Image-based biophysical modeling predicts cortical potentials evoked with subthalamic deep brain stimulation

Abstract

Background: Subthalamic deep brain stimulation (DBS) is an effective surgical treatment for Parkinson's disease and continues to advance technologically with an enormous parameter space. As such, in-silico DBS modeling systems have become common tools for research and development, but their underlying methods have yet to be standardized and validated.

Objective: Evaluate the accuracy of patient-specific estimates of neural pathway activations in the subthalamic region against intracranial, cortical evoked potential (EP) recordings.

Methods: Pathway activations were modeled in eleven patients using the latest advances in connectomic modeling of subthalamic DBS, focusing on the hyperdirect pathway (HDP) and corticospinal/bulbar tract (CSBT) for their relevance in human research studies. Correlations between pathway activations and respective EP amplitudes were quantified.

Results: Good model performance required accurate lead localization and image fusions, as well as appropriate selection of fiber diameter in the biophysical model. While optimal model parameters varied across patients, good performance could be achieved using a global set of parameters that explained 60% and 73% of electrophysiologic activations of CSBT and HDP, respectively. Moreover, restricted models fit to only EP amplitudes of eight standard (monopolar and bipolar) electrode configurations were able to extrapolate variation in EP amplitudes across other directional electrode configurations and stimulation parameters, with no significant reduction in model performance across the cohort.

Conclusions: Our findings demonstrate that connectomic models of DBS with sufficient anatomical and electrical details can predict recruitment dynamics of white matter. These results will help to define connectomic modeling standards for preoperative surgical targeting and postoperative patient programming applications.

Keywords: Biophysical modeling; Deep brain stimulation; Electrocorticography; Evoked potentials; Parkinson’s disease; Subthalamic nucleus.

Figure A.1.. Positional uncertainty was reduced with structural MRI lead localization.

(A) Average displacement between contact centers ($\Delta {\overline{d}}_{\mathit{move}}$) when the leads were localized with a postoperative T1-weighted (T1_post) image or an intraoperative CT (CT_intra) image. The black arrow points to Patient 2 depicted in the top panel. L = lateral, A = anterior, and S = superior. (B) The change in model performance compared to the magnitude of the positional shift when relocalized with T1_post. R² = coefficient of determination, CSBT = corticospinal/bulbar tract, and HDP = hyperdirect pathway. (C) Model performance across the cohort with T1_post or CT_intra. R² were indeterminate for CSBT in Patient 7, 10, and 11 because EP₀ was zero for all their settings.

Figure 1.. Individualized connectomic estimates of direct axonal activation.

(A) Anatomical models of corticospinal/bulbar tract (CSBT, reds) and hyperdirect pathway (HDP, blues) with the subthalamic nucleus (STN, green) overlaid. (B) Pathways warped into Patient 3’s preoperative T1w space with their lead overlaid. (C) Closeup of Panel B. Directions: L = lateral, S = superior, A = anterior. (D) Extracellular voltages applied to the pathways from a 1 mA of current applied between an active cathodic contact (2−, magenta) and a distal large return electrode on the contralateral shoulder (C+, not shown). Examples of (E) percent co-activation of CSBT and HDP, and (F) selective activation of HDP at 10 Hz.

Figure 2.. Electrocorticographical evaluation of direct axonal activation.

(A) Evoked potentials (EPs) recorded with subdural electrocorticography (ECoG) during subthalamic deep brain stimulation (DBS). The electrode strip spanned the premotor cortex, primary motor cortex (M1), primary sensory cortex (S1), and superior parietal lobule. White arrow points at the central sulcus. The bottom panel depicts an averaged EP trace for monopolar and bipolar electrode configurations, demonstrating that EPs are distinct from the stimulation artifact. EP₀ and EP₁ peaks are denoted. (B) EP₀ amplitude was correlated with modeled activation of the corticospinal/bulbar tract (CSBT, red) and EP₁ amplitude with the hyperdirect pathway (HDP, blue). Data from Patient 3. (C) Linear correlations between the EPs and the model pathway activation from Panel B. R² = Coefficient of Determination. Stimulation settings: IDs of anode (+) and cathode (−) / current amplitude / stimulus pulse width. Contact 0 is nearest to the tip of Medtronic Lead 3389.

Figure 3.. Model performance improved with increasing fiber diameter.

(A) Linear variation in evoked potential (EP) amplitudes explained by respective estimates of pathway activation. R² = coefficient of determination, CSBT = corticospinal/bulbar tract, and HDP = hyperdirect pathway with a diameter ratio of collateral to body of 1:3. (B) Accuracy in predicting activation (true positives) versus no activation (true negatives). Black arrows point to the median fiber diameter. (C) Top: individual examples of model performance by diameter and patient. Bottom: model performance with a general fiber diameter (12 μm, black arrows) compared to model performance when the optimal diameter was selected per patient (D_optimal). Patients 7, 10, and 11 are excluded (n = 8) for CSBT cases because their EP₀ was zero and unvarying, so R² was indeterminate.

