///I LIBRARY

Michigan Stab
University

 

This is to certify that the

thesis entitled

FREQUENCY DOMAIN FEATURES OF BACKSCATTEREO ACOUSTIC
RADIATION‘FROM BIOLOGICAL TISSUE

presented by

CHARLES JOSEPH deSOSTOA

has been accepted towards fulfillment
of the requirements for

M.S. degreein Electrical Eng. 8 Sys.
Sci.

 

 

0%W

Major professor

Date H/II ./7?

0-7639

 

 

 

OVERDUE FINES ARE 25¢ PER DAY
PER ITEM

Return to book drop to remove
this checkout from your record.

 

 

 

FREQUENCY DOMAIN FEATURES OF BACKSCATTERED ACOUSTIC

RADIATION FROM BIOLOGICAL TISSUE

By

Charles Joseph deSostoa

A THESIS

Submitted to

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

MASTER OF SCIENCE

Department of Electrical Engineering
and Systems Science

1979

ABSTRACT

FREQUENCY DOMAIN FEATURES OF BACKSCATTERED ACOUSTIC

RADIATION FROM BIOLOGICAL TISSUE

By

Charles Joseph deSostoa

This thesis represents a preliminary investigation into the
feasibility of indentifying tissue types based on spectral properties
of ultrasound echoes. Toward this end, diffuse ultrasound echoes from
in 3339 human liver and spleen were investigated in order to develop
spectral tissue signatures for these organs. The interrogation was
performed by a broadbanded 1 MHz transducer operated in the pulse/echo
mode. A 5 MHz sampling rate was used to digitize the backseattered
signal and the digital data was stored onto magnetic tape for
postprocessing. The postprocessing of data collected consisted of the
following two procedures; first, Fourier Transformation of the
digitized waveforms, and second, calculation of statistical measures
of the spectra. Various combinations of these statistical measures
were studied in order to assist in tissue classification. The two
classifiers investigated were the scatter plot method and minimum
Mahalanobis distance method. Data generated from a single subject as

well as from a group of 5 subjects was used for testing the two

classification methods. For the scatter plot method and two
dimensional feature space, succesful classification rates of 0.73 and
0.83 were achieveable for group and individual data sets respectively.
Applying the Mahalanobis method to the group of 5 subjects yielded
success rates ranging from 0.72 to 0.79 for the more successful
combinations of features. Attenuation factors have been applied to the
backseattered spectra to correct for overlying tissue effects. A
slight increase in the effectiveness of the features to facilitate
tissue classification was observed and indicates that more exact
methods for applying attenuation correction factors could prove

useful.

TO MADELYN AND X

ACKNOWLEDGMENTS

The author extends his greatest gratitude to Dr. D. K. Reinhard,
his thesis advisor, who has been a constant source of guidance and
support. Sincere appreciation is expressed to Dr. G. I. Harris and
Mr. D. A. Gift for their valued advice. Appreciation is also expressed
to Dr. R. Nettleton, a member of the guidance committee, for his review
of and suggestions to this thesis.

A very special thanks is extended to Dr. H. R. Zapp for his
extensive review of this thesis and numerous suggestions during the
course of this research.

Additional thanks are expressed to Dr. T. Adams, Mr. M. Steinmetz,

and Mr. B. Johnston for their help and support.

TABLE OF CONTENTS

LI 8 T 0F TABLE S O O O O O O O O O O O O O O O O O O O 0

LIST OF FIGURES O O O O O O O O O O O O O O O O O O O O O O

I 0 INTRODUCTION 0 I l O O O O O O O O O O O O O O O O O O 0

Previous WOrk . . . . . . . . . . . . . . . .
Wave Metion . . . . . . . . . . . . . . . . .
Characteristic Impedance . . . . . . . . . .
Acoustic Scattering . . . . . . . . . . . . .
Attenuation . . . . . . . . . . . . . . . . .

II. THEORETICAL CONSIDERATIONS . . . . . . . . . . . . . .

Homogeneous Medium . . . . . . . . . . . . .
Weakly Inhomogeneous Medium . . . . . . . . .
wave Attenuation . . . . . . . . . . . . . .
Linear Modeling . . . . . . . . . . . . . . .
The Steady State Transducer Field . . . . . .
Ideal Scatterers . . . . . . . . . . . . . .

III. EXPERIMENTAL PROCEDURE AND RESULTS

3.
3.
3

1
2
3

Experiment Procedure . . . . . . . . . . . .
Backscatter From a Metal Block . . . . . . .
The Mahalanobis Distance . . . . . . . . . .

IV. BIOLOGICAL TISSUE ANALYSIS

4.1
4.2
4.3

4.4

Biological Tissue Data Collection and Post
Processing . . . . . . . . . . . . . . . . .
Feature Space Representation . . . . . . . .
Tissue Differentiation by the Mahalanobis
Method . . . . . . . . . . . . . . . . . . .
Introduction of Attenuation Correction Factor

V. CONCLUSION . . . . . . . . . . . . . . . . . . . .

APPENDIX A

APPENDIX B

BIBLIOGRAPHY

O O O O O O O O O O I O I O O O O O O 0 O

O O O I O O O O O O O O I O O O Q C Q Q 0

iv

Page

vi

H

WNQUIN

F‘P‘

15
16
20
21
23
26
37
37

4O
53

57

57

62

66
71

74

81

94

98

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

3.1

4.1

4.2

LIST OF TABLES

Propagation velocities of some biological
materials 0 O O O O O O O O C O O O C O C 0

Characteristic impedance of some biological
materials 0 O O O O O I O O O O O O O O O O 0

Biological attenuation coefficients
Point scatterer . . . . . . . . . . . . . .
Cylinderical scatterer . . . . . . . . . . .
Plane scatterer . . . . . . . . . . . . . .
Rank order of measures from least to most

sensitive to 10% change in overlying tissue

attenuation coefficient . . . . . . . . .

Rank order of measures from least to most
sensitive to scatterer type . . . . . . . .

Mahalanobis distances and classification for
all sample points of Figure 3.11 . . . . .

Classification by Mahalanobis method . . . .

Classification by Mahalanobis method attenuation

intrOduced C O O O O O O O O O O O O O O O I

14

31

32

33

35

36

55

7O

73

Figure

Figure
Figure
Figure

Figure
Figure

Figure

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

1.1

1.2
2.1
2.2

2.3

2.4

3.1

3.2

3.3A

3.33

3.4

3.5

3.6

3.7

3.8

3.9

LIST OF FIGURES

Variation of propagation velocity with temperature
in water . . . . . . . . . . . . . . . . . . . . .

Reflection and transmission of acoustic wave . . .
Definition of coordinates . . . . . . . . . . . .
Relations involved in linear modeling . . . . . .

The ultrasonic field for a 1.5 MHz transducer of
radius r =

1 cm. 0 O O O O O O O O O O O O O O 0

Polar plot of 1.5 MHz transducer field of radius

r 8 1 cm 0 O O O O O O O O O O O O O O O I O O 0
Data collection system and postprocessing . . . .

Experimental setup for investigation of the
ultrasonic field spatial dependence . . . . . . .

Typical sampled backscattered waveform from
metal bIOCk O O O O O O O O I I O O I O O O O O O

Expanded view of Figure 3.3A between t1 and

t2 0 o o o o o o o o o o o o o o o o 0

Frequency spectra for reflection from a metal
block at same position but different records . . .

Frequency spectra of reflections from a metal
block for distances d c 2.3 cm and d - 3.8 cm . .

Intradistance spatial variations of mean and
variance . . . . . . . . . . . . . . . . . . . . .

Intradistance spatial variations of skewness
and kurtosis . . . . . . . . . . . . . . . .

Intradistance spatial variations of first and
second partial sums . . . . . . . . . . . . . . .

Intradistance spatial variations of third and
fourth partial sums . . . . . . . . . . . . . . .

vi

11
19

22

24

26

4O

42

44

45

46

47

49

50

51

52

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

3.10

3.11

3.12

4I1

4.2

4.3

4.4

4.5

4I6

4.7

Bivariate density plot of two arbitrary classes

in the feature space (f1,f2) . . . . . . . . .

Example of two well ordered classes in feature
Space (f1, f2) 0 o o o o o o o o o e o o o o o

a) Classification using euclidean distance
methOd I I I I I I I I I I I I I I I I I I

b) Classification using Mahalanobis distance
me thOd I I I I I I I I I I I I I I I I I I

Sampled backscattered waveform from liver
tissue I I I I I I I I I I ‘I I I I I I I I I I

Sampled backscattered waveform from spleen
tissue I I I I I I I I I I I I I I I I I I I I

Interrogated volume defined by time window
Of Figure 4 I 1 I I I I I I I I I I I I I I I I

Spectrum of backscattered ultrasound from
liver tissue I I I I I I I I I I I I I I

Spectrum of backscattered ultrasound from
spleen tissue . . . . . . . . . . . . . . . .

Scatter plot of liver and spleen samples
for a single individual . . . . . . . . . . .

Scatter plot of liver and spleen samples
for five subjects . . . . . . . . . . . . .

53

54

56

56

59

6O

61

63

64

67

68

CHAPTER I

INTRODUCTION

In recent years much research has been conducted in the field
of biomedical ultrasonics. In particular, considerable interest and
effort has been directed toward quantifying the interaction between
various ultrasonic interrogation beams and certain biological tissues.
The ultimate goal of such studies is the determination of a set of
quantifying features that would enable the researcher to discriminate
between normal and pathological states of a given tissue. The in-
vestigation of quantifying features, commonly referred to as sig-
natures, includes signal amplitude analysis, impediography, time delay
spectroscopy, investigation of frequency dependent absorption, and
frequency and angle dependent scattering. The above techniques represent
only a cross-section of those developed to date, rather than a compre-
hensive list.

This thesis investigates properties of the spectral energy
distribution of ultrasound backscattered from biological tissue.
First, a brief examination of the basic nature by which sound energy
propagates and is scattered will be presented. Second, a mathematical
model for both the interaction of ultrasound radiation with tissue
and the effects of overlying tissue on this model will be discussed.
The model is applied to idealized scatters including point, cylinder,
and plane sources. Finally, classification of samples will be
performed using feature spaces defined by subsets of eight statistical

measures determined from the tissue spectra. The effects of overlying

tissue will be noted on the ability of the classifier to interpret
the information correctly. Two different biological tissues were
studied experimentally, namely; human liver, and human spleen.
1.1 PREVIOUS WORK

In recent years a variety of advanced techniques designed to
extract information about the acoustical properties of soft-tissue
structures have been investigated. Of these techniques, those
employing frequency domain analysis have received much attention and
have proven successful in the differentiation of certain tissue states.

Lele, et al.1 have demonstrated tissue pathology discrimination
by considering the state dependence of the attenuation coefficient.
Comparing the backscattered frequency spectrum of a known reflector
(i.e. glass plate) with and without intervening tissue, they observed
an alteration of the spectral energy distribution. It was noted that
different tissue states demonstrated detectable changes in the
attenuation coefficient as a function of frequency. Lele1 has in-
vestigated this phenomenon for skeletal muscle with localized areas
of heat necrotization and infarction by vascular occlusion and from
in gitgg experiments on specimens of normal myocardium and anemic
infarcts. In addition, Lizzi, et al.2’3’“ have demonstrated the
pathology frequency dependence of the attenuation coefficient for
vitrious hanorraging of the eye 39:2}!2, Results from both studies
have proven to be relatively successful in determining tissue state
differentiation features.

Lizzi3 has also observed spectrum shaping due to pathologies

characteristic of well defined, thin membranes. More specifically,

it was noted that the frequency domain of an acoustic pulse scattered
from a detached retina exhibited a scalloped spectrum. The scalloped
form was due to the destructive interference between reflections from
the anterior and posterior surfaces.

Cepstral signal processing of reflected acoustic waves from
tissue structures has been investigated by Fraser, Birnholtz, and Kinos.
The cepstra corresponds to the Fourier transformed log power spectrum
of a signal and therefore allows the processing of backscattered
spectra in a linear, additive manner. These authors concluded that
information about the distribution of spacing between reflectors may be
seperated from the information about the incident wave itself and in-
vestigated. In addition, they noted that two potentially useful para-
‘meters for tissue characterization in 3132 are the shape of the cepstrum
obtained from soft tissue echoes, and attenuation coefficient estimation
by the cepstral smoothing of the log power spectra.

Chu and Raeside6 adopted a frame work for automated pattern recog-
tfltionapplied to MPmode cardiac scans. 'The steps involved in the analysis
consist of processing, feature extraction, and classification. The pro-
cessing of anterior mitral leaflet waveforms consisted of determining
the Fourier series of each waveform obtained from a sample space of 88
subjects (57 normal volunteers and 31 confirmed cases of mitral stenosis).
The power spectrum generated by the Fourier series was used to form a 21
component feature vector. Feature ranking was carried out to eliminate
less informative components, thus reducing the feature vector to only
two componenets. Utilizing this vector Chu and Raeside6 attempted to
establish an effective algorithum for the automated classification of

anterior mitral leaflet waveforms of unknown pathology.

Investigated were the nearest-neighbor and Bayes' classifiers. Both
classifiers proved extremely successful (not a single miscalculation
occurred within the 88 applications).

Preston, Czerwinski, and Leb7 have investigated sixty-five features
based on the shape and statistical properties of the power spectrum, the
rectified waveform, and the raw waveform. These features were then
processed in order to select the best discriminators between groups of
data. Upon application of the discrimination features to the backs
scattered signals from normal and pathological (acute pyelonephritis)
rabbit kidneys the best results were derived from the frequency spectrum,
in particular, from the total energy in the range 0 to 1.8 MHZ and 1.9
to 2.8 MHZ, and from theyfirstamoment;of thegpowerzspectrum.

