Mixed Integer Linear Programming for Active Contact Selection in Deep Brain Stimulation

TL;DR

This paper addresses the challenge of efficiently programming deep brain stimulation by formulating it as an optimization problem over target and constraint regions in the subthalamic nucleus. It introduces a mixed integer linear programming (MILP) framework that allows dissimilar current distributions across active contacts, and compares it to a linear programming (LP) baseline using data from ten Parkinson's disease patients. The MILP approach yields better adherence to the predefined activation profile, but incurs higher computational cost and shows limits when target regions are ill-defined or lead placement is suboptimal; LP offers far faster solutions and may align more closely with clinical practice under certain relaxation settings. The work demonstrates the trade-offs between activation accuracy and computation time and discusses future directions, including hybrid LP-MILP strategies and refined target definitions that incorporate patient-specific maps and white matter tracts to improve practical utility.

Abstract

Deep brain stimulation (DBS) programming remains a complex and time-consuming process, requiring manual selection of stimulation parameters to achieve therapeutic effects while minimizing adverse side-effects. This study explores mathematical optimization for DBS programming, using functional subdivisions of the subthalamic nucleus (STN) to define the desired activation profile. A Mixed Integer Linear Programming (MILP) framework is presented allowing for dissimilar current distribution across active contacts. MILP is compared to a Linear Programming (LP) approach in terms of computational efficiency and activation accuracy. Results from ten Parkinson's disease patients treated with DBS show that while MILP better matches the predefined stimulation target activation profile, LP solutions more closely resemble clinically applied settings, suggesting the profile may not fully capture clinically relevant patterns. Additionally, MILP's limitations are discussed, including its reliance on precisely defined target regions and its computational burden for larger target sets.

Figures (7)

• Figure 1: (a) An eight-contact Boston Scientific Vercise Cartesia™ Directional lead relative to the functional subdivisions of the STN Ewert2018 along with target (blue) and constraint (orange) points. The original set of points were taken from an atlas Ewert2018 and downsampled using a voxel filter with a voxel length of $0.95mm$. (b) The Abbot's Medical Infinity™ Directional lead with the contact nomenclature used in this study. The upper and lower contact rows are ring contacts, while the two middle rows consist of three segmented contacts (A,B,C) each.
• Figure 2: The distribution of current through all contacts under clinical settings. Values range between zero (light blue) and one (dark blue). Patient ID -- $x$-axis. Active contact -- $y$-axis.
• Figure 3: Dice-Sørensen coefficients comparing VTAs directly computed from the solution of the COMSOL model with VTAs reconstructed via superposition of individual contact solutions. The boxplot statistics were computed from a total of $23$ contact configurations across amplitudes from $0.5mA$ to $5mA$, including adjacent segmented contacts, three-segment rings, ring-segment pairings, and vertically misaligned combinations.
• Figure 4: The optimized current distributions for all ten patients, obtained using the LP formulation in \ref{['eq:LP']}, are shown for six different values of the constraint parameter $\theta$. The parameter $\theta$ determines the percentage of points in $\Omega_{\mathrm{c}}$ that must remain below the threshold $E_{\mathrm{th,c}}$. The color gradient from light blue ($\theta = 0$) to dark blue ($\theta = 1$) represents the proportion of the total applied current allocated to each contact.
• Figure 5: Optimized current distributions across all eight contacts computed from the MILP approach given in \ref{['eq:MILP']}. The values range from zero (light blue) to one (dark blue), representing the proportion of the total applied current allocated to each contact.