Efficient Uncertainty Modeling for Additively Manufactured Polymer Scaffolds in Bone Tissue Engineering

该项目涉及在多变制造不确定因素下骨支架设计的优化方法的发展。在严重创伤、骨质疏松症或骨肉瘤的情况下，可能会发生临界大小的骨丢失，在传统治疗下，骨不愈合的可能性很高(即再生的骨组织无法成功桥接引入的空洞)。在这种情况下，必须引入支架形式的多孔材料来填补这一缺口。由于目前的黄金标准护理，即自体移植，确实有相当大的缺点，人们正在探索人工制造的替代品。最有前景的此类替代材料包括可生物吸收、生物兼容、聚合物基、可添加制造的多孔骨支架。在新骨基质的再生阶段，这种支架需要在生理载荷条件下保持空洞部位的结构完整性，同时不阻止细胞扩散和血管形成-这导致了相互竞争的优化目标。形状优化是一种自然的工具，以便为此类支架找到最佳满足给定标准的微结构和空间孔隙率分布的设计。由于这种微观结构所涉及的尺度很小，因此在这种应用中，添加剂制造工艺接近其当前的技术极限，从而引入了相当大的印刷产品与设计的偏差。具体地说，虽然这种不确定性中的一些可能是任意类型的，即遵循很好表征的概率分布，但是在打印过程中引入的一些误差更难量化，因此属于认知类别，其中例如只能建立概率的界限(例如，由于使用计算机层析成像打印支架的困难)。因此，我们需要转向多态不确定性量化的方法。因此，我们的主要目标是利用最近在定量随机均化方面的数学突破，推导出有效的不确定性估计器和定制的周期性骨支架的数值方法，所述周期性骨支架在小长度尺度上具有材料特性的随机任意扰动，在中观尺度上具有几何偏差。这些估计器将被用作简化的替代模型(在数字验证之后)，从而允许有效地处理骨支架形状优化算法中的多态不确定性。

This project concerns the development of optimization methods for the design of bone scaffolds under polymorphic manufacturing uncertainties. In the event of major trauma, osteoporosis, or osteosarcoma, a critical-size bone loss can occur, where - under conventional therapy - the likelihood for non-reunion (i.e., the failure of regenerated bone tissue to successfully bridge the introduced void) is high. In such cases, a porous material in the form of a scaffold has to be introduced to fill this gap. Since the current gold-standard of care, an autograft, does have considerable disadvantages, artificially manufactured replacements are being explored. Among the most promising such replacements are bioresorbable, biocompatible, polymer-based, additively manufactured, porous bone scaffolds. Such scaffolds need to maintain the structural integrity under the physiological loading conditions of the void site during the regeneration phase for new bone matrix, while not prohibiting cell diffusion and vascularization - this leads to competing optimization goals. Shape optimization is a natural tool in order to find designs for microstructures and spatial porosity distributions for such scaffolds that optimally fulfill the given criteria. Due to the small scales involved in such microstructure, the additive manufacturing process is near its current technology limits in such applications, whereby fairly large deviations of the printed product from the design are introduced. In particular, while some of this uncertainty may be of aleatoric type, i.e., following a well-characterized probability distribution, some errors introduced in the printing process are more difficult to quantify and thus fall in the epistemic category where for example only bounds on probabilities can be established (e.g., due to difficulties in imaging the printed scaffolds using computer tomography). We thus need to turn to the methods of polymorphic uncertainty quantification.Our main goal is thus to use the recent mathematical breakthroughs in quantitative stochastic homogenization to derive effective uncertainty estimators and tailor-made numerical methods for periodic bone scaffolds with a random aleatoric perturbation of material properties on small length scales and deviations of geometry on mesoscales. These estimators will be used as much simplified surrogate models (after numerical validation), thus allowing for an efficient treatment of the polymorphic uncertainty in shape optimization algorithms for bone scaffolds.