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Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Published on: August 12, 2018

Brain state in a convex body.

M Bohner¹, S Hui

¹Abteilung Math. V, Ulm Univ.

IEEE Transactions on Neural Networks

|January 1, 1995

Summary

This summary is machine-generated.

This study generalizes the brain-state-in-a-box (BSB) model for nonlinear systems with states in convex bodies. It provides conditions for stable equilibrium points, applicable to image reconstruction with multi-valued pixels.

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Area of Science:

Dynamical Systems Theory
Convex Geometry
Computational Neuroscience

Background:

The classical brain-state-in-a-box (BSB) model is limited to hypercube state spaces.
Generalizing BSB dynamics to arbitrary convex bodies offers broader applicability.
Nonlinear discrete dynamical systems are fundamental in various scientific fields.

Purpose of the Study:

To generalize the brain-state-in-a-box (BSB) model to systems with states in arbitrary convex bodies.
To characterize equilibrium points and stability conditions for these generalized systems.
To explore applications in areas like image reconstruction.

Main Methods:

Utilizing the support function of convex bodies to analyze equilibrium points.
Developing sufficient conditions for identifying stable equilibrium points.
Investigating the specific case of polytope state spaces for simpler results.

Main Results:

Characterizations of equilibrium points for generalized BSB models in convex bodies.
Sufficient conditions for stability of equilibrium points derived.
More precise and simpler results obtained for polytope state spaces compared to general convex bodies.
The generalized model provides a framework for multi-valued pixel states in image reconstruction.

Conclusions:

The generalized BSB model extends classical dynamics to complex state spaces.
The study provides analytical tools for understanding stability in nonlinear systems.
This work offers a novel approach for image reconstruction problems involving multi-valued data.