Comparison of Brain Temperature Distribution in Mathematical and Solid Models of Head Thermal Characteristics

Abstract

SUMMARY Accurate temperature control of brain tissue during hypothermia treatment is necessary in order to prevent secondary brain damage and to avoid various side effects. Thus, the visualization of the intracerebral temperature distribution in hypothermia treatment was studied at the fundamental level. For this purpose a virtual reality technology was used to create a mathematical model that reflects metabolic heat production and Fourier heat conduction in a brain with the necessary parameters based on various clinical models. In the present study, an experimental system was developed to examine a mathematical simulation of the blood flow in a human head by using a solid brain model constructed using silicon rubber in the shape of a brain based on MRI data, taking into account the metabolic heat given off by three film heaters and including six sensors for the measurement of regional brain temperature. The mathematical simulation describes the internal temperature distribution in a brain with a similar structure to the brain solid model. The results of mathematical simulations and experiments using the brain solid model were quite consistent in the steady state, including control of regional temperature. This allows for the performance of heat conduction experiments under conditions similar to those of a living body, in which the internal temperature is clinically difficult to observe. Thus, the mathematical simulation is confirmed to be useful together with experiments using the solid model for the study of future brain hypothermia treatment.

Regular Tetrahedral Lattice Coordinate System for an Equivalent Arrangement of Bio‐mathematical Models Reflecting Objects’ Shape

“…12, studies using mathematical models with continuous arrangement of regular tetrahedrons [1,13,14], same as in the present study, showed relatively good agreement between simulated and measured results for different algorithms of temperature control. 12, studies using mathematical models with continuous arrangement of regular tetrahedrons [1,13,14], same as in the present study, showed relatively good agreement between simulated and measured results for different algorithms of temperature control.…”

“…The proposed method was verified for dynamic models [1,2,9] and thermodynamic models [10,13,14]; the method combines a number of features advantageous for a wide variety of biomathematical simulations. Besides, continuous state distributions can be visualized because most of space is defined as computable domain.…”

“…Normally, connection between nodes is expressed by links; however, in some cases such as spring models [1,2,9] and heat transfer models [10,13,14], connection elements should express energy transfer, attenuation, and accumulation as well. Nodal points represent mass, temperature, and other material characteristics around them.…”

“…Nodal points represent mass, temperature, and other material characteristics around them. Normally, connection between nodes is expressed by links; however, in some cases such as spring models [1,2,9] and heat transfer models [10,13,14], connection elements should express energy transfer, attenuation, and accumulation as well. Thus in this study, we define channels to conceptually represent connections and respective energy transfer.…”

“…On the other hand, node allocation in lattice coordinates created by continuous arrangement of regular tetrahedrons was employed to propose dynamic models based on a visco-elasto-plastic model [1,2,9] and visualized models of temperature distribution in human head using a thermodynamic model [10]. Particularly, results of thermodynamic simulations using the latter model [13,14] showed good agreement with results of experimental measurement, thus proving feasibility of accurate simulations with biomathematical models. However, regularity of node placement in such lattice coordinates was reported only fractionally [15], while calculation method was not described.…”