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

Abstract

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...

A Mathematical Model to Solve Bio-Heat Transfer Problems through a Bio-Heat Transfer Equation with Quadratic Temperature-Dependent Blood Perfusion under a Constant Spatial Heating on Skin Surface

“…The maximal value of 0 ω , 0 γ , and 0 δ are 4 7 10 − × , 4 1.9 10 − × and 6 7 10 − × , respectively [6]. The the arterial blood temperature 37 C a T =  is used.…”

3D numerical simulations on GPUs of hyperthermia with nanoparticles by a nonlinear bioheat model

“…The steady-temperature is so important that it can be used, for instance, to diagnose in a non-invasive manner tumors by the measure of the temperature at the skin surface, especially those near to skin [13,21]. Nevertheless, the skin-surface temperature may also be employed in inverse analyses to estimate either the location and size of tumors or some of the tissue properties such as the blood perfusion rate [22,23,24,25].…”

Extended Generalized Riccati Equation Mapping for Thermal Traveling-Wave Distribution in Biological Tissues through a Bio-Heat Transfer Model with Linear/Quadratic Temperature-Dependent Blood Perfusion

“…Temperature distributions for two individual patients calculated on coarse and fine spatial grids were compared. Most recently, Partridge et al [35] presented an inverse analysis procedure based on a coupled numerical formulation first to identify the coefficients of linear and quadratic variations of blood perfusion, and then to investigate temperature distribution at the skin surface for tumor perfusion. Their procedure has the advantage of not requiring the calculation of derivatives or sensitivities, or an initial estimate of these values.…”

“…We assume in this work a linear and a quadratic temperature-dependent blood similar to the expression identified respectively by Gowrishankar et al [36] and Partridge et al [35] [37,38] to reduce it to a linear Schrödinger spectral problem. Riccati Equation (1.3) appears in many fields of applied mathematics, in many instances when we can find exact solutions of nonlinear partial differential equations.…”