once (mm)
157mm 173mm 176mm 157mm 173mm 176mm
Day1 Average 157.21 173.60 176.01 156.84 173.80 176.56
S.D. 0.878 0.311 1.640 0.523 0.387 0.574
Day 2 Average 157.35 173.80 176.50 156.98 173.88 176.65
S.D. 0.741 0.301 0.341 0.808 0.554 0.362

 

The next two tables show length and angle calculations for two calibration
triangles. These consisted of a solid piece of wood with 3 markers affixed at fixed
distances and angles from one another. For all data shown here, lengths are measured in

millimeters and angles are measured in degrees.

 

Small Triangle
Length Length Length Angle Angle Angle
AB BC CA ABC BCA CAB
(mm) (mm) (MM) (dog) (dog) (dog)
Day 1 Average 171.23 243.42 172.00 44.96 44.70 90.34
S.D. 0.903 1.061 0.896 0.340 0.218 0.339
Day 2 Average 171.19 243.50 172.31 44.67 45.04 90.29
S.D. 0.946 0.901 0.726 0.246 0.298 0.381
Blg Triangle
Length Length Length Angle Angle Angle
AB BC CA ABC BCA CAB
(mm) (mm) (mm) (deg) (deg) (deg)
Day 1 Average 410.25 428.46 469.51 68.04 54.14 57.82
S.D. 0.561 0.715 0.670 0.118 0.098 0.126
Day 2 Average 410.60 428.46 469.68 68.04 54.17 57.79
S.D. 0.634 0.578 0.506 0.094 0.094 0.098

87

 

A4. Lumbar radius calculation

 

 

 

 

 

 

 

Figure 29. Diagram for radius calculation

Given a triangle with sides of arbitrary lengths a, b, and c, as seen in Figure 29, it is
possible to draw a line perpendicular to side c that will give the height of the triangle,
which will be called h. The triangle is now divided into two different right triangles with
height h, and base lengths d and c-d. Using this, and Pythagorean’s Theorem, it is

possible to solve both triangles for h2 as seen in equations 12 and 13.
h 2 = b2 — d 2 (12)

h2 =a2—(c-d)2 (13)

Setting these two equations equal to one another allows for solving of length d in terms of

the known quantities a, b, and c, seen in equation 14.

_—a2+b2+c2

2c

d

 

(14)

88

A4 (cont.).
Once d is known, it can be entered back into equation 12 such that h can be solved for in

the following manner, seen as equations 15-18.

 

 

 

 

 

2
_ 2 2 2
h2=b2—[ a +b +c ] (15)
2c
4 4 4 2 2_ 2 2 2 2
h2=b2- a +b +c 2a b2 2a c +2b c (16)
4c
2 —a4 —b4 —c4 +2a2b2 +2a2c2 +2b2c2
h = 2 (17)
4c
1 —a4 —b4 —c4 +2a2b2 +2a2c2 +2b2c2
11:- (13)
2 c2

Once h is described in terms of the known values, a, b, and c, the area of the triangle can

be found by using the equations 19-21.

A = %(base)(height) = £611 (19)

 

 

_4_4_4 22 22 22
l l\/a b c +2ab +2ac +2bc (20)

A=—c—
22 ,2

 

A =i-J—a4 —b4 —c4 +2a2b2 +2azc2 +2b2c2 (21)

89

A4 (cont.).

Equation 21 is commonly known as Heron’s formula, which gives the area of a triangle

given the lengths of each of the sides of the triangle. Alternative forms of Heron’s

formula are shown in equations 22 and 23.

 

A=-:I\/(a2 +192 +c2)2 —2(a4 +b4 +c4)

 

A=-:I\/(a+b+c)(a+b—c)(a—b+c)(—a+b+c)

Another method to solve for the area of the triangle is to use equation 24.

A = gab sin WC

The Law of Sines states:

a b c —2r

sintt/A _ sint/IB — sintt/B —

 

 

(22)

(23)

(24)

(25)

Equations 22, 24, and 25 can then be combined to solve for r in terms of the known

lengths a, b, and c shown as equations 26-28.

90

(26)

 

A4 (cont.).

,=___ on

_ abc
r—J(a+b+c)(a+b—c)(a—b+c)(—a+b+c)

 

(28)

 

91

A5. Dynamic Openness and Lumbar Angles (deg)

$01
0
83.8
83.9
83.9
84.2
84.4
84.6
84.9
85.1
85.5
85.9
86.1
86.5
86.9
87.1
87.5
87.9
88.3
88.5
88.7
89.3
89.3
89.6
90.2
90.4
90.7
91.2
91.6
91.9
92.1
92.7
93.1
93.6
94.1
94.7
95.1
95.5
95.8

 

0.

-3.3
-3.4
-3.2
-4.1
-3.9
-3.0
-2.9
-2.6
-2.0
-l .3
-l .3
-l .4
-l .8
-1.4
-3.0
-3.4
-3.0
-2.1
-2.2
-0.7
-0.9
-0.5
0.2
1.0
2.3
1.5
-0.1
0.5
0.7
0.4
1.4
2.8
3.6
3.9
3.3
4.9
3.6

 

96.3
96.8
97.0
97.3
97.6
97.7
97.9
98.0
98.1
98.2
98.3
98.5
98.6
98.8
98.9
99.0
99.2
99.4
99.5
99.7
100.0
100.4
100.8
101.0
101.1
101.2
101.4
101.5
101.5
101.3
101.2
101.1
100.9
100.9
100.8
100.7
100.7

5.1
4.7
3.4
3.4
4.4
6.1
4.5
3.7
4.4
4.4
3.7
3.5
3.6
5.8
3.6
3.6
5.0
3.3
5.3
6.0
7.0
7.1
7.1
6.1
5.8
6.8
6.4
6.9
8.5
7.3
6.4
6.5
7.0
7.4
7.2
7.4
7.6

 

100.6
100.8
101.0
101.1
101.2
101.2
101.2
101.3
101.2
101.1
101.0
101.0
100.9
100.8
100.7
100.6
100.6
100.6
100.6
100.6
100.6
100.6
100.6
100.6
100.6
100.5
100.5
100.4
100.6
100.4
100.5
100.3
100.3
100.2
100.2
100.1
99.8

7.4
7.1
7.8
7.6
7.0
7.3
6.9
6.9
5.5
6.6
5.9
5.4
7.1
6.3
6.4
5.9
5.6
6.1
7.0
6.9
6.9
5.9
6.3
6.3
5.6
6.4
6.7
7.0
6.4
6.6
6.0
6.3
5.9
7.4
6.4
5.8
5.6

 

99.6
99.5
99.3
99.4
99.0
98.6
98.2
98.1
97.6
97.1
96.7
96.1
95.6
95.0
94.4
93.7
93.3
93.0
92.7
92.3
91.8
91.6
91.3
91.0
90.7
90.3
89.8
89.4
89.1
88.9
88.7
88.6
88.1
87.6
87.3
87.1
86.8

92

5.2
3.5
3.0
2.9
3.8
3.9
3.3
3.0
3.2
3.4
3.4
3.0
3.1
2.6
1.9
2.5
-0.3
-O.3
1.4
0.4
0.6
2.5
2.4
2.5
2.4
1.1
0.2
0.4
0.7
-O.1
-1.0
-0.8
-0.1
-0.7
-2.2
-l.7
-l.6

 

86.6
86.2
85.7
85.0
84.3
84.1
83.7
83.2
82.8
82.6
82.4
82.0
81.8
81.4
81.1
81.0
77.6
77.5
77.3
77.3
77.2
77.2
77.1
77.0
76.9
76.8
76.7
76.8
76.7
76.8
76.8
76.8
76.8
76.7
76.7
76.7
76.7

-1.2
-l.l
-1.2
-l.0
-O.5
-3.0
—2.7
-2.0
-2.3
-2.2
-2.4
-2.6
—2.7
-2.7
-2.5
-2.7
-3.1
—2.7
-2.7
-l.2
-4.2
-2.0
-5.0
-l.7
-O.8
-3.9
-4.8
-3.6
-4.6
-4.6
-4.8
-4.6
-5.0
-4.9
-4.0
-4.2
-3.5

 

0

76.8
76.7
76.6
76.7
76.6
76.5
76.5
76.5
76.6
76.6
76.6
76.5
76.6
76.5
76.6
76.6
76.6
76.6
76.7
76.8
76.7
76.7
76.7
76.7
76.7
76.7
76.8
76.8
76.8
76.7
76.8
76.7
76.7
76.8
76.8
76.8
76.8

(1

-5.4
4.7
-2.7
-4.8
-3.3
-2.9
4.0
4.4
4.5
4.4
4.5
-4.6
4.3
4.0
4.5
4.5
4.3
4.5
—4.6
4.5
4.6
4.7
4.5
4.6
4.9
4.7
-5.4
-5.0
-3.0
-5.2
4.5
4.4
4.5
4.3
4.0
4.2
-3.9

 

A5 (cont.).

S01
0
76.8
76.8
76.8
76.8
76.8
76.8
76.8
76.8
76.8
76.8
76.9
76.9
77.1
77.2
77.2
77.2
77.2
77.3
77.4
77.5
77.5
77.5
77.5
77.6
77.8
78.0
78.3
78.5
78.7

 

0.

—4.6
-4.9
-5.4
-4.8
-5.0
-4.3
-4.3
-4.5
-4.3
-4.6
-4.7
—4.7
-5.2
-4.8
-4.3
-4.7
—4.2
-4.6
-4.8
-4.4
-4.9
-4.7
-3.1
-3.5
-6.2
-l.O
—4.6
-4.0
-4.2

 

93

A5 (cont.).