The above review has been concerned with those techniques using
frequency domain analysis. It is, however, important to realize that
the frequency domain does not contain any new information about the
time domain signal, since it is derived from the latter. Frequency
domain analysis is used in this thesis for two reasons: first, the
work done by Preston, et al.7 seems to indicate that frequency domain
features tend to be better discriminators; and, second, the attenuation
effects of overlying tissue are more readily discerned in the frequency
domain.

The following sections of this chapter outline some fundamental
physical concepts regarding the interaction of ultrasound with

biological tissue.

1.2 WAVE MOTION

In the following sections of this chapter it will be assumed that
the energy of an acoustic wave exists at a single frequency unless
otherwise stated. Additionally, the medium through which this wave
travels is presumed to be isotropic and perfectly elastic. The mode
of the wave considered is longitudinal; that is, the particle motion
is in the same direction as the energy flow. Additional assumptions
will be presented when appropriate to the development.

The mechanisms by which sound energy propagates can be attributed
to the elasticity and to the density of the medium. The elasticity,
represented by the adiabatic compressibility (K) of the medium,
accounts for the restoring forces that a volume exhibits against
compression. The density is represented by the inertia of the mass
which results in an overshoot of the particles from their mean position.
The resultant particle motion is thus harmonic.

For perfect gasses it can be shown that the group velocity+ of
the wave is proportional to the square root of the mean-squared

molecular velocity (Ingarde):

CO. V <V2>

where <v2> is the mean-squared molecular velocity.

For liquids and solids the velocity of sound is considerably
greater than the root-mean-square velocity of a molecule about its
equilibrium position. For lonitudinal waves the velocity of sound

can be shown to be (Ingarde):

+ Group velocity is the speed at which energy propagates through a
medium.

,Ka' , 1'
C a — = —
o no

where Ka - adiabatic bulk modulus,

p = mean density of medium,

K 8 adiabatic compressibility.
The velocity of sound is independent of the amplitude and frequency of
the wave to the extent that the excess pressure associated with the
ultrasound wave is small compared with the equilibrium pressure. This
is required to keep the compressibility, K, from exhibiting an excess
pressure dependence.

It has been observed experimentally that the velocity of sound is

dependent on the temperature of the transmitting medium. This may be

 

 

 

 

 

 

 

 

 

 

 

1550 /L 'K\
1500
A /
U
Q)
U)
\
E
v
>~1|+50
U
'H
U
O
H
0)
>
1400
0 20 1&0 60 80 100

Temperature (°C)

Figure 1.1 Variation of propagation velocity with temperature in
water. Wells 1969.

attributed to the temperature dependence of the elasticity and density
of the medium. Generally, the relationship between velocity and
tenperature can be quite complex. Figure 1.1 shows the acoustic
velocity versus temperature dependence in distilled water.

Another experimentally observed phenomenon, velocity dispersion,
occurs due to the frequency dependence of the acoustic velocity.
Velocity dispersion,although measurable, is insignificant for bio-
logical tissues in the frequency range of interest (f < 2.5 MHZ). The
velocity of sound for a few types of biological materials are presented

in Table 1.1.

TABLE 1.1

Propagation Velocities of some Biological Materials*.

 

 

Tissue Mean Velocity
m/sec
Fat 1450'
Human tissue, mean value 1540
Brain 1541
Liver 1549
Kidney 1561
Spleen 1566
Blood 1570
Muscle 1585
Skull-bone ' 4080

 

*
From P.N.T. Wells9

1.3 CHARACTERISTIC IMPEDANCE
The characteristic impedance of a medium expresses the relation-
ship between the pressure and phase velocity+ associated with

propagating acoustic waves. It is defined as:

Z 3 pc 31’2.
K

where p = density,
c a group velocity,
and K a adiabatic compressibility.
The characterisitic impedance of a mediumrmay be complex (Herzfeld
and Litovitz10 although for biological tissue the imaginary component
is negligible (Wells“). The relationship between the pressure and

phase velocity of the acoustic wave is given by:

P = Zu
where P = pressure
u 8 phase velocity,
and 2 - characteristic impedance.

The characteristic impedances of a few biological tissues have been

tabulated below.

+ Phase velocity is the same as the particle vibrational velocity.

TABLE 1.2

Characteristic Impedance of Some Biological Materials*

 

 

Tissue 2(8/cm2 - sec) x 10-5

Fat 1.38
Brain 1.58
Kidney 1.62
Human tissue, mean value 1.63
Spleen 1.64
Liver 1.65
Muscle 1.70
Skull-bone 7.8

 

*
From P.N.T. Wellsg

For plane waves incident on a planar interface between two media
the characteristic impedances on either side of the interface may be
used to define reflection and transmission coefficients. The appli-
cation of Snell's Law, along with appropriate boundary conditions,
lead to an expression for the ratio of the pressure reflected to
pressure incident (reflectivity) and the pressure transmitted to the

pressure incident (transmissivity). The required boundary conditions

are:
1> 92 .§
dt + dt

where

2)

N+ m N+

10

the displacement vector

= 0- is medium 1 side of boundary

0+ is medium 2 side of boundary.

P(o') - p<d+)

where P(x) - pressure of acoustic wave at x.

Thus, the particle velocity and acoustic pressure are continuous at

the boundary between two media. The reflectivity and transmissivity

are (Ingarde):

and

Pr ‘ 22 cosei - Zl coset

P1 22 cosei + 21 coset

I

 

Pt 2 22 cosei

 

P1 22 cosei + 21 coset

characteristic impedance of medium 1
characteristic impedance of medium 2

incident angle of acoustic wave from the normal
to the planar interface

angle of transmitted acoustic wave from the normal
to the planar interface.

Snell's law defines the relationship between the angles of incidence

and transmission and the acoustic velocity of each medium:

where c

1

sin 61 Cl

sin at C2

acoustic velocity in medium 1
acoustic velocity in medium 2
angle of incidence

transmitted angle

11

Figure 1.2 below indicates the angles involved.

Medium 1 Medium 2

c1901 c29p2

reflected

       
   

transmitted

 

 

incident

 

“VV\\\\V‘

5‘:
II
C

Figure 1.2 Reflection and transmission of acoustic wave.

For the case of normal incidence we have:

 

 

91 = 6t 3 0
thus

Pi 22+Zl
and

it. .. “2

P1 22+Zl

A similar relationship for the intensity reflection coefficient, (Yr),

and the intensity transmission coefficient, (Tt)’ may be developed:

2
22 cosei - Zl coset

2
V g Pr
22 cosei + 21 coset Pi

r:

 

12

and

T =

2
4 22 Z1 cos 61 = 21(Pt)2
t _ —

(22 cosei + 21 6089192 22 P1

Reflections from certain tissue surfaces and large interfaces may be

treated approximately in this manner.

1.4 ACOUSTIC SCATTERING

Usually, the scattering processes associated with biological
tissue are extremely complex due to the randomness of the size, shape,
distribution, orientation, density, and compressibility variations of
the scattering centers. As a first step, the solution to the single
body scattemeris formulated. Then, utilizing the linearity of the
wave equation describing the propagation properties of the medium,
the principle of superposition is used to describe multiple body
scattering. Unfortunately, even problems of relative simplicity
generate rather complex solutions as will be seen in Chapter 2. A
more tractable approach to modeling random reflectors in biological
tissue is that of Kuc et al.11 who model the reflectors as a random
linear filter. The filter is assumed to have an impulse response
that is a zero mean, white Gaussian process. The advantage of
this type of approach is that probability and statistics
may be applied to the macrostate of the scattering volume, as opposed
to a prohibitively complex microstate approach which would attempt to

analyze each acoustic wave-reflector interaction separately.

13

1.5 ATTENUATION

A change in the average cross-sectional acoustic beam intensity
may be attributed to either spatial dispersion in the medium through
which the wave propagates or to the spatially dependent shape of the
acoustic beam characteristic of the transducer itself. This latter
phenomenon will be discussed in Section 2.6. Ultrasound attenuation
may be due to the combined effects of several different mechanisms,
however in certain situations one particular mechanism may predominate.
The following section reviews those mechanisms applicable to biological
tissue.

A mechanism of attenuation, characteristic of the transmission
medium, is the elastic scattering suffered by an acoustic wave as it
impinges on discontinuities within the interrogated volume. This
leads to a dispersion of the amustical energy from the original beam
direction. Mechanisms of attenuation due to active absorption, howb
ever, are related to the visosity, thermal conductivity, relaxation,
and elastic hysteresis. Of these mechanisms relaxation is the pre—
dominant factor involved in attenuation for biological tissue.

Attenuation due to the transmission of ultrasound through

biological tissue is well characterized experimentally by the relation:

= -a(f)d
I Ioe

where Io = initial intensity of acoustic beam,

d

total transmission distance through attenuation medium,

and a(f) = attenuation coefficient characteristic of medium.

14

In general, the frequency dependence of the attenuation coefficient

(a) in biological tissues is linear (Lizzi et al.“)

where

a = a f
o

no - attenuation per cm at l MHZ

and f - frequency of acoustic wave in MHZ.

A table of biological tissues and their corresponding attenuation

coefficients are given below. In this table, the absorption

coefficient is expressed in terms of dB/cm, rather than inverse

 

 

centimeters.
TABLE 1.3
*
Biological Attenuation Coefficients
o/f Temp. Frequency
Tissue dB/cm . MHZ oC MHZ Com.

Liver, Human 1.17 body 1.5 in vivo
Liver, Human 1. 24 40°C 0. 97 fresh
Liver, Porcine 1.18 25°C 4 fresh
Liver, Porcine 0.23 24.8OC 4 homogenated
Spleen, Human o. 50 18.2°C 1. 6 fixed
Fat, Human 0.6 37°C 1 fresh
Muscle, Human 0.64 37°C 1.5 in vivo
Abdominal Wall 2.94 - 1 fat & muscle
Abdominal Wall 1-2 - 1 mainly fat

 

From Comprehensive Compilation of Emperical Ultrasonic Properties
of Mammalian Tissue12

CHAPTER II
THEORETICAL CONSIDERATIONS
It is instructive to review an approach describing the propagation
and scattering of acoustic energy by the appropriate wave equation and
boundary conditions. In this chapter the wave equation approach is
used to provide a foundation on which to base a linear model. This
model provides a useful conceptual tool for analyzing the ultrasound/

tissue interaction.

2.1 HOMOGENEOUS MEDIUM

The wave equation approach is often described in terms of a
continuous wave field, although ultrasonic excitations generated in
practice are of a transient nature. It has been shown, however, that
the transient (pulse-echo) and steady state (continuous wave) formula-
tions are equivalent (Goldberg and Watsonls).

Consider first the wave equation for longitudinal waves in a

homogeneous elastic medium for which there is no Scattering (Ingards):
v2p-—-—-——-o (1)

where the pressure, p, is a function of both time and spatial

coordinates, and c is the group velocity of he acoustic wave.

0

Seperation of the variable ? (spatial vector) and t (temporal variable)

leads to:

vsz?) + k3,, p(‘r*) = o (2)

15

16

where kon is the wave number, equal to 217/1n and An is the wavelength
of the propagating wave. The magnitude of the acoustic wave is

assumed to be small so that the velocity and thus wave number are
essentially independent of the wave amplitude (i.e. the compressibility
and density of the medium do not vary significantly from their mean
values). This assumption is valid for intensity levels used in this
research and in clinical diagnostic systems. The solution of equation

(2) is:

+

p(f) = An ejkon. ? (3)

where A.n is the wave amplitude and kén is the propagation vector.
Introducing the time dependence yields the total solution of the wave

equation:

jdton; ? - aunt)

(4)

Pn('r*,t) = An e

where

”n = C0 kon
By superposition, a more general expression for propagating continuous

waves satisfying equation (1) is given by:

pa.) = 2 An ej<kon~r - cont) (5)

n:

2.2 WEAKLY INHOMOGENOUS MEDIA

The 'diffuse' echoes observed in a backscattered acoustic wave
from biological tissue samples may be attributed to small inhomo-
geneities within the tissue volume. The wave equation approach be-

comes complex for such scattering and requires linearization to attain

17

tractable solutions. An approach of this kind still proves useful
in modeling such complex scattering phenomenon.

Consider the case where the compressibility and density of a
well defined volume embedded in a homogeneous medium vary as a function
of location and thus produce a spatially varying acoustic velocity
within the subvolume. The refractive index reflects this variation,

as shown in the following expression:

n(?) =

 

co

em ' “0 + “13) (6)
where Co is the speed of sound for the homogeneous medium and c(f) is
the speed of sound at a specific location. The no term represents
the nominal refractive index for the medium, and n(?) represents

small variations about the mean. Starting with equation (2) of the

previous section, the Helmholtz equation becomes:
v2p<’r’) + 1:260:36?) = o (7)

where k2(f) may be expressed as:

2 2 2
k2?) - “’ - .9. _c_°- . 2 2
r 2765 e3 e6?) Mum)

Substituting this into equation (7) yields:
vsz) + kg(no + n1(?))2p(?) = 0 (8)

One may choose, without loss of generality, no = 1 (i.e., the nominal
acoustic velocity of the inhomogeneous volume is the same as that of
the surrounding homogeneous medium). In addition, by the small var-

iation assumption (n1<<no) the n1 terms may be neglected. Equation

l8

(8) becomes:

V2p(r) + k §p(?) - -2 n1(r)k§ p(r) (9)

For weak scattering the total pressure field within the inhomogenous
volume may be written as the sum of the incident and weakly scattered

fields (Gore and Leemanls):

pt = P1 + 133 (10)

The homogeneous wave equation (2) together with equation (10) results

in the following relation:

stp (r) + k2 Osp c?) = -2 n1(i-*)k§{pi(?> + 1:86)} (11)

It is possible to formulate the solution for the backscattered acoustic
pressure described by (11) at a point, R, using a Green's function.
In the far field wagg et al., have shown that the scattered wave may

be expressed as:

+ 1‘22" jk OR _,, I "
ps<r> = e —9—R—J{p,(? >+ pse'nnluwefiko? 'zdv' (12)

This expression assumes that the observation point is sufficiently
removed from the scattering volume to justify the Fraunhofer con—
dition:

kod2 << 1
212

 

(13)

Figure 2.1. depicts the geometry appropriate to equation (12).

