Efficient Uncertainty Modeling for Additively Manufactured Polymer Scaffolds in Bone Tissue Engineering
Abstract
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.
Bone tissue engineering, scaffold structures, additive manufacturing, quantitative stochastic homogenization, shape optimization.
