Model-Based Comparison of Deep Brain Stimulation Array Functionality with Varying Number of Radial Electrodes and Machine Learning Feature Sets

Abstract

Deep brain stimulation (DBS) leads with radially distributed electrodes have potential to improve clinical outcomes through more selective targeting of pathways and networks within the brain. However, increasing the number of electrodes on clinical DBS leads by replacing conventional cylindrical shell electrodes with radially distributed electrodes raises practical design and stimulation programming challenges. We used computational modeling to investigate: (1) how the number of radial electrodes impact the ability to steer, shift, and sculpt a region of neural activation (RoA), and (2) which RoA features are best used in combination with machine learning classifiers to predict programming settings to target a particular area near the lead. Stimulation configurations were modeled using 27 lead designs with one to nine radially distributed electrodes. The computational modeling framework consisted of a three-dimensional finite element tissue conductance model in combination with a multi-compartment biophysical axon model. For each lead design, two-dimensional threshold-dependent RoAs were calculated from the computational modeling results. The models showed more radial electrodes enabled finer resolution RoA steering; however, stimulation amplitude, and therefore spatial extent of the RoA, was limited by charge injection and charge storage capacity constraints due to the small electrode surface area for leads with more than four radially distributed electrodes. RoA shifting resolution was improved by the addition of radial electrodes when using uniform multi-cathode stimulation, but non-uniform multi-cathode stimulation produced equivalent or better resolution shifting without increasing the number of radial electrodes. Robust machine learning classification of 15 monopolar stimulation configurations was achieved using as few as three geometric features describing a RoA. The results of this study indicate that, for a clinical-scale DBS lead, more than four radial electrodes minimally improved in the ability to steer, shift, and sculpt axonal activation around a DBS lead and a simple feature set consisting of the RoA center of mass and orientation enabled robust machine learning classification. These results provide important design constraints for future development of high-density DBS arrays.

Keywords: DBS; DBS lead; DBS programing algorithms; Deep brain stimulation; computational modeling; machine learning; neuromodulation.

Figure 1

DBSA lead design. DBSA leads were designed with two to nine electrodes per row. DBSA electrode width and radial separation were calculated for each lead design using Equations (1, 2). The DBSA–e3–h1.5 lead design is shown. Electrode height was 1.5 (shown), 1.0, or 0.5 mm.

Figure 2

Modeling axonal activation. Tissue voltage during stimulation was modeled for each stimulation configuration using the finite element method (A). The multi-compartment axon model population superimposed with extracellular potentials derived from the tissue voltage predictions (B). A spatial axonal activation profile, or region of activation (RoA) plot resulting from stimulation at 2.5 mA (C). RoA quantification using regional properties calculated from a closed binary image of the RoA plot (D).

Figure 3

Machine learning feature set generation. Machine learning features were extracted from simulation results spanning 15 monopolar stimulation configurations at simulation amplitudes ranging from 1 to 5 mA in 0.1 mA increments.

Figure 4

Stimulation amplitude limits. Maximum stimulation amplitude (for a biphasic waveform with a 90 μs initial pulse) was calculated for each lead design using a charge storage capacity of 150 μC/cm² and a safety factor limit of k = 2.0 (A). RoAs resulting from stimulation amplitude limits for several example DBSA lead designs (B).

Figure 5

Monopolar single-cathode lateral shift and aspect ratio. RoA lateral shift and aspect ratio for monopolar single-cathode stimulation using DBSA lead designs with 1.5 mm electrode height within the range of 1–5 mA. Similar RoAs were produced from all DBSA designs (A). As stimulation amplitude was increased, lateral shift and aspect ratio both increased at similar rates (B,C).

Figure 6

Monopolar single-cathode steering. Angular shift for monopolar single-cathode stimulation using DBSA lead designs with 1.5 mm electrode height within the range of 1 to 5 mA. DBSA leads with more electrodes were capable of finer RoA CoM angular shifting (A) in accordance with electrode angular separation (B).

Figure 7

Steering toward an offset target region. Steering activation toward a target region between electrodes was investigated using DBSA–e4–h1.5 with single-cathode and multi-cathode stimulation configurations (A). The multi-cathode configuration performed best with a 45° angular shift (B) and exhibited the largest overlap and smallest overspill for any given stimulation amplitude (C).

Figure 8

Incremental CoM shifting using monopolar multi-cathode stimulation. Monopolar stimulation currents were uniformly split across an increasing number of radial electrodes for each DBSA (A). DBSAs with more radial electrodes enabled shifting within the same range but at improved resolution (B). Aspect ratio decreased initially for DBSAs with more than 4-radial electrodes and increased from ~0.5 to 1 as the proportion of active electrodes increased (C).

Figure 9

Multi-cathode, non-uniform current shifting of the CoM. Monopolar stimulation currents uniformly split across an increasing number of radial electrodes using DBSA–e8–h1.5 compared to monopolar stimulation non-uniformly split across electrodes using DBSA–e4–h1.5 (A). Non-uniform configurations using DBSA–e4–h1.5 resulted in improved shifting resolution in comparison to uniform configurations using DBSA–e8–h1.5 (B). Aspect ratio profile was similar for the two strategies but was shifted for non-uniform current shifting indicating more circular RoAs were generated from non-uniform shifting (C).

Figure 10

Classification accuracy. Mean classification accuracy and accuracy standard error (represented by error bars) were calculated for each classifier/feature set combination across 10-folds. Perfect classification of monopolar stimulation settings was achieved with the random forest classifier using any of the three feature sets. The neural network, naïve Bayes and random forest classifiers achieved perfect or near perfect accuracy using the region properties feature set.

Figure 11

Feature importance. Sequential forward selection accuracy converged to one after the addition of features 1, 2, and 4 using both the neural network and naïve Bayes classifiers. From the random forest algorithm, the effect on classification error was increased most by the random permutation of features 1, 2, 3, and 4. Features 1: CoM x-coordinate, 2: CoM y-coordinate, and 4: ellipse fit orientation were found to be the most important features and using only these three features in combination with the neural network and naïve Bayes classifiers enabled perfect classification.