An excessive volume of normal tissues may be irradiated due to respiratory displacement in current standard radiation therapy of lung cancer. If motion of the lung can be predicted using biomechanical simulation, tumor tissues can be irradiated more accurately and precisely. A two-dimensional lung model is created from exhalation Computed Tomography (CT) images using image processing techniques. Lung deformation is modeled as an elastic material and simulated by a particle method. Influence of thoracic breathing and heartbeat are given as the boundary condition. The calculation results are compared with those of 4DCT data to evaluate calculation accuracy quantitatively.

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In this paper we deal with a discrete-time optimal control problem and propose a new algorithm which is mainly based on the solutions of Riccati equations of the associated accessory optimal control problems. In this algorithm the scheme for the existence of Riccati solutions is included in a simple and practical fashion. Some simulation experiments are illustrated to show the effectiveness of the proposed algorithm.

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