3D-visualized Model of Temperature Distribution in the Brain for the Investigation of Brain Cooling Effect

Abstract

Brain hypothermia requires controlling its temperature within an appropriate range, considering the change of body temperature in a long period. Various mathematical models have been used for the study of control and cooling capability of brain temperature in hypothermia. In the previous models, a hemisphere in a lumped parameter of a uniform temperature has been assumed as a simplified brain without considering the temperature distribution. In the present study, however, a new model is proposed to visualize the temperature distribution in the brain. The model has an approximate shape of each organ in a head based on MRI data, and may well reflect the properties such as heat transfer coefficients, metabolic heat production and heat capacity of human organs. The model has a pseudo-blood-flow model in which any temperature can be set as initial value at the starting place of blood flow. Some simulations using this model are performed with its controlled temperature by the introduction of Ringer's solution into any of the four arteries to the brain. The results of simulation suggests that the various cooling effects are made clear in every region of brain, and that the temperature distribution can be known for the application of controlling brain temperature in a concerning part.

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

“…A method of representing heat transfer between the inflowing blood and the brain tissue by a mathematical heat conduction model, as shown in Fig. 2, in order to reproduce the temperature distribution has been proposed [15]. In this model, nodes are placed at the vertices of continuously connected regular tetrahedra, and heat conduction is assumed to occur between adjacent nodes.…”

“…In vivo heat transfer occurs by heat conduction, convection, and advection in blood, but previous investigations [8,17] presented results obtained by representing the above factors by heat conduction. Honma et al [15] also created a mathematical model that takes these mechanisms into consideration. Heat conduction between nodes proceeds in accordance with Fourier's law, and the effects of convection are not taken into account.…”

“…The temperature T 0 (t + 1) at node 0 at time t + 1 can be calculated by means of Eq. (3) from the metabolic heat production M 0 (t) at node 0 and the heat transfer coefficient k i0 between node 0 and nodes i [15]. The heat transfer coefficient k expresses the rate of heat transfer of the nodes calculated from the thermal conductivity λ. Node 0 represents an arbitrary node in the three-dimensional lattice, and consequently, the nodes i corresponding to each node are uniquely determined.…”

“…In a mathematical model of the brain, for example, this means a set of nodes providing the shapes and parameters of brain tissue. Based on continuously captured MRI image data for the human head, we created tissue models of the brain, skull, and eyeballs [15]. However, the brain is a single continuous system consisting of the cerebrum, cerebellum, and medulla oblongata; other tissues such as the facial muscles and the parotid glands are included in the skull; and the cerebrospinal fluid (CSF) is assumed to fill the space between the mathematical model of the brain and that of the head.…”

“…They proposed a method of three-dimensional representation in addition to representation in sagittal or transverse section, creating a human head model that combined the shape data of the physical model with a heat conduction model, showing the temperature distribution by color gradations [15]. They used this model to perform a mathematical simulation oriented to selective brain hypothermia [16] and showed that temperature control in an arbitrary part of the brain is possible.…”