The Modeling Analysis on Porous Media Hepatic Cancer for Microwave Ablation of an Interstitial Helix-Antenna

This research is concerned with microwave ablation analyses using a 2.45 GHz four-tine (4T) antenna for hepatic cancer tissue. In the study, three-dimensional finite-element models were utilized to examine the tissue temperature distributions during and after MW ablation. A preliminary study was first carried out with regard to the specific absorption rates along the 4T antenna insertion depths and the temperature distributions inside the solid and porous liver models with either 3 cm-in-diameter tumor or 5 cm-in-diameter tumor. Based on the preliminary results, the porous models were further examined for the effect of varying blood flow velocities (0–200 cm/s) with a 1 cm-in-diameter blood vessel next to the antenna and also for the effect of vessel-antenna locations (0, 0.8, and 1.3 cm) with a constant blood flow velocity of 16.7 cm/s. All scenarios were simulated under temperature-controlled mode (90°C). The findings revealed that the blood flow velocity and vessel location influence the ablation effectiveness and that increased blood flow inhibits heat transfer to the vessel wall. At the nearest and farthest vessel-antenna locations (0 and 1.3 cm), approximately 90.3% and 99.55% of the cancer cells were eradicated except for the areas adjacent to the vessel. In addition, total tissue thermal displacement is 5.9 mm which is 6.59% of the total length of the overall model.

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Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202518500252 ◽

2018 ◽

Vol 28 (05) ◽

pp. 953-978 ◽

Cited By ~ 16

Author(s):

Tobias Köppl ◽

Ettore Vidotto ◽

Barbara Wohlmuth ◽

Paolo Zunino

Keyword(s):

Porous Media ◽

Source Term ◽

Stationary Flow ◽

Porous Matrix ◽

Coupling Scheme ◽

Dimensional Model ◽

Modeling Analysis ◽

Flow Processes ◽

Darcy Equations ◽

Second Order Elliptic Problems

Many biological and geological systems can be modeled as porous media with small inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of such systems. In these applications, tissue, soil or rocks are considered to be porous media, while blood vessels, roots or fractures form small inclusions. To model flow processes in thin inclusions, one-dimensional (1D) models of Darcy- or Poiseuille type have been used, whereas Darcy-equations of higher dimension have been considered for the flow processes within the porous matrix. A coupling between flow in the porous matrix and the inclusions can be achieved by setting suitable source terms for the corresponding models, where the source term of the higher-dimensional model is concentrated on the center lines of the inclusions. In this paper, we investigate an alternative coupling scheme. Here, the source term lives on the boundary of the inclusions. By doing so, we lift the dimension by one and thus increase the regularity of the solution. We show that this model can be derived from a full-dimensional model and the occurring modeling errors are estimated. Furthermore, we prove the well-posedness of the variational formulation and discuss the convergence behavior of standard finite element methods with respect to this model. Our theoretical results are confirmed by numerical tests. Finally, we demonstrate how the new coupling concept can be used to simulate stationary flow through a capillary network embedded in a biological tissue.

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