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Abstract
Abstract Patient-specific surgical simulations require the patient-specific identification of the constitutive parameters. The sparsity of the experimental data and the substantial noise in the data (e.g., recovered during surgery) cause considerable uncertainty in the identification. In this exploratory work, parameter uncertainty for incompressible hyperelasticity, often used for soft tissues, is addressed by a probabilistic identification approach based on Bayesian inference. Our study particularly focuses on the uncertainty of the model: we investigate how the identified uncertainties of the constitutive parameters behave when different forms of model uncertainty are considered. The model uncertainty formulations range from uninformative ones to more accurate ones that incorporate more detailed extensions of incompressible hyperelasticity. The study shows that incorporating model uncertainty may improve the results, but this is not guaranteed.
Highlights
Constitutive models of soft tissues are crucial for computer-aided surgery, surgical training simulators, functional tissue engineering, and traumatic brain injury simulations (Humphrey, 2003; Madireddy et al, 2015; Hauseux et al, 2018; Bui et al, 2019; Duprez et al, 2020; Magliulo et al, 2020)
Six model uncertainty formulations are considered: 1. A random variable associated with a normal distribution with a constant mean and variance; 2
A random variable associated with a normal distribution with a linear input-dependent mean; 3
Summary
Constitutive models of soft tissues are crucial for computer-aided surgery, surgical training simulators, functional tissue engineering, and traumatic brain injury simulations (Humphrey, 2003; Madireddy et al, 2015; Hauseux et al, 2018; Bui et al, 2019; Duprez et al, 2020; Magliulo et al, 2020). Conventional probabilistic identification frameworks can identify parameter uncertainties, they are traditionally not formulated to account for the fact that the model itself is limited to describe the data. A well-accepted approach to include the uncertainty of models in probabilistic identification settings was presented by Kennedy and O’Hagan (KOH) (Kennedy and O’Hagan, 2001) This “KOH” framework was, for instance, employed in (Arhonditsis et al, 2008; Higdon et al, 2008; McFarland and Mahadevan, 2008; Sankararaman et al, 2011; Arendt et al, 2012). Different model uncertainty formulations have been considered These formulations range from uninformative to probabilistically more advanced ones, and from input-independent forms to formulations based on more advanced incompressible hyperelasticity. In this contribution, we consider synthetic data, so that we can make a quantitative comparison with the reference input. As this study is exploratory, we limit ourselves to tensile and compression data for which the model responses can be described by closed-form expressions
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