Graph Total Variation for Cardiac Surface Potential Reconstruction
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Solution Overview
Problem
Current methods for reconstructing cardiac surface potentials from body surface measurements, such as those using the method of fundamental solutions or Tikhonov regularization, suffer from smoothing effects that lose sharp spatial details, leading to inaccurate representations of electrophysiological signals.
Innovation Solution
The use of graph total variation (GTV) regularization, which incorporates information about the graph structure of the heart surface and imposes sparsity constraints on neighboring nodes, allows for the calculation of derivatives on irregular meshes and provides a fast solver to compute inverse solutions more accurately, thereby recovering sharper R waves and reducing smoothing effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional reconstruction methods (method of fundamental solutions or Tikhonov regularization) are used, then the reconstruction process is computationally simpler, but the spatial resolution and sharpness of electrophysiological signals are degraded due to smoothing effects
Solution Approach 1:
The patent changes the regularization parameter from traditional L2-norm (Tikhonov) to graph total variation norm, which fundamentally alters the mathematical properties of the reconstruction. This parameter change enables preservation of sharp spatial details while maintaining computational tractability through the graph-based formulation that exploits the discrete structure of cardiac surface meshes
Solution Approach 2:
The patent replaces traditional continuous mathematical operators with discrete graph-based operators suitable for irregular meