Human skin is a complex material to test and model as its physical and geometric properties depend on a host of parameters and conditions: thickness, location, age, ethnicity, hydration, etc. Skin tension plays a pivotal role in clinical settings, affecting scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension. Destructive testing of skin samples only gives a partial picture, as harvesting skin dehydrates the sample and releases its residual stress, which is likely to alter its behaviour significantly. Knowledge of the in vivo tension in skin will aid in preoperative reconstructive surgery planning, e.g., by providing safe limits of skin stress or accurately estimating the skin area required for repairs. Here, we develop and validate two methods to quantify the in vivo tension in skin using acoustic measurements. We find that it is possible to determine the difference in residual stress along in-plane directions on a patient-specific basis, using a simple in vivo measurement technique. Additionally, we find that coupling elastic wave measurements with machine learning (ML) models is a viable non-invasive method to determine in vivo skin tension.
Firstly, we model the skin as an incompressible, anisotropic hyperelastic material with one family of fibres, where the principal pre-stress is aligned along the fibres. A detailed analysis of the theoretical model reveals that the in-plane stress difference is related to the surface wave speeds, via a simple formula with a known error of less than 9%. The proposed formula is universal and depends on neither a specific energy density function nor material properties. We validate the formula with finite element (FE) simulations. We replicate the in vivo stress by applying a pre-stretch and induce a wave using an instantaneous impulse. We measure the wave speeds parallel and perpendicular to the fibres at various levels of pre-stress. We find that the error between the actual stress difference and that calculated with the formula is less than 3% for the simulations, which is within the range determined by the analytic model.
Secondly, we train a ML model that uses surface wave speed measurements to predict the in vivo skin tension. We create a large dataset consisting of simulated wave propagation experiments using an FE model. We then train a Gaussian process regression model to solve the inverse problem of predicting stress and pre-stretch in skin using the wave speed measurements. The ML model demonstrated good predictive performance, highlighting the feasibility of the method.
In vivo stress is difficult to estimate in general, however, the methods proposed here will enable on-demand patient-specific measurement of the in vivo stress in skin in a non-invasive manner. They are based on easily accessible parameters and could replace existing qualitative techniques with more accurate quantitative measurements, aiding preoperative reconstructive surgery planning and ultimately improving surgical outcomes.
This is joint work with Matt Nagle, Christelle Vedel, Wenting Shu, Michel Destrade, Michael Fop and Aisling Ní Annaidh.
