Constrained Varying-Coefficient Model for Time-Course Experiments in Soft Tissue Fabrication

Abstract

In the fabrication of artificial soft tissues, novel biomaterials with the required properties are obtained by appropriately adjusting process parameters during material synthesis. One key step in finding the desired material is understanding the relationship between the process parameters and the material properties, and time-course experiments are typically conducted for this purpose. This article proposes a constrained varying-coefficient modeling method for such data in which expert knowledge is properly accommodated in the model estimation to make the modeling practically meaningful. The proposed model has a semiparametric structure and incorporates expert knowledge in the form of constraints on model coefficients. Estimation algorithms based on a smoothing spline and a weighted smoothing spline are also provided. Finally, the proposed method is compared with existing methods in a case study and a numerical study.

KEYWORDS:

• Biomaterial fabrication
• Constrained modeling
• Time-course experiment
• Varying-coefficient model
• Weighted smoothing spline

Supplementary Materials

Online supplementary materials for this article include technical proofs, algorithms, and the data and R code used in the case study and the numerical study.

Acknowledgments

The authors sincerely thank the associate editor and two anonymous reviewers for their valuable comments and suggestions that helped improve this article.

Additional information

Funding

This work is supported by the National Science Foundation under grant CMMI-1634858.