Computational advances for big data analytics and medical decision making
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With the increase in volume and complexity of data and evidence, medical decision making can be a complex process. Many decisions involve timeliness, uncertainties, and tradeoffs, and can have serious consequences for patients and the clinical practice. This dissertation aims to develop computationally efficient methods for big data analytics and medical decision making. We investigate three topics: the double pivot simplex method to advance linear programming solution techniques, the multiple isocenter selection problem in radiation therapy treatment planning, and the multi-objective treatment planning optimization problem. Chapter 1 advances the computation aspects of the double pivot simplex method by improving its computational efficiency and stability. The double pivot simplex method is a recent advancement to the simplex method which optimally solves linear programs. During any iteration, this algorithm pivots up to two variables at a time instead of one. An efficient implementation of double pivots is developed into LPSOL, a simplex solver for linear programs. We discuss a procedure to handle double pivots and bounded variables, a strategy to update the basis factorization with two variables simultaneously, and other topics related to numerical instability. On average, this implementation enabled double pivots to solve benchmark problems with nearly 30% fewer pivots and in better than 25% less time than the classical single pivots. In Chapter 2, we study the multiple isocenters placement problem in external beam radiation therapy treatment planning. In current treatment strategies, most plans use a single isocenter. Multiple isocenters can improve the dose conformity but their number and locations are difficult to determine. To address this issue, we propose a mathematical model which incorporates the tumor’s geometric characteristics to determine the number of isocenters. An approximation heuristic approach is developed to solve the isocenter selection problem. With the optimized isocenters, the treatment plans can achieve better conformity compared to single isocenter plans. In Chapter 3, we propose a radiation therapy treatment planning framework for stereotactic body radiation treatment (SBRT). Beam angles and the final aperture shapes are critical in developing feasible and deliverable radiation treatment plans. Here we propose the first treatment planning framework that combines the two by integrating the warm-start simultaneous beam angle and fluence map optimization (BAFMO) and direct aperture optimization (DAO). Both problems are multiple objective optimization problems. We introduce the matrix reduction technique to handle dense dose matrix for BAFMO and an approximation scheme for column generation in DAO. We further investigate the benefit of utilizing the optimized beam angle from the BAFMO and show that the final plans use 20% less total modular units (MU) of typical radiation doses.