504
0
70.0
70.3
70.9
71.4
72.3
73.1
73.8
74.4
75.5
76.1
77.0
77.7
78.5
79.2
80.1
80.8
81.5
82.1
82.7
83.1
83.3
83.6
83.9
84.2
84.5
84.8
85.0
85.4
85.5
85.8
86.0
86.0
86.2
86.3
86.4
86.4
86.7

 

4.2

5.3

5.4

5.2

5.2

5.9

5.1

5.4

6.9

6.8

11.5
11.1
7.7

10.0
11.0
11.3
12.0
10.9
10.5
10.8
12.1
11.9
13.0
13.9
15.5
15.1
14.6
15.7
14.7
14.2
15.3
16.8
17.0
17.4
16.5
17.9
19.3

 

0

86.8
87.1
87.4
87.8
88.0
88.2
88.3
88.5
88.7
88.7
88.9
88.9
89.0
89.1
89.2
89.4
89.6
89.8
89.8
91.3
91.3
91.3
91.3
91.2
91.3
90.3
89.9
89.8
89.5
89.0
88.5
88.1
87.4
86.7
86.5
86.0
85.8

0.

18.7
19.0
19.6
19.3
20.3
20.5
20.0
21.3
21.5
21.8
21.0
22.6
21.4
22.6
23.8
23.4
25.0
24.9
25.8
26.6
27.2
26.4
26.3
26.4
26.5
24.1
23.3
22.6
22.2
21.2
21.0
21.1
21.7
17.6
17.6
17.8
17.1

 

9

85.3
85.0
84.5
84.1
83.8
83.0
82.2
81.4
80.4
79.7
79.0
78.6
78.0
77.3
76.5
75.9
75.2
74.5
73.5
72.9
72.1
71.5
70.9
70.5
70.1
69.5
69.0
68.5
68.2
67.8
67.2
66.5
65.8
65.4
65.1
64.6
64.3

0.

18.1
17.3
17.9
17.0
15.1
16.5
14.4
13.0
11.5
10.2
11.4
10.8
11.2
11.1
11.7
11.0
11.4
9.4
11.6
9.8
8.3
9.2
8.2
7.5
7.5
8.0
6.5
4.7
4.0
3.1
5.4
2.9
2.8
1.0
-4.6
0.8
0.7

 

63.9
63.6
63.3
63.0
62.8
62.6
62.4
62.1
61.8
61.6
61 . 1
60.9
60.8
60.5
60.5
60.4
60.4
60.3
60.1
60.0
60.0
59.9
59.8
59.9
59.9
59.9
60.0
60.0
60.0
60.1
60.1
60.2
60.2
60.1
60.2
60.2
60.4

94

0.7

0.1

0.7

0.6

0.0

-3.1
-4.1
-6.1
-5.6
-5.3
-5.4
-5.8
-5.7
-6.2
-6.5
-6.8
-6.4
-6.4
-6.4
-6.8
-6.9
-6.7
-6.3
-5.9
-6.7
-6.2
-6.9
-7.2
-7.1
-7.5
-7.0
-5.8
-6.7
-6.4
-5.6
-6.4
-5.8

 

0

60.3
60.3
60.4
60.3
60.3
60.3
60.3
60.5
60.7
60.8
60.9
61.1
61.4
61.7
62.3
62.6
62.3
62.5
62.9
63.4
63.8
64.1
64.4
64.8
65.3
66.1
66.4
66.7
66.8
72.8
73.0
73.3
73.6
73.7
73.9
74.1
74.1

a

-5.6
-4.9
-4.6
-4.4
-4.4
-4.8
-5.2
-6.0
-5.6
-6.3
-5.6
-5.7
—7.0
-7.9
-6.0
-6.2
0.3
-4.5
-3.8
-3.8
-4.4
-3.4
-3.5
2.3
2.8
2.3
0.9
1.5
2.1
5.8
5.7
6.7
7.0
6.9
7.1
7.3
7.1

 

74.2
74.4
74.6
74.8
75.1
75.2
75.2
75.2
75.2
75.2
75.1
75.0

9.2
7.6
8.9
9.2
9.6
9.8
7.3
7.2
7.4
7.1
7.2
7.2

 

 

AS (cont.).

$08
6

87.3
87.3
87.4
87.4
87.4
87.6
87.9
88.6
89.0
89.4
89.8
90.3
90.6
91 . 1
91.5
92.0
92.2
92.8
93.7
94.1
94.7
95.3
95.9
96.3
96.5
96.7
96.9
97.2
97.5
98.2
99.2
99.9
100.7
101.1
101.3
101.4
101.4

4.8
4.9
4.6
4.6
4.8
7.6
5.0
11.1
8.9
5.5
5.2
6.3
6.5
7.9
8.2
7.2
7.7
10.9
12.3
10.4
13.8
15.8
14.6
15.4
19.5
18.0
16.0
17.7
19.4
21.1
23.7
24.2
26.9
27.8
28.0
29.1
29.7

 

0

101.6
101.6
101.7
101.7
101.9
102.0
102.1
102.2
102.2
102.3
102.3
102.3
102.3
102.3
102.3
102.2
102.2
102.2
102.3
102.1
102.2
102.1
102.2
102.2
102.2
102.1
102.2
102.1
102.2
102.1
102.2
102.2
102.2
102.2
102.2
102.2
102.3

a

28.7
29.0
29.6
29.7
28.0
30.0
28.1
30.0
30.8
30.2
28.2
30.3
30.7
30.3
30.2
30.7
30.1
30.0
30.6
29.6
29.8
30.6
30.1
27.7
29.7
28.7
29.7
29.0
30.7
30.7
27.3
30.7
29.8
30.3
29.6
29.7
28.8

 

0

102.3
102.3
102.3
102.2
102.3
102.3
102.3
102.3
102.5
102.3
102.4
102.4
102.4
102.5
102.4
102.4
102.4
102.4
102.3
102.4
102.3
102.4
102.2
102.2
102.1
101.9
101.8
101.7
102.1
101.1
100.7
100.4
99.5

98.7

97.8

96.9

96.0

(I

30.3
30.1
30.3
31.7
32.6
31.8
31.5
32.8
33.5
32.3
31.9
31.0
31.5
31.3
31.1
31.4
31.4
31.3
31.7
32.8
31.0
31.7
31.2
30.9
32.4
32.8
31.6
31.8
31.4
30.6
28.7
27.2
26.9
24.3
21.9
20.7
17.9

 

95.1
94.0
93.1
92.0
91.1
89.9
88.7
87.8
86.7
85.4
84.2
83.1
82.0
81.2
80.0
79.0
77.9
76.8
76.0
75.0
74.4
73.5
72.6
71.7
70.8
69.9
68.9
67.9
67.0
66.2
65.4
64.9
64.3
63.7
63.2
62.5
62.0

95

a

17.1
16.3
12.7
12.9
14.0
6.5
10.8
6.5
8.1
5.0
2.3
1.5
4.0
4.4
6.3
0.5
2.6
0.6
1.6
-6.5
-7.5
-8.0
-8.4
-8.6
-9.9
-10.6
~12.l
-l 1.3
-l 1.1
-12.4
~13. 1
-13.7
-l4.2
—14.3
-l4.7
-l4.5
-l4.8

 

61.4
60.8
60.4
59.8
59.3
59.1
58.7
58.4
57.9
57.7
57.1
56.9
56.7
56.7
56.5
56.5
56.4
56.3
56.3
56.4
56.5
56.4
56.4
56.5
56.7
56.6
56.6
56.9
57.2
57.7
58.1
58.4
58.5
58.7
58.6
58.6
58.6

(1

-15.2
-l4.6
-15.1
-15.0
-15.8
-15.2
~15.6
-15.7
-15.8
~16.4
-15.8
-l6.0
~16.1
-16.1
-15.8
-16.2
-l6.3
-l6.6
-17.0
-15.8
-16.2
-16.0
-15.9
-l6.1
-16.3
-l6.3
-16.0
-16.4
-16.3
-15.6
-15.6
-15.8
-l6.0
-16.3
-16.3
-17.0
-16.7

I L“- .1-

 

 

A5 (cont.).

$08
9
58.6
58.5
58.5
58.6
58.7
58.8
58.7
58.8
59.1
59.1
59.2
59.3
59.5
59.6
59.7
59.8
59.8
59.9
60.0
60.0
60.1
60.2
60.3
60.5
60.7
61.2
61.6
62.3
62.6
63.1
63.9
64.4
64.9
65.4
65.8
66.2
66.7

 

0.

-16.4
-16.3
-15.6
-15.8
-l6.3
-17.3
-l7.3
-16.3
~16.0
-15.7

-15.8'

-15.4
-15.8
-15.9
-15.8
-15.3
-15.8
-16.0
-15.7
-16.3
-l6.1
-16.0
-15.7
-15.9
-15.4
-15.4
-15.6
-14.7
-15.9
-15.5
-15.0
-13.8
-14.1
-13.8
-17.9
-13.9
-l4.0

 

67.5
68.3
68.7
69.6
70.5
71.5
72.4
73.2
73.9
74.5
75.4
76.4
77.4
78.2
78.6
78.7
78.9
79.2
79.6
80.2
80.9
81.2
81.9
82.5
82.9
83.6
84.0
84.6
85.2
85.7
86.2
86.5
86.7
87.0
87.4
88.1
88.8

(1

-12.9
-12.9
-14.0
-12.8
-12.4
-10.8
-lO.l
-8.0
-7.5
-12.2
-7.1
3.3
-8.4
1.7
2.0
2.0
0.7
1.0
3.2
3.4
3.2
4.5
10.0
9.7
7.8
7.0
5.0
7.0
5.5
4.5
6.2
6.6
7.2
6.6
7.3
9.2
11.8

 

89.0
89.5
90.0
90.3
90.7
91.0
91.3
91.7
92.0
92.5
92.6
92.6
92.6
92.2
92.1
92.0
92.0
92.0

8.0
8.6
10.6
8.0
8.8
9.7
8.6
8.9
10.3
15.2
15.7
15.5
14.9
9.5
7.3
11.0
8.7
11.3

 

96

 

A5 (cont.).

