Fig 1.
Flowchart diagram of OSS-DBS with its main CAD/CAE modules.
Communication between and within the modules is conducted via various Python scripts, which form the core of the platform. Solid line parallelograms depict mandatory input data, while dashed ones are optional.
Fig 2.
Example of an initial human brain discretization in OSS-DBS.
The model is divided into the region of interest (ROI), the vicinity of contacts and the rest of the tissue (ROT). All three have their own submeshes with different element size requirements. Additionally, submeshes are defined for the electrode contacts and the encapsulation layer away from them. Controlled surface refinement of the contacts leads to a highly dense submesh around the electrode. Here, the active contacts are depicted in red, while the floating conductors are presented as blue cylinders.
Fig 3.
Representation of axon arrays in OSS-DBS.
In the volume conductor model, an axon is defined as a sequence of points (nodes of Ranvier and internodal segments), with spacing dependent on axonal morphology. If at least one segment lies in the encapsulation layer (in red), cerebrospinal fluid or outside of the computational domain, the axon is excluded. (A) Ordered axon array employed for VTA estimations. (B) Realistically placed axons passing in the vicinity of the subthalamic nucleus derived from the fiber tractography of the rat brain [13].
Fig 4.
Dielectric properties of brain tissue in the frequency spectrum of a 60 μs rectangular pulse with a repetition rate of 130 Hz.
(A) Conductivity of grey and white matter. (B) Capacitive effect of brain tissue (ωε).
Fig 5.
Distribution of the rat brain tissue [13], mapped onto a tetrahedral mesh using OSS-DBS.
Grey and white matter are depicted with the corresponding colors, CSF is shown in blue and the encapsulation layer in red. The electrode lead is considered to be a perfect conductor and subtracted from the computational domain. (A) Tissue map for the whole brain. (B) Local mapping of the tissue before (left) and after (center) CSF refinement. The unmapped cells are depicted in green. For comparison, the segmented MRI data are shown on the right.
Fig 6.
Flowchart of adaptive mesh refinement.
Table 1.
Dielectric properties of brain tissue at 520 Hz [17].
Fig 7.
Results of voltage-controlled stimulation in the human brain tissue.
(A) Distribution of the brain tissue and a floating conductor (in green) on the adaptively refined mesh and the electric potential distribution on transversally aligned axons shown in one plane. Note that one of the axons was subtracted due to unrealistic placement. (B) Distribution of the electric potential magnitude on the ordered axon array. (C) Distribution of the electric field magnitude in the computational domain (log scale). The shape is evidently distorted by highly conductive CSF.
Fig 8.
Results of current-controlled stimulation in the rat brain tissue.
(A) Distribution of the brain tissue on the adaptively refined mesh. Note the coarse discretization on the periphery of the computational domain which is sufficient due to the fast decay of the electric field away from the electrode contacts. (B) Distribution of the electric potential magnitude on the realistically placed axons in the vicinity of the STN. (C) Electric potential magnitude difference on the axonal compartments computed with the OSS-DBS and COMSOL models.
Fig 9.
Electric potential distribution on a single axonal compartment during DBS with different computational models.
(A) Current-controlled stimulation in the rat model, computed with the EQS and the QS formulations, both without CPE. The difference arises from the capacitive charging in the former formulation. (B) Voltage-controlled stimulation with and without CPE in human model for the EQS formulation. The shape of the potential is affected by the high impedance of the electrical double layer at low frequencies.