A generative model of hyperelastic strain energy density functions for multiple tissue brain deformation.

Purpose: Estimation of brain deformation is crucial during neurosurgery. Whilst mechanical characterisation captures stress-strain relationships of tissue, biomechanical models are limited by experimental conditions. This results in variability reported in the literature. The aim of this work was to demonstrate a generative model of strain energy density functions can estimate the elastic properties of tissue using observed brain deformation.

Methods: For the generative model a Gaussian Process regression learns elastic potentials from 73 manuscripts. We evaluate the use of neo-Hookean, Mooney-Rivlin and 1-term Ogden meta-models to guarantee stability. Single and multiple tissue experiments validate the ability of our generative model to estimate tissue properties on a synthetic brain model and in eight temporal lobe resection cases where deformation is observed between pre- and post-operative images.

Results: Estimated parameters on a synthetic model are close to the known reference with a root-mean-square error (RMSE) of 0.1 mm and 0.2 mm between surface nodes for single and multiple tissue experiments. In clinical cases, we were able to recover brain deformation from pre- to post-operative images reducing RMSE of differences from 1.37 to 1.08 mm on the ventricle surface and from 5.89 to 4.84 mm on the resection cavity surface.

Conclusion: Our generative model can capture uncertainties related to mechanical characterisation of tissue. When fitting samples from elastography and linear studies, all meta-models performed similarly. The Ogden meta-model performed the best on hyperelastic studies. We were able to predict elastic parameters in a reference model on a synthetic phantom. However, deformation observed in clinical cases is only partly explained using our generative model.