Source term prediction in a multilayer tissue during hyperthermia

An Optimized Control Approach for HIFU Tissue Ablation Using PDE Constrained Optimization Method

High-intensity focused ultrasound (HIFU) is a widely used technique capable of providing noninvasive heating and ablation for a wide range of applications. However, the major challenges lie in the determination of the position and the amount of heat deposition over a target area. In order to assure that the thermal area is confined to tumor locations, an optimization method should be employed. Sequential quadratic programming and steepest gradient method with closed-form solution have been previously used to solve this kind of problem. However, these methods are complex and computationally inefficient. The goal of this article is to solve and control the solution of inverse problems with partial differential equation (PDE) constraints. Therefore, a distinguishing challenge of this technique is the handling of large numbers of optimization variables in combination with the complexities of discretized PDEs. In our method, the objective function is formulated as the square difference between the actual thermal dose and the desired one. At each iteration of the optimization procedure, we need to develop and solve the variation problem, the adjoint problem, and the gradient of the objective function. The analytical formula for the gradient is derived and calculated based on the solution of the adjoint problem. Several factors have been taken into consideration to demonstrate the robustness and efficiency of the proposed algorithm. The simulation results for all cases indicate the robustness and the computational efficiency of our proposed method compared to the steepest gradient descent method with the closed-form solution.

Estimation of the optimum number and location of nanoparticle injections and the specific loss power for ideal hyperthermia

Hyperthermia is one of the most appealing methods of cancer treatment in which the temperature of tumor is elevated to reach a desired temperature. One of the methods of increasing tissue temperature is injection of nanoparticle fluids to tumor and applying alternative magnetic field, which is called magnetic nanoparticle hyperthermia method. The total number of injection points, as well as the their location within a tissue play a significant role in this method. Furthermore, the power of heating of a magnetic material per gram or specific loss power (SLP) is another important factor which needs to be investigated. As the uniform temperature of 43 °C is effective enough for a tumor regression in certain specific tissues, the inverse method is applied to find out both the number of injection points and their location. Furthermore, the effective amount of heat generated by nanoparticles is investigated by this technique. Two-dimensional cancerous brain tissue was considered, zero gradients on boundary conditions were assumed, and diffusion equation and Pennes equation, which is regarded as energy equation, were solved, respectively. Conjugate gradient technique as a one way of inverse methods is applied, and unknowns are investigated. The results illustrate that three-point injection with the best injection sites cannot induce a uniform temperate distribution of 43 °C, and although four-point injection can create a uniform temperature elevation, the amount of it cannot reach the 43 °C. Finally, the optimum locations of five-point injection which are ((0.80,3.24), (0.80,0.84), (2.00,2.00), (3.20,3.24), (3.32,0.84)) (all dimensions are in mm) in the studied domain with special loss power of 420 W/g, all of which are obtained after 36 iterations, demonstrate that these conditions can meet the requirements of the magnetic fluid hyperthermia and can be considered for the future usage of researchers and investigators.