Biomedical Modelling and Simulation -towards Individual Models of the Human Cardiovascular System

• Yair Censor, University of Haifa ([email protected]). A unified approach to physical and equivalent uniform dose constraints in intensity-modulated radiation therapy (IMRT) via the split feasibility problem. Abstract The multiple-sets split feasibility problem requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. We propose and study a unified model for handling physical dose constraints and equivalent uniform dose (EUD) constraints appearing in the inverse problem of intensity-modulated radiation therapy (IMRT) treatment planning in a mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function but the optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraints sets. This guarantees convergence to a feasible solution if the split feasibility problem is consistent (i.e., has a solution) and convergence to a solution that minimally violates the physical dose constraints and the EUD constraints – otherwise. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme. • Magnus Borga, Linköping University ([email protected]). Canonical Correlation Analysis (CCA) and Adaptive Filtering Techniques in Functional Magnetic Resonance Imaging (fMRI) Abstract The functional processes of the human brain are still poorly understood although much effort has been focused on revealing its secrets. A relatively new and promising tool for this purpose is functional magnetic resonance imaging (fMRI). The purpose of fMRI is to map sensor, motor and cognitive functions to specific areas in the brain. The physical basis of the method is that oxygenated and deoxygenated blood have different magnetic properties, a difference that can be measured in an MR-scanner. As it is essential to capture the state of the brain at each volume acquisition, a very fast imaging sequence called echo planar imaging (EPI) is used. Unfortunately the EPI images suffer from low signal to noise ratio which makes the detection of active brain regions a challenging problem. Typically, less than 5the brain activity. Furthermore, the shape of the temporal activity pattern that is searched for is partly unknown. To cope with these problems, adaptive filtering methods can be employed.