In-vitro measurements coupled with in-silico simulations for stochastic calibration and uncertainty quantification of the mechanical response of biological material
Makaleler > Tam Makale · 2025
Yazarlar: Mahmut PEKEDİS
arXiv, physics.med-ph, Hakemsiz Dergi, Uluslararası, Diğer Endeksler, 2025, cilt 0, ss 1-34
DOI: 10.48550/arXiv.2503.09900
Özet
<p>In the standard Bayesian framework, a likelihood function is required, which can be difficult or computationally expensive to derive for non-homogeneous biological materials under complex mechanical loading conditions. Here, we propose a simple and practical approach based on in-vitro measurements and in-silico simulations 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 this 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 separately 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, the bounds of these parameters are used as priors, uniformly sampled, and coupled with in-vitro data in simulation-based approximate Bayesian computations to calibrate and quantify the uncertainty parameters for three loading cases. The results demonstrate that increasing the number of loading scenarios improves the accuracy of the specimen-specific best- fit parameter set. Furthermore, approximate Bayesian inference shows that in-silico simulations using the posterior parameters, 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.</p>