Boundary element method (BEM) for solving normal or inverse bio-heat transfer problem of biological bodies with complex shape

The identification of the space-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. While Dirichlet boundary conditions are assumed, the additional measurement necessary to render a unique solution is either a heat-flux measurement or a time-average temperature measurement inside the space region of interest. A numerical approach based on the Crank-Nicolson finite-difference scheme combined with the first-order Tikhonov's regularization method is developed. Numerical results are presented and discussed.

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“…In the one-dimensional case, the Pennes bio-heat conduction equation, [1,4,5], in its non-dimensional form, is given by…”

Section: Introductionmentioning

confidence: 99%

Space-dependent perfusion coefficient identification in the transient bio-heat equation

2009

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“…GAs are ideally suited to the inverse problem of identifying the parameters used in the temperature-dependence expansions for blood perfusion (Ren et al, 1995;Majchrzak and Paruch, 2004). The method is of an evolutionary type, based on the process of natural selection, requiring no initial guess about the values of the parameters.…”

Section: Procedures For Identification Of Blood Perfusion Parametersmentioning

confidence: 99%

“…Previous works on inverse analysis of biological bodies were carried out by Ren et al (1995), who applied the Boundary Element Method (BEM) to identify heat sources in biological bodies based on the simultaneous measurement of temperature and heat flux at the skin surface, by Majchrzak and Paruch (2004), who estimated the (constant) thermophysical parameters of a tumour using a least-squares algorithm based on sensitivity coefficients, and by Partridge and Wrobel (2007), who presented a BEM inverse analysis based on a Genetic Algorithm (GA) (Goldberg, 1989;Goldberg et al, 1997) to identify the position and size of shallow tumours using skin temperature measurements. This paper extends the algorithm developed by Partridge and Wrobel (2007) for the identification of the coefficients of linear and quadratic variations of blood perfusion.…”

Section: Introductionmentioning

confidence: 99%

“…Herein, a numerical technique for identification of the temperature-dependent blood perfusion parameters in Pennes' equation is proposed based on the Dual Reciprocity Method (DRM), which has already been used for the direct solution of the bioheat equation (Deng and Liu, 2000;Deng and Liu, 2004a;Deng and Liu, 2004b;Lu et al, 1998;Liu and Xu, 2000). It is assumed that the size and location of the tumour are known from previous diagnostics; in the DRM, the tumour is treated as a sub-region and in addition to the nodes used to model the boundary of the tumour, no other internal points are required.Previous works on inverse analysis of biological bodies were carried out by Ren et al (1995), who applied the Boundary Element Method (BEM) to identify heat sources in biological bodies based on the simultaneous measurement of temperature and heat flux at the skin surface, by Majchrzak and Paruch (2004), who estimated the (constant) thermophysical parameters of a tumour using a least-squares algorithm based on sensitivity coefficients, and by Partridge and Wrobel (2007), who presented a BEM inverse analysis based on a Genetic Algorithm (GA) (Goldberg, 1989;Goldberg et al, 1997) to identify the position and size of shallow tumours using skin temperature measurements. This paper extends the algorithm developed by Partridge and Wrobel (2007) for the identification of the coefficients of linear and quadratic variations of blood perfusion.…”

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A coupled dual reciprocity BEM/genetic algorithm for identification of blood perfusion parameters

Partridge

Wrobel

2009

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The paper presents an inverse analysis procedure based on a coupled numerical formulation through which the coefficients describing non-linear thermal properties of blood perfusion may be identified. Design/methodology/approach -The coupled numerical technique involves a combination of the Dual Reciprocity Boundary Element Method and a GeneticAlgorithm for the solution of the Pennes bioheat equation. Both linear and quadratic temperature-dependent variations are considered for the blood perfusion. Findings -The proposed DRBEM formulation requires no internal discretisation and, in this case, no internal nodes either, apart from those defining the interface tissue/tumour. It is seen that the skin temperature variation changes as the blood perfusion increases, and in certain cases flat or nearly flat curves are produced. The proposed algorithm has difficulty to identify the perfusion parameters in these cases, although a more advanced GA may provide improved results.Practical implications -The coupled technique allows accurate inverse solutions of the Pennes bioheat equation for quantitative diagnostics on the physiological conditions of biological bodies and for optimisation of hyperthermia for cancer therapy.Originality/value -The proposed technique can be used to guide hyperthermia cancer treatment, which normally involves heating tissue to 42-43 o C. When heated up to this range of temperatures, the blood flow in normal tissues, e.g. skin and muscle, increases significantly, while blood flow in the tumour zone decreases. Therefore, the consideration of temperature-dependent blood perfusion in this case is not only essential for the correct modelling of the problem, but should provide larger skin temperature variations, making the identification problem easier Keywords Boundary element method, Dual reciprocity method, Genetic algorithm, Inverse analysis, Tumours, Blood perfusion Paper type Research paper IntroductionIt is well known that the body surface temperature is controlled by blood circulation, local metabolism and heat transfer between the skin and the environment (Deng and Liu, 2004a). It is also known that several types of tumours, e.g. skin or breast, can lead to an increase in local blood flow, and thus to an increase in the local temperature (Liu and Xu, 2000). On the other hand, thrombosis or vascular sclerosis decreases the blood flowing to the skin, resulting in lower skin temperatures (Liu and Xu, 2000).The Pennes bioheat equation can be used for the quantitative diagnostics of physiological conditions on biological bodies, e.g. for simulations of regional hyperthermia for cancer therapy (Tompkins et al., 1994;Erdmann et al., 1998;Lang et al., 1999). The parameters considered in Pennes' equation are usually assumed to be constant except for the blood perfusion, which varies with temperature (Tompkins et al., 1994;Erdmann et al., 1998;Lang et al., 1999;Rai and Rai, 1999;Liu and Xu, 2000). Herein, a numerical technique for identification of the temperature-dependent blood perfusi...

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“…However, at macroscopic level, the blood perfusion is considered to be a directionless quantity due to the very complex nature of the pathways through which it evolves. In the one-dimensional case, the temperature and the spacewise-dependent blood perfusion coefficient P f (x) > 0 are related through the Pennes bio-heat conduction equation, [2,10,13], which, in non-dimensional form, in the absence of sources, is given by:…”

Section: Introductionmentioning

confidence: 99%

Inverse space-dependent perfusion coefficient identification

Trucu¹,

Ingham²,

Lesnic³

2008

J. Phys.: Conf. Ser.

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Boundary element method (BEM) for solving normal or inverse bio-heat transfer problem of biological bodies with complex shape

Cited by 33 publications

References 7 publications

Space-dependent perfusion coefficient identification in the transient bio-heat equation

Space-dependent perfusion coefficient identification in the transient bio-heat equation

A coupled dual reciprocity BEM/genetic algorithm for identification of blood perfusion parameters

Inverse space-dependent perfusion coefficient identification

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