Bayesian Inference Framework to Identify Skin Material Properties \textit{in vivo} from Active Membranes

Accurate in vivo characterization of skin mechanical properties is essential for diagnostics and treatment planning across dermatological and surgical applications. Existing noninvasive techniques are limited in capturing the nonlinear and anisotropic behavior of skin. In this work, we propose a Bayesian inference framework that leverages active membranes to induce desired deformations and infer patient-specific skin properties from a measured strain field. A finite element model of skin-membrane interaction, parameterized using the Holzapfel-Gasser-Ogden model, is used to generate strain field data under various membrane actuation conditions. To overcome the computational cost of repeated simulations required for Bayesian sampling, we construct a data-driven surrogate using principal component analysis for dimensionality reduction and Gaussian process regression for rapid evaluation. Our approach enables probabilistic inference of key skin parameters, including shear modulus, fiber stiffness, dispersion, and orientation. An advatange of the proposed method is that inference of skin biomechanics does not require direct force measurements. Rather, the method relies on known properties of active membranes (which can be tested ahead of time). The method does require strain field measurements. Through synthetic studies, we demonstrate that our method accurately recovers most model parameters even under moderate levels of spatially correlated noise, and that multi-frame or multi-membrane observations significantly enhance identifiability. These results establish the potential of active membranes as a viable platform for noninvasive, in vivo skin biomechanics assessment.