The purpose of the study was to develop a simulation approach for laser-induced thermotherapy (LITT) that is based on mathematical models for radiation transport, heat transport, and tissue damage. The LITT ablation was applied to ex vivo pig liver tissue. Experiments were repeated with different laser powers, i.e., 22-34 W, and flow rates of the cooling water in the applicator system, i.e., 47-92 ml/min. During the procedure, the temperature was measured in the liver sample at different distances to the applicator as well as in the cooling circuit using a fiber optic thermometer. For validation, the simulation results were compared with the results of the laser ablation experiments in the ex vivo pig liver samples. The simulated and measured temperature curves presented a relatively good agreement. The Bland-Altman plot showed an average of temperature differences of -0.13 C and 95%-limits-of-agreement of ±7.11C. The standard deviation amounted to ±3.63 C. The accuracy of the developed simulation is comparable with the accuracy of the MR thermometry reported in other clinical studies. The simulation showed a significant potential for the application in treatment planning.
We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three‐dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived via a homogenization of the geometry in 3D and a transformation of the three‐dimensional models to two dimensions. A shape optimization problem based on the tracking of heat absorption by the cooler and the uniform distribution of the flow through the microchannels is formulated and adapted to all models. We present the corresponding shape derivatives and adjoint systems, which we derived with a material derivative free adjoint approach. To demonstrate the feasibility of the reduced models, the optimization problems are solved numerically with a gradient descent method. A comparison of the results shows that the reduced models perform similarly to the original one while using significantly less computational resources.
We consider the optimization of a chemical microchannel reactor by means of PDE-constrained optimization techniques, using the example of the Sabatier reaction. To model the chemically reacting flow in the microchannels, we introduce a three- and a one-dimensional model. As these are given by strongly coupled and highly nonlinear systems of partial differential equations (PDEs), we present our software package cashocs which implements the adjoint approach and facilitates the numerical solution of the subsequent optimization problems. We solve a parameter identification problem numerically to determine necessary kinetic parameters for the models from experimental data given in the literature. The obtained results show excellent agreement to the measurements. Finally, we present two optimization problems for optimizing the reactor’s product yield. First, we use a tracking-type cost functional to maximize the reactant conversion, keep the flow rate of the reactor fixed, and use its wall temperature as optimization variable. Second, we consider the wall temperature and the inlet gas velocity as optimization variables, use an objective functional for maximizing the flow rate in the reactor, and ensure the quality of the product by means of a state constraint. The results obtained from solving these problems numerically show great potential for improving the design of the microreactor.
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