510
0
87.7
88.1
88.4
88.8
89.6
90.5
91.8
93.0
94.5
96.1
97.7
99.2
101.3
103.4
105.1
106.8
108.8
110.3
111.7
113.1
114.4
115.5
116.5
117.3
118.5
119.5
120.5
121.2
122.0
122.4
123.1
123.7
124.0
124.2
124.3
124.3
124.4

7.8
8.7
7.9
7.2
7.9
12.4
12.4
13.8
14.3
18.5
20.6
24.2
23.0
24.3
28.1
28.8
34.9
33.2
31.7
33.0
35.2
35.2
36.5
36.6
38.7
38.0
40.2
40.5
41.5
45.5
45.5
46.3
43.8
45.1
44.8
47.6
48.3

 

0

124.4
124.4
124.4
124.5
124.5
124.4
124.3
124.3
124.2
124.1
124.1
124.1
124.1
124.0
124.0
123.9
123.9
123.8
123.8
123.8
123.7
123.6
123.6
123.4
123.5
123.3
123.2
123.3
123.3
123.3
123.2
123.3
123.4
123.4
123.4
123.3
123.4

(I

46.8
45.3
47.1
48.0
48.7
47.7
48.3
48.9
47.8
48.7
48.7
48.5
50.8
49.8
48.6
50.1
50.6
50.6
50.0
50.0
51.3
49.9
50.9
48.7
48.4
48.8
48.8
48.3
50.1
48.8
48.8
49.5
49.1
45.5
48.3
49.5
49.0

 

0

123.3
123.0
122.8
122.6
122.0
121.5
120.9
120.2
119.5
118.7
117.7
116.4
114.2
111.9
109.8
107.1
104.6
102.0
98.9
95.8
93.0
90.7
88.3
86.1
84.1
82.4
80.8
79.1
77.8
76.6
75.6
75.1
74.6
74.2
75.1
75.2
74.9

0.

48.3
48.0
48.7
47.3
47.5
47.3
46.5
45.7
44.9
42.3
42.4
40.6
41.2
35.5
35.8
32.2
31.7
33.1
25.5
22.9
21.7
21.9
22.0
21.5
17.7
18.2
18.7
19.3
19.7
19.2
19.7
20.0
17.1
15.1
18.2
19.0
18.3

 

0

75.0
74.9
75.1
74.8
78.3
78.0
77.7
77.6
77.5
77.5
77.5
77.5
77.5
77.3
77.4
77.3
77.3
77.4
77.3
77.4
77.5
77.6
77.8
77.9
78.0
78.1
77.9
77.8
77.8
77.9
77.9
77.8
77.8
78.1
78.2
78.6
79.3

97

0.

19.8
18.4
21.0
17.9
19.8
19.2
19.3
19.8
19.6
20.5
18.7
18.3
19.4
18.6
16.0
16.0
16.4
15.4
19.3
18.8
18.5
17.7
17.2
17.7
18.0
17.6
17.0
17.6
19.6
18.1
18.2
18.4
19.3
18.9
18.4
20.6
19.6

 

0

79.7
76.8
77.8
79.1
80.6
81.8
83.2
84.6
86.0
87.1
88.3
89.5
90.7
91.9
93.1
94.1
95.3
96.0
96.9
97.9
98.9
99.7
100.8
101.6
102.4
102.9
103.3
103.2
103.3
103.4
103.3
103.1
102.8
102.7
102.5

a

21.8
20.6
22.5
21.8
21.7
22.8
27.2
27.9
26.3
27.4
27.3
28.0
28.0
29.2
30.4
31.6
28.8
32.3
31.6
31.5
33.7
31.8
33.7
35.3
37.8
38.1
37.4
35.4
34.6
36.0
35.7
34.7
33.0
31.7
31.4

 

A5 (cont.).

811
0
82.3
83.0
83.6
84.4
85.3
86.3
87.3
88.3
89.2
90.3
91.2
92.5
93.4
94.2
95.2
96.1
96.8
97.3
98.1
98.9
99.7
100.7
102.1
103.9
105.5
106.5
107.7
108.6
109.5
110.1
110.5
111.5
112.0
112.8
113.6
114.5
115.2

 

(1

15.4
15.5
14.7
16.2
18.8
18.9
20.3
18.1
18.2
20.1
21.3
21.9
22.5
24.0
21.8
22.3
22.8
23.6
22.7
25.3
26.2
26.1
28.9
30.2
27.7
32.8
34.0
33.1
34.3
34.6
34.3
32.5
33.3
32.9
31.5
31.0
30.1

 

0

115.8
116.1
116.2
116.6
116.6
116.6
116.8
117.0
117.2
117.1
117.3
117.4
117.4
117.6
117.7
117.8
118.0
117.9
117.9
117.9
117.9
117.7
117.7
117.7
117.7
118.0
118.2
118.3
118.3
118.5
118.8
118.9
119.1
119.1
118.8
118.3
117.9

(I

27.8
27.1
26.7
26.6
25.4
21.0
20.1
19.3
19.5
20.8
19.7
18.4
18.0
16.0
16.8
16.2
17.9
18.6
18.2
15.6
14.4
15.2
13.2
13.1
12.3
12.1
7.2
8.4
8.0
8.1
9.7
7.5
10.6
11.3
10.5
10.0
10.1

 

0

117.7
117.4
117.1
117.0
117.0
116.9
116.9
117.0
117.2
117.1
117.0
117.1
116.9
116.9
116.8
116.9
116.5
116.6
116.2
116.0
115.8
115.5
115.4
115.1
114.9
114.4
113.8
113.3
112.6
112.1
111.1
110.0
108.9
107.8
106.8
105.2
103.9

0.

11.5
10.9
10.6
10.4
9.7

10.5
9.9

10.0
9.5

9.9

10.1
10.1
9.7

10.3
10.1
10.6
10.8
9.5

9.2

12.0
11.8
10.3
10.8
7.3

8.0

8.8

6.8

12.3
12.2
15.1
12.8
13.7
11.7
11.6
13.1
10.2
10.7

 

0

102.5
101.2
99.8
98.5
97.4
96.4
95.2
93.8
92.6
91.7
90.9
90.0
88.9
87.9
87.1
86.4
85.7
85.3
85.2
84.8
84.2
83.9
83.6
82.9
82.6
81.7
81.2
80.7
80.2
79.8
79.6
79.3
79.2
79.0
78.8
78.8
78.2

98

(1

10.8
10.8
9.8
7.0
10.0
8.9
10.0
9.5
7.1
6.4
6.7
7.2
6.1
6.9
6.3
6.5
5.7
5.1
7.7
5.7
5.7
5.9
4.6
4.2
7.0
5.5
5.1
3.4
4.7
6.0
6.1
4.3
3.7
3.7
3.3
4.3
5.1

 

78.0
77.8
77.7
77.6
77.8
77.8
77.8
77.7
77.5
77.3
77.3
77.3
77.1
76.7
76.5
76.4
76.1
75.6
75.3
74.8
74.2
73.7
73.3
72.9
72.6
72.4
72.1
71.8
71.2
70.7
70.2
69.8
69.8
69.3
69.1
68.7
68.4

5.3
6.4
4.8
5.7
6.1
4.0
4.4
5.3
5.4
5.3
5.1
5.6
5.9
4.9
5.3
4.7
5.2
6.1
5.8
6.3
8.8
5.5
5.8
3.8
3.4
5.5
3.5
5.5
3.6
3.8
3.6
2.9
2.6
3.3
2.9
2.5
2.9

 

A5 (cont.).

$11
9

68.2
68.0
67.9
67.9
68.2
68.3
68.4
68.6
68.7
68.8
68.9
68.9
69.0
69.1
69.1
69.1
69.0
69.3
69.5
69.4
69.4
69.3
69.4
69.4
69.5
69.6
69.7
69.7
69.8
69.8
69.8
69.9
69.9
70.1
70.1
70.6
71.2

 

2.7
2.6
2.6
2.5
2.1
3.0
2.5
3.4
4.8
3.6
3.5
3.2
2.1
2.7
2.4
3.2
3.5
1.0
1.5
3.3
0.9
1.3
1.4
1.8
1.8
1.5
2.0
2.0
2.7
1.9
1.7
1.8
3.5
2.3
1.5
3.4
4.2

 

71.7
72.5
72.8
73.3
74.1
74.6
75.6
76.1
76.6
77.4
78.2
79.1
79.8
80.7
81.7
82.8
83.7
84.2
85.0
85.5
86.1
86.4
86.7
87.0
87.4
87.6
87.9
88.1
88.4
88.5
88.5
88.8
88.7
88.9
88.8
88.7
88.6

4.5
5.1
5.2
5.9
6.9
4.9
6.8
6.2
5.5
7.8
12.0
10.9
7.2
10.0
14.3
16.8
18.2
16.8
16.1
16.4
18.0
19.5
20.5
21.4
20.9
21.7
20.1
19.1
18.4
21.0
19.8
18.3
17.1
16.9
17.2
19.2
16.6

 

99

A5 (cont.).

$12
9

80.6
81.3
82.1
82.9
84.4
86.1
87.7
88.9
90.1
91.9
93.4
94.6
96.2
97.3
98.9
100.2
101.6
102.5
103.5
104.5
105.6
106.4
107.0
107.5
107.9
108.4
108.7
109.0
109.0
109.2
109.4
109.6
109.5
109.4
109.3
109.5
109.4

 

9.8
10.8
14.5
12.0
17.1
15.2
17.6
19.5
17.8
20.2
20.6
22.8
20.7
24.0
25.1
27.8
25.0
26.5
26.8
29.5
31.4
34.0
31.6
32.8
31.4
31.2
31.6
31.8
32.1
32.3
32.6
33.4
33.2
34.0
33.7
34.5
34.4

 

0

109.2
109.3
109.1
109.1
109.0
108.9
108.9
108.8
108.7
108.6
108.6
108.7

109.0 '

109.1
109.1
109.0
109.2
109.2
109.3
109.5
109.6
109.6
109.4
109.4
109.4
109.3
109.4
109.4
109.4
109.4
109.4
109.4
109.5
109.5
109.5
109.5
109.6

0.

