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

Alejandro Granados, Fernando Perez-Garcia, Martin Schweiger, Vejay Vakharia, Sjoerd B Vos, Anna Miserocchi, Andrew W McEvoy, John S Duncan, Rachel Sparks, Sébastien Ourselin

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
JournalInternational Journal of Computer Assisted Radiology and Surgery
Early online date9 Nov 2020
Publication statusE-pub ahead of print - 9 Nov 2020


  • Biomechanics
  • Brain deformation
  • Gaussian Processes


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