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

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High intensity focused ultrasound (HIFU) is a widely used technique capable of providing non-invasive heating and ablation for a wide range of applications. However, the major challenges lie on 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 paper is to solve and control the solution of inverse problems with Partial Differential Equation (PDE) constrains. 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 of the actual thermal dose and the desired one. At each iteration of the optimization procedure, we need to develop and solve the variation problem, 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 simulations 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.

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering

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