A flux-conservative finite difference scheme for the numerical solution of the nonlinear bioheat equation

We present a flux-conservative finite difference (FCFD) scheme for solving the nonlinear (bio)heat transfer in living tissue. The proposed scheme deals with steep gradients in the material properties for malignant and healthy tissues. The method applies directly on the raw medical image data without the need for sophisticated image analysis algorithms to define the interface between tumor and healthy tissues.

[1]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[2]  Mehdi Ghommem,et al.  Real-time tumor ablation simulation based on the dynamic mode decomposition method. , 2014, Medical physics.

[3]  Taras Gerya,et al.  Introduction to Numerical Geodynamic Modelling , 2010 .

[4]  J C Bischof,et al.  Investigation of the thermal and tissue injury behaviour in microwave thermal therapy using a porcine kidney model , 2004, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[5]  P R Stauffer,et al.  Phantom and animal tissues for modelling the electrical properties of human liver , 2003, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[6]  G. Bourantas,et al.  A meshless point collocation treatment of transient bioheat problems , 2014, International journal for numerical methods in biomedical engineering.

[7]  John G. Webster,et al.  Measurement and Analysis of Tissue Temperature During Microwave Liver Ablation , 2007, IEEE Transactions on Biomedical Engineering.

[8]  J. Zee.  Heating the patient : a promising approach ? , 2002 .

[9]  Jan J W Lagendijk,et al.  Prostate perfusion in patients with locally advanced prostate carcinoma treated with different hyperthermia techniques. , 2002, The Journal of urology.

[10]  K. Delman,et al.  The role of hyperthermia in optimizing tumor response to regional therapy , 2008, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[11]  Chris J. Diederich,et al.  Hyperthermia classic commentary: ‘Arrhenius relationships from the molecule and cell to the clinic’ by William Dewey, Int. J. Hyperthermia, 10:457–483, 1994 , 2009, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[12]  H. H. Pennes.  Analysis of tissue and arterial blood temperatures in the resting human forearm. , 1948, Journal of applied physiology.

[13]  Guirong Liu.  Mesh Free Methods: Moving Beyond the Finite Element Method , 2002 .

[14]  Karol Miller,et al.  Modified moving least squares with polynomial bases for scattered data approximation , 2015, Appl. Math. Comput..

[15]  B. Hooper.  Optical-thermal response of laser-irradiated tissue , 1996 .

[16]  I. Sbalzarini,et al.  Using DC PSE operator discretization in Eulerian meshless collocation methods improves their robustness in complex geometries , 2016 .

[17]  Gregory E. Fasshauer,et al.  Meshfree Approximation Methods with Matlab , 2007, Interdisciplinary Mathematical Sciences.

[18]  Ashleyj . Welch,et al.  Optical-Thermal Response of Laser-Irradiated Tissue , 1995 .

[19]  Louis Moresi,et al.  The accuracy of finite element solutions of Stokes's flow with strongly varying viscosity , 1996 .

[20]  Punit Prakash,et al.  Theoretical Modeling for Hepatic Microwave Ablation , 2010, The open biomedical engineering journal.