Developing a modeling and simulation framework for human thermoregulation for voxelized domains

Abstract

Since the 1980s, various models have been developed to simulate human thermoregulation. These models have undergone many modifications, maturing from simple geometrical shapes to more advanced polygon meshes. However, state-of-the-art models still lack the flexibility to be person specific and simulate thermoregulation with anatomical accuracy. Computational human phantoms (CHP), such as voxel phantoms, are anthropomorphic models developed from person-specific medical imaging data. These models provide the flexibility to represent a person-specific simulation domain with anatomical accuracy. However, using voxel phantoms for thermoregulation is challenging. This dissertation focuses on the challenges of using voxel phantoms for thermoregulation simulation and proposes solutions to overcome them. The first challenge associated with voxel phantoms is the stair-step effect introduced due to the cuboidal nature of voxels. To understand and quantify the surface area error due to the stair-step effect, a sphere was used, as a sphere represents the worst-case scenario for 3D curved domains. The overestimation of surface area for a sphere was found to be 50 %. Many solutions are available in the literature to reduce this error, but all of them rely on an unstructured mesh. To maintain the structured nature inherent in voxel phantoms, a structured cleaving method was developed. This method divides a pixel into four triangles and a voxel into 24 tetrahedrons. Using the smoothing method described in this dissertation, the overestimation of the surface area of a sphere was reduced to 16 %. This method was further tested on four tumors obtained from MRI scans. The overestimation of surface area for these tumors was reduced from 47% to 17% on average using the structured cleaving method. The second challenge of thermoregulation models lies in the multiphysics aspect of thermoregulation. Blood flow in vasculature is predominantly modeled as one-dimensional, whereas the blood flow in capillary beds is modeled as three-dimensional. This results in a mixed-dimensional mesh of vasculature and the tissue-capillary bed. This mixed-dimensional coupling was addressed using the Dirac distribution function and algorithm obtained from the literature. This algorithm was further advanced by adding multiscale coupling due to the difference in mesh resolutions of segmented vasculature and tissue voxels. The mixed-dimensional, multi-scale mesh was used to create a blood flow - heat transfer coupled solver and simulate this multi-physics phenomenon on frog tongue data obtained from the literature. The resulting framework is called the Voxelized Multi-Physics Simulation Framework (VoM-PhyS), which provides a strong foundation for a full-body thermoregulation simulation. The third challenge with any voxel domain generated from imaging data is associated with voxel resolution. Due to the dimensional scale of blood vessels, not all vessels are captured in a given voxel resolution. This loss of segmentable vascular data results in discontinuous blood vessels. The pre-capillary vessels, like arterioles, provide the highest resistance to blood flow. Due to the resolution limitations, these pre-capillary vessels are modeled with the tissue as a porous domain. In other words, using the porous media method, pre-capillary vessels get modeled with a capillary bed in a tissue voxel. This results in a loss of information that could have been modeled if the pre-capillary vessels were segmented and modeled distinct from capillary bed. The vessels can only be modeled if a very high image resolution is used, which would also increase the computational cost of the entire simulation domain. Instead, a mathematical representation of the pressure drop induced in these unsegmented blood vessels is used. A part of this dissertation focuses on developing a mathematical equation to calculate the pressure drop parameter, which can be used to accurately model the flow resistance offered by pre-capillary vessels and simulate blood flow. This dissertation provides the equations to calculate the pressure drop parameters for any given vasculature and tissue domain, provided the total pressure drop across the simulation domain and the total blood steady-state flow rate are known. These equations provide deeper insight into vascular resistance and strengthen the VoM-PhyS Framework by allowing the flexibility to reduce the mesh size and computational memory requirements. The effect of substituting segmented vessels with mathematical pressure drop parameters on heat transfer is analyzed by simulating a 3D vascular domain of 32 terminal vessels and five generations of bifurcation. Each generation is successively removed and substituted with the pressure drop parameter to analyze the error in heat transfer due to a lack of segmentation data. To reduce this error, two methods are proposed and demonstrated to show considerable energy error reduction.