Stochastic modeling of tissue engineering scaffolds with heterogeneous porosity levels
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In this thesis, the internal architecture of the scaffolds is optimized based on a given distribution and porosity level function. The discrete porosity levels are used to determine required expected number of pores for each region of the scaffold. Random design variables are used to model the distribution of pores biomimetically. Because of the randomness of the distribution of pores, overlapped pores must be determined for calculating the porosity levels accurately. A new computational method based on simulation has been developed to calculate the expected overlapped volumes. A numerical method also developed to check the accuracy of the computational method on a simple example. Using the calculated overlapping factors, the required numbers of spheres are determined to satisfy the required porosity levels at each region. The presented methods are implemented in a computing environment and implementations are presented.