33.6
33.8
31.2
32.9
33.3
33.1
32.4
32.5
32.5
32.4
32.5
32.7
33.6
32.9
33.6
35.3
34.9
33.3
32.8
33.0
34.9
33.4
33.7
33.0
33.0
34.9
33.1
33.2
33.2
33.4
33.2
33.8
33.3
34.1
34.0
33.9
34.1

 

0

109.6
109.5
109.5
109.5
109.4
109.4
109.5
109.4
109.5
109.5
109.5
109.4
109.4
109.4
109.3
109.2
108.9
108.6
108.5
108.2
107.9
107.5
107.1
106.5
105.7
104.2
102.3
100.2
98.0

95.1

92.4

90.2

87.7

84.7

82.6

80.1

78.1

(I

34.3
33.9
34.3
34.6
34.0
33.1
34.6
35.5
34.7
34.3
34.5
35.1
34.2
34.1
43.3
33.4
33.1
33.4
34.9
36.2
36.4
35.8
36.5
37.6
39.3
37.6
35.2
38.0
37.9
32.1
28.0
26.1
24.2
21.3
19.5
15.8
13.0

0

76.5
74.7
73.1
71.5
70.1
68.7
67.3
66.0
64.9
64.2
63.8
63.6
63.3
63.3
63.4
63.5
63.8
63.8
64.1
64.3
64.2
64.3
64.6
64.6
64.6
64.8
64.8
64.8
64.9
64.8
64.7
64.5
64.5
64.5
64.5
64.5
64.5

 

100

0.

14.6
13.4
9.6
9.8
6.8
9.6
8.3
7.7
6.7
4.6
4.4
8.6
9.4
12.3
11.3
9.5
11.3
11.1
11.0
7.1
6.8
6.5
6.0
5.6
4.9
8.7
5.3
8.1
5.3
5.2
5.0
4.6
5.1
5.1
5.6
6.2
5.9

 

64.5
64.2
64.2
64.3
64.1
64.1
64.0
64.1
64.1
64.0
64.1
64.1
64.2
64.1
64.1
64.0
64.0
64.1
64.1
64.0
64.0
63.9
63.9
63.8
63.8
63.8
63.6
63.6
63.6
63.5
63.6
63.7
63.6
63.6
63.5
63.6
63.5

6.4
6.4
6.5
9.8
6.4
9.5
5.7
5.6
6.2
6.1
5.9
5.8
6.0
7.3
5.8
6.2
6.5
6.4
10.4
5.7
5.6
6.0
6.0
5.9
9.2
6.2
6.0
8.4
5.9
5.8
5.7
6.7
5.5
6.1
5.9
6.1
6.2

 

63.6
63.4
63.5
63.8
64.2
64.9
66.0
67.2
68.4
69.5
70.9
72.4
73.7
75.5
77.0
78.3
79.3
80.7
81.8
83.0
84.2
84.8
85.4
85.6
85.6
85.0
84.6
84.0
83.5
83.0

6.5

5.9

6.2

5.6

7.0

7.4

11.0
11.7
9.7

7.2

11.0
10.9
11.6
10.4
11.5
14.4
10.5
12.1
16.2
13.9
11.9
12.6
12.5
11.4
13.2
12.8
12.3
10.5
10.1
12.1

 

A5 (cont.).

813
9
72.3
73.2
74.1
74.9
75.9
76.9
77.7
79.1
80.0
81.1
82.2
83.3
84.6
85.8
87.3
88.7
89.8
91.2
92.7
94.1
95.5
96.9
98.1
99.7
100.6
102.0
103.0
104.2
104.9
105.9
106.9
107.7
108.4
108.7
109.0
109.3
109.4

 

0.

-l4.8
-15.6
-15.9
-l3.9
-13.8
-l3.2
-13.9
—13.2
-12.2
-l3.9
-12.5
-12.1
-9.0
-10.3
-10.5
-9.5
-6.0
-8.0
-9.1
-9.9
1.9
2.6
2.9
5.0
1.4
0.3
3.7
5.5
5.4
5.9
4.1
5.2
4.6
2.2
3.4
3.8
3.6

 

109.4
109.4
109.4
109.4
109.4
109.4
109.5
109.5
109.5
109.5
109.5
109.4
109.4
109.3
109.4
109.3
109.4
109.4
109.4
109.4
109.5
109.4
109.4
109.4
109.4
109.4
109.4
109.4
109.4
109.4
109.4
109.3
109.3
109.3
109.3
109.2
109.3

4.2
4.8
4.4
4.5
4.0
5.0
3.9
4.2
4.5
4.0
4.4
4.6
3.8
3.8
4.5
4.0
3.3
4.1
4.4
4.5
4.5
4.3
4.2
4.1
5.4
3.9
4.4
4.1
4.8
4.2
5.5
3.7
4.5
4.6
3.7
4.4
4.5

 

109.2
109.2
109.2
109.2
109.1
109.1
109.2
109.2
109.2
109.1
109.1
109.1
109.0
108.9
108.9
108.7
108.7
108.4
108.2
107.6
107.3
106.9
106.1
105.4
104.7
103.9
102.8
101.3
100.3
98.8

97.0

95.5

93.1

91.3

89.8

88.3

87.0

4.1
3.8
3.3
3.8
3.2
3.8
3.6
4.0
4.3
4.2
3.6
3.3
4.0
3.7
2.9
3.7
2.6
1.7
-5.6
0.1
2.4
2.2
3.3
1.6
-5.7
0.9
0.5
-9.2
-10.7
~10.4
-8.2
-9.6
-11.6
-10.7
-7.5
-7.8
-11.2

101

 

0

85.3
83.3
81.1
79.2
77.4
75.9
74.3
72.3
70.0
68.0
66.3
64.5
63.0
62.1
61.8
61.8
61.8
62.1
62.2
62.3
62.4
62.5
62.7
62.9
63.0
63.0
63.1
63.2
63.2
63.4
63.2
63.3
63.2
63.4
63.5
63.6
63.7

a

-11.3
—lO.5
-10.3
-13.6
-l4.1
-13.9
-14.5
-13.1
-13.9
-14.6
-16.2
—l7.2
-17.0
-l8.4
-19.7
-l9.1
-l9.5
-l9.2
-19.9
-18.9
-18.9
-l9.1
-19.4
-18.9
-20.3
-l9.0
-l9.0
-19.4
-19.6
-19.5
-19.8
-19.8
-l8.9
-19.2
-18.3
—l8.2
-18.l

 

63.7
63.8
64.0
63.9
64.2
64.4
64.5
64.7
64.5
64.5
64.6
64.7
64.6
64.6
64.7
64.6
64.6
64.6
64.6
64.6
64.5
64.4
64.3
64.2
64.3
64.0
64.0
64.1
63.8
63.7
64.0
63.7
63.7
63.7
63.8
63.8
63.5

a

-18.3
-18.4
-18.1
-18.0
-18.1
-18.3
—18.0
-18.5
-l7.8
-18.2
-18.1
-18.3
-17.7
-17.8
-l7.7
-18.0
-17.9
-l8.6
-17.8
-17.7
-l6.0
-17.5
-17.9
-18.4
-16.5
~17.3
-18.4
-17.6
-18.3
-18.9
-17.7
-17.7
-17.9
-l7.9
-17.7
-l7.8
-17.7

 

 

A5 (cont.).

513
6
63.5
63.5
63.6
63.7
63.4
63.4
63.4
63.3
63.4
63.4
63.4
63.6
63.6
63.5
63.5
63.4
63.5
63.4
63.7
63.6
63.9
64.1
64.4
64.8
65.3
65.9
66.5
67.4
68.3
69.2
70.4
71.4
72.4
73.4
74.8
76.2
77.4

 

0.

-17.7
-l7.7
-18.1
-17.8
-l7.5
-18.0
-l9.2
-18.0
-18.0
-18.0
-18.0
-18.0
-17.8
-18.0
-l7.7
-18.2
-l8.3
-l8.0
-17.9
-l9.4
-l8.4
-l7.6
-l8.4
-19.2
-19.9
-20.9
-18.7
-l7.4
-15.2
-15.3
-16.9
-15.8
-12.9
-l4.2
-11.1
-13.6
-10.7

 

79.1
80.3
81.5
82.2
82.8
82.9
82.9
82.5
82.0
81.4
81 . 1
80.8
80.4
80.2
80.0

(I

-10.0
-10.1
-10.1
-10.7
-9.5
-9.9
-10.8
-10.2
-10.7
-10.6
-13.2
-10.1
-lO.9
-10.0
-9.5

 

102

 

A5 (cont.).

S17
0
99.6
100.8
102.2
103.3
104.4
105.4
106.4
107.4
108.3
108.8
109.4
110.1
110.7
111.4
112.2
113.5
114.7
115.9
117.0
118.3
119.3
120.0
120.7
121.5
122.3
122.9
123.5
123.8
124.1
124.3
124.5
124.6
124.8
124.9
125.1
125.3
125.6

0

16.5
25.1
24.9
25.1
29.7
22.1
27.9
27.2
32.8
29.0
28.3
27.0
29.4
29.7
29.3
32.1
30.5
32.5
32.0
38.6
37.7
35.0
38.2
36.8
39.0
42.9
41.9
40.5
40.4
39.9
40.3
40.4
39.8
39.1
39.4
40.1
39.3

 

0

126.0
126.1
126.2
126.1
126.1
126.0
125.9
125.8
125.7
125.5
125.4
125.4
125.6
125.8
125.8
125.8
125.9
126.0
126.0
126.1
126.1
126.2
126.3
126.5
126.7
126.8
127.0
127.0
127.0
127.1
127.1
127.1
127.0
127.0
126.9
126.8
126.7

(I

39.9
40.1
43.7
44.1
44.3
44.9
44.7
44.3
44.5
44.9
45.5
45.0
48.3
48.0
48.3
48.5
50.7
50.2
50.2
49.9
49.0
48.5
48.1
48.3
48.7
47.5
47.5
44.7
43.2
44.1
44.3
46.7
44.0
42.1
42.2
42.4
42.8

 

0

126.7
126.6
126.6
126.5
126.6
126.5
126.5
126.5
126.4
126.4
126.3
126.2
126.2
126.2
126.2
126.2
126.2
126.1
126.1
126.1
126.0
126.0
125.9
125.9
125.8
125.7
125.6
125.4
125.1
125.0
124.7
124.2
123.5
122.7
121.9
121.2
119.9

(1

43.3
43.1
44.2
42.5
42.7
41.6
42.1
43.4
42.0
44.0
43.5
42.9
44.1
42.7
43.7
43.0
43.4
42.0
43.9
43.9
42.4
42.4
42.9
43.0
43.3
42.9
44.7
42.7
44.3
42.9
43.8
47.7
49.8
50.5
47.8
43.7
41.4

0

118.8
117.7
116.6
115.9
115.1
114.2
112.8
111.6
110.2
108.6
106.9
105.2
103.7
102.9
102.8
102.1
101.6
100.4
99.2
97.6
96.2
95.0
94.1
92.9
91.9
91.0
90.5
89.9
89.5
89.0
88.6
87.9
87.5
87.1
86.8
86.5
86.4

 

103

0.

