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Laser-induced thermotherapy is a local, minimally invasive treatment for liver tumors, which uses laser radiation to destroy targeted tissue. Many factors, such as the placement of the applicator(s), the length of the treatment and the amount of radiation introduced, affect the success of the treatment. In this work, we focus on controlling the amount of laser power applied during the treatment. This results in a PDE-constrained optimal control problem. Because such problems are computationally expensive to solve directly, a space-mapping approach is used. The coarse model used in the space-mapping method is derived through a novel linearization of the constraining equations and subsequently reduced using proper orthogonal decomposition. An example problem shows the viability of this approach. |
