The Explicit Green’s Approach with stability enhancement for solving the bioheat transfer equation

Abstract

The aim of this paper is to propose a strategy for performing a stability enhancement into the Explicit Green's Approach (ExGA) method applied to the bioheat transfer equation. The ExGA method is a time-stepping technique that uses numerical Green's functions in the time domain; these functions are here computed by the FEM.Basically, a new two nonequal time substeps procedure is proposed to compute Green's functions at the first time step. This is accomplished by adopting the standard explicit Euler scheme and an optimized procedure to yield the best stability constraint, allowing a reduction into the number of time steps without loss of accuracy. In addition, the concept of local numerical Green's functions is introduced and explored aiming at reducing the computational effort of nodal Green's functions calculation. Two examples are presented in order to show the potentialities of the proposed methodology, one to illustrate the accuracy and another applied to skin burn simulations.

Q-r curve of thermal tomography and its clinical application on breast tumor diagnosis

“…Based on the principle of black body radiation, the medical infrared detector can detect the thermal distribution information of body surface, display the temperature field of human body with false-color image, and record the infrared information that can't be identified by naked eyes with thermal image in real time [14]. However, the method taking the temperature distribution and temperature difference information of body surface as the basis for diagnosis of diseases has many limitations, because it is ignored that the internal thermal distribution of lesion in human body carries lots of valuable disease information, which is of great importance for the diagnosis of diseases [15][16][17][18]. At present, the medical imaging technologies being commonly used such as magnetic resonance imaging (MRI), X-CT imaging, ultrasonic imaging etc., can provide some related biochemical and pathologic information, nevertheless these technologies have a fundamental constraint, that is they can only display the shape changes of body tissue, but not reflect functional changes of body tissue [19,20].…”

“…In order to mine the valuable 3-dimensional heat distribution data based on temperature distribution of body surface, many research groups have carried out in-depth studies and made a series of achievements [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This present paper aims to acquire the q-r characteristic curve of the heat intensity varying with depth of tomography based on the temperature distribution characteristics of tumor in different stages.…”

Commentary on the clinical and preclinical dosage limits of interstitially administered magnetic fluids for therapeutic hyperthermia based on current practice and efficacy models

“…Given these parameters, various theoretical models exist that describe the expected biophysical heat flows in different conditions, which we can use to predict in silico the temperature increase DT at and around the injection site. Surveying a selection of recent publications on such models in the field of magnetic hyperthermia [65][66][67][68][69][70][71][72], two things are apparent: (i) that the methods that different authors adopt to address the problem are many and varied, and can be mathematically very complex; and (ii) they all take as their starting point the "Pennes equation":…”

“…In this paper, it is not our intention to critique the various available bioheat models for magnetic heating, nor do we wish to introduce a comprehensive but complex model that covers multiple scenarios such as time-dependent effects, thermally-varying perfusion or variations in metabolic rate between tumour tissue and healthy tissue. Such considerations have been covered in other works, including those already cited [65][66][67][68][69][70][71][72]. Instead, we present here a simple analytical model that enables a "first approximation" predictive step to be taken in the translation of magnetic hyperthermia, directed towards treatment planning.…”

Diagnosis of breast tumor using thermal tomography q − r curve

“…[10][11][12][13] In order to detect the temperature changes as early as possible, specialized medical inspection equipment has to be used. [14][15][16][17][18] At present, the medical imaging technologies being commonly used, such as ultrasonic imaging, magnetic resonance imaging, X-computed tomography imaging etc., can display the shape changes of lesions, but cannot reflect functional changes of body tissues. 19,20 When the pathological changes become structural lesions, qualitative changes have taken place in the human body.…”