43.6
42.7
45.4
41.7
42.7
40.0
35.8
33.9
37.7
34.1
29.3
24.8
31.6
31.5
18.9
22.5
25.5
19.5
23.1
15.7
19.2
17.3
19.3
18.7
18.5
18.2
18.3
16.9
15.2
14.3
15.8
14.1
13.7
13.3
12.1
12.5
12.4

 

0

86.2
86.1
86.0
86.0
85.8
85.4
85.2
84.9
84.6
84.3
83.9
83.6
83.4
83.0
82.8
82.7
82.6
82.5
82.3
82.3
82.2
82.0
81.7
81.4
81.1
81.0
80.9
80.9
80.9
80.8
80.7
80.7
80.5
80.5
80.5
80.4
80.5

a

14.3
14.7
14.7
15.3
16.1
15.2
14.5
15.6
14.5
15.4
13.8
13.7
14.4
13.6
13.5
12.2
12.6
13.0
13.6
13.5
13.5
13.2
10.1
12.7
10.9
11.0
10.3
11.5
11.3
11.4
11.5
11.4
11.3
10.8
11.4
11.7
11.3

 

0

80.5
80.6
80.6
80.7
80.8
80.8
80.9
80.8
81.0
81.0
81.0
81.0
80.8
80.9
80.8
80.8
80.7
80.7
80.8
80.9
80.9
80.9
80.8
81.0
81.1
81.0
81.0
81.1
81.4
81.6
81.9
82.3
83.2
84.1
85.1
86.2
87.4

a

11.2
12.1
11.4
11.7
11.7
11.9
12.1
11.6
12.0
11.5
11.6
11.8
11.7
11.7
8.6
10.3
12.0
11.2
11.3
11.7
11.8
12.2
12.3
12.3
9.9
9.6
9.6
11.2
9.4
9.5
10.1
10.6
10.2
13.6
15.3
15.3
16.7

 

 

A5 (cont.).

$17
0
88.3
89.4
90.5
91.3
92.0
92.9
93.6
94.5
95.4
96.4
97.5
98.7
99.3
99.9
100.6
101.3
101.7
102.3
102.8
103.4
104.1
104.7
105.1
105.7
106.2
106.7
107.2
107.4
107.8
108.1
108.2
108.4

a.

18.3
17.2
18.1
17.7
18.0
16.9
18.4
20.8
19.2
17.0
18.0
19.5
21.0
21.9
23.0
23.7
24.6
24.5
24.7
24.4
27.2
22.7
23.1
27.8
25.0
33.7
31.9
33.1
33.4
26.5
29.7
30.3

 

104

A5 (cont.).

$18
0
71.6
72.0
72.8
74.3
75.9
78.0
79.5
80.5
81.2
81.2
82.0
82.7
83.2
83.4
83.7
84.1
84.6
85.0
85.5
86.2
86.3
86.5
86.8
87.4
87.9
88.3
88.6
88.9
89.2
89.3
89.4
89.5
89.6
89.6
89.7
89.6
89.7

 

a

-12.2
-12.9
-ll.3
-11.0
-12.0
-10.5
-13.9
-13.5
-12.5
-13.4
-l3.2
-12.5
-14.7
-15.1
-16.7
-16.5
-17.2
-17.2
-17.6
-17.3
-18.5
-18.2
-16.4
-17.7
-l6.2
-16.0
-15.6
-16.5
-14.6
-l6.2
-l3.2
-15.2
-l3.8
-14.8
-13.9
-13.5
-13.8

 

89.7
89.8
90.0
90.1
89.9
90.0
90.2
90.2
90.4
90.4
90.5
90.9
90.9
91.0
91.2
91.4
91.5
91.6
91.7
91.7
91.8
91.9
92.0
92.1
92.1
92.1
92.2
92.2
92.2
92.2
92.2
92.2
92.1
92.1
92.0
91.9
91.8

(1

-13.9
-145
-l6.7
-14.7
-16.3
-14.8
-14.3
—14.2
-14.6
-142
-144
-144
-14.1
-14.7
-143
-144
-16.7
-14.1
-14.1
-145
-12.8
-14.5
—15.0
-142
-12.8
-14.6
-144
-15.3
44.2
-14.4
-14.4
-14.6
-14.7
-15.2
-152
-153
-15.0

 

91.7
91.6
91.6
91.5
91.4
91.3
91.0
91.1
90.8
90.8
90.8
90.7
90.7
90.6
90.6
90.5
90.5
90.5
90.4
90.4
90.3
90.2
90.2
90.1
90.2
90.0
90.0
89.9
89.8
89.9
89.7
89.7
89.7
89.6
89.6
89.6
89.5

0.

-15.0
-15.4
~15.4
-18.0
-17.0
-16.4
-l8.5
-l8.8
-19.0
-18.2
-18.1
-l8.1
-18.5
-18.6
-18.7
-18.0
~19.3
-16.0
-19.0
-17.7
-l7.7
-17.2
-14.1
-16.6
-12.4
-15.0
-14.2
-l3.7
-13.3
-12.7
-12.5
-12.5
-14.6
-13.6
-13.2
-l3.l
-12.9

105

 

89.4
89.3
89.2
88.9
88.7
88.7
88.2
87.8
87.1
86.5
85.9
85.2
84.3
83.5
82.2
80.8
79.0
76.9
75.1
73.3
72.2
70.8
69.6
68.2
66.7
65.7
64.7
63.7
63.1
62.6
62.3
62.0
61.5
61.1
60.6
60.4
60.0

a

-12.7
-14.3
-13.4
-14.0
-13.4
-12.8
-l3.3
-12.6
-11.5
-12.7
-10.2
-12.9
-13.0
-12.7
-12.9
-13.5
-13.0
-11.6
-16.5
-12.6
-12.3
-11.7
-12.6
-11.6
-11.5
-11.4
-10.5
-9.6
-11.1
-9.3
-12.5
-10.2
-10.2
-11.6
-11.0
-10.4
-10.3

 

59.9
59.5
58.9
58.4
58.2
58.1
58.0
57.9
57.9
57.7
57.5
57.3
57.5
57.4
57.3
57.1
57.1
57.2
57.1
57.2
57.2
57.2
57.2
57.1
57.2
57.2
57.4
57.3
57.4
57.6
57.9
58.2
58.2
58.3
58.4
58.6
58.7

(1

-10.2
-10.9
-10.5
-11.1
-11.4
-ll.8
-11.3
-10.9
-9.9
-10.1
-9.7
~10.3
-lO.1
-10.2
-9.5
-9.2
-9.7
-10.2
-11.4
-10.9
-11.9
-ll.6
-11.3
-10.2
-12.6
-11.4
-7.0
-13.4
-10.0
-9.1
-11.4
-9.5
-11.7
-10.9
—13.2
-9.7
-11.5

 

A5 (cont.).

818
0
58.9
59.1
59.3
59.5
59.6
59.7
59.9
60.0
60.2
60.3
60.6
60.5
60.6
60.7
60.9
60.9
61.1
61.0
61.2
61.2
61.3
61.4
61.3
61.5
61.4
61.6
61.5
61.6
61.5
61.5
61.5
61.6
61.8
61.8
61.9
62.1
62.4

 

(1

-10.6
-ll.7
-11.5
-11.0
-l3.3
-12.7
-12.6
-10.9
-1 1.1
-1 1.1
-9.2

-11.2
-13.5
-10.3
-10.9
-10.5
-11.0
-10.6
-11.0
-10.8
-13.3
-12.5
-10.6
-9.9

-10.6
-10.2
-11.3
-8.1

-10.8
-10.3
-10.5
-10.2
—11.4
~10.7
-10.9
-12.6
—1 1.1

 

62.9
63.4
64.1
64.4
64.9
65.1
65.2
65.4
65.5
65.7
65.9
66.2
66.7
67.3
67.9
68.2
68.5
69.0
69.2
69.6
69.8
70.0
70.8
71.1
71.3
71.6
72.2
72.6
73.0
73.2
73.5
73.8
74.3
74.6
75.0
75.2
75.4

0.

~10.2
-7.8
-6.3
-8.5
-9.8
-8.6
-9.1
-9.4
-11.1
-10.8
-11.2
-10.9
-ll.2
-12.6
-12.9
-12.0
-12.1
-11.7
-12.0
-ll.8
-11.1
-11.0
-lO.5
-10.0
-10.9
-9.7
-10.4
-10.8
-10.9
-11.4
-ll.7
-11.6
-10.0
-11.8
-8.5
-8.1
-8.1

 

6

75.6
75.6
75.5
75.3
74.9
74.5
74.2
74.1
74.2

a

-8.4
-7.8
-8.4
—5.5
-9.7
-7.9
-6.4
-6.0
-6.1

 

106

 

A5 (cont.).

$19
9
70.5
70.6
70.7
70.9
71.1
71.3
71.7
72.0
72.5
72.6
72.9
73.3
73.6
74.3
74.5
74.7
75.4
75.7
75.9
77.9
78.1
78.3
78.8
79.1
79.5
79.9
80.4
80.9
81.5
83.1
83.4
83.7
83.9
84.1
84.3
84.5
84.7

 

0.

