Mathematical Models of Bioheat Transfer

Charny, Caleb K.

doi:10.1016/s0065-2717(08)70344-7

Cited by 182 publications

(149 citation statements)

References 52 publications

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“…The BHT thus offers a simple and practical solution if applied to tissue under appropriate conditions, as is required even with more sophisticated models that attempt to reflect heat transfer by perfusion more accurately (21). Without the need to model the complex geometry of larger vessels, the BHT has been successfully implemented in therapeutic hyperthermia and heat clearance methods for measuring perfusion (22). It has been shown to yield valid results if measurements are made in tissue regions far away from large vessels that may introduce local convection and when the assumption of uniform perfusion is justifiable.…”

Section: Theorymentioning

confidence: 99%

Tissue thermal conductivity by magnetic resonance thermometry and focused ultrasound heating

Cheng

Plewes

2002

Magnetic Resonance Imaging

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Purpose:To investigate the combined use of magnetic resonance (MR) temperature imaging and focused ultrasound (FUS) for the noninvasive determination of tissue thermal properties. Materials and Methods:Brief, spatial impulses of temperature elevation were created in tissue using a spherical, air-backed transducer operating at 1.68 MHz and measured using MR temperature imaging in a 1.5-Tesla clinical scanner. A novel technique based on thermal washout is applied in an analysis of the acquired MR temperature images to estimate tissue thermal conductivity and perfusion.Results: Numerical simulations and experiments in vitro and in vivo demonstrate that thermal conductivity can be measured to within 10% of the true value with MR thermometry at 1.5 Tesla. With the temperature precision available at 1.5 Tesla, however, robust perfusion estimation is feasible only in highly perfused organs or tumors. Conclusion:This study has developed a method for determining tissue thermal properties specific to the patient and organ at the site of interest, and allows repeated application. This capability is relevant in thermal therapy planning of tumor ablation using MR-guided FUS systems.

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Section: Theorymentioning

confidence: 99%

Tissue thermal conductivity by magnetic resonance thermometry and focused ultrasound heating

Cheng

Plewes

2002

Magnetic Resonance Imaging

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“…(Chen & Holmes, 1980a;b); (Chato, 1980); (Valvano et al, 1984); (Weinbaum & Jiji, 1985); (Arkin et al, 1986); (Hirst, 1989) (see also e.g. (Charney, 1992) for a review on mathematical modeling of the influence of blood perfusion). Recently, some studies have shown the important role of porous media in modeling flow and heat transfer in living body, and the pertinence of models including this parameter have been analyzed, see e.g.…”

Section: Problem Definitionmentioning

confidence: 99%

Thermal Therapy: Stabilization and Identification

Belmiloudi¹

2011

Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology

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44 pages, In "Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology", A. Belmiloudi (Ed.), InTech (Open Access Publisher), Vienna, 2011 - ISBN 978-953-307-550-1International audienceMotivated by topics and issues critical to human health and safety of treatment, the problem studied in this chapter derives from the modeling and stabilizing control of the transport of thermal energy in biological systems with porous structures. First, the modeling of thermal transport by perfusion within the framework of the theory of porous media is presented and the governing equations are established. The thermal processes within the tissues are predicted by using some generalized uncertain evolutive nonlinear bioheat transfer type models with nonlinear Robin boundary conditions, by taking into account porous structures and directional blood flow. Afterwards the existence, the uniqueness and the regularity of the solution of the state equation are presented as well as stability and maximum principle under extra assumptions. Second, we introduce the initial perturbation problem and give the existence and uniqueness of the perturbation solution and obtain a stability result. Third, the real-time identification and robust stabilization problems are formulated, in different situations, in order to reconstitute simultaneously the blood perfusion rate, the porosity parameter, the heat transfer parameter, the distributed energy source terms and the heat flux due to the evaporation, which affect the effects of thermal physical properties on the transient temperature of biological tissues, and to control and stabilize the desired online temperature and thermal damage provided by MRI measurements. Because, it is now well-known that a controlled and stabilized temperature field does not necessarily imply a controlled and stabilized tissue damage. This work includes results concerning the existence of the optimal solutions, the sensitivity problems, adjoint problems, necessary optimality conditions and optimization problems. Next, we analyse the case when data are measured in only some points in space-time domain, and the case where the body Ω is constituted by different tissue types which occupy finitely many disjointed subdomains. Some numerical strategies, based on adjoint control optimization , in order to perform the robust control, are also discussed. Finally, control and stabilization problems for a coupled thermal, radiation transport and coagulation processes modeling the laser-induced thermotherapy in biological tissues, during cancer treatment, are analyzed

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“…Charny (1990Charny ( , 1992 showed that the bleed-off from the largest countercurrent vessels can be described by the Pennes equation. These bleed-off vessels in muscle tissue can be as large as 300 µm.…”

Section: Thermal Modelsmentioning

confidence: 99%

“…Self-heated thermistor techniques to measure perfusion have been investigated in recent years (Chato 1968, Balasubramaniam 1977, Holmes 1980, Valvano 1984, Patel 1987, Anderson 1992 , Holmes 1980, and Xu 1991), a KEFF model , Roemer 1987, Patel 1987 and the Weinbaum-Jiji model (Weinbaum 1985, Song 1987, Valvano 1990, Charny 1990, Xu 1991, Charny 1992.…”

Section: Introductionmentioning

confidence: 99%