In view of the complex vascular architecture and the intricate physical heat transfer processes in the human body, convective heat transfer via the blood is generally described by simple substitutional processes ("non-vascular models"). The classical "bioheat" approach of Pennes (J. Appl. Physiol. 1: 93-122, 1948), defining the heat flow to or from the tissue as being proportional to the product of perfusion rate and the difference of arterial and tissue temperature, has been seriously questioned after having been used for > 40 yr in many applications. In our laboratory, we have at our disposal a complex three-dimensional vascular model for the special case of tissue in a human extremity. This was used to test the performance of simple nonvascular models. It turned out that the Pennes approach may deliver acceptable results if the body is in the thermoneutral zone or if heat stress acts uniformly on the whole body. However, when cold stress or local hyperthermia is present, unreliable results must be expected. As the vascular model is not generally practicable because of its extreme complexity, we offer the efficiency function concept as a simple way of correcting the classical bioheat approach by factor multiplication. Efficiency function is determined as a function of perfusion rate and tissue depth in a way that compensates for the deficiencies of the Pennes bioheat term. The results are reasonable compared with those of the vascular model and experimental results.
Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open-source C++ software toolbox for the numerical computation of forward solutions in bioelectromagnetism. Building upon the DUNE framework, it provides implementations of modern fitted and unfitted finite element methods to efficiently solve the forward problems of electro- and magnetoencephalography. The user can choose between a variety of different source models that are implemented. The software’s aim is to provide interfaces that are extendable and easy-to-use. In order to enable a closer integration into existing analysis pipelines, interfaces to Python and MATLAB are provided. The practical use is demonstrated by a source analysis example of somatosensory evoked potentials using a realistic six-compartment head model. Detailed installation instructions and example scripts using spherical and realistic head models are appended.
A three-dimensional thermal model is presented in which convective heat transfer is defined in terms of the physical details of the vascular system. The convective heat exchange between prearteriole and postvenule vessels and the tissue across the vessel walls is calculated explicitly without using shape factors. Conduction in x-, y-, and z-direction is considered. This vascular model is applied to a human extremity. The spatial variations in the arterial, venous and tissue temperatures under basal conditions, hyperthermic conditions and in a cold environment are computed. Conclusions are drawn as to the validity of bioheat approaches.
Abstract-Objective: The purpose of this study is to introduce and evaluate the unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving the electroencephalography (EEG) forward problem. Methods: This new approach for source analysis does not use a geometry conforming volume triangulation, but instead uses a structured mesh that does not resolve the geometry. The geometry is described using level set functions and is incorporated implicitly in its mathematical formulation. As no triangulation is necessary, the complexity of a simulation pipeline and the need for manual interaction for patient specific simulations can be reduced and is comparable with that of the FEM for hexahedral meshes. In addition, it maintains conservation laws on a discrete level. Here, we present the theory for UDG-FEM forward modeling, its verification using quasi-analytical solutions in multi-layer sphere models and an evaluation in a comparison with a discontinuous Galerkin (DG-FEM) method on hexahedral and on conforming tetrahedral meshes. We furthermore apply the UDG-FEM forward approach in a realistic head model simulation study. Results: The given results show convergence and indicate a good overall accuracy of the UDG-FEM approach. UDG-FEM performs comparable or even better than DG-FEM on a conforming tetrahedral mesh while providing a less complex simulation pipeline. When compared to DG-FEM on hexahedral meshes, an overall better accuracy is achieved. Conclusion: The UDG-FEM approach is an accurate, flexible and promising method to solve the EEG forward problem. Significance: This study shows the first application of the UDG-FEM approach to the EEG forward problem.
We developed a three-dimensional thermal model in which convective heat transfer in a human extremity is explicitly quantified by taking into account the physical details of the vascular system. The spatial pattern in the arterial, venous and tissue temperature is computed during hyperthermia treatment. As such a complex vascular model is not generally applicable, a comparative study of the results of simpler, substitutional, non-vascular concepts applied to hyperthermia was carried out. It turned out that classical bioheat approaches may lead to wrong conclusions. Satisfactory results are to be expected from an approach suggested by Wissler/Baish and Charny/Levin, and by a far simpler efficiency function (EF) concept, developed by us, that can be used as easily as the simple classical Pennes approach while avoiding its deficiencies. The EF model is used to predict whether the temperature of the entire volume of vascularized muscle tissue will be raised to a therapeutic level. With the help of the vascular model, local thermal non-uniformities near individual blood vessels are analysed. Underheating in small volumes of tissue near the vessel walls is detected. This might explain tumour regrowth following local hyperthermia treatment in the tissue adjacent to blood vessels.
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