Bayesian computer-aided experimental design of heterogeneous scaffolds for tissue engineering

L. E. Weiss, C. H. Amon, S. Finger, E. D. Miller, D. Romero, I. Verdinelli, L. M. Walker, P. G. Campbell

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


This paper presents a Bayesian methodology for computer-aided experimental design of heterogeneous scaffolds for tissue engineering applications. These heterogeneous scaffolds have spatial distributions of growth factors designed to induce and direct the growth of new tissue as the scaffolds degrade. While early scaffold designs have been essentially homogenous, new solid freeform fabrication (SFF) processes enable the fabrication of more complex, biologically inspired heterogeneous designs with controlled spatial distributions of growth factors and scaffold microstructures. SFF processes dramatically expand the number of design possibilities and significantly increase the experimental burden placed on tissue engineers in terms of time and cost. Therefore, we use a multi-stage Bayesian surrogate modeling methodology (MBSM) to build surrogate models that describe the relationship between the design parameters and the therapeutic response. This methodology is well suited for the early stages of the design process because we do not have accurate models of tissue growth, yet the success of our design depends on understanding the effect of the spatial distribution of growth factors on tissue growth. The MBSM process can guide experimental design more efficiently than traditional factorial methods. Using a simulated computer model of bone tissue regeneration, we demonstrate the advantages of Bayesian versus factorial methods for designing heterogeneous fibrin scaffolds with spatial distributions of growth factors enabled by a new SFF process.

Original languageEnglish (US)
Pages (from-to)1127-1139
Number of pages13
JournalCAD Computer Aided Design
Issue number11
StatePublished - Sep 15 2005
Externally publishedYes

Bibliographical note

Funding Information:
The authors gratefully acknowledge the funding of the Office of Naval Research (Grant no. N000140110766), the National Science Foundation (Grants no. CTS-0210238, CTS-0103082, and DMI-9800565), the National Institutes of Health (Grant no. 1 R01 EB00 364-01), the Pennsylvania Infrastructure Technology Alliance (PITA), a partnership of Carnegie Mellon, Lehigh University and the Commonwealth of Pennsylvania's Department of Community and Economic Development (DCED), the Health Resources and Services Administration (Grant no. 1C76 HF 00381-01), and the Scaife Foundation. We wish to thank Aventis Behring, L.L.C. (King of Prussia, PA) for their generous gift of lyophilized human fibrinogen and thrombin, and Matthews International Corp. (Pittsburgh, PA) for their generous donation of inkjet solenoid valves. We also acknowledge Dr Jeffrey Hollinger, Director of The Bone Tissue Engineering Center at Carnegie Mellon, for his insight on bone regeneration; Mr Larry Schultz and Dr Jason Smith for their assistance in the fabrication of matrices; and, Dr Greg Fisher for his assistance in imaging the scaffolds.


  • Bayesian modeling
  • Heterogeneous designs
  • Solid freeform fabrication
  • Tissue engineering


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