Constrained hierarchical modeling of degradation data in tissue-engineered scaffold fabrication

In tissue-engineered scaffold fabrication, the degradation of scaffolds is a critical issue because it needs to match with the rate of new tissue formation in the human body. However, scaffold degradation is a very complicated process, making degradation regulation a challenging task. To provide a scientific understanding on the degradation of scaffolds, we propose a novel constrained hierarchical model (CHM) for the degradation data. The proposed model has two levels, with the first level characterizing scaffold degradation profiles and the second level characterizing the effect of process parameters on the degradation. Moreover, it can incorporate expert knowledge in the modeling through meaningful constraints, leading to insightful inference on scaffold degradation. Bayesian methods are used for parameter estimation and model comparison. In the case study, the proposed method is illustrated and compared with existing methods using data from a novel tissue-engineered scaffold fabrication process. A numerical study is conducted to examine the effect of sample size on model estimation.