19

I

Figure 2.1. Definition of coordinates. Observation point is at
location 0. The R direction lies in the unit vector,
2, direction.

Equation (11) may be linearized by dropping the scattered pressure
term from the integral, consistent with the assumption of weak

scattering, thus:

k R + *
kzej 0 k t.
p86?) = €71;— J’pi<ic*')nl<‘r*')ej 0‘ z «W (14)

Consider a plane wave with amplitude A incident on volume V'such

that:

jk 22-?

131(1’?) 3 A8 0 (15)

The solution for the backscattered radiation, ps(f), is (wagg17)=

+ k2 _ “fr:
Ps(r) = {AejkoRH 2?; J‘v'nlfit'h “02 r dV'} (16)

20

or
+ + kg -> -jk02°?'
Ps(r) p1(r) {m n1(r')e dV' } (17)
v!
The bracketed term in equation (17) represents the reflection
coefficient for the scattering volume V'. In general the reflection
coefficient is a complex quantity that may be characterized by a
magnitude and phase. The important result of equation (17) is the

linear relation between the scattered and incident acoustic waves.

2.3 WAVE ATTENUATION

The attenuation of acoustic energy as it propagates through
biological tissue has not been considered thus far. Attenuation may
be phenomenologically introduced into the above relation by introducing
a complex wave number, k - kr + jki. The imaginary part of k is
often refered to as the attenuation coefficient, a. The introduction

of this factor modifies equation (17) as follows:

_ _) k2 _ “‘4‘:
p8(r) = {e “R 1 p1(r) {fifnlé'h “02 r dv'} (18)
or '
psm = Am R(f) p16?)
where

a = aof as in section 1.4,

A(f) = the first bracketed term, represents the effect
of overlying tissue attenuation, and

R(f) = the second bracketed term, represents the
reflection coefficient.

21

2.4 LINEAR MODELING

The wave equation approach reviewed in the previous sections
indicates that an appropriate linear model may be formulated so as
to characterize the ultrasound/tissue interaction. This model pro-
vides a concise description of the system from which each contributing
factor is easily identified.

Figure 2.2 below illustrates the various components involved in
the formulation of the linear model. The received signal from a

reflector internal to the tissue volume may be written as:
y(t) = e(t)*h(t)*b1(t)*a(t)*r1(t)*a(t)*b2(t)*h(t) (20)

where all processes are assumed linear, '*' denotes convolution, and
e(t) - transducer excitation waveform,
h(t) - impulse response of piezoelectric transducer,
b1(t) - transmissivity impulse response for water/tissue interface,

a(t) - impulse response function accounting for attenuation through
overlying tissue,

ri(k) - reflectivity impulse response associated with the ri
scattering volume, and

b2(t) - transmissivity impulse response for tissue/water interface.

22

e(t)

    
 
  

transducer
x
h(t) h(t)

a(t) ' a(t)

La

scatterer

 
 

tissue

 

 

  
   

 

 

 

Figure 2.2. Relations involved in linear modeling.

Equation (20) may be written in the frequency domain as:
Y(f) = E(f) H2(f) A2(f) 31(f) 32(f) R1(f) (21)

Where capitalized letters denote Fourier transforms of their corres-
ponding time domain functions.

Equation (21) shows explicity the dependence of the received
signal not only on scattering and attenuation parameters associated
‘with the tissue but also on the form of the interrogating beam. The
first two terms may be consolidated to form one term representing the

interrogation beam:

X(f.d) = R(f) H2(f.d) (22)

The distance dependence, d, not as yet considered, has been introduced
here and will be discussed in the following section.

The transmissivity coefficients for water/tissue and tissue/water

23

interfaces are both nearly unity so that equation (21) may be

simplified as follows:

Y(f,d) = X(f,d) A2(f) Rim (23)

The transfer or 'tissue signature' function, TS, may be defined as

the ratio of the received signal to the interrogating beam signal, or:

Y(f,d) =

TS(f,d) =
X(f,d)

2
A (f) Ri(f) (24)
Equation (24) indicates that TS(f,d) may be obtained from Y(f,d), if
X(f,d) is observable by deconvolution of Y(f,d) and X(f,d). In
addition, equation (24) emphasizes the fact that tissue signatures
of backscattered ultrasound are due both to the scattering element

and the overlying tissue.

2.5 THE STEADY STATE TRANSDUCER FIELD

For practical transducers the acoustic field is rather complex,
exhibiting a spatial dependence characterized by two distinct regions,
namely; the near (Fresnel) and far (Fraunhofer) zones. A relationship
for the central axis intensity distribution may be formulated by
assuming that the transducer is a cophasally vibrating piston, and

is given by (Wellsg):

1x = Io {sinzq-(Jr: + x5'- x))} (25)

24

where Io = maximum wave intensity,
I = wave intensity at a distance x from the transducer,
r = radius of transducer,
A - wavelength in propagating medium 8 c/f,
c - acoustic velocity in medium,
and f ' cyclic frequency.

In addition, the beam cross-section intensity exhibits a trans-
verse spatial variation which is dependent upon the distance from the
transducer, x, and the ratio r/l. The number of maxima increase with
decreasing values of x and increasing values of r/A. Figure 2.3 .

demonstrates both spatial variations for a 1.5 MHz transducer with a

radius of 1 cm.

E

 

A—e==::::""—‘—"——————flfifl—’
\41—\-

(a)

(11) (iV) (vi)

cl

Ix/IO H

 

 

(i) (111) (v)

WWMAMMZA

(ii) (iii) (iv) (vi)

cFIGURE 2.3. The ultrasonic field for a 1.5 MHz transducer of
radius r=1 cm. (a) most of energy lies within limits
shown in this diagram; (b) relative intensity distri-
bution along central axis; (c) relative cross-section
intensity distribution for positions indicated in (b).

25

Axial maxima and minima.may be determined using equation (25) and

are given by:

 

= r2 _ nZAZ (26)

xn,min 2n1

and

4r2 - 12 2m+1
xmmax = ( ) (27)
’ 4A(2m+1)
where
x a position of axial minimum amplitude,
n,min

x 8 position of axial maximum amplitude,
m,max

n 2 1,2,3 I I I
and m = 0,1,2 . . . .
The directivity function for the far field of the transducer

may be defined as (Wellsg):

2.11 (k rain 6)

DS = k rain 6 ' (28)

 

where
J1 = Bessel's function of the first kind,
and
k = 2n/l is the wave number.
At the roots of the Bessel's function the directivity function goes
to zero. This indicates that for any angle 6 such that k rsine is

a root of Jl the intensity on the surface of a cone defined by the

angle 6 is zero. The angle of the first null is:

3.83
e = sin'1{ — } (29)
kr

26

Figure 2.4 is a polar plot for the far field (for an acoustic velocity

of c - 1540 m/sec) of the transducer considered in Figure 2.3.

12.57° o
9.567 6.5820

3.5890

 

 

.410 .688
.538

FIGURE 2.4. Polar plot of 1.5 MHz transducer field of radius
r = 1 cm. The velocity of sound in the medium is
1540 m/sec.

2.6 IDEAL SCATTERERS

The effects of attenuation due to overlying tissue are invest-
igated for the backscattered power spectrum of three ideal scatterers
' in this section. To quantify these effects, closed form solutions
for eight statistical measures of the spectral power distribution are
developed, namely; the mean frequency, variance, skewness, kurtosis,

and first through fourth partial sums.

27

CASE 1: Point Scatterer
For a point scatterer, one whose dimension is much smaller than
the acoustic wavelength, the intensity of the secondary scattered
wave exhibits an f1+ frequency dependence (i.e. Rayleigh scattering).
Attenuation of the acoustic beam due to lossy intervening tissue may
—2ad

be introduced by an attenuation factor, e . The backscattered

wave is thus:

-2ad

sp(f) = R0 f“d (30)

where d is the round trip distance traveled by the wave through the
attenuating tissue, and R0 is an arbitrary amplitude factor. Normal-
ization of the above power density function is accomplished by dividing

equation (30) by N, defined as:
fu‘ 4 2nd
N -J Rof e ‘ df (31)
f2

where
fu = highest frequency component of interest
and

fz = lowest frequency component of interest.

Values for the eight statistical measures of the backscattered power
spectrum are given by the following expressions (for ad > 0 and.

fl < f < fu):

MEAN=f =
P IZp/Ilp’ _ (32)

VARIANCE = ogp = { I - 2?1 + f2: }/1 (33)

3P 2p 1p lp’

28

e ;’ 3 e - “ "2
SKEWNESS Ep{(f fp) } {I4p 3pr3p + 3£p12p

- ‘8 3
prIp}/Ilp(°fp) s

e g— u . - “ ‘2
KURTOSIS Ep{(f fp) } {ISp 4pr + 6fp13p

4p

.. 4?3 + —‘§ 1+
pxzp prIP}/Ilp(ofp) .

f f
“+1 / I1 I “ (n = 1.2.3.4) .

P
fn f2

PARTIAL sums - PS = I |
up 1p

where
fn = (fu - f£)(n - 1)/4 + f2 ,
fu -2 df
I = f“e “0 df ,
1p f
2
and
fm+3 -2a df f8 (m+3)
I - -—— e o l +--———-I
mp 200d f 200d (m-1)p
u

(m = 2.3.4.5) .

(34)

(35)

(36)

(37)

(38)

(39)

29

CASE 2: Cylindrical Scatterer

For a long thin cylinder with a diameter much smaller than the
acoustic wavelength, the scattered power spectrum is proportional to
£3. Following a similar development as that for the point scatterer,

the normalized backscattered power spectrum may be expressed as:

Rof3e-zaodf

SNC(f) " fu . (40)

f1

 

Rof3e‘2“°df df

The eight statistical measures for the cylindrical scatterer
possess the same general form as equations (32) through (38) for the
point scatterer, with the exception that the Imp's are replaced with

the following expressions:

f“ 2 df
e 3 - a

11¢ j fe ° df. (41)

f2
and
I _ fm+2 e-Zaodflfl + (n+2)
mc -— m—l
200d fu Zaod ( )C (42)

(ID = 2.3.4.5).

CASE 3: Planar Scatterer

Specular reflection from a plane with dimensions much larger
than the acoustic wavelength is frequency independent. The normalized
backscattered spectrum together with attentuation due to overlying

tissue may be written as:

30

-2a df
R e 0
SNp1(f) a f o (43)
u -2
Roe aodf
f2
As with the cylinderical scatterer, the statistical measures charac—

 

df

terizing the backscattered power spectrum have the same general form

as the point scatterer, with the Imp's replaced by:

f
u "2aodf

Ilpl a 8 df (44)

f1
and

-1

I 3 fm e-Zaodflfl + (In-1)]:

mp1 2aod f 2aod (m-1)p1 (45)

u

(m = 2,3,4,5) .

The above relations for the point, cylinder, and plane scatterers
have been applied to the following situations,
1) no overlying tissue {i.e. ad I 0},

2) 3 cm of overlying tissue with an attenuation of 0.9 dB/cm -
MHz (i.e. ad 8 1.38f where f is in MHz),

3) 3 cm of overlying tissue with an attenuation of 1.0 dB/cm -
MHz (i.e. ad = 1.38f where f is in MHz).

Two different frequency ranges have been considered, viz., the
range from .4 to 1.6 MHz, and the range from 2.9 to 4.1 MHz. The
results have been tabulated for the point scatterer in Table 2.1, for
the cylindrical scatterer in Table 2.2, and for the plane scatterer

in Table 2.3.

