Cryolipolysis is a noninvasive clinical procedure to locally reduce adipose tissue. During the procedure, paddles that are maintained at a prescribed temperature (commonly -14 ℗ʻC and 3.1 ℗ʻC) are placed in good thermal contact with the skin. Cryolipolysis was inspired by panniculitis observed in a pediatric patient. The goal is to cool the adipose tissue to 10.4 ℗ʻC in order to induce apoptosis in adipocytes, presumably by the crystallization of the intracellular triglycerides. The dermal cells between the cooled paddle and the adipocytes are colder than the adipocytes, but are less susceptible to death due to cooling. Thus, when properly administered, cryolipolysis leaves the dermis and epidermis unharmed. There are some adverse outcomes, e.g. transient neuropathy and rare adipose hyperplasia. The clinical cooling protocol has been based largely on animal experiments and subsequent clinical experience. A mathematical model could aid clinicians by providing insight into the temperature history of the tissues, potentially allowing optimization of the procedure. A model is here presented based on the Pennes bioheat transfer equation. Scaling the equation reveals two parameters in the Pennes equation: the Fourier number and a blood perfusion parameter. This scaled equation has the form of a 1D transient fin equation. Green's function solutions were used to model the temperature profile. The model revealed that the 30 min and 60 min treatment protocols often used clinically would give similar temperature profiles. Moreover, the effect of the blood perfusion rate was more noticeable for the end temperature than for the transient temperatures. The range of thermal conductivities typical for tissue, which is largely a function of tissue hydration, had little net effect on the temperature profile. This justified the use of the one-layer model. In addition to other insights, the results showed that the -14 ℗ʻC paddle cooled more of the tissue to the desired temperature than did the 3.1 ℗ʻC, as would be expected. For optimizing treatments, the relationship between temperature and time required to trigger apoptosis in adipocytes needs to be quantified and coupled with the temperature model.
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