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

本项目关注在多晶制造不确定性下骨支架设计的优化方法的发展。在重大创伤、骨质疏松或骨肉瘤的情况下，可能发生临界大小的骨质流失，在常规治疗下，不团聚的可能性很高（即再生骨组织无法成功地桥接引入的空隙）。在这种情况下，必须引入支架形式的多孔材料来填补这个空隙。由于目前护理的黄金标准，自体移植物，确实有相当大的缺点，人工制造的替代品正在探索中。其中最有前途的替代品是生物可吸收的、生物相容性的、聚合物基的、添加剂制造的多孔骨支架。这种支架需要在新骨基质再生阶段保持空洞部位生理负荷条件下的结构完整性，同时不妨碍细胞扩散和血管化，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，可以为这些支架找到微结构和空间孔隙度分布的设计，以最佳地满足给定的标准。由于这种微结构涉及的规模较小，增材制造工艺在此类应用中接近其当前的技术极限，从而引入了与设计相当大的打印产品偏差。特别是，虽然这种不确定性中的一些可能是任意类型的，即遵循一个特征良好的概率分布，但在打印过程中引入的一些错误更难以量化，因此属于认知范畴，例如只能建立概率的界限（例如，由于使用计算机断层扫描对打印支架进行成像的困难）。因此，我们需要转向多态不确定度量化的方法。因此，我们的主要目标是利用最近在定量随机均质化方面的数学突破，为具有小长度尺度上材料特性随机任意扰动和中尺度上几何偏差的周期性骨支架导出有效的不确定性估计器和量身定制的数值方法。这些估计器将用作简化的替代模型（经过数值验证），从而允许有效地处理骨支架形状优化算法中的多态性不确定性。

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.