Mathematical study of temperature distribution model in human males and females dermal part

Abstract

Heat transfer problems are related with various disciplines including biomedical sciences and have a role both in treatment and diagnosis. Such problems can aid in predicting the time in the course of treatment or giving information on the temperature where, thermometry is lacking. The balance between the heat generation and loss from the body to environment is very important to maintain body core temperature. Any physiological abnormality will disturb the homeo- static conditions for the temperature. Therefore, the study of heat transfer under normal and abnormal conditions will be useful for various clinical conditions. The study of body skin temperature is an essential aspect to understand temperature regulation in human. Skin temperature is usually not uniform over the body surface, because it varies with the surrounding conditions. Skin temper- ature is one of the major factors determining heat exchange with the environment. It provides the thermoregulatory system with important information about the need to conserve or dissipate heat. There are clear statistical facts indicating the importance of evaluating individual temperature distribution. The _rst such fact is apparent: all human beings have more or less individual body composition and di_erent tissue types (e.g. bone, muscle, fat and skin), their amount and distributions. The second relevant fact is that di_erent tissue types have di_erent orders of magnitude in metabolic heat generation, perfusion and perspiration, and individual body com- position are the major factors for thermo regulation in human males and females body. About 50% 􀀀 80% of the heat ow in the tissue is carried in or out of the tissue by the blood ow [74]. Skin is a complicated structure with many functions and if any one of the functions could not work, rash or abnormal sensation is the result. Thermally signi_cant blood vessels are generally in a thermal scale of less than 300_m [48]. So it has been di_cult to make temperature measuring devices with su_cient resolution to measure temperature uctuation. In all cases, exper- imental results could not possible, modeling should be necessary. Actually, our body is divided in to the inner and outer cells. Temperature is relatively uniform in the core, but outer cell (skin and subcutaneous tissue) temperature is not uniform over the body surface. It varies with surrounding condition. If our body core temperature aries around 41_ death will occurs. On the other hand, if the core temperature reaches 33_C, the person becomes un- conscious, below this level death will occur [85]. So, it is important to know how the human body behaves under di_erent surrounding conditions. Besides a large number of publications dealing with thermoregulation of males body, very few are the females. It can therefore be argued that conclusions regarding sex-related di_erences in temperature regulation remain limited and the mathematical modeling should be necessary. The present thesis deals with variational _nite element techniques for one and two dimensional steady states and transient temperature distribution model of human males and females dermal part. The modi_ed form of Pennes bio-heat equation has been used in the model for temperature distribution in the layers. The shape function for temperatures in the layers has been considered as a linear function of depth. The thickness of layers has been measured perpendicularly from the outer skin surface towards body core. It is assumed that the outer sur- face of the skin is exposed to the environment and the loss of heat from the skin surface is assumed due to convection, radiation and sweat evaporation. In our study, thickness of the fatty part of females subcutaneous tissue is considered slightly thicker as compared with males due to greater amount of subcutaneous fat of females. The human skin layer is discretized, namely stra- tum corneum, stratum germinativum, papillary region, reticular region, fatty and muscle parts of subcutaneous tissue. In two dimensional analysis, the skin layer is divided into 180 nodal elements with triangular shape having total 114 nodes for males and 200 nodal elements with triangular shape having total 126 nodes for females. The thesis is divided into six chapters. chapter-wise brief description of the present study is as follows: Chapter 1 deals with the general introduction of human males and females skin layer anatomy and physiology. It also deals heat transform mechanisms in human males and females skin layers namely conduction, convection, radiation, evaporation, perfusion and metabolism. It covers physical and physiological dif- ferences of heat regulation in human males and females skin. The derivation of Pennes bio-heat equation with its signi_cance of the model has been discussed. At the end of this chapter, the literatures review of the earlier researcher in this area has been carried out. Chapter 2 deals with the mathematical discussion of _nite element method. It covers the basic theory of _nite elements, calculus of variations, weak formu- lations and _nite element model discretization. The _nite element procedure for bio-heat equation has been discussed. Chapter 3 describes the study of metabolic e_ect relying on dermal thick- nesses of males and females for temperature distribution of the layers of dermal part at various atmospheric temperatures. The study has been carried out for one and two dimensional steady states and transient cases using _nite element method. Lower percentage of muscle mass and higher percentage of adipose tissue in subcutaneous part of females result lower metabolic rate and higher subcuta- neous fat compared to males. Metabolism is considered as a heat source within the body tissue. The study delineates that males and females would di_er in their physio- logical responses in temperature distribution due to di_erences in metabolic heat production between gender. The result shows that steady state temperature of each nodal is achieved earlier in case of males in comparison to females. The thinner layers of males lead to higher values of skin temperature than thicker layer of females. Thickness plays signi_cant role for temperatures distribution in human males and females bodies. Convergence of temperature values due to metabolism is carried out by varying the mesh sizes. The numerical results are compared with past general human body simulated results. Chapter 4 describes the comparative mathematical model of perfusion ef- fect analysis for temperature distribution in human males and females bodies in di_erent thermal environments. Both, one and two dimensional steady states and transient cases are studied. The solution of the mathematical model is presented on the basis of variational _nite element method. The Pennes bio-heat equation has been used for the study of the model that it incorporates the blood perfusion or volumetric ow rate within the tissue. The appropriate physical and phys- iological parameters together with suitable boundary conditions that a_ect the heat regulations have been incorporated in the model. The loss of heat from the outer surface of body to the environment is taken due to convection, radiation and sweat evaporation. The result shows that steady state and transient temperature of each nodal is slightly higher and is achieved earlier in case of males in comparison to females. Convergence of temperature values due to perfusion by varying the mesh sizes has been carried out. The validation of the numerical results have been checked. Chapter 5 deals with comparative study of thermoregulation of human males and females under hot zone due to sweating. The solution is presented on the basis of variational _nite element method for one and two dimensional steady and transient cases. Sweating is considered as a heat loss within the body by evaporation of water inside the body. The sweating rate for male is calculated by the relation: E = 8:47 _ 10􀀀5(0:1 _ Tsk + 0:9 _ Tb) 􀀀 36:6_C [kg=m2=sec] where, Tsk = T0 (Outer skin surface temperature), Tb = 37_ (Body core temper- ature). The sweat rate in females is less compared to males due to the lower density of sweat gland and hormonal pattern in females. So, coe_cient of Tb is considered as 0:7 instead of 0:9 in above relation for females [44]. The analysis sought out that tissue temperature in males is slightly higher as compared to females when atmospheric temperature T1 is less than body core temperature. But, the females tissue temperature is higher, when T1 exceeds 37_C. The steady state nodal temperature is achieved earlier in case of males in comparison to females. Convergence of temperature values due to sweating is carried out by varying the mesh element size. The numerical results are compared with past simulated general human body (male) results. Chapter 6 describes one and two dimensional mathematical models for tissue temperature distribution during follicular and luteal phases of females. The study is further carried out for the temperature distribution results of these phases as compared to males temperature distribution. The analysis presents that during the luteal phase of females, the tissue temperature is lower as compared to males, when atmospheric temperature T1 falls below the body core tempera- ture. Likewise, females luteal phase temperature is slightly higher as compared to males, when T1 exceeds the body core temperature. But, females follicular phase temperature is lower as compared to females luteal phase and males body temperature either T1 is greater or less than the body core. The above di_er- ences of females compared to males under the same atmospheric conditions may be the causes of females hormonal variation during the menstrual cycle phases.