-5.9
-5.7
-6.3
-5.4
-5.7
-6.0
-6.9
-7.2
-8.6
-8.6
-8.7
-9.2
-8.4
-7.5
-7.7
-6.2
-6.3
-5.9
-5.8
-6.1
-6.2
-6.2
-5.8
-5.9
-5.9
-5.5
-4.0
-4.2
-2.8
-3.8
-5.7
-7.8
-4.1
-6.0
-3.4
-4.7
-3.8

 

84.9
85.2
85.3
85.4
85.5
85.6
85.8
85.9
85.9
86.1
86.1
86.2
86.3
86.3
86.4
86.5
86.6
86.6
86.7
86.7
86.8
86.8
86.8
86.8
86.9
86.9
86.8
86.8
86.6
86.7
86.6
86.4
86.4
86.3
86.3
86.4
86.4

0.0
-4.1
-4.5
-4.4
-4.6
-4.0
-4.4
-3.8
-3.9
1.6
2.4
2.0
1.8
2.1
2.1
1.8
1.8
1.9
-3.7
0.3
0.3
0.2
0.6
-4.2
0.3
0.3
0.2
-4.3
-3.9
-4.2
0.1
-3.9
2.1
2.0
1.4
2.0
1.4

 

86.4
86.4
86.5
86.5
86.6
86.5
86.6
86.5
86.5
86.5
86.5
86.5
86.5
86.5
86.4
86.4
86.4
86.4
86.4
86.3
86.3
86.2
86.1
86.1
86.0
85.8
85.8
85.7
85.6
85.5
85.4
85.2
85.0
84.8
84.6
84.3
84.0

1.9
-4.2
0.7
-4.8
-4.2
-4.4
-4.8
-4.5
-4.5
-4.5
-4.2
-4.5
-4.2
-4.4
-4.6
0.1
0.0
2.0
2.1
2.4
2.2
2.4
-3.7
0.0
2.7
4.5
2.3
2.3
2.5

1.7

1.9
-2.9
-2.7
-3.3
-2.9
-3.2
-4.5

 

0

83.8
83.7
83.5
83.4
83.1
82.7
82.3
81.7
81.3
81.0
80.7
80.4
78.9
78.3
77.8
77.1
76.5
75.8
75.3
74.9
74.5
74.0
73.7
73.3.
72.8
72.3
71.9
71.4
71.1
70.7
70.6
70.3
69.9
69.6
69.1
68.9
68.6

107

(I

4.7
-5.0
-52
-50
4.4
-5.1
4.7
4.2
-1.8
0.3
-22
-4.6
4.6
4.5
-5.1
-5.1
-5.0
-3.8
-3.5
4.0
4.4
4.7
-4.6
-6.6
-8.1
-7.5
-6.5
-7.0
-7.5
-7.1
-7.2
-7.7

_ -8.1

-7.6
-5.8
-6.9
-6.2

 

0

68.6
68.4
68.2
68.1
68.0
68.0
68.0
68.0
68.1
68.2
68.3
68.3
68.3
68.3
68.3
68.3
68.5
68.3
68.3
68.3
68.3
68.4
68.5
68.5
68.6
68.4
68.4
68.5
68.4
68.3
68.3
68.3
68.3
68.3
68.2
68.3
68.0

a.

-6.7
-6.3
-6.8
-6.7
-6.1
-6.4
-6.4
-7.0
-7.0
-6.1
-5.4
-6.5
-6.6
-6.5
-6.2
-8.9
-5.7
-7.0
-6.8
-7.1
-6.9
-6.7
-6.4
-6.7
-6.1
-6.0
-6.9
-5.7
-6.3
-6.6
-6.9
-6.9
-6.8
-6.9
-6.8
-5.0
-5.8

 

0

67.9
67.7
67.6
67.4
67.4
67.3
67.4
67.3
67.2
67.2
67.2
67.3
67.4
67.3
67.3
67.3
67.4
67.4
67.5
67.6
67.8
67.8
67.9
68.1
68.1
68.1
68.2
68.5
68.6
68.6
69.0
69.3
69.7
69.9
70.1
70.6
71.2

0.

-6.0
-5.6
-6.5
-6.6
-6.5
-6.1
-6.6
-6.7
-6.3
-6.9
-7.0
-8.2
-6.3
«6.8
-6.5
-7.1
-6.5
-6.6
-6.7
-6.8
-5.9
-7.1
-5.8
-5.9
-7.1
-6.4
-6.5
-6.5
-6.1
-5.8
-6.3
-6.3
-5.5
-5.7
-5.3
-7.3
-6.4

 

AS (cont.).

$19
0
71.6
72.3
72.7
73.0
73.0
73.1
73.0
73.0
72.8
72.8
73.0

 

(I

-6.3
-6.9
-4.5
-6.1
-6.4
-5.9
-6.2
-4.6
-3.6
-3.3
-4.0

 

108

A5 (cont.).

$21
0
74.2
74.7
75.3
75.7
76.6
77.3
77.7
78.3
79.1
79.6
80.8
83.6
86.5
87.1
87.9
88.8
89.5
90.1
90.8
91.8
93.0
95.4
96.8
97.8
100.3
101.3
102.2
102.9
103.7
104.3
104.4
104.7
105.0
105.4
107.4
109.6
108.3

 

(I

-9.6
-9.1
-7.0
0.1
0.7
2.6
3.2
4.4
6.3
7.9
9.9
12.7
13.2
13.3
15.2
19.5
22.6
24.5
26.0
25.5
28.5
32.2
32.2
35.7
38.6
41.0
42.9
43.7
45.5
46.3
46.7
46.2
48.0
48.2
48.9
49.1
49.6

 

0

107.1
109.6
110.3
110.8
111.8
112.6
113.7
114.2
114.6
115.2
115.4
115.8
115.9
116.2
116.4
116.6
116.6
116.7
116.8
116.8
116.9
116.9
117.0
116.9
116.8
116.9
116.7
116.7
117.1
117.1
117.1
117.0
117.1
117.1
117.1
117.1
117.1

(I

50.2
47.9
50.2
51.3
52.2
53.2
51.7
51.7
54.5
53.4
55.5
56.9
56.7
57.5
57.9
58.6
59.1
59.0
58.9
59.2
59.8
59.7
59.9
64.2
64.9
65.0
64.5
64.6
66.0
64.7
64.2
64.8
65.1
64.7
62.8
62.9
64.6

 

9

117.1
117.1
117.1
117.2
117.1
117.1
117.1
117.1
117.1
117.2
117.2
117.2
117.3
117.3
117.4
118.3
118.4
118.5
118.6
118.6
118.7
118.7
118.8
118.8
117.8
117.8
117.9
117.9
117.9
117.9
117.9
117.8
117.8
117.8
117.7
117.5
117.3

a

60.0
61.5
62.0
61.6
61.3
61.5
61.6
62.1
61.0
61.7
61.6
59.9
61.2
61.2
60.1
61.6
57.6
57.6
57.7
64.5
66.7
67.0
58.9
56.0
57.7
58.7
58.8
58.7
58.7
58.8
58.3
58.4
66.3
58.6
59.3
67.4
67.9

0

117.2
116.9
116.7
116.4
116.0
115.6
115.4
115.0
114.5
113.7
113.8
111.9
109.1
110.1
109.2
106.5
105.8
104.8
103.9
102.9
100.0
97.0
95.6
94.4
93.1
91.9
88.5
85.3
84.3
83.1
82.2
81.2
77.7
74.9
74.0
72.9
61.5

 

109

a

67.4
58.8
59.7
63.1
63.8
63.3
63.1
62.1
62.7
62.4
65.8
61.4
61.7
61.2
61.0
59.6
59.1
58.9
58.7
62.9
62.6
61.4
57.8
55.3
51.0
48.6
45.1
42.2
36.9
34.1
28.0
23.4
28.7
27.9
25.2
18.3
-7.7

 

63.3
61.9
59.3
60.7
59.5
59.6
59.3
58.8
61.5
55.9
55.4
55.4
54.4
51.5
51.5
51.8
52.0
53.5
54.0
54.4
54.3
54.2
52.1
51.1
51.5
52.9
52.1
52.4
52.5
52.5
52.6
52.8
52.8
53.0
52.9
52.5
52.9

a

-9.0
-4.1
-8.1
-10.7
-14.3
-l9.6
-l4.4
-34.2
-24.4
-16.4
—16.8
-18.6
-14.8
-30.4
-28.0
-26.6
-26.5
-25.1
-23.8
-24.2
~37.4
-34.6
-22.7
-23.5
-24.2
-41.9
-40.8
-38.3
-35.5
-34.9
-33.1
-30.2
-22.8
-23.8
-24.2
-25.0
-26.1

 

A5 (cont.).

S21
0
53.1
52.9
53.0
53.1
53.2
53.4
53.3
53.6
53.3
53.4
53.5
53.5
53.5
53.8
53.6
53.4
53.6
53.6
53.5
53.4
53.5
53.5
53.5
53.5
53.5
53.5
53.8
53.9
53.9
54.2
54.2
54.3
54.3
54.3
54.3
54.3
54.2

 

(1

-24.2
-23.9
-23.4
-22.9
-22.7
-22.5
-22.3
-22.5
-23.1
-23.5
-22.9
-23.6
-24.1
-24.0
-23.8
-23.8
-23.6
-23.5
-23.1
-22.8
-23.3
-22.8
-23.5
-23.2
-23.9
-23.4
-23.6
-23.6
-23.4
-23.6
-23.6
-23.5
-23.7
-24.0
-23.7
-24.0
-24.4

 

54.1
54.0
53.9
54.0
54.1
54.1
54.2
53.9
53.6
53.6
53.6
53.6
53.7
53.5
53.7
53.3
53.7
54.4
54.5
55.2
55.3
55.9
55.8
56.0
58.3
58.5
60.5
64.3
62.6
64.9
64.4
65.3
68.4
71.3
70.7
72.2
73.4

a

-24.5
-244
-245
-24.6
-24.6
-24.9
-25.0
-250
-244
-242
-237
-237
-237
-292
-309
-33.1
-35.6
-37.7
42.4
-21.8
-34.6
-22.6
-19.6
-21.6
-24.8
4.2
44.7
-18.8
-8.8
-12.6
1.2
10.8
2.3
4.9
6.8
8.1
10.9

 

0

76.2
77.3
77.0
78.0
79.1
82.0
85.0
85.7
86.1
86.8
87.3
87.9
88.5
89.0
91.3
92.2
92.7
94.7
94.9
95.0
95.1
95.2

(I

11.8
15.8
18.1
20.9
23.5
26.0
28.7
28.7
30.1
32.4
34.8
36.7
37.9
37.5
38.0
39.1
40.2
41.6
41.8
42.2
42.3
43.1

 

110

A5 (cont.).