31

 

woa.o mNH.o <wm.o oom.o Ham.o noo.o sum Hmauumm summon
mma.o owH.o omN.o. mNm.o mam.o mmN.o 85m Hmauumm ouHSH
HwN.o NwN.o mHH.o mNN.o mo~.o mno.c 55m Hmwuumm vacuum
Hq¢.o noq.o hma.o Nao.o who.o mHo.o 85m Hmfiuumm umuqh
0mm.N mam.~ oHH.N «mN.N woe.~ mnm.m maneuunm
n¢0.1 emm.o mo¢.¢1 «H¢.01 om¢.01 N¢H.HI mmmnamxm
mmo.o noa.o moa.o wwo.o «wo.o omo.o ooamwum>
cum.m aqm.m Nm0.m aqH.H on.H anm.H smmz
IW.H m. o o.H m. o

«mane em: H.e I e.~

um: I Eo\mo ca aoaumosouu<

emcee em: e.H 1 e.o

um: I EU\mv :« mafiumaamuu<

muommmz

 

mummafi<om HzHom

H.N mAm<H

32

 

mac.o «ca.o 0mm.o Ho~.o Hm~.o oom.o «mm
nma.o NNH.o onw.o me.o «om.o <m~.o mmm
uhu.o omN.o MH~.c mn~.o me.o oHH.o Nmm
am¢.o ¢¢¢.o HoH.o o~a.o weH.o mmo.o Hmm
oom.N 50¢.N nwm.H mwm.H Han.N mom.m mumouusu
woh.o m¢0.o 0mm.o: mHH.o1 NMN.OI Huo.al mmmaBmxm
«mo.o OOH.o MHH.o OOH.o mmo.o moo.o mommfium>
NmN.m aHm.m Hoo.m woo.H who.H owN.H cum:
o.H m. o o.H m. o

manna em: fie .. m.~

um: I Eo\mo :H coaumscouu<

mmemm mm: m; .. ed

an: 1 ao\mv ca soaumsnmuu<

ousmmmz

 

mmmuae<om A<UHmGZHAMU

N.N mum<H

33

 

0e0.0 000.0 0m~.0 0e0.0 mm0.0 0mN.0 «mm
NHH.0 mNH.0 0w~.0 NHH.0 mHN.0 0m~.0 mmm
mnN.0 m0~.0 0nN.0 mmN.0 m0N.0 0nN.0 Nmm
«00.0 Nmm.0 0mN.0 c0m.0 Nnm.0 0m~.0 Hmm
00m.m 00H.m 000.H 000.0 00H.m 000.H maneuusx
m00.H 000.0 000.0 m00.H 000.0 000.0 mmmnamxm
mno.0 H00.0 H00.0 mno.0 H00.0 0NH.0 moamfium>
NH~.m amm.m 00m.m nam.0 mmn.0 000.H emu:
0.H 0. 0 0.H m. 0

mwcmm mm: H.¢ I 0.N

um: I ao\mv ca coauusnouu<

006mm um: 0.H I ¢.0

um: I ao\mm aw eoaumscouum

ousmmmz

 

mmmmwfi<om mz<4m

m.N mqm<H

34

In general, the ability of features to differentiate between
scatterer types is dependent upon their sensitivity to scattering
properties and relative insensitivity to overlying tissue effects.
This has been investigated for the ideal scatterers considered above,
and the results tabulated below. From these tables it is observed
that there are no features that exhibit the most favorable conditions
for both attributes simultaneously. There is a trade off between
sensitivity to scatter type and insensitivity to overlying tissue
effects. For example the skewness of the power spectrum exhibits high
sensitivity to both scatterer type and changes in overlying tissue
attenuation (see Tables 2.4 and 2.5). Conversely, the mean frequency
is relatively insensitive to both factors. However, it should be noted
that, for these ideal reflectors, the sensitivity of each feature to
scatterer type is, for the mostpart, greater than that for a 1001
change in overlying tissue attenuation.

The backscattered power spectra from biological tissue will be

much more complex than those considered here.

m.~ announu H.N moHDmH mo manna one can mosBHou scum consumes» mum manna many so muasmmm
.unufloammooo coaumsaouum wnu as mucosa N0H m cu mounowuuum summons a“ masons usmuumn cu Momma mmwmuamuumn muons

35

 

owcmm hucmsumum um: H.e I m.~

mwamm hucwsvaum um: 0.H I «.0

enme.mev ewe Aumm.eev ewe Auoe.mev m Auee.eev emm Aue5.eev m ANNH.AHV a m
Auoe.oev mmm Anuo.mev m Anne.nav ewe Auoe.oH0 mmm Anem.eev a Ammm.eev m e
RNNH.e0 m anue.mv mmm “Nee.m0 mmm ANNH.eV m Auee.uav Hme AumH.eHv Ham 8
Anem.mv a Anem.ev Hem Auee.ev Hme Aeem.mv a anen.oev ewe Aueo.mv mmm m
“use.ev Ne Auoo.e0 Ne Amm~.ev e Auee.ev we Auee.mv «we ANme.ev emm e
Amme.m0 Hmm “Nem.au a Auee.mv Ne Anme.mv Hmm Anne.~v mmm imam.e0 «e m
Aneo.mV «mm ANeo.Hv Nmm anem.cv z Aueo.mV mmm Anoe.~v z Ammo.~0 z N
Ammo.ov z ANHm.ov z Anem.ov «mm enme.~v z Auoe.ov Ne ANHm.ovV «mm H
I seam
muuaom muusom wousom muusom muusom ouuoom
woman Homewaho unaom woman noocfifiho uswom

 

«mflMDm4mz m0 mmnmo ¥z<m

e.~ mgm<k

uooaofimmmoo nowumscouum osmmfiu wcwhauo>o a“ owcmno N0H ou m>fiuwmnom once so ummma aoum

36

wawmaum>o ou one coaumosouu<

.n.~ nwsounu H.~ madcap no one menace scum owumuonmw www.maamu menu so muasmmm
.mmnmu mousom awesome mousmmoa men a“ omnmso usmuuma ago no woman mmwmuaouume oumnz

.Nmz au\m00 on On vasommm we wanna»

em

 

38.80 w £3.30 w $8.80 w 93 .e3 ewe w
Aeo~.wev ewe anew.eev ewe Aeoo.ew0 ewe Aeow.ewv «we e
auoe.ewv ewe Anee.ev ewe ANoe.we0 ewe ANwo.m~V Ne w
Anoe.o~v ewe Anew.wv ewe Aeww.ewv ewe Aeew.~ev ewe w
enme.eev e Auwe.wv e Anew.ww0 we Aeow.oev w e
Anee.eev we eNNe.eV we Aewe.ewv a ANow.wV mwe w
heee.oev wwe Auwe.ev wwe Aueo.w~0 a Aewo.ev z N
Aeww.wv z Aeww.e0 : ANee.m0 ewe Aeew.mv a e
menee emeeeeeu memee nemeeeeu sane
\usfiom \uuwom \uawom \uswom

mwomm honosumum um: H.e I 0.N mwaum huamsvoum an: 0.H I «.0

 

one» Houumom ou m>fiuwmoom once on ummma scum

ammmbm<m= ho amaze Mz<m

m.N MAO<H

CHAPTER III

EXPERIMENTAL PROCEDURE AND RESULTS

The spectral energy distribution of backscattered ultrasound
ratiation depends not only on thetintrinsic properties of the tissue
(e.g. s and K) but also on the interrogating pulse shapele. There-
fore, it is necessary to investigate the characteristics of the ultra-
sonic beam as a function of frequency and distance. For this purpose,
analysis of backscattered radiation from a thick metal block, assumed
to be a perfect reflector, was performed. The results are presented
in Section 3.2.

The remainder of this chapter contains material covering data
collection procedures, and tissue differentiation techniques. Section
3.1 outlines the general data collection procedure and post processing
of information. Section 3.3 discusses the Mahalanobis distance as

applied to tissue differentiation.

3.1 EXPERIMENTAL PROCEDURE

Figure 3.1 depicts the general data collection and signal process-
ing system used for tissue analysis in this thesis. Details of the
system operation and performance are contained in previous worksl3’1“
and also in the appendix. A brief outline is presented below.

Data collection is completely synchronized by the Varian 74
minicomputer. The user has the ability, via the Varian 74, to obtain
160 separate '1ooks' per data file of either Avmode or B-mode scans.

Each 'look' corresponds to an echo train generated by a single excitation

38

of the piezoelectric transducer (see Figure 3.3A). The time varying
voltage signal, which is proportional to the backscattered radiation
is band limited (low passed at 1.8 MHz with a flat passband and sharp cutoff
filter, :40 dB. octave and highpassed at 100 KHz) and amplified (selectable
gain from 0 to 62 dBO. Analog/Digital Conversion (AID) is accomplished at
5 MHz, with each sample quantized into one of 256 levels (i.e. 8 bit samples).
Each record, containing 2048 samples/waveform, is then stored on
magnetic tape for further signal processing.

Software developed for the analysis of backscattered waveforms is
discussed extensively in Appendix A. The following is a list of the
software features:

A.1) a subroutine to plot the raw data of the backscattered
radiation,

A.2) time weighting functions to suppress frequency domain
sidelobes,

A.3) the ability to calculate either the amplitude or power
spectrum of the weighted time signal via an FFT algorithm,

A.4) subroutines to plot the frequency domain response,

A.5) the ability to calculate ratios between frequency domain
distributions (i.e., deconvolution),

A.6) user defined attenuation correction factor that is applied
to the frequency domain (i.e., exp (ad) ),

A.7) a subroutine to calculate eight statistical measures of
the spectral distribution, namely; the mean, variance,
skewness, kurtosis, and first through fourth partial sums.

In addition, software has been developed to analyze groups of

statistics that have been generated by the spectral analysis of
backscattered waveforms originating from the same class of scatterers

(e.g. liver, spleen, metal block). The following is a list of features

for this software:

39

B.1) subroutine to calculate the mean and variance for each
group of statistics (see A.7 of previous list),

B.2) subroutine to etermine the covariance matrix for any
feature vector of the class,

B.3) algorithm" for determining the Mahalanobis distance
between a sample point and any given test set.

The Mahalanobis distance is defined mathematically as:

T -
d2 = {ul - uz} Z 1 {ul - uz}

where “1 = coordinate vector of the centroid of a test set in
the given feature space, ‘
“2 = coordinate vector of the sample point in the same
feature space,
and id'= the inverse covariance matrix of the test set.

Heuristically, the Mahalanobis distance assigns the number, d, to a
sample whose relative magnitude may beinterpreted as a measure of how
similar that sample point is to a given test set. The Mahalanobis

distance is discussed further in Section 3.3.

+The feature vector is any subset of the eight statistical measures
characterizing the spectra of a class (see A.7 of previous list).

40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VARIAN 74
Amplifier A/D
& HPF 5 MHz 8 Software
bits for
spectral &
statistical
analysis
graphics—
terminal
-transducer diSk
"‘J drive
mag.
tape

 

FIGURE 3.1 Data Collection System and Post Processing.

3.2 BACKSCATTER FROM A METAL BLOCK
The radiation field of a practical transducer exhibits a spatial
dependence. This has been investigated for the transducer used in
this thesis by analyzing the backscattered radiation from a thick metal
block. The block was positioned at various distances in the near field
of the transducer.
The experimental procedure is outlined below (see Figure 3.2).
l) A metal block (4 cm x 15 cm x 15 cm) was placed at the
bottom of a large tank (56 cm x 58 cm x 61 cm) partially
filled with distilled water at 27 C.
2) The transducer, supported by a laboratory chemical stand,
was positioned at various distances from the metal block.

The distances varied from 2 cm to 5 cm in 3 mm increments.

3) With the pulsar-receiver continuously pulsing the trans—
ducer (2 once every 1.2 msec) the output of the amplifier

41

was monitored with an oscilloscope. The amplifier gain

was set at 29 dB. The transducer's angular position was
varied while the distance from the metal block was held
constant so as to produce maximum peaks in the backscattered
waveform, indicating normal incidence to the metal block.

4) After achieving proper transducer positioning the pulser-
receiver was set to external trigger mode, and data
collection was executed via the Varian 74. Two files per
transducer position, each containing 95 seperate waveforms,
were recorded on magnetic tape.

It should be noted that the transducer is not capable of unabiguously
detecting spatial variations of the acoustic wave that are equal to

or less than the transducer face dimensions. Therefore, although the
near field produces a complicated interference pattern, the waveform
produced by the transducer is theintegrated result of all localized

field components incident on the entire transducer face,. Thus: localized
nulls or peaks .can' not be detected.

A typical backscattered time domain waveform from the ‘metal block
is presented in Figures 3.3A and B. The transmitted signal occurs at
t-O seconds and the first reflection from the front face of the metal
block occurs approximately 52 microseconds later. Additional pulses
are due to multiple reflections from both the front and backside of the
metal block (see Figure 3.2).

The definition of terms presented here pertain to the remaining
discussion on spectral variations of the backscattered radiation from

a metal block.

Intradistance spectral class v the set of all spectra determined
from the metal block held fixed in orientation and distance with
respect to the transducer.

Interdistance spectral class - the set of all spectra determined
from one and only one backscattered waveform originating from
the metal block placed at each 3 mm increment between 2 cm and 5
cm inclusive with the same orientation (i.e., normal incidence).

42

1 MHz transducer

to P/R

500 coaxial cable

 

 

k.

 

 

 

d face

 

primary fromV
front inter-

water level

distilled water
@ T=27 C
c=1540 m/sec.

 

/

 

 

“I

 

7’3/
::/// c=3250 m7gegTI‘

/ / / /
Metal Block
/ /

Higher order

reflections

 
  

\

 

 

‘bottom of tank, \ \

«L J

 

 

 

\J
I

1

 

Figure 3.2. Experimental set up for investigation of the
ultrasonic field spatial dependence.

43

Intradistance meafiure matrix - the N x 8 matrix whose i-jth

element the j statistical measure (see A.7 of Section 3.1)

of the i spectrum belonging to an intradistance Spectral class.

N is the number of different spectra in each class (N=190-2 files

each containing 95 records per distance).

variations in the spectra of backscattered ultrasound from a metal
block at constant orientation and distance due to random noise have
been investigated. In Figure 3.4 the spectra of six different signal
records have been superimposed. Each record was taken at the same position.
The results shown in this figure are typical of intradistance spectral
classes. Note that most of the variatiOn occurs at the lower frequencies,
viz., 0.4 to 0.6 MHz.

The superimposed spectra of two signal records taken at different
distances are presented in Figure 3.5. This figure indicates that for
reflectors in the near field of the transducer the spectral variations
of records belonging to intradistance classes are of the same magnitude
as those for interdistance classes.

