Geometric Paradigm for Nonlinear Neural Dynamics Modeling
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current technologies fail to precisely model and control nonlinear neural dynamics, which are crucial for understanding brain functions and treating neuropsychiatric disorders like depression and anxiety, as they lack a geometric paradigm for nonlinear modeling and decoding.
Innovation Solution
A geometric paradigm is introduced that identifies a nonlinear manifold using topological data analysis, learns dynamic models over this manifold, and creates geometric decoders and controllers to achieve precise control of neural dynamics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional linear modeling approaches are used for neural dynamics, then the model is simple and easy to implement, but it cannot accurately capture nonlinear brain network dynamics
Solution Approach 1:
The patent applies manifold learning to transform neural data from linear Euclidean space to curved nonlinear manifolds, allowing the model to capture the intrinsic geometric structure of neural dynamics. This curvature-based approach enables accurate representation of nonlinear brain network dynamics while maintaining computational tractability through geometric transformations.
Solution Approach 2:
The patent introduces covering spaces that map nonlinear manifolds to higher-dimensional linear spaces where standard linear modeling techniques can be applied. By lifting the problem to another dimension, the method combines the accuracy of nonlinear manifold representation with the simplicity of linear modeling in the covering space.
2Reliability
If open-loop deep brain stimulation is applied, then the system is simple to operate, but it lacks precision in controlling neural dynamics and achieving therapeutic effects
Solution Approach 1:
The patent implements closed-loop control by continuously monitoring neural dynamics through recorded signals, comparing them against the geometric model predictions, and adjusting stimulation parameters in real-time based on the deviations. This feedback mechanism enables precise control of neural dynamics to achieve desired therapeutic effects while adapting to individual patient responses.
Solution Approach 2:
The patent performs preliminary learning of the geometric dynamic model during a calibration phase before actual therapy delivery. This preliminary action establishes the patient-specific neural dynamics model and optimal control parameters in advance, enabling more effective and personalized treatment during subsequent therapeutic sessions.
Data Source
AI summary
A method for nonlinear modeling, decoding, and control of neural dynamics includes identifying, based on neural time-series samples, a type of a manifold as a base for a neural model. The method further includes learning, based on a covering space, a dynamic model that is fit on the manifold to create the neural model. The method further includes creating, using the neural model, a geometric decoder and a geometric controller.