Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

In-vitro measurements coupled with in-silico simulations for stochastic calibration and uncertainty quantification of the mechanical response of biological materials

Mahmut Pekedis

TL;DR

The work addresses the challenge of calibrating constitutive models for biologic tissues with high inter-sample variability by coupling in-vitro tendon measurements with in-silico finite-element simulations using a likelihood-free approximate Bayesian computation (ABC) framework. A fiber-reinforced viscoelastic tendon model is calibrated specimen-by-specimen via Bayesian optimization and then used within ABC to quantify parameter uncertainty across distal, middle, and proximal sites from diabetic Achilles tendons. Results show rapid convergence of the optimization, identification of key parameters governing mechanical response (notablyEf, Em, and alpha_f), and posterior distributions that reproduce the observed variability in measurements. The approach provides a general, likelihood-free framework for stochastic calibration of constitutive models under varied geometries and loading conditions, with potential implications for personalized tendon mechanics and device design.

Abstract

This study proposes a simple and practical approach based on in-vitro measurements and in-silico simulation using the likelihood-free Bayesian inference with the finite element method simultaneously for stochastic calibration and uncertainty quantification of the mechanical response of biological materials. We implement the approach for distal, middle, and proximal human Achilles tendon specimens obtained from diabetic patients post-amputation. A wide range of in-vitro loading conditions are considered, including one-step and two-step relaxation, as well as incremental cyclic loading tests. In-silico simulations are performed for the tendons assuming a fiber-reinforced viscoelastic response, which is modeled for the ground matrix and fiber components. Initially, the calibration of the specimen-specific parameters is predicted using Bayesian optimization and the sensitivity of each parameter is evaluated using the Sobol index and random forest. Then, these parameters are used as priors, and coupled with in-vitro data in simulation-based approximate Bayesian computation to calibrate and quantify the uncertainty parameters for three loading cases. The results demonstrate that in-silico simulations using the posterior parameters of approximate Bayesian computation can capture the uncertainty bounds of in-vitro measurements. This approach provides a useful framework for stochastic calibration of constitutive material model parameters without the need to derive a likelihood function, regardless of the specimen's geometry or loading conditions.

In-vitro measurements coupled with in-silico simulations for stochastic calibration and uncertainty quantification of the mechanical response of biological materials

TL;DR

The work addresses the challenge of calibrating constitutive models for biologic tissues with high inter-sample variability by coupling in-vitro tendon measurements with in-silico finite-element simulations using a likelihood-free approximate Bayesian computation (ABC) framework. A fiber-reinforced viscoelastic tendon model is calibrated specimen-by-specimen via Bayesian optimization and then used within ABC to quantify parameter uncertainty across distal, middle, and proximal sites from diabetic Achilles tendons. Results show rapid convergence of the optimization, identification of key parameters governing mechanical response (notablyEf, Em, and alpha_f), and posterior distributions that reproduce the observed variability in measurements. The approach provides a general, likelihood-free framework for stochastic calibration of constitutive models under varied geometries and loading conditions, with potential implications for personalized tendon mechanics and device design.

Abstract

This study proposes a simple and practical approach based on in-vitro measurements and in-silico simulation using the likelihood-free Bayesian inference with the finite element method simultaneously for stochastic calibration and uncertainty quantification of the mechanical response of biological materials. We implement the approach for distal, middle, and proximal human Achilles tendon specimens obtained from diabetic patients post-amputation. A wide range of in-vitro loading conditions are considered, including one-step and two-step relaxation, as well as incremental cyclic loading tests. In-silico simulations are performed for the tendons assuming a fiber-reinforced viscoelastic response, which is modeled for the ground matrix and fiber components. Initially, the calibration of the specimen-specific parameters is predicted using Bayesian optimization and the sensitivity of each parameter is evaluated using the Sobol index and random forest. Then, these parameters are used as priors, and coupled with in-vitro data in simulation-based approximate Bayesian computation to calibrate and quantify the uncertainty parameters for three loading cases. The results demonstrate that in-silico simulations using the posterior parameters of approximate Bayesian computation can capture the uncertainty bounds of in-vitro measurements. This approach provides a useful framework for stochastic calibration of constitutive material model parameters without the need to derive a likelihood function, regardless of the specimen's geometry or loading conditions.

Paper Structure

This paper contains 14 sections, 15 equations, 20 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. In-vitro measurements
  4. Fiber reinforced visco elastic model
  5. In-silico simulations
  6. Bayesian optimization and sensitivity analysis
  7. Approximate Bayesian Computation
  8. Implementation procedures
  9. Results
  10. Bayesian optimization
  11. Sensitivity analysis
  12. Approximate Bayesian computation
  13. Discussion and Conclusions
  14. Acknowledgments

Figures (20)

  • Figure 1: Typical experimental in-vitro measurements observed for a specimen. (a) One-step relaxation. (b) Two-step relaxation. (c) Incremental cyclic loading
  • Figure 2: Specimen-specific parameter calibration steps using in-vitro measurements, in-silico simulations, and Bayesian optimization
  • Figure 3: Stochastic parameter calibration steps using in-vitro measurements, in-silico simulations and approximate Bayesian computation
  • Figure 4: Typical convergence plot of a specimen during Bayesian optimization
  • Figure 5: In-vitro (ground truth) and in-silico (simulation) observations of a typical sample with parameters tuned with Bayesian optimization.
  • ...and 15 more figures