Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

• Type of Material: Article
• Authors: Babak N Safa, Emory University; Michael H Santare, University of Delaware; Christopher Ethier, Emory University; Dawn M Elliott, University of Delaware
• Language: English
• Date: 2021-02-25
• Publisher: ELSEVIER SCI LTD
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
• License: Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International
• Final Published Version (URL): http://dx.doi.org/10.1016/j.actbio.2021.01.006
• Title of Journal or Parent Work: ACTA BIOMATERIALIA
• Volume: 123
• Start Page: 197
• End Page: 207
• Grant/Funding Information: NIBIB-NIH R01 EB002425, NEI-NIH R01 EY025286, and the Georgia Research Alliance.
• Keywords: Identifiability; Technology; Stress mechanics; Engineering; Science & Technology; Tendon; Optimization; Materials Science; Engineering, Biomedical; Materials Science, Biomaterials; Sclera

Abstract

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the “identifiability” or “uniqueness” of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.