$23
0

76.0
77.1
78.2
80.8
82.5
85.0
85.7
87.0
88.0
88.6
89.7
90.5
91.1
93.0
93.7
94.6
95.3
96.3
97.8
100.2
101.1
102.2
103.3
104.2
104.9
107.2
108.8
110.3
111.8
113.0
114.2
115.4
117.0
118.0
118.8
120.0
121.3

 

9.5
9.7
21.4
13.8
16.8
18.1
18.4
21.3
23.3
23.2
21.5
24.7
25.7
26.0
28.1
30.7
28.0
30.0
30.6
35.2
33.1
35.0
35.1
39.3
42.1
39.8
43.5
44.2
48.9
49.3
48.9
51.0
53.8
56.4
59.5
63.7
66.4

 

0

122.2
123.0
123.9
124.4
124.7
124.9
125.0
125.1
125.0
124.8
124.6
124.4
124.4
124.4
124.4
124.4
124.3
124.4
124.2
124.2
124.1
124.0
124.0
124.1
124.1
124.1
124.1
124.2
124.4
124.4
124.3
124.4
124.4
124.4
124.5
124.5
124.6

a

69.6
71.7
76.1
78.2
79.5
80.9
81.4
81.5
80.6
79.7
79.8
80.4
79.6
79.4
77.7
78.3
78.2
78.2
77.4
75.5
75.5
74.8
74.8
74.0
72.8
71.8
71.8
73.0
74.3
74.5
74.2
74.8
74.6
74.6
74.4
75.7
74.8

 

0

124.5
124.6
124.6
124.7
124.7
124.8
125.6
125.6
125.6
125.6
125.6
125.7
125.6
125.5
125.5
125.5
125.5
125.5
125.5
125.4
125.4
125.4
125.4
125.3
125.3
125.2
125.1
125.0
124.7
122.5
121.1
118.5
117.2
115.6
113.8
110.9
108.5

(1

74.1
74.3
75.0
75.4
75.5
74.8
75.6
76.4
77.0
79.2
78.9
78.2
78.0
78.9
78.9
78.9
78.6
79.7
78.7
79.6
80.1
78.6
79.4
78.7
77.5
78.6
78.8
76.7
77.7
76.5
70.8
66.4
66.0
62.8
59.0
55.5
53.8

 

0

106.3
103.9
101.3
98.5
95.1
91.6
89.5
85.3
81.8
80.7
80.1
79.6
78.7
77.8
75.3
74.3
73.2
72.1
70.8
68.7
67.5
65.4
64.4
63.3
61.9
61.3
58.7
56.9
56.0
55.9
55.6
54.2
54.9
53.5
52.8
52.5
52.2

111

a

56.9
53.4
51.0
55.7
53.9
52.5
53.5
50.6
46.7
46.3
44.6
41.0
39.7
34.7
32.8
28.1
25.8
22.5
20.2
14.1
23.1
10.8
12.0
14.7
12.9
9.9
3.3
1.7
2.1
4.6
5.4
2.3
0.6
-25.6
2.2
2.9
-8.5

 

53.1
52.3
53.8
53.7
53.8
53.8
53.8
53.8
53.7
53.6
53.7
53.7
53.5
53.6
53.6
53.6
53.7
53.8
53.8
53.9
53.9
53.8
54.2
53.0
54.0
54.3
54.2
54.1
54.1
54.4
53.4
52.4
52.5
52.5
52.5
52.6
52.5

1.1
0.5
2.3
1.6
1.9
1.8
2.5
1.8
1.9
2.3
2.0
1.9
2.3
1.7
1.4
0.8
0.6
1.3
2.5
1.8
2.6
2.4
1.8
1.8
2.3
1.3
2.0
1.2
2.1
2.4
1.8
1.3
1.6
1.5
1.1
2.2
~10.5

 

52.4
52.6
52.6
52.6
52.5
52.4
52.5
52.4
52.4
52.4
52.4
52.4
52.4
52.4
52.4
52.4
52.5
52.5
52.4
52.3
52.4
52.5
52.4
52.5
52.5
52.5
52.6
52.9
54.7
55.2
56.2
52.2
54.0
55.0
55.7
56.4
57.4

1.8
2.5
1.4
3.7
3.0
3.2
3.8
3.8
4.2
4.5
4.0
3.5
4.9
4.4
4.6
4.6
3.9
4.7
4.3
4.3
4.5
4.9
4.4
5.1
5.0
4.9
4.5
5.0
5.6
4.3
3.6
2.4
3.9
8.4
8.2
10.8
9.3

 

 

A5 (cont.).

823
0
58.2
60.1
61.1
61.6
62.2
62.7
63.6
64.1
64.1
64.4
65.4
67.3
68.1
69.0
69.9
70.6
71.2
72.7
73.1
73.2
73.4
73.4
73.4
73.5
73.4

0.

10.8
15.9
10.2
13.3
16.9
12.3
11.8
17.9
12.4
13.0
13.6
13.3
13.4
12.7
15.2
15.8
14.8
16.4
15.7
14.6
13.8
11.8
12.2
12.1
10.8

 

112

A5 (cont.).

$26
0
74.4
75.2
75.9
77.5
79.3
80.7
82.1
83.9
85.7
87.2
88.7
90.2
91.8
93.0
94.6
95.7
97.0
98.2
99.6
100.6
101.6
102.3
119.9
120.6
121.1
121.4
121.7
121.9
122.0
122.2
122.4
122.4
122.5
122.6
122.8
122.9
122.8

 

a
-7.1
-4.9
-7.5
-2.6
-2.9
5.9
6.4
1.3
4.5
6.7
9.7
7.6
6.6
10.4
17.7
19.6
18.4
16.9
15.9
16.0
18.6
16.6
28.0
27.8
27.2
26.7
27.2
25.9
27.8
26.9
27.2
27.8
26.8
27.5
27.4
26.2
26.9

 

0
122.9
122.9
122.8
122.0
121.7
121.5
121.2
120.9
120.6
120.4
120.0
119.8
119.6
119.4
119.3
119.2
119.0
118.8
118.4
117.9
117.2
116.0
114.6
112.7
110.9
108.6
106.4
104.2
101.7
98.8
96.8
95.1
92.9
90.8
89.1
87.4
85.5

a
26.4
26.9
27.5
32.2
35.1
34.7
33.0
34.3
35.3
34.4
34.2
33.8
33.7
33.6
31.0
33.7
34.4
35.7
34.1
32.3
31.1
32.0
32.8
33.9
30.7
28.2
32.2
33.3
25.3
23.3
21.6
26.9
26.8
25.3
20.2
13.9

7.6

 

83.5
81.7
80.2
78.4
76.2
74.9
73.4
72.1
70.6
69.0
67.3
65.6
63.8
62.4
61.7
61.4
61.4
61.5
61.7
61.8
61.9
61.9
62.0
61.8
62.0
61.9
61.7
61.5
61.5
61.6
61.7
61.9
61.9
61.7
61.7
61.6
61.6

4.6
3.5
0.3
-l.4
-3.2
—4.3
-5.8
-5.8
-6.3
-6.7
-8.6
-6.6
-9.1
-12.5
-9.2
-12.0
-11.7
-11.2
-11.1
-ll.3
~12.6
-12.8
-l3.5
-13.1
-16.0
-l3.6
-11.0
-ll.7
-ll.1
-lO.2
-10.5
-l3.8
-11.4
-10.8
-12.6
-12.9
~12.4

0

61.6
61.7
61.7
61.7
62.2
62.2
62.5
62.6
62.6
62.5
62.7
63.0
63.2
63.3
63.6
63.7
63.7
64.4
64.2
64.1
64.0
63.9
64.0
64.1
64.1
64.1
64.2
64.2
64.1
64.2
64.2
63.6
63.6
63.7
63.7
64.3
63.7

 

113

a

-14.3
-14.7
-14.3
-15.0
-13.9
-l4.2
-15.2
-15.0
-l3.1
-15.5
-12.4
-12.2
-13.8
-13.6
-12.3
-11.9
-l2.6
—12.6
-13.2
-13.2
-l3.6
-13.7
-13.2
-ll.4
-14.0
-l3.7
-12.4
-ll.9
-12.3
-12.4
-12.3
-12.8
-12.1
-12.3
-11.7
-11.7
-12.4

 

0
63.5
63.5
63.6
63.4
63.3
63.3
63.5
63.8
64.4
65.1
65.8
66.8
67.9
68.8
70.1
70.8
71.8
72.8
73.6
74.6
75.6
76.6
77.5
78.5
79.4
80.3
80.9
81.4
81.8
82.2
82.4
82.7
82.7
82.5
82.3
82.0
81.6

o.
-13.2
-14.5
-14.3
-13.4
-12.9
-11.9
-13.7
-12.3
-l3.0
-10.9
-10.3

-7.6
-7.5
-8.8
-5.8
-4.8
-4.1
-4.9
-3.4
—5.1
-7.7
-5.7
-5.3
-4.7
2.2
3.8
4.1

2.9
2.3

-6.0
-3.1
-1.4
0.6
0.3

4.0
4.1

2.2

 

81.3

2.0

 

 

A5 (cont.).

