Approximate lumped parameter model for bioheat equation
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Date
2023
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Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2023.
Abstract
Lumped parameter modeling is a good alternative for analytical and numerical models, providing simple, and accurate results in many applications, including analysis of biological systems in the human body. However, the use of lumped parameter models in the bioheat transfer is very limited, as the thermal resistances are only valid for systems with no heat generation and biological tissues often have metabolic heat production. This study shows that the lumped parameter models can be used for examining the bioheat transfer in the human body. For this purpose, the arms, legs, and head were modeled and temperatures of the tissues within these body parts are determined by using analytical, numerical, and lumped parameter modeling. The models are examined for resting and exercise conditions. 4- layered cylindrical and spherical models are used for representing the limbs and the head, respectively. These models include the blood flow, convection, radiation, and perspiration. Comparison of the results obtained with analytical, numerical, and lumped parameter methods showed that the deviations between the results of different methods are not significant. Maximum error for the limbs during rest is determined as 0.4°C, and it is not more than 1°C, during exercise. The error for the head is slightly higher, but does not exceed 1.5°C. Maximum deviations are observed at the fat and bone tissue for limbs and head, respectively. The errors for skin and core are much lower. Furthermore, the effects of thermoregulatory systems such as blood flow, sweating, radiation, and convection are also examined throughout the analysis. It is observed that the effect of blood flow is very dominant at the core, but other mechanisms are more effective at the outermost layers than the core instead. Lumped parameter method will be more useful when more complex systems with pulsating blood flow and transient changes are considered.