Interdistance spectral variations of the backscattered radiation in
the near field of the transducer have been investigated further. Eight
statistical measures (see A.7 of Section 3.1) have been calculated for
each member of the intradistance spectral classes. The mean and variance
for each column of the intradistance measure matrix have been calculated
and plotted versus distance in Figures 3.6 through 3.9. The vertical
scaling of each figure is identical to facilitate the comparison of
magnitude variations between intradistance mean values of the statistics.
Spatial variations of the mean value for the intradistance mean,

variancelfirst partial sum, and fourth partial sum are significantly

less than those for the intradistance skewness and kurtosis, and to a lesser

44

.aoauoaamau mumeaue ecu ou moaoamouuoo Nu can do :aa3uao saunas mafia any
.xooan Hausa Baum anoma>m3 vauauuaomxomn oaaaaam Managua <m.m muomam

Aoaaav mafia .
ace 00 co 0e cm 0

 

p p p — b — _ b b P b — p _ b p p p — F OOfil

 

 

0mI

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,; -_ .P1 ’ .I
1. . 11-.. .‘ 111-11111 - .. e
_ : r
w 1 1
m 1 1|
II.om
. Ne H
ee 1 I
ooe
en en

apnnttdmv aAem

aIevs IInJ)

(snIoA s

45

.N

u mam Hu awesome <m.m muswfim mo 30H> movemexm mm.m auswwm

Aoaanv mafia

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N0 mm em on 0% Ne
— I—I P1 . _ OOH!
1|
0ml
4 o
fi-
0m
fix I
00~

 

 

 

(SJIOA g = 31233 {Tug} spnandmv BABM

46

.aouooau
unauawuao usn aowuwmoa mama um Mooan Hmuma a Scam sowuuaamau sow muuoaam hoaasomum

Aumzv hoaasvaum
0.N 0.H 0.H «.0

— _
. — _

-—

.¢.m MMDUHm

 

 

9P“3TIdi GATJPIBH

 

 

47

.au 0.m n 0 one
So m.~ n 0 maoamuaao Haw xuoan amuaa m scum acoauumawau mo muuomaa uoaasoaum .m.m mmDUHm

Anmzv aoaaooaum
o.~ e.e o.e e.e

— p —
_ d _

 

 

i
i
apnnIIdmv aAtneIau

 

Eu 0.m n o \
Eu m.~ u 0

 

 

48

extent for the second and third partial sums. This would indicate
that the former measures would also exhibit greater stability for
reflections from a more complex scatterer that was randomly placed
within the near field of the transducer. The ill behaved nature of
the intradistance skewness, kurtosis, second and third partial sums
presents a problem when the order of magnitude between variations
due to reflector type (e.g. liver and spleen) is the same as that

for interdistance variations.

49

.00GGHHG? Ufiw fimme MO mfiOuHaQHHMKr HMfiqum MUGmumflflQHUEH econ WMDUHW

A300 moamumen
o.w he e.e fie w.w w.w Na TN fa TN o.~
b b . i- F
_ a — 1 _

 

—L
‘P

--

~0.H

 

 

 

2. {1V1

2. 8;
E
.m-
mee. :4

 

/ {1| \ 24

moz<Hm<>

am.

 

 

we. a w:

 

 

SKEWNESS

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.15

3.13

3.11

3.09

3.07

3.05

3.03

3.01

-.39
/\
[\KURTOSIS [\
-.43 r V
-.45 I fi
-.47
-.49
-.51 \j ‘ A
753 A\fl V
SKEWNESS
1L1 I I I I I. 114 114 14
I 1’ ‘1 l I I l I
2.0 2.3 2.6 2.9 3.2 3.5 3-8 4.1 4.4 4.7
Distance (cm)
FIGURE 3.7 Intradistance spatial variations of skewness and kurtosis.

SISOLHHX

51

mm.

B
N
o

0N.

SECOND PARTIAL SUM

fin.

mm.

.masm Hmauoa 0:06am mam umuam mo aaoeuawua> Hmeuoam ooamumwomuuaH

A800 monoumen

 

 

 

 

 

 

 

 

.0.m MMDUHm

o.w e.e e.e e.e w.w w.w ~.w e.e w.~ TN e.e
t. .r n u .r u w w “
we.
saw .255; eweee
:.
esw 432$ ezooew
we.
we.
2.

 

 

HHS TVIIHVJ ISHIJ

52

FOURTH PARTIAL SUM

0d.

N
PI!
0

<r
—I

0e.

0.m

.ma—fim HQHUHGQ Subs—JON flaw UHHSU MO QGOflUmHHGKr Hwfiumflm QUCMumfiUwHuH—H .m.m.. EDEN—“h

AEOV museum“:

e.e e.e e.e m.m m.m ~.m a.~ o.~ m.~ o.~
. e _ . PI _ _ _ .
_ e _ u . a U lq A

 

 

 

2.3m damn—“gm GMHIH. >\
<

 

 

 

 

me.

me.

#0.

mm.

NOS TVIIHVd GHIHI

53

3.3 THE‘MAHALANOBIS DISTANCE

This section reviews the concept of the Mahalanobis distance as
it applies to tissue differention. Two illustrative examples consist-
ing of well ordered classes will be presented.

Consider two arbitrary classes whose densities in a two dimensional
feature space are contained within the closed contours of Figure 3.10.
This figure is not typical of density plots obtained from the analysis
of echoes orginating from biological tissue for the features considered

in this thesis. It is only presented here as an example.

 

 

 

£1 +

FIGURE 3.10 Bivariate density plot of two arbitrary classes in the
feature space (f , f ). The area within the closed
contours indicates regions of nonzero density for both
classes.

54

Consider the sample point, T1, in the above figure. Let the measures
d1 and d2 be the Euclidean distances from T1 to the centroids of
classes C1 and C2 respectively. One method for classigying T1 would
be to assign it to the closest class (i.e., to C1 if d1 < d2, and to
C2 if d2 < d1). The sample point T1 would be classified as a member
of C2 by this method, which is incorrect. In fact, any point lying

in the shaded region of C1 would be incorrectly classified.

Another method for classifying sample points in a feature space
would be to use the same criterion as above with the Mahalanobis
distance substituted for the Euclidean distance. The advantage of the
Mahalanobis distance is that it takes into account the spread of the
classes about their centroids (see equation 3.1). Consider the well

ordered classes of Figure 3.11.

 

 

1.0J[ . . .
o ' ‘ ..T3
+ T
‘HN T . 4
2I
“T5
0 T6
oT7T
' 8
T9,
'T1 '3
1.0
fl +

FIGURE 3.11. Example of two well ordered classes in feature space
(fl’f2)o

55

The Mahalanobis distances for all T 's have been calculated and are

tabulated below.

'MAHALANOBIS DISTANCES AND CLASSIFICATION

1

TABLE 3.1

for all sample points of Figure 3.11

 

Sample Point

Mahalanobis Distance

 

to C1 to C2 Classification
T1 10.893 11.096 Cl
T2 10.484 11.088 Cl
T3 10.030 11.101 C1
T4 10.328 11.090 C1
T5 10.650 11.075 C1
T6 10.758 10.883 C1
T7 10.861 10.883 C1
T8 10.842 10.925 C1
T9 10.878 10.728 C2

 

Even for classes that overlap, the Mahalanobis method performs better

than does the euclidean as demonstrated by the sketches of Figure 3.12.

 

I.v.i 31-10.0901?-

 

 

56

  
 

miscalled Cl's

 

 

 

 
   

miscalled Cl's

 

miscalled Cz's

 

 

f1+

Figure 3.12 a) Classification using the euclidean distance
method. Shaded region indicates area where
miscalls would occur.

h) Classification using the Mahalanobis dis-
tance method. Shaded region indicates areas
where miscalls would occur.

CHAPTER TV
BIOLOGICAL TISSUE ANALYSIS

The analysis of backscattered ultrasound from biological tissue
is discussed in this chapter. Two types of tissue were investigated,
namely; human liver and spleen. The data base gathered for this thesis
consisted of five individuals, all of which were assumed to have normal
healthy organs.

The rationale behind choosing the liver and spleen organs is two—
fold; first, the anatomical placement of both organs is quite similar
(i.e. both are adjacent to the abdominal wall), and second, the sono-
anatomy of liver is significantly different than that of the spleen.
The spleen is quite sono-lucent compared to the liver. The similarities
in overlying tissue and differences in acoustic properties of the liver
and spleen should facilitate the differentiation between these organs.

The first section of this chapter outlines the data collection
procedure and the post processing of collected data. Results obtained.
from the spectral analysis of liver and spleen echoes are presented in
Sections 4.2 and 4.3. Also investigated were the effects of introducing
a correction factor (for attenuation due to overlying tissue) to the
frequency domain of the transformed tissue echoes. .The results of this

analysis are contained in Section 4.4.

4.1 BIOLOGICAL TISSUE DATA COLLECTION AND POST PROCESSING
Human liver and spleen data was collected ig_vivo from five
healthy subjects. The procedure is outlined below:

1) The subject was positioned on a firm, horizontal table,

58

prone for spleen experiments and supine for liver.

2) An acoustic gel was applied to the transducer and to the
skin directly above the organ to provide a good acoustic
match at the interface.

3) The pulser/receiver was set to maximum energy and damped
such that the transducer range for two to three cycles,

4) While monitoring the reconstructed waveform from the AID
converter, the transducer's location and angular orientation
were varied so as to achieve proper positioning.

5) Upon locating the proper organ, the subject was requested
not to breathe while a single file containing 160 records
was taken. A file required approximately five seconds for
collection and recording onto the minicomputer's semi-
conductor‘memory.

6) The data collected was transfered automatically under soft—
ware control from semiconductor memory to magnetic tape for
post processing.

Backscattered waveforms from the liver and spleen experiments are
presented in Figures 4.1 and 4.2. The following criteria were established
for determining a time window appropriate for both types of backscattered
waveforms.

1) The window must be sufficiently long to minimize spreading

in the frequency domain.

2) The window must be sufficiently short to ensure that only
the organ of interest contributes to the frequency domain

distribution.

59

00~

00

.oommfiu um>HH scum anoma>m3.wauauumomxoan vuaaamm

Aoamnv mafia
00 . 0e 0N

30953 1 Hw>HH
05“» mo uaouu

 

e.e ouswam

00ml

00HI

00H

00m

epnartdmv antistau

60

00a

00

caaaam
mo xomn

.aommwu aoaaam scum anoma>a3 mauauuaonxoao oaaaaam

Aoamnv mafia
ow oe . ow

scones aaaaam
08%» mo uaoum

 

e.e eeewee

00ml

00~I

c>
spnnrtdmv aArasIsg

00H

00w

61

3) The window must be positioned such that, for a fixed window
length determined by l and 2 above, the entire window lies
within the organ of interest for all subjects.

A window starting position and width that meets all three of the above
criteria is indicated in Figures 4.1 and 4.2 by the heavy vertical
lines. These lines correspond to a window 18 microseconds long starting
56 microseconds after the transmitted ultrasound pulse was generated.
Assuming an average acoustic velocity of 1540 m/second, this window
would correspond roughly to a pill box type volume of radius 0.95 cm
with a depth of 1.39 cm located 3.54 am from the abdominal wall/trans—
ducer interface (see Figure 4.3). Due to the dispersive nature of the
medium and acoustic beam and to the finite temporal width of the ultra—
sound pulse, the actual interrogated volume does not have such well

defined boundaries as indicated by this figure.

abdominal wall

transmission
gel

 

0.95 cm

  
 

interrogated volume

 

I“
é

transducer

 

 

 

3.54 am 1.39

FIGURE 4.3. Interrogated volume defined by time window of
Figure 4.1.

62

A Hanning weighting function was applied to 35 echoes per organ
per individual defined by the above time window. The spectral density
for each weighted echo was determined,thus establishing two classes,
namely; a global liver spectral class, and a global spleen spectral
class. The spectrum of Figure 4.1 (member of liver class) is presented
in Figure 4.4, while the spectrum of Figure 4.2 (member of spleen class)
is presented in Figure 4.5.

Eight statistical measures were calculated for each member of
both spectral classes, thus establishing a liver measure matrix and
spleen measure matrix. The statistical measures were calculated in
the frequency range 0.4 MHz to 1.6 MHz, and are listed here as a ref-
erence for the remaining material of this chapter.

Ml - The mean frequency of the spectral density.

M2 - The variance of the spectral density.

M3 - The skewness of the spectral density.

M4 - The Rurtosis of the spectral density.

M5 - The first partial sum (i.e. the ratio of the energy in the
range from 0.4 MHz to 0.7 MHz to the energy in the range
from 0.4 MHz to 1.6 MHz).

M6 - The second partial sum (0.7 MHz to 1.0 MHz).

M7 - The third partial sum (1.0 MHz to 1.3 MHz).

M8 - The fourth partial sum (1.3 MHz to 1.6 MHz).

4.2 FEATURE SPACE REPRESENTATION

For the purpose of tissue differentiation it would be ideal if a
feature space was definable such that tissue classes‘did not over«
lap in the space. This is not the case for the feature spaces in«

vestigated in this thesis. Consider the feature subspace defined by

.A~.¢ ouowam oomv
wsmmwu uo>fia aoum vasommuuas woumuuwomxomn mo annuomam wouaamauoz .c.q mmsuHm

$sz SEEM—me
o.~ e; o; e.e
J“

p —
1 _

ooo.o

db

moo.o

 

63

 

 

 

 

:

 

 

 

 

 

 

 

\ f¥ mfio.o

 

owo.o

 

HGfllITdNV

64

1
J-

.A~.¢ wuowfim ommv
mammau nomadm Eoum vasommuuas vmumuumomxomn mo abuuommm vmufiamauoz

3:5 Ezuaommm
9N a; o; e.e

P r
q a

"F'

/

 

 

 

 

 

 

 

 

 

 

 

 

.m.q mmame

000.0

mco.o

o~o.c

 

 

 

 

m~o.o

 

0No.o

EGHLITJNV

65

skewness and kurtosis. A scatter plot of liver and spleen sample
points obtained from the spectral and statistical analysis of echoes
from one individual is presented in Figure 4.6. Note that although
the two centroids of the two classes are distinct the spreads of both
classes are sufficiently large to cause an overlap. A scatter plot
for all five individuals together with the same two classes, and
feature space is presented in Figure 4.7. The overlap in this figure
is even more pronounced, to the extent of rendering this approach
together with the above feature space virtually useless.

The spread of a class may be attributed to the variation in
properties of successive echoes andvariance introduced by different
individuals. Variance in the spectra of successive echoes may be
attributed to tissue dynamics such as changes in blood pressure and
respiration, or to changes in transducer positioning during the course
of data collection. Variations due to different individuals may be
caused by changes in overlying tissue effects among other things. At
any rate, Figures 4.6 and 4.7 indicate that variations due to different
individuals tend to be greater than those caused by tissue dynamics and
transducer positioning.

