Data-guided brain deformation modeling: evaluation of a 3-D adjoint inversion method in porcine studies

Biomechanical models of brain deformation are useful tools for estimating parenchymal shift that results during open cranial procedures. Intraoperative data is likely to improve model estimates, but incorporation of such data into the model is not trivial. This study tests the adjoint equations method (AEM) for data assimilation as a viable approach for integrating displacement data into a brain deformation model. AEM was applied to two porcine experiments. AEM-based estimates were compared both to measured displacement data [from computed tomography (CT) scans] and to model solutions obtained without the guidance of sparse data, which we term the best prior estimate (BPE). Additionally, the sensitivity of the AEM solution to inverse parameter selection was investigated. The results suggest that it is most important to estimate the size of the variance in the measurement error correctly, make the correlation length long and estimate displacement (over stress) boundary conditions. Application of AEM shows an average 33% improvement over BPE. This paper represents the first evidence of successful use of the AEM technique in three dimensions with experimental data validation. The guidelines established for selection of model parameters are starting points for further optimization of the method under clinical conditions.