Variational finite element approach to study the thermal stress in multi-layered human head

Abstract

The human head is one of the most sensitive parts of human body due to the fact that it contains brain. Any abnormality in the functioning of brain may disturb the entire system. One of the disturbing factors of brain is thermal stress. Thus, it is imperative to study the effects of thermal stress on human head at various environmental conditions. For the thermoregulation process, the human head is considered to be a structure of four layers viz.; brain, cerebrospinal fluid (CSF), skull and scalp. A mathematical model has been formulated to estimate the variation of temperature at these layers. The model is based on radial form of bio-heat equation with the appropriate boundary conditions and has been solved by variational finite element method. The rate of metabolic heat generation and thermal conductivity in this study have been assumed to be heterogeneous. The results were compared with the experimental studies for their coincidence and it has been observed theoretically and experimentally that the human head has greater resistance to compete with the thermal stress up to large extent.

Mathematical Simulation and Numerical Computation of the Temperature Profiles in the Peripherals of Human Brain during the Tepid Sponge Treatment to Fever

“…To display the results graphically, it becomes indispensable to get the numerical approximations by using the numerical values of the parameters. The numerical values of all the associated parameters (see Table 7 ) have been taken from the various research papers which include Khanday et al [ 14 ], Janssen et al [ 21 ], Aijaz et al [ 18 ], Shirkavand and Nazif [ 22 ], Melo et al [ 23 ], de Dear et al [ 24 ], and Giering et al [ 25 ]. It is to be noted that there is a small variation in the values of the thickness of scalp, skull, and CSF, depending on the age and geographical factors.…”

“…It is to be noted that k , p , and c have specific constant values in each layer of the domain and, hence, take distinct values in scalp, skull, and CSF as demonstrated by Aijaz et al [ 18 ]. Thus, in the numerical computation, their numerical values will be taken according to the positions of nodal points pertaining to T i , j , k in the numerical discretization of the domain (see Figure 1(b) ).…”

“…Further, various physiological parameters have a remarkable impact on the heat transfer through tissue as assessed by Ley and Bayazitoglu [ 16 ]. Therefore, for the formulation of the mathematical model, Pennes' bioheat equation [ 17 ] is the most appropriate equation as discussed by Aijaz et al [ 18 ]. Therefore, the rate of heat flow through the human head is also dependent on the layer under study.…”

Energy Balance Approach to Study the Role of Perspiration in Heat Distribution of Human Skin

“…To deal with the complex structure of the human body, different methods have been used for heat transfer by many researchers. Aijaz et al [6,9] used the variational finite element method for the numerical solutions of the bioheat equation and justified their claim that this method gives optimum results for irregular geometrical patterns. In the present case, we shall use the surface energy balance method to determine the heat transfer.…”

“…Earlier, Khanday et al [5] estimated the effects of thermal stress on the behaviour of fluid concentrations in human dermal regions by formulating a mathematical model based on the diffusion equation along with appropriate boundary conditions and solving the model by the variational finite element method. Mir Aijaz et al [6] used the variational finite element approach to study the thermal stress in multilayered human head.…”