S28
0
55.4
56.8
57.2
58.0
58.8
60.2
61.9
64.9
67.9
71.1
73.0
74.7
78.1
80.6
83.5
85.2
87.1
88.8
91.8
93.4
95.9
97.4
98.8
99.9
101.3
102.2
103.2
104.1
104.8
106.5
107.2
107.5
107.6
107.7
107.7
107.6
107.4

a
-25.4
-23.8
-25.7
-24.6
-25.3
-21.4
-22.5
-22.1
-21.9
-21.4
-l6.0
-16.6
-l4.l
-13.1
-13.1

-8.7
-8.7
-6.5
-1.8
0.5
1.2
9.3
10.1
11.7
11.5
9.6
17.0
15.0
12.0
13.3
13.4
14.0
13.4
13.5
13.7
13.4
13.2

 

0
107.2
107.1
106.9
106.8
106.9
106.9
106.8
106.7
106.7
106.6
106.5
106.5
106.4
106.3
106.3
106.2
106.3
106.3
106.3
106.3
106.2
106.2
106.1
106.1
106.0
105.9
105.8
105.8
105.6
105.4
104.6
104.4
104.4
104.5
104.5
104.6
104.6

a
12.9
13.9
12.8
13.4
13.1
12.8
12.7
12.9
12.6
12.6
12.2
12.2
12.4
12.8
12.4
12.8
19.3
14.6
13.3
13.6
18.0
13.7
18.2
13.1
13.2
12.4
11.9
12.1
11.7
11.5
11.5
11.1
15.9
16.3
16.9
17.0
17.2

 

0
104.8
104.8
105.0
105.1
105.1
105.1
105.2
105.2
105.3
105.2
105.2
105.2
105.2
105.2
105.1
105.1
105.1
105.1
105.0
105.0
105.0
105.0
104.9
104.7
104.5
104.0
103.5
102.5
101.1
100.0
98.5
97.1
94.3
92.5
89.9
87.8
85.6

a
17.8
17.6
18.7
12.7
12.5
13.5
12.6
12.6
14.0
13.8
21.9
13.6
13.5
14.0
13.9
20.1
13.6
13.1
13.3
19.4
18.3
19.7
18.9
18.8
20.1
17.8
16.9
14.6
13.5
11.2
11.4

7.0
3.7
2.6
0.0
-3.9
-4.3

 

0
83.7
80.2
77.3
75.4
72.6
70.8
67.6
64.8
61.6
58.7
56.7
54.5
51.1
48.9
45.6
44.1
42.9
41.6
40.7
39.4
39.1
38.1
37.9
37.9
38.0
37.8
37.1
37.0
36.8
36.7
36.6
36.5
36.5
36.6
36.6
36.7
36.8

114

a
-7.3
-12.1
-l4.1
-l4.7
-l6.4
-l7.2
-l9.8
-17.7
-23.1
-27.4
-25.0
-26.7
-23.9
-27.4
-26.1
-28.2
-27.4
-27.3
-28.8
-25.4
-26.0
-23.0
-23.6
-20.9
-22.2
-21.3
-22.3
-22.6
-22.0
-21.6
-21.2
-22.1
-21.6
-22.0
-22.2
-21.9
-22.3

 

0
36.6
36.6
36.7
36.7
36.6
36.6
36.6
36.6
36.6
36.7
36.7
36.7
36.7
36.8
36.8
36.8
36.9
36.7
36.9
36.9
36.9
36.9
36.9
36.8
36.8
36.9
36.8
36.7
36.7
36.7
36.7
36.7
36.8
36.7
36.6
36.6
36.6

a.
-23.0
-23.2
-23.0
-23.2
-22.3
-25.5
-23.6
~23.1
-23.5
-23.9
-23.5
-23.7
-23.4
-23.1
-22.9
-23.0
-25.7
-22.2
-23.5
-25.7
-23.1
-23.4
-23.4
-23.4
-23.3
-22.9
-23.4
-23.2
-23.3
-23.9
-23.0
-22.6
-22.2
-23.6
-23.7
-22.8
-23.5

 

0
36.6
36.6
36.5
36.5
36.5
36.5
36.6
36.6
36.6
36.6
36.6
36.7
36.9
36.9
37.2
38.0
37.8
38.8
40.3
42.1
43.1
44.1
45.3
47.7
48.8
49.6
50.2
50.5
50.8
51.0
51.1
51.2
51.2
51.3

a.
-24.1
-24.6
-24.1
-24.4
-24.2
-24.9
-24.4
-24.4
-24.6
-24.5
-24.6
-23.2
-24.4
-22.8
-25.8
-28.2
-34.5
-32.8
-30.4
-24.3
-22.9
-23.2
-18.3
-20.4
—19.1
-17.0
-17.3
-18.3
-17.1
-19.4
-17.2
-l9.4
-l8.3
-23.4

 

A5 (cont.).

S30
0
78.2
79.0
79.5
79.9
80.7
81.6
82.5
83.5
85.1
86.3
87.4
88.7
89.7
90.6
91.5
92.2
93.1
94.1
95.0
96.1
97.1
97.9
98.6
99.5
100.0
100.8
101.6
102.2
103.2
104.0
104.8
105.5
105.9
106.3
106.9
107.6
108.3

 

5.6
11.7
13.3
10.6
7.2
7.9
10.2
11.8
12.2
14.0
12.8
15.7
15.7
18.2
19.6
18.0
23.8
18.8
19.2
19.8
25.3
21.7
22.5
22.9
19.1
20.4
21.9
16.9
27.6
22.8
12.7
20.6
26.8
22.4
25.4
28.8
27.1

 

108.6
108.9
109.4
109.7
110.2
110.5
110.6
111.0
111.2
111.4
111.6
111.9
112.3
112.4
112.6
112.8
112.9
113.0
113.1
113.2
113.4
113.6
113.8
113.9
114.1
114.3
114.3
114.7
114.9
114.9
115.0
115.3
115.2
115.2
115.1
115.0
115.0

(1

24.5
18.1
21.6
21.8
20.9
21.0
20.0
21.0
21.6
21.6
21.6
18.8
19.5
20.3
20.4
20.1
19.6
19.7
21.1
19.5
19.8
19.5
20.0
22.2
22.9
23.3
24.3
24.2
23.6
22.0
20.1
20.3
20.9
21.1
22.4
23.4
23.7

 

114.9
114.8
114.7
114.7
114.7
114.7
114.7
114.6
114.6
114.6
114.5
114.5
114.5
114.5
114.4
114.4
114.3
114.3
114.2
114.1
114.0
114.0
114.0
114.0
113.9
114.1
114.0
114.3
114.1
114.1
114.2
114.2
114.2
114.1
113.3
113.2
113.2

a

21.9
22.9
22.8
22.2
22.3
22.1
22.4
22.3
22.4
23.0
22.8
22.5
21.9
22.3
22.1
22.0
21.4
22.4
21.4
21.1
21.7
21.6
21.9
21.0
21.0
25.4
26.0
23.2
22.8
22.1
22.9
27.5
27.2
27.4
14.4
21.4
20.0

115

 

113.0
113.0
112.6
112.0
111.4
110.4
109.4
108.3
107.0
105.6
104.2
102.4
101.0
99.3
97.3
95.1
93.3
91.3
88.9
86.8
84.9
82.8
80.6
78.2
75.8
73.7
72.0
71.2
70.8
70.7
70.7
70.5
70.5
70.2
69.5
69.1
68.6

(I

18.7
22.0
19.1
17.4
22.4
22.8
25.4
15.8
16.7
17.5
20.7
17.4
15.1
16.7
13.5
8.9
10.2
9.4
2.8
0.4
0.4
3.6
2.8

-15.2 '

-15.3
-15.7
-17.8
-14.9
-15.0
-l4.2
-14.2
-14.9
-16.8
-14.2
-13.9
-13.9
-14.3

 

67.9
67.7
67.4
66.8
66.8
66.5
66.5
66.6
66.5
66.5
66.4
66.1
65.9
65.7
65.4
65.5
65.2
65.1
65.0
65.0
64.9
64.9
64.7
64.6
64.6
64.8
64.5
64.3
64.3
64.2
64.3
64.0
64.1
64.1
64.0
64.2
64.0

a

-l4.6
-17.1
-16.7
-15.4
-15.0
-14.5
~14.7
-14.8
-l4.1
-17.7
-15.4
-16.1
-16.5
-16.5
-l4.6
-16.5
-15.5
-14.7
-14.9
-15.4
-15.5
-15.0
-14.9
-15.2
-15.9
-15.3
-15.8
-15.7
-15.9
-15.1
~15.0
-14.2
-15.0
-15.0
~15.3
-15.1
-15.6

 

 

A5 (cont.).

S30
9
64.0
64.0
64.1
64.2
64.5
64.5
64.7
64.8
64.9
64.6
64.7
64.5
64.6
64.6
64.6
64.6
64.7
64.7
64.8
64.9
64.9
65.1
64.9
65.0
64.8
64.8
64.6
64.6
64.9
64.9
65.0
65.1
65.0
65.0
65.0
65.0
65.0

a
-15.3
-15.3
-15.7
«15.6
-16.6
-16.3
-16.5
-16.6
~16.5
-16.5
-l6.4
-17.1
-l7.3
—l6.7
-16.9
-l7.1
-16.1
-15.4
-16.8
-16.7
-l6.2

0.2
-13.7
-14.4
-14.8
-16.9
-16.8
-16.7
-16.1
-16.6
-16.7
-l7.0
-l7.5
~17.5
-l7.4
-l6.3
-l6.8

 

0
65.1
65.3
65.7
66.2
66.6
67.4
67.9
69.1
70.2
71 . 1
72.2
73.4
74.7
75.9
76.8
77.8
79.0
80.1
81.0
81.8
82.2
82.8
83.0
83.5
83.8
83.9
84.1
84.0
83.9
83.7

a
-16.8
-14.6
-13.9
-13.5
-13.5
-l4.4
-13.5
-13.4
-ll.8

1.3
1.2
1.7
0.8
2.0
2.5
8.3
8.7
7.1
8.3
10.1
10.8
11.3
11.1
11.0
11.6
11.0
16.1
15.5
13.3
13.4

 

116

10.

11.

12.

BIBLIOGRAPHY

Kopec, J., E. Sayre, and J. Esdaile, Predictors of back pain in a general
population cohort. Spine (Phila Pa 1976), 2004. 29(1): p. 70-7; discussion 77-8.

Schneider, S. and S. Zoller, [Physical movement - Is it good for the back? .'
Nationwide representative study on different eflects of physical activity at the
workplace and in leisure time. ] . Orthopade, 2009.

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