Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.13452

In Silico Study for Optimizing Intensity and Focality Electrode Configurations for Directional DBS Under Uncertainty Using Metaheuristic L1L1 Method

Fernando Galaz Prieto·Antti Lassila·Maryam Samavaki·Sampsa Pursiainen
View original source ↗Read source document ↗Export metadata ↓

Abstract

Background and Objective: As Deep Brain Stimulation (DBS) advances toward directional leads and optimization-based current steering, selecting electrode contact configurations becomes complex. This study formulates configuration selection as an inverse mapping between target activation and electrode currents using metaheuristic L1-norm regularized L1-norm fitting (L1L1). L1L1 incorporates lead-field uncertainty arising from electrode placement, tissue properties, and forward modeling assumptions. Methods: The framework introduces lead-field perturbations and restricts the controllable domain through a sensitivity-based feasibility criterion within a finite element formulation derived using the Complete Electrode Model. Current distributions were optimized for 8- and 40-contact leads. Performance was evaluated using focused current density, nuisance current density, and their ratio under safety and sparsity constraints. Results: L1L1 was evaluated using noiseless and noisy lead fields, with noise selected to reflect attenuation within the volume of tissue activated. The method produced sparse, spatially selective stimulation patterns across perturbation levels. Hyperparameter optimization yielded bipolar or multipolar configurations. Compared with the Reciprocity Principle (RP), which produced strictly bipolar configurations, and Tikhonov-regularized least squares (TLS), which produced more distributed solutions, L1L1 enabled controlled transitions between sparse and multipolar patterns. It concentrated stimulation within the target while limiting unintended current spread, particularly under noisy conditions. Conclusions: L1L1 can assist specialists in optimizing DBS configurations. By incorporating uncertainty directly into optimization, it provides robust and interpretable current steering across lead configurations while accounting for forward-model variability.

Explore related subjects

math.OCcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Fernando Galaz Prieto, Antti Lassila, Maryam Samavaki, Sampsa Pursiainen. 2026-08-13. In Silico Study for Optimizing Intensity and Focality Electrode Configurations for Directional DBS Under Uncertainty Using Metaheuristic L1L1 Method. https://arxiv.org/abs/2506.13452

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Subpath-Based Column Generation for Electric Vehicle Routing Problems

Motivated by widespread electrification targets, this paper studies an Electric Vehicle Routing Problem with Time Windows and Nonlinear Charging (EVRPTWNL) that jointly optimizes routing-scheduling decisions and charging decisions given vehicle capacities, time windows and battery capacities. We develop a column generation scheme with a subpath-based label-setting algorithm that decomposes the pricing problem into two phases: (i) generating subpaths between charging stations, and (ii) combining subpaths into paths while optimizing charging decisions in between. We formalize a domination framework to establish the convergence and exactness of the algorithm, and prove that the methodology can solve a range of EVRP variants (e.g., with vehicle capacities, time windows, and nonlinear charging) and relaxation-tightening strategies (e.g., ng-relaxations and subset-row cuts). Computational results show improvements over path-based benchmarks in both computational time and solution quality, especially when time windows become wider, when vehicles can perform multiple tasks on a single charge and when vehicles still need to recharge several times across the planning horizon. Ultimately, the methodology can scale to otherwise intractable instances with up to 100 customers, thereby enhancing fleet management capabilities across electrified logistics areas.

math.OC↗
arXiv2026

Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they do not address \emph{complexity}: for broad operator classes described only through regularity (e.g.\ uniform continuity or $C^r$-regularity), information-theoretic lower bounds imply that minimax-optimal NO approximation rates scale \emph{exponentially} in the reciprocal accuracy $1/\varepsilon$. This has shifted the focus of NO theory toward identifying additional problem-specific structure, beyond regularity, under which suitably tailored NO architectures can leverage to unlock polynomial scaling in $1/\varepsilon$. We exhibit the first polynomial-scaling regime for NO approximations of solution operators in stochastic analysis; by identifying structured families of \emph{non-Markovian} BSDEs with randomized terminal condition parameterized by the Sobolev-regular terminal condition and by Sobolev-regular additive nonlinear perturbations of the generator. We prove that their solution operator can be approximated (uniformly over the family) by a tailored NO whose number of trainable parameters grows \emph{polynomially} in $1/\varepsilon$. We unlock this polynomial scaling regime by \emph{informing the NO's inductive bias} by factoring out the singular part of the associated semilinear elliptic PDE Green's function and by incorporating the Doléans--Dade exponential of the BSDE's common non-Markovian factor into the NO's decoding layers. As a byproduct, we extend polynomial-scaling guarantees from families of linear elliptic PDEs on regular domains to the semilinear setting.

math.OC↗
arXiv2026

The Competive Spectral Radius of Families of Nonexpansive Mappings

We consider a new class of repeated zero-sum games in which the payoff is the escape rate of a switched dynamical system, where at every stage, the transition is given by a nonexpansive operator depending on the actions of both players. This generalizes to the two-player (and non-linear) case the notion of joint spectral radius of a family of matrices. We show that the value of this game does exist, and we characterize it in terms of an infinite dimensional non-linear eigenproblem. This provides a two-player analogue of Mañe's lemma from ergodic control. This also extends to the two-player case results of Kohlberg and Neyman (1981), Karlsson (2001), and Vigeral and the second author (2012), concerning the asymptotic behavior of nonexpansive mappings. We discuss two special cases of this game: order preserving and positively homogeneous self-maps of a cone equipped with Funk's and Thompson's metrics, and translations of a finite dimensional normed space.

math.OC↗