Consider first the scatter plot for a single individual (Figure
4.6). A linear boundary has been drawn in this feature space to
partition it into two subspaces; one in which a majority of points
originate from liver samples, and the other in which a majority of

points originate from spleen samples.

66

The boundary was drawn so as to maximize the total number of
sample points in the correct subspace (i.e., liver sample points in
liver subspace and spleen sample points in spleen subspace). A
success rate may be determined by taking the ratio of organ sample
points in the proper subspace to the total number of sample points
for that organ in the entire feature space. The success rates for
this individual, boundary, and feature space are; liver success rate =
0.76, spleen success rate = 0.83, and total success rate (average of
previous two) = 0.80.

Consider next the scatter plot for all five individuals. A
piece—wise linear boundary has been drawn in this feature space to
partition the liver and spleen classes. Again the boundary was
chosen so as to maximize the total number of sample points in the
correct subspace. The success rates as defined above are; liver
success rate = 0.69, spleen success rate . 0.78, and total success

rate . 0.73.

4.3 TISSUE DIFFERENTIATION BY THE MAHLANOBIS METHOD

The method for tissue differentiation demonstrated in the previous
section (i.e. drawing the scatter plot and partitioning the feature
space) has a few drawbacks. First, the plots are time consuming and
tedious. Second, it lacks a certain preciseness in choosing exactly
how to partition the feature space. Finally, scatter plots in three

dimensions or higher are prohibitively complex to draw. The Mahalanobis

KURTOSIS (ARBITRARY SCALE)

 

67

x liver
. spleen

 

   

liver subspace

 

XXx 0
‘ O
x
x x spleen subspace
’5 x
x
x
x
x
SKEWNESS (ARBITRARY SCALE)
FIGURE 4.6. Scatter plot of liver and spleen samples for a single

individual.

KURTOSIS (ARBITRARY SCALE)

68

liver subspace . .

 

 

liver

X
x [- spleen

spleen subspace

 

SKEWNESS (ARBITRARY SCALE)

FIGURE 4.7.
individuals.

Scatter plot of liver and spleen samples for five

69

method does not suffer these disadvantages, although it does lack a

few of the desireable attributes enjoyed by the scatter plot method.

For example, the latter method allows one to observe the global

relationship of all data points simultaneously whereas the former does

not. At any rate, tissue differentiation utilizing the Mahalanobis

method has been investigated for all feature subspace defined by

combinations of M1 through M8 of order three or less.

The procedure for testing the ability of certain feature spaces

to facilitate discrimination of classes through the Mahalanobis method

is outlined below.

1)

2)

3)

4)

5)

6)

The appropriate columns of the liver and spleen measure
matrices were used to define the two classes in the feature
space of interest.

A sample point was systematically chosen from one of the
classes.

The entries of the chosen sample point were deleted from
the appropriate class matrix (i.e. the class matrix considered
the sample point as an unknown).

The Mahalanobis distance was calculated from the sample
point to the centroid of each class.

The sample point was classified as a member of the class to
which it lie closest (i.e. its Mahalanobis distance was
smallest).

Knowing a priori which class the sample point came from,

it was noted whether the Mahalanobis method classified the

sample correctly or not.

 

.11..

153.14.»! .

70

Steps 2 through 6 were repeated for every other member in both
spectral classes. Selected results obtained from this testing are

presented in Table 4.1. A more comprehensive list is given in

 

 

Appendix B.
TABLE 4.1
CLASSIFICATION BY MAHALANOBIS DISTANCE
Feature Liver Spleen Overall
Space 2 Correct Calls Z Correct Calls 2 Correct Calls

m2,m3,m4,m6,m7 89.77 64.77 77.27
m2,m3,m4,m6 87.50 65.91 76.91
m2,m4,m7 88.64 62.50 75.57
m2,m4,m6 88.64 56.82 72.73
ml,m2,m4 82.95 61.36 72.16
m3,m4 88.64 53.41 71.03
m6 54.55 64.77 59.66

 

Results presented in Table 4.1 indicate that liver samples were
'easier' to identify than spleens, except for the M6 feature space.
In other words, the measures investigated here were biased toward
'classifying unknown sample points as members of the liver class. This
trend was observed for the vast majority of feature subspace investi-
gated. However, the apparent 'ease' by which a class is called
correctly may not be a desireable attribute in and of itself. Consider
the feature space, F8, in which a certain class, C1, is successively

differentiated 95% of the time. It is entirely possible for a second

71

class, C2, (different from C1) to also be classified as a.member of
Cl 95% of the time. In other words, a majority of samples in F5,

whether they belong to C or C2, are classified as members of C

l 1'
Therefore, for classes Cl and C2 the feature space, FS, would not
facilitate the differentiating between them. This phenomenon has been
observed for several feature subspace investigated. For example, the
feature space defined by M4 and M5 classified 93.182 of the liver
samples and 96.59% of the spleen samples as belonging to the liver

sample space.

4.4 INTRODUCTION OF ATTENUATION CORRECTION FACTOR

The analysis of the previous section has been repeated here for
the first five feature spaces listed in Table 4.1, with the exception
that an attenuation correction factor has been introduced (see Appendix
A for details). Two different cases of attenuation due to overlying
tissue have been investigated, they are:

1) Attenuation due to overlying tissue was assumed to be

the same forboth liver and spleen experiments, and

2) Attenuation due to overlying tissue for liver experiments

was assumed to be different than that for spleen.
Case 1.

As a first approximation, an assumed attenuation of 1.24 dB/cm—MHz
was introduced for both liver and spleen experiments. This involved
multiplying the backscattered spectra by exp (0.143 f d). The factor
d is a constant and represents the round trip distance traveled by the
ultrasound pulse through the attenuating tissue. The factor f represents

the frequency in megahertz. Classification of members from both corrected

72

spectral classes was performed using the Mahalanobis method and
procedure outlined in the previous section. The results are pre-

sented in Table 4.2.

Case 2.

As a second approximation, different attenuation factors were
assumed for the liver and spleen experiments. Correction for the
liver spectral class was the same as in Case 1 (i.e. 1.24 dB/cm - MHz).
Consider the backscattered time waveform for spleen samples illustrated
in Figure 4.2. In Figure 4.3 the abdominal wall/spleen interface and
the position of the time window have been labeled. Note that for the
round trip distance from transducer to interrogating volume the ultra—
sonic pulse must travel through approximately 1.6 cm of abdominal wall
tissue and 1.9 cm of spleen tissue. Attenuation due to spleen tissue
was assumed to be relatively small compared to the liver as evidenced
by the strong reflections originating from behind the spleen. There-
fore, for Case 2, the overlying tissue attenuation for spleen was taken
to be 1.14 dB/cm — MHz.+

In general, an across the board application of an attenuation
correction factor (see Case 1) did not tend to increase the success
rate of the classifier, while selectively applying an attenuation
correction factor did (see Case 2). In either case, the changes in
marginal success rates were not great, except for feature space (Ml,

M2,M4). For this feature space a significant decline in the liver

success rate was accompanied by a significant rise in the spleen success

+There is a lack of published data on attenuation for in_vivo spleen.
The value 1.14 dch MHz used for Case 2 spleen is rather arbitrarily
chosen.

rate. Overall, the total success rate did not change drastically for

either Case 1 or Case 2 and all feature spaces considered.

TABLE 4.2

CLASSIFICATION BY‘MAHALANOBIS DISTANCE

ATTENUATION INTRODUCED*

 

Feature
Space

Liver

2 Correct Calls

Spleen

2 Correct Calls

Overall

2 Correct Calls

 

m2,m3,m4,m6,m7
m2,m3,m4,m6
m2,m4,m7
m2,m4,m6

ml,m2,m4

90.91 (92.05)

'87.50 (90.91)

89.77 (89.77)
92.05 (93.18)

75.00 (77.27)

62.50 (65.91)
60.23 (64.77)
51.14 (52.27)
53.41 (56.82)

68.18 (69.32)

76.71 (78.98)
73.87 (77.84)
70.46 (71.02)
72.73 (75.00)

71.59‘(73.30)

 

*
The numbers in parenthesis correspond to Case 2 results.

CHAPTER V
CONCLUSION

The spectral distribution or backscattered ultrasound from
biological tissue has been investigated. The motivation for this
study has been the prospect of determining a set of discriminant
features that would facilitate differentiation between tissue classes:
Also investigated were the effects of applying a correction factor
accounting for attenuation due to overlying tissue to the spectral
distributions of backscattered diffuse echoes.

The biological tissues investigated were human liver and spleen.
The experiments were performed in zigg on five subjects, all of which
were assumed to have normal healthy organs. The spleen and liver
were chosen for two reasons. First, the type of overlying tissue and
propogation distances through this tissue were similar for both liver
and spleen examinations (i.e. the overlying tissue was approximately
2 cm deep and consisted primarily of fat and muscle tissue). This
de-emphasized but did not eliminate variations between in gizg liver
and spleen spectra that were not intrinsic to the organs themselves.
Second, as reported in the literaturelg’20 the liver and spleen
possess significantly different sonoanatomies, thus facilitating
discrimination between them based on properties of the organ.

The spectral distributions of diffuse echoes recorded for both
liver and spleen organs were determined using a Fast Fourier Transform
(FFT). Prior to transformation, a Banning weighting function was

applied to a time window corresponding to diffuse echoes originating

an

75

from the organ of interest. This weighting function suppressed
sidelopes in the frequency domain introduced by time limiting the
backscattered waveform. To characterize the backscattered echoes

eight statistical measures of the spectral distribution were determined;
they were, the mean frequency, variance, skewness, kurtosis, and first
through fourth partial sums. All measures were defined on the frequency
range 0.4 MHz to 1.6 MHz.

Two methods for tissue classification were investigated; namely,
the scatter plot method and Mahalanobis method. These classifiers
were applied to feature spaces defined by subsets of the statistical
measures listed above. The Mahalanobis method was applied to all
feature spaces of order three or less. In addition, a few higher order
feature spaces were investigated. A scatter plot was drawn for the
two dimensional feature space in which the Mahalanobis method performed
best. Additional scatter plots have also been investigated but were
not presented, however, they exhibited similar results as those
observed forthe scatter plot presented in Section 4.2.

The scatter plot method was useful in gaining insight into the
sources of difficulty associated with differentiating between tissue
classes using the features chosen in this study. A few observations
are listed below.

1. The feature spaces that were investigated using the scatter

plot method exhibitted varrying degrees of overlap between
the classes.

2. Class overlap was more extensive when considering a group

of subjects as opposed to a single individual.

76

3. For a single individual a linear boundry was sufficient to
seperate the tissue classes while maintaining an overall
success rate above 0.80.

4. A piece-wise linear boundary was required for scatter plots

in which all five subjects were considered to maintain an
overall success rate above 0.70.

The above observations are related to the variance and close proximity
of the tissue classes. The variance associated with an individual may be
attributed to tissue dynamics (e.g., blood pressure or respiration), or
alternations in transducer position during data collection, or noise
introduced by the data collection system (e.g., quantization error by
AID). Variance associated with a group may be attributed to such things
as varying properties of overlying tissue between individuals (e.g., more
fat than muscle contributing to the overlying tissue), or basic differences
in the properties of the investigated organs (e.g., density-or compressi-
bility variations of the tissue). Close proximity of the tissue classes
may be attributed to a moderate sensitivity of the discriminate features
to liver andspleen tissue and/or similar tissue signatures for both liver
and spleen organs.

As stated above, moderate success rates (>O.70) could be achieved
using the scatter plot method for both single individual and group tissue
classes. However, the success rates for group classes were noticeably
less than those for a single individual, as expected, due to additional
variance introduced by the group. This suggests that for much larger
groups this method may prove less useful for tissue differentiation.

An alternative approach may be to consider only one individual at a time.

77

For example, consider the problem of diagnosing the pathology of a
portion of a patient's liver. Most likely this type of differentia—
tion would be much more difficult than liver/spleen differentiation
due to the subtlety of the tissue variations than that considered in
this research. At any rate, one may approach this task by attempting
to establish a 'normal' liver tissue class from analysis of a portion
of the organ known to be healthy (e.g., the left lobe if the right
lobe is suspected of being deseased). Comparison of echo analysis
results from the suspected deseased tissue with those from the 'normal'
class may reveal the pathology of the suspect isssue, assuming a good
set of differentiating features could be established.

The Mahalanobis distance provided a faster, more precise method for
classifying tissue samples than the scatter plots. A few observations
from the results of theMahalanobis method are listed below (the liver
and spleen tissue classes considered were those that accounted for all
five subjects). I

1. For feature spaces of order three or less the overall

success rate never exceeded 0.76.

2. The liver success rates were almost always greater than

the spleen success rates.

3. In general, the higher the order of the feature space

the better the success rate was, however, the success
rate did not increase significantly as the order increased.

The success rates using the Mahalanobis method and the feature

space defined by the skewness and kurtosis agreed relatively well with

that determined by the scatter plot method. The overall success rates

78

for these two methods were 0.71 and 0.73 respectively.

The Mahalanobis method has also been applied to tissue classes
for which a correction factor accounting for attenuation due to over-
lying tissue has been applied. It was found that an across the board
application of an approximately determined correction factor did not
improve the effectiveness of the classifier. Instead, a slight decrease
in success rates was observed. Conversely, when a correction factor
reflecting the difference in attenuation due to overlying tissue for
liver and spleen echoes was applied a slight increase in success rates
was observed. The approach used in this study for applying correction
factors intended to offset effects due to overlying tissue has not been
very rigorous, although results obtained indicate that a more precise
application of correction factors may prove very usefull in increasing
the effectiveness the classifiers studied. Methods for determining
attenuation factors have been established for in 2132 experiments and
are relatively accurate. Application of these methods to the classifier
and feature spaces considered here should prove interesting.

