Numerical modelling for simulation and treatment planning of prostate thermal therapy

Abstract

A 2D transmission line matrix model is used to study thermal transfer in living tissues exposed to laser energy. Damage size because of thermal coagulation in thermal treatment of benign prostate hyperplasia is determined quantitatively. Results show a quasilinear dependency of blood perfusion on temperature at the beginning of coagulation. Immediately thereafter, blood perfusion decreases considerably until it shuts down when the tissue under investigation has been coagulated. Increase in perfusion rate (ω) leads to high values of t 100 , which is the time required to reach a primary zone temperature of about 100°C, and reflects the increased cooling created by perfusion. The transmission line matrix numerical model predicts the coagulation damage contours; that way, it has a clinical interest in therapy as an aid for clinicians because damage cannot be easily measured within patients. Results are validated through comparison with other researches.

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

“…This paper presents a general TLM formulation for bio‐heat transfer that can be simplified to previously published formulations . This formulation assumes that the unit vector normal to the border of the node is similar to the unit vector pointing from the center of the node to the midpoint of the border (Equation ), which becomes exact for regular geometries such as rectangles and parallelepipeds.…”

“…It is important to note that, with minor modifications, Equations to can be simplified to the previously published formulations …”

“…It is important to note that, with minor modifications, Equations 3 to 15 can be simplified to the previously published formulations. [11][12][13][14][15][16][17][18][19] 2.2 | Scattering, connection, boundary conditions, initial conditions, temperature calculation, and heat flux calculation Scattering is computed as the resultant voltage in the impedances Z n of the Thévenin's equivalent circuit ( Figure 3) of the general TLM node circuit ( Figure 2):…”

“…Calculations were performed using the software TLMBHT 10 34 Because the formulation described in this study reduces to published formulations, it can be said that the following node geometries are already validated: lines [14][15][16]19 and graded lines 11 in 1-D; squares, [14][15][16][17][18] rectangles, 11 and triangles 12 in 2-D; cubes, [14][15][16] parallelepipeds, 11 and tetrahedrons 13 in 3-D. The validation performed in this paper is for non-previously described node elements, which are irregular quadrangle in 2-D ( Figure 4A), irregular hexahedron in 3-D ( Figure 4B), and pyramids in 3-D ( Figure 4C).…”

“…[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).…”