Figure 4.. Model performance was optimal with all anatomical subdivisions.

(A) Anatomical subdivisions of the corticospinal/bulbar tract (CSBT, reds) and (B) the respective model performance using these subdivisions. Subthalamic nucleus (green). R² = coefficient of determination, L = lateral, P = posterior, and S = superior. ‘All’ is the combination of motor and limbic subdivisions (left), and the motor subdivision is further subdivided into the primary motor cortex (M1), supplementary motor area (SMA), and premotor cortex (right). (C and D) The same as A and B except for the hyperdirect pathway (HDP, blues). Asterisks denote statistical differences with a Kolmogorov-Smirnov test (α = 0.05). Note, Patients 7, 10, and 11 are excluded (n = 8) for CSBT cases because their EP₀ was zero and unvarying, so R² was indeterminate.

Figure 5.. Model errors were minimal with omnidirectional stimulation of pathways.

(A) Relative errors ((predicted value – actual value) / actual value) of evoked potential 1 (EP₁) collapsed across patients, and subdivided by electrode configuration (top) or type (bottom). (B) Model fits in patients with directional leads using all data (left), only data acquired during omnidirectional stimulation with a monopolar, ring electrode (middle), or only data acquired during directional stimulation with bipolar or segmented electrodes (right). R² = coefficient of determination. (C) Comparative model performance with only data from omnidirectional stimulation cases. Data from patients in B are emphasized (black arrow and lines). R² were indeterminate for CSBT in Patient 7, 10, and 11 because EP₀ was zero for all of their settings.

Figure 6.. Evoked potential (EP) amplitudes were maximal in the posterior STN.

(A) Variation in EP₀ (circles) and estimates of corticospinal/bulbar tract (CSBT) activation (squares) at 3 mA across the four (pseudo-)ring contacts in monopolar cathodic configurations. (B) The same as Panel A except for EP₁ and the hyperdirect pathway (HDP). (C and D) Similar to A and B, except for segmented contacts at three current amplitudes. Contact orientations: A = anterior, PM = posteromedial, PL = posterolateral, with PL and PM flipped across hemispheres. The six points per each combination of orientation and amplitude are the data collected from the two segmented contacts in Patients 4–6 with steerable DBS leads. Data from Patients 7, 9, and 11 are excluded (n = 8) because their data were only collected with bipolar contact configurations. Bonferroni corrections were applied to the Kolmogorov-Smirnov tests to account for multiple comparisons: α < 0.05 / 6 for A and B (4 rings choose 2) and α < 0.05 / 3 for C and D (3 segments choose 2).

Figure 7.. Patient-specificity was necessary for good model performance.

(A) Linear correlations between the normalized evoked potential (EP) amplitudes and their respective pathway activations aggregated across the entire cohort, where EP₀ (reds) and EP₁ (blues) were normalized by the respective range of amplitudes in each patient (i.e., (value – minimum value) / range of values) and expressed as a percentage. For comparison, the distribution of individual linear regression fits (dashed lines) for all patients are shown. R² = coefficient of determination, CSBT = corticospinal/bulbar tract (n = 8, left), and HDP = hyperdirect pathway (n = 11, right). (B) R² for aggregate fits (open squares) compared to respective patient-specific fits (filled circles). The black arrows point to the respective R² for aggregate fits.

Figure 8.. Eight standard ring settings explained the majority of variance in EP amplitudes.

Correlations between CSBT and the respective evoked potential (EP₀) amplitude for (A) Patient 1 and (B) all patients using all stimulation settings (red), only four monopolar ring electrode configurations (C+0−, C+1−, C+2−, and C+3−, maroon), only four bipolar ring configurations (1+0−, 2+1−, 3+2−, and 2+3, pink), or both monopolar and bipolar ring settings combined (gold). For restricted cases, the regression model was fit to only four or eight settings (enlarged and outlined in black), and then the coefficient of determination (R²) was calculated for all points. Pulse width = 60 μs, and amplitude = 5 mA unless specified otherwise (see Sources of variance). For electrode configurations, C, +, and − denote stimulation case, anode, and cathode, respectively. (C–D) The same as A–B for EP₁ and HDP, with the same stimulation setting for the full (blue) and restricted models (teal, purple, and cyan). CSBT = corticospinal/bulbar tract (n = 8), and HDP = hyperdirect pathway (n = 11). Asterisks denote statistical differences with a Kolmogorov-Smirnov test (α = 0.05).