Dosimetry and hyperthermia computation in human tissues in presence of EM-waves using TLM method

Ijjeh, Abdelrahman; Makhlouf, Oualid; Cueille, Marylène; Dubard, Jean-Lou; Ney, Michel

doi:10.23919/eucap.2017.7928541

Cited by 3 publications

(2 citation statements)

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“…[7][8][9] Because of these advantages, TLM has become an increasingly popular method to solve problems in heat transfer in biological tissues. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] The limitation of the TLM method is that, for every control volume geometry, a new circuit node must be developed. The first developed TLM node formulation was for regular geometries (squares and cubes) 15,16 and was later expanded to include graded elements (rectangles and parallelepipeds) 11 and orthogonal curvilinear elements (such as cylinders).…”

Section: Introductionmentioning

confidence: 99%

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General node for transmission‐line modeling (TLM) method applied to bio‐heat transfer

Milan

Gebremedhin

2018

Int J Numerical Modelling

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Transmission‐line modeling (TLM) is a numerical method used to solve coupled partial differential equations in time domain. Using TLM, the equations of the problem and a small control volume are represented by an electric network composed of nodes. In this paper, a general TLM node theory for bio‐heat transfer that simplifies to existing node formulations is presented. This formulation allows for the use of irregular node geometries, such as irregular quadrangles and hexahedrons, which are necessary to accurately model complex geometries of biological systems. Using irregular hexahedron nodes, solutions of skin‐surface temperatures of a breast with tumor are demonstrated. This theory is based on 2 assumptions. The first is that the unit vector perpendicular to the border of the node is similar to the unit vector from the center of the node to the midpoint of its border, which is exact for regular geometries (eg, rectangles in 2‐D, and parallelepipeds in 3‐D) and approximated for most irregular geometries used in practice (eg, triangles and quadrangles in 2‐D, and tetrahedrons and hexahedrons in 3‐D). This first assumption does not, however, hold for all geometries such as 3‐D pyramids. The second assumption, which is controlled by an error parameter, is that the dispersive effect intrinsically modeled by the transmission‐line inductor is negligible compared with the diffusive effect modeled by the resistor of the node. This general TLM node formulation facilitates algorithm development and increases flexibility, increasing the applicability of TLM to solve complex geometric problems typical of most biological systems.

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Section: Introductionmentioning

confidence: 99%

“…The properties of the node and its elements give TLM its main advantages, which are stability and non‐requirement of matrix inversion for time‐domain solutions . Because of these advantages, TLM has become an increasingly popular method to solve problems in heat transfer in biological tissues …”

Section: Introductionmentioning

confidence: 99%