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Influence of Uncertainties in the Material Properties of Brain Tissue on the Probabilistic Volume of Tissue

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Christian Schmidt, Peadar Grant,  Madeleine Lowery,  Ursula Van Rienen
Volume: 60, Issue: 5, Page: 1378 – 1387

Deep brain stimulation (DBS) has evolved as a widely employed procedure to treat the symptoms of motor skill disorders such as Parkinson’s disease, essential tremor and dystonia. Although successfully employed across various clinical fields, the fundamental mechanisms of the action of DBS remain uncertain. Starting in the last decade, many computational models to gain insight into these mechanisms have been developed. However, the model parameters are subject to uncertainty and knowledge on how this uncertainty influences the predicted neural activation is scarce. This additional information on the probability distribution of the extent of neural activation could help engineers as well as clinicians in evaluating the actual activated area and rating the likelihood of undesired activation. However, uncertainty quantification for these models with classical methods such as Monte Carlo simulation is computational intensive.

We propose the application of the polynomial chaos technique for the uncertainty quantification of the neural activation in a human brain model for DBS. A non-intrusive projection method  was used to approximate the probabilistic volume of tissue activated (VTA)  by a multi-dimensional polynomial expansion. The method has the advantage to require only the evaluation of the deterministic model on the nodes of a multi-dimensional cubature grid used for the computation of the expansion coefficients, which substantially reduces the computational intense if only a small number of uncertain model parameters is considered. The deterministic model combines a finite element model based on a digital brain atlas and a multi-compartmental model of mammalian nerve fibres. The material properties of brain tissue were modelled as uniform random parameters using data from several experimental studies. The results suggest that the major contribution to the uncertainty of the VTA arises from uncertainties in the conductivity of brain tissue and lead to the conclusion that the uncertainty in these model parameters should be considered in volume conductor models of DBS.

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