The research conducted for this thesis has been preliminary in
nature. That is, the main objective has been to determine a set of
discriminating features that could be used for discerning tissue class.
In addition, the effects of overlying issue have been addressed. Results
generated from the spectral analysis of backscattered radiation are
encouraging and warrent further research into the tissue differentiation
methods presented in this thesis.

The application of a more exact measure of the attenuation
coefficient for overlying tissue should prove useful in increasing the

effectiveness of the discriminatory features. Experiments performed

79

.igsvitgg are more appropriate for estimation of attenuation correction
factors than in 2333. For example, consider the task of classifying
the state (e.g., fresh, frozen, fixed, etc.) of excised porcine liver.
If one were to analyze diffuse echoes from anywhere except directly
beneath the water/liver interface there would be attenuation of the
backscattered radiation due to overlying liver tissues. The attenuation
coefficient may be determined by the following procedure.

With a suspended sample of porcine liver above a thick metal block
(block normal to ultrasound beam) execute a Bpmode scan of the tissue
(i.e., spatially sweep the transducer across the liver while pulsing
and receiving at intermediate stationary positions). Determine the
round trip distance through the tissue for each intermediate position
at which data was taken. After removing the liver specimen collect

backscatter echoes from the metal block with no intervening tissue over

C‘

"

an area that was covered by the B—mode scan.l The ratio of the spectral
distribution determined from the backscattered echo originating from

the metal block's front surface with intervening tissue to that without
yields the attenuation. Dividing the above attenuation by the round
trip distance through the tissue will yeild the attenuation coefficient
(a) as a function of frequency with units of inverse centimeters.
Application of this factor on an echo by echo basis to the backscattered
spectral distribution should eliminate the affect of overlying tissue

on the discrimination problem. Also it would be instructive to experi-
mentally study feature subset properties for various known reflectors,
such as planes, thin cylinders, and point like reflectors. Such further
work should contribute to an appreciation of the relative role of the

various contributors to quantitative measures of backscattered ultrasound.

80

and is imperative to the optimum application of tissue signature

techniques.

APPENDICES

APPENDIX A

The postprocessing and analysis of backscattered ultrasound from
various reflectors is performed with the aid of two interactive Fortran
programs; namely, PLOTS3 and FTRSB. The following sections outline the

usage of these programs.

A.l PLOT83 DOCUMENTATION

PLOTSS must be run from the TEKTRONIX graphics terminal. The user
requests tasks to be run via 2 letter mnemonic commands, which are input
when the '$' prompt appears on the terminal. Most tasks require additional
input, these are discussed below. If an illegal command or input is
entered the program will request the input again. The following is a

list of commands and the associated tasks.

MNEMONIC NAME SECTION TASK

RD READ A.1.l Reads ultrasound data from user
specified disk file.

PL PLOT ULTRASOUND A.1.2 Plots ultrasound data as continuous
DATA waveform as a function of sample
interval.
FT FAST FOURIER A.1.3 Performs an FFT on user specified
TRANSFORM weighted sample window.
PS POWER SPECTRUM A.1.4 Calculates the power spectrum
(amplitude squared) from FFT reslts.
RT SPECTRA RATIO A.1.5 Determines the ratio between two
discrete frequency spectra (i.e.,
deconvolution).
NR NORMALIZE FRE- A.1.6 Normalizes the sum of the spectral
QUENCY SPECTRUM components in,a specified frequency

range to unity.

81

82

MNEMONIC NAME SECTION TASK
AT ATTENUATION A.1.7 Applies a user specified attenuation
CORRECTION correction factor to the frequency
FACTOR spectrum.
PF PLOT FREQUENCY A.1.8 Plots frequency spectrum.
MD . MINIDRIVER A.1.9 Calculates statistical measures of

the spectral distribution for a user
specified set of ultrasound records
and stores results on disk file.

ST STOP ———- Terminates PLOTS3

PLOT83 exists on the third partition of the ultrasound disk. To
start execution of the program enter the following input at the graphics
terminal; ‘

;SCHED,PLOT83,p,ww

where
p = priority (usually 5)

ww = logical unit number Of the third partition of the removable
platter drive in which the ultrasound disk has been placed.

The following output will appear at the graphics terminal;

INPUT FILE #‘S 0F ULTRASOUND DISK

F1 F2
XX Y?
where '
xx - user input indicating the second partition of the ultrasound
disk,
(and yy 8 user input indicating the third partition of the ultrasound
disk.

If disk drive D013 is used, ww = 26, xx = 25, and yy = 26.

A.1.l READ

The following sequence of inputs will instruct the program to read
an ultrasound data record from a disk file. Outputs to the terminal are
signified by upper case characters, inputs by the user are signified by

lower-case characters.

83

$rd

FILE NAME AND DATA TYPE (1 numerator, 2 denominator)
NNNNNN T

nnnnnn t

 

where
nnnnnn 8 name of data file. There are six data
files that currently exist on the ultra-
sound disk. They are ULTRAl through
ULTRA6.

and t - 1 or 2 as indicated above. This input
is used to flag the spectral distribution
associated with the ultrasound data when
a ratio between distributions is requested.
See RT command.

RECORD NUMBER
NNN
nnn

 

where _
nnn - the number of the record that is to be
read from the ultrasound file. This
number must lie between 2 and 160.

DOES THIS FILE HAVE A HEADER? (T OR F)
X
x
If the file does have a header it will be output following a'T'input.

where x - T if the file does have a header, and

F if the file does not have a header.

ENTER START OF WAVE ARRAY
ISTR
ssss

 

where .

ssss - Each data record contains 2048 words of
of data. Only 1024 of these words are
stored into the programs common memory to
conserve on memory space. It is therefore
necessary to indicate where the first word
of the 1024 block should start in the 2048
block. 'ssss' should never exceed 1024.

A.1.2 PLOT ULTRASOUND DATA
The following inputs will instruct the program to plot the raw ultra-
sound data previously read. This task allows the user to choose an

appropriate time window by displaying the backscattered waveform. The

84

horizontal axis is directly proportional to time. To determine the cor-
responding time, multiply the horizontal axis number by the appropriate
sampling period (in most cases this should be 0.2 usec.). The user should
be aware of the implicit sample (or time) offset introduce by reading

only a portion of the data record as mentioned above (i.e., if ssss - 10,

then 1 on the horizontal axis corresponds to the 10th sample).

 

$p1

INPUT LAST ARRAY POS. TO PLOT
LLLL

1111

 

where
1111 t the last sample point in the ultrasound

data to be plotted. This number must be
less than 1024.

A.1.3 FAST FOURIER TRANSFORM

The user may request that an FFT be calculated for any specified
sequence of sample points less than 512 words long. Before calculating
the FFT a user specified weighting function is applied to the sequence
of data points and zero filled so that the FFT always calculates the
spectral components for a time sequence 512 words long. The following

inputs and outputs are associated with an FT command.

 

$ft
ENTER WORD RANGE OF TIME WINDOW
WFWD WSWD

Jocxxyyyy

 

where
xxxx = the first sample point of the window
(this is the offset value on the raw
data plot).

yyyy - the last sample point of the window
(this also is the offset value on the
raw data plot).

85

YOUR CHOICES OF WINDOW FUNCTIONS ARE:

FUNCTION CODE
HANNING 01
HAMMING 02
TRIANGULAR 03
BLACKMAN O4

RECTANGULAR 05
ENTER CODE OF WINDOW FUNCTION --
CC

 

where
cc I 01 through 05. Note that the weighting
function code must not be preceeded by
any blank spaces. If an illegal code
is entered the rectangular weighting
will be used.

ENTER NORMALIZED FREQUENCY RANGE.
F.1-F.2

xxxyyy

 

where
xxx I the lowest frequency component of in-
terest. This number must be a real num-
ber and is rounded off to the tenths
position. The frequency is assumed to be
in MHz.

yyy I the highest frequency component of in-
terest. This number must also follow
the guide lines as xxx.

 

The above inputs are all that is necessary. A typical output as

shown below will follow the last input.

FRSTF - .39 SCNDF - 1.60
WINDOW TYPE USED: HANNING
MEAN FREQUENCY I .823 FIRST PARTIAL SUM I .400
STANDARD DEVIATION I .301 SECOND PARTIAL SUM I .283
SKEWNESS I .500 THIRD PARTIAL SUM I .243
EXCESS I 2.34 FOURTH PARTIAL SUM I .740E-01

FRSTF is the lowest frequency considered and SCNDF is the highest fre-

quency considered. -

A.1.4 POWER SPECTRUM
The power spectrum is calculated by squaring the results of an FFT.

The inputs and outputs are indentical to those presented in section A.1.3.

86
A.1.5 SPECTRA RATIO

The ratio between two spectral distributions may be calculated. This
operation corresponds to deconvolving the two associated time domain
sampled waveforms. Before a ratio may be requested the following tasks
must be performed.

1) read an ultrasound data record and flag the data
as the numerator (i.e., data type I 1).

2) request either an FT or PS,

3) read another ultrasound data record and flag the
data as the denominator (i.e., data type I 2),

4) request the same task as in 2 with the same para-
meters (e.g., same time window, weighting function,
etc.).

The following is an example of an RT command.

 

$rt

STATISTICS ARE PERFORMED ON RATIO OF NORMALIZED
DATA IN THE FREQUENCY RANGE .4 T0 1.6
WINDOW TYPE USED: HANNING

MEAN FREQUENCY I .994 FIRST PARTIAL SUM I .244
STANDARD DEVIATION I .354 SECOND PARTIAL SUM I .246
SKEWNESS I -.256E-1 THIRD PARTIAL SUM I .243

EXCESS I 1.79 FOURTH PARTIAL SUM I .267

 

A.1.6 NORMALIZE FREQUENCY SPECTRUM

After any spectral distribution has been calculated the user may re-
quest that the results be normalized. Normalization of all spectral lines
in the frequency range specified by the user in the previous FT or PS
command sequence will be performed as follows;

1) all spectral components in the specified frequency
range are summed,

2) the result of step 1 is divided into each spectral
component of the specified frequency range.

The results are stored in the same array that the original spectral dis-

tribution existed in.

87

A.1.7 ATTENUATION CORRECTION FACTOR

An attenuation correction factor of the form exp(ad) may be applied
to the frequency domain to offset effects of overlying tissue. The user
must specify the attenuation per centimeter per megahertz, the acoustic
velocity of the overlying tissue, and the first sample point that cor-
responds to the beginning of the overlying tissue. The AT command is as

follows. This command must preceed an FT command.

 

$at A

ATTEN. COEFF. (DB/CM MHZ), VELOCITY (M/SEC) AND FIRST POSITION OF TARGET
ATTEN VELOCITY FRST

aaaaa vvvvvvvv ffff

 

where
aaaaa I attenuation coefficient with units of db/cm-MHZ.

vvvvvvvv I the velocity of sound in the overlying tissue,
this number must be real and have units of
meters/sec.,

ffff I the first sample point corresponding to the be-
ginning of the overlyingrtissue.
A.1.8 PLOT FREQUENCY
The following input instructs the program to plot the calculated
frequency distribution. The spectrum is plotted only in the frequency

range specified by the user previously.

$pf

A.1.9 MINIDRIVER

The MD command allows the user to analyze a set of backscattered
echoes from the same class and store the results onto disk file with a
minimum requirement of user inputs. The following sequence of inputs

are necessary for the minidriver task.

88

$md

ENTER FILE NAME -_

NNNNNN

nnnnnn (see section A.1.1)
ENTER WORD RANGE --

WFWD WSWD

xxxx yyyy (see section A.1.3)
ENTER WINDOW CHOICE --

WC

cc (see section A.1.3)
ENTER FREQUENCY RANGE --

F.1 F.2

xxx yyy (see sectiom A.1.3)
ENTER START OF WAVE ARRAY ..
ISTR

ssss (see section A.1.1)
ENTER FILE TO BE WRITTEN ON (l-SAVSTT Z-SAVSTS)
F

f

There are two files (SAVSTT and SAVSTS) that exist on
the ultrasound disk that were explicitly created for
this purpose. In additon there are two other files
(SAVSTA and SAVSTB) that may be used for storing this
type of data. The user may use the graphics editor to
transfer data from the former two files to the later
two files.

ENTER RECORD INCREMENT --
IN
ii
ENTER NUMBER OF RECORDS --
NR
fin

 

where
ii I the increment by which records will be
read (e.g., if ii I 5, then the 2nd,
7th, 12th, etc. records will be analyzed).

nn I the number of records to be read and
analyzed.

After entering the last input the program will execute the following
set of tasks without further user inputs.

1) Execute an RD task for the appropriate record and file as spec-
ified above.

2) Execute an FT task.

3) Store all calculated statistical results onto the appropriate
file as specified above.

Typically MD is used to obtain a set of statistical measure for a class

'-

89

that may be used to test the effectiveness of the measures coupled with

a classification technique to discriminate between classes.

A.2 FTRS3 DOCUMENTATION
FTRS3 should be run on the TEKTRONIX graphics terminal. To start
execution of the program enter the following input;

;SCHED,FTRS3,p,ww
where
p I priority (usually 5),

and ww I logical unit number of the fourth parti-
tion of the ultrasound disk. If disk
drive D013 is used then ww I 27.

The following sequence of outputs and appropriate inputs should follow.

 

DATA FILES ARE ON? --- SAVSTT & SAVSTS -1, OR SAVSTA & SAVSTB -2
r
where
r I 1 if the sets of statistical measures are

stored on SAVSTT and SAVSTS, or 2 if the
sets of statistical measures are stored
on SAVSTA and SAVSTB. Note that the
user's responce is typed in column 1.

