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.

中文翻译：

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多组织脑变形的超弹性应变能量密度函数生成模型

 目的

脑变形的估计在神经外科手术中至关重要。虽然机械表征捕获了组织的应力-应变关系，但生物力学模型受到实验条件的限制。这导致文献中报道的变异性。这项工作的目的是证明应变能密度函数的生成模型可以使用观察到的大脑变形来估计组织的弹性特性。

 方法

对于生成模型，高斯过程回归从 73 篇手稿中学习弹性势。我们评估了 Neo-Hookean、Mooney-Rivlin 和 1 项 Ogden 元模型的使用，以保证稳定性。单个和多个组织实验验证了我们的生成模型在合成大脑模型和八个颞叶切除病例中估计组织特性的能力，其中在术前和术后图像之间观察到变形。

 结果

合成模型的估计参数接近已知参考，单组织和多组织实验的表面节点之间的均方根误差 (RMSE) 分别为 0.1 毫米和 0.2 毫米。在临床病例中，我们能够从术前和术后图像中恢复脑变形，将脑室表面的 RMSE 差异从 1.37 毫米减少到 1.08 毫米，切除腔表面的差异从 5.89 毫米减少到 4.84 毫米。

 结论

我们的生成模型可以捕获与组织机械特性相关的不确定性。当拟合来自弹性成像和线性研究的样本时，所有元模型的表现相似。 Ogden 元模型在超弹性研究中表现最好。我们能够预测合成模型上参考模型中的弹性参数。然而，使用我们的生成模型只能部分解释临床病例中观察到的变形。