# OF RECORDS IN SAVSTT AND SAVSTS (or SAVSTA AND SAVSTB)?
FTT FTS
xxx xxx
where
xxx I the number of data records in SAVSTT or
SAVSTA,

and yyy I the number of data records in SAVSTS or
SAVSTB.

INPUT NUMBER OF DATA BLOCKS (AS DEFINED BY FTT ABOVE)

TO SKIP ON INPUT FILE.

NUM

nnn

where
nnn I an -integer number of data blocks to skip.

A data block is defined as the number of
input records specified by FTT. By using
various combinations of FTT and NUM the
user may access different blocks of data
from both input files.

90

Do you wish the statistics and covariance matrix printed out? (T or F)
r
where
r I T for true or yes, and F for false or no.
If a T is entered the statistics and co-
variance matrix are printed out on the
line printer..

Do you wish to classify a group of points? (T or F)
r

where
r I T forgyes and F for no.

If a group of sample test points are not to be classified the following

sequence of outputs and appropriate inputs shbuld follow.

 

ENTER SAMPLE #, SAMPLE FILE, AND FEATURE SPACE (l-SAVSTT 2-SAVSTS)
NUM S S
nnn x y
where
nnn I record number from sample file that is
to be tested against the set of records
in the feature space,

x I 1 if the sample file (i.e., the file
from which the sample record is taken)
is SAVSTT or SAVSTA, and 2 if the sample
file is SAVSTS or SAVSTB,

y I 1 if the feature space (i.e., the file
that the sample record is tested against)
is file SAVSTT or SAVSTA, and 2 if the
feature space is file SAVSTS or SAVSTB.

A set of feature vectors will be request at this point. The user

may enter as many as 10 seperate feature vectors. The following example

illustrates the input of a set of feature vectors.

91

ENTER FEATURE VECTOR
F1 F2 F3 F4 F5 F6 F7 F8
a1 a2 a3 a4 a5 a6 a7 a8
ENTER FEATURE VECTOR
F1 F2 F3 F4 F5 F6 F7 F8
b1 b2 b3 b4 b5 b6 b7 b8

ENTER FEATURE VECTOR

F1 F2 F3 F4 F5 F6 F7 F8

no entries (i.e., a return with no numbers inputted is entered, this
terminates the request for additional feature vectors)

where »
a1 - a8 any combination of 01 through 08.
b1 - b8 - 01 - mean 05 - first partial sum
... 02 - variance 06 - second partial sum

03 - skewness 07 — third partial sum
04 - kurtosis 08 — fourth partial sum
Note that if 10 feature vectors are
entered the program will automatically
' terminate additional requests for
feature vectors, and proceed with pre-
viously entered set of feature vectors.

After completion of the feature vector inputs the program will cal-
culate the Mahalanobis distance between the test point (indicated by the
specified sample file and record number) and centroid of the feature space

file. A sample output is presented below.

 

.27813OE-07
MAHAL DSTN I 5.722 1 2 3 0 O O O O FSPACE I 1
SSPACE I l SNUM I 3

 

The first number is the determinate of the covariance matrix.
The validity of the output is suspect if this number is a few orders of
magnitude less than that shown here.for this indicates that the matrix
is becoming singular and the method for determining the inverse fails.
The number after 'MAHAL DSTN' is the calculated Mahalanobis distance be-

tween the test point and feature space class centroid. The eight integers

92

following this number are the feature components used for the calculations.
FSPACE is the file that was specified for the feature space and SSPACE
and SNUM are the file and record number used as the test point. After
outputing the results for all feature vectors requested the progtam will
loop back to the request for a change of feature vector. The program
then continues from this point as described above.

If a group of sample test points are to be classified the following

sequence of outputs and appropriate inputs should follow.

 

INPUT # 0F SAMPLES, INCREMENT, AND SAMPLE SPACE
NUM IN S
nnn ii 3
where
nnn I the number of samples to be classified
using the least Mahalanobis distance
method,

ii I the increment by which the test points
are to be taken from the sample space
file,

3 I 1 if the sample space file is SAVSTT or
SAVSTA, and 2 if the sample space file
is SAVSTS or SAVSTB.

The above input performs the following task;

1) Determine which record is to be used for the test point.

' 2) Delete this record from the apprOpriate file.

3) Calculate the Mahalanobis distance from this test point to the cen-
troids of both input files.

4) If specified, tally the number of correct classifications obtained.

5) Loop back to 1 until all test points as specified by nnn above have
been classified.

The user may specify that either the results of all distance cal-
culations be outputted to the line printer or that just the percentage
of correct classifications be outputted to the graphics terminal. Results
printed on the line printer are formatted the same as described on the

preceeding page for all distance calcualtions. The following is an ex-

ample of the output of the percentage.

93

SAMPLE SPACE IS 1 AND 2 OF CORRECT CALLS WAS 83.33
where
SAMPLE SPACE I 1 if the test points came
from SAVSTT or SAVSTA, and
2 if the test points came
from SAVSTS or SAVSTB.
After classifying all test points the program loops back to the
request for if the statistics and covariance matrix should be printed out.

The program proceeds as before from this point. The program.may be ter-

minated by sending two returns in a row to the computer.

APPENDIX B

The success rates for all feature spaces of order three or less
have been determined using the Mahalanobis method and procedure out-
lined in Section 3 -- for liver and spleen tissue classes. These
classes contained 35 samples per organ per subject. There were five
subjects, thus each tissue class contained 185 feature vectors. The
components of the feature spaces were chosen from the following list

of measures determined from the backscatter tissue spectra.

 

MEASURE* MNEMONIC
BEEN FREQUENCY M1
VARIANCE M2
SKEWNESS M3
KURTOSIS M4
FIRST PARTIAL SUM M5
SECOND PARTIAL SUM M6
THIRD PARTIAL SUM M7
FOURTH PARTIAL SUM M8

 

All measures were calculated in the frequency range 0.4 MHz
to 1.6 MHz ‘

The following table presents the results obtained. The first
column lists the mnemonics for the feature space components, the
second and third columns list the marginal success rates for the
liver and spleen classes respectively, and the fourth column is the
total success rate for that feature space (average of columns 2 and
3).

94

95

TABLE 3.1

SUCCESS RATES USING MAHALANOBIS METHOD

 

Feature Space

Liver Success

Spleen Success

Total Success

 

Rate Rate Rate
M1 .511 .580 .546
M2 .568 .602 .585
M3 .580 .648 .614
M4 .977 .057 .517
M5 .921 .182 .551
M6 .546 .648 .600
M7 .693 ‘ .409 .551
M8 .591 .534 .563
M1 M2 .648 .602 .625
M1 M3 .625 .591 .608
M1 M4 .830 .375 .602
M1 M5 .784 .546 .665
M1 M6 .739 .523 .631
M1 M7 .648 .523 .585
Ml M8 .648 .466 .557
M2 M3 .636 .705 .671
M2 M4 .841 .557 .699
M2 M5 .705 .557 .631
M2 M6 .784 .557 .671
M2 M7 .727 .580 .653
M2 M8 .682 .602 .642
M3 M4 .886 .534 .710
M3 M5 .716 .557 .636
M3 M6 .716 .580 .648
M3 M7 .716 .557 .636
M3 M8 .568 .682 .625
M4 M5 .932 .034 .483
M4 M6 .830 .455 .642
M4 M7 .943 .205 .574

Feature Space

Liver Success

96

Spleen Success

Total Success

 

Rate Rate Rate
M4 M8 .682 .443 .563
M5 M6 .761 .546 .654
M5 M7 .966 .148 .557
'M5 M8 .705 .489 .597
M6 M7 .727 .466 .597
M6 M8 .841 .500 .641
M7 M8 .839 .534 .636
M1 M2 M3 . 614 . 750 . 682
M1 M2 M4 .830 .614 .722
M1 M2 M5 . 841 . 534 . 688
M1 M2 M6 .830 .534 .682
M1 M2 M7 . 705 . 534 . 619
M1 M2 ‘M8 .852 .534 .693
M1 M3 M4 . 841 . 500 . 671
M1 M3 M5 . 602 . 705 . 653
M1 M3 M6 . 614 . 659 . 636
M1 M3 M7 . 659 . 557 . 608
M1 M3 M8 . 682 . 614 . 648
M1 M4 M5 . 898 . 500 . 699
M1 M4 M6 .864 .534 .699
M1 M4 M7 .841 .432 .636
M1 M4 M8 .773 .398 .585
M1 M5 M6 . 671 . 681 . 676
M1 M5 M7 . 885 . 546 . 716
M1 M5 M8 . 909 . 455 . 682
M1 M6 M7 . 807 . 477 . 642
M1 M6 M8 .875 .443 .659
M1 M7 M8 .727 .534 .631
M2 M3 M4 . 841 . 500 . 671
M2 M3 M5 .761 .636 .699
M2 M3 M6 .800 .568 .684
M2 M3 M7 .807 .602 .705

Feature Space

Liver Success

97

Spleen Success

Total Success

 

Rate Rate Rate
M2 M3 M8 .659 .659 .659
M2 M4 M5 .807 .557 .682
M2 M4 M6 .886 .568 .727
M2 M4 M7 .886 .625 .756
M2 M4 M8 .830 .568 .699
M2 M5 M6 .818 .511 .665
M2 M5 M7 .841 .511 .676
M2 M5 M8 .796 .500 .648
M2 M6 M7 ..898 .455 .676
M2 M6 M8 .830 .557 .693
M2 M7 M8 .761 .523 .642
M3 M4 M5 .898 .534 .716
M3 M4 M6 .864 .511 .688
M3 M4 M7 .852 .534 .693
M3 M4 M8 .773 .591 .682
M3 M5 M6 .716 .580 .648
M3 M5 M7 .886 .489 .688
M3 M5 M8 .705 .580 .642
M3 M6 M7 .852 .489 .671
M3 M6 M8 .727 .602 .655
M3 M7 M8 .614 .636 .625
M4 M5 M6 .886 .477 .682
M4 M5 M7 .977 .091 .534
M4 M5 M8 .841 .409 .625
M4 M6 M7 .943 .375 .659
M4 M6 M8 .864 .489 .676
M4 M7 M8 .830 .511 .671
M5 M6 M7 .886 .477 .682
M5 M6 M8 .886 .477 .682
M5 M7 M8 .886 .477 .682
M6 M7 M8 .886 .477 .682

BIBLIOGRAPHY

10.

11.

98

BIBLIOGRAPHY

P.P. Lele, and N. Senapati, "The Frequency Spectra of Energy

Backscattered and Attenuated by Normal and Abnormal Tissue",

Recent Advances in Ultrasound in Biomedicine, Volume 1, 1977,
D.N. White, Editor.

F.L. Lfizzi, M.A. Laviola, and D.J. Coleman, "Ultrasonic Tissue
Characterization Using Spectrum Analysis", Proceedings of the
Society of Photo-Optical Instrumentation Engineers, Volume 96,
1976.

F.L. Lizzi. and M.A. Laviola, "Tissue Signature Characterization
Utilizing Frequency Domain Analysis", Ultrasonics Symposium
Proceedings, 1976, IEEE Cat. #76 CHllZO-SSU.

F.L. Lizzi, L. Katz, L. St. Louis, and D.J. Coleman, "Applications
of Spectral Analysis in Medical Ultrasonography", Ultrasonics,
March 1976.

J. Fraser, and 6.8. Kino, "Cepstral Signal Processing for Tissue
Signal Analysis", Second International Symposium on Ultrasonic
Tissue Characterization, 1977.

W.K. Chu, and D.E. Raeside, "Fourier Analysis of the Echocardiogram",
Phys. Med. Biol, Volume 23, No. 1, 100-105, 1978.

M.G. Czerwinski, D.E. Leb, and K. Preston, Jr., "Ultrasonic
Characterization of Pyelomephritis in the Rabbit", Third
International Symposium on Ultrasonic Imaging and Tissue
Characterization, 1978.

P.M; Morse, and K.U. Ingardfi, Theoretical Acoustics", Internations
Series in Pure and Applied Science, McGrawIHill Book Company,
1968.

P.N.T. Wells, "Physical Principles of Ultrasonic Diagnosis",
Academic Press, 1969.

Karl F. Herzfeld and Theodore A. Litovitz, "Absorption and
Dispersion of Ultrasonic Waves", Academic Press, 1959.

Roman Kue, Mischa Schwartz, Nathaniel Finby, and Frank Dain, "
"Livertissue Characterization Using Reflected Ultrasonic Signals ,
Submitted for publication to IEEE Transactions on Biomedical

Engineering.

12.

l3.

14.

15.

16.

17.

18.

19.

20.

99

S.A. Goss, R.C. Johnston, and F. Dunn, "Comprehensive Complication
of Empirical Ultrasonic Propeties of Mammalian Tissue", J.
Acoustic Association of America, 1978.

Mark Robert Funk, "A Digital Ultrasound System for Data Collection,
Imaging, and Tissue Signature Analysis", Masters Thesis, Electrical
Engineering and System Science, Michigan State University.

Phillip Chemento, Michigan State University. ULTRA documentation,
Unpublished.

Goldberg and Watson, "Collision Theory", John Wiley, 1964.

J.C. Gore and S. Leeman, "Ultrasonic Backscattering from Human
Tissue: A Realistic Model", Physical Medical Biology, 1977. '

R.C. wagg, RJM. Lerner and R. Gramak, "Swept - Frequency Ultra-
sonic Determination of Tissue Macrostructures", Proceedings of
NSF - NBS Seminar on Tissue Characterization.

Duds and Hart, "Pattern Classification and Scene Analysis",
Wiley Interscience, 1973.

N. Hassani, "Hepatic Sonography", Ultrasonography of the Abdomin,
1976 C

N. Hassani, "Splenic Sonography", Ultrasonography of the Abdomin,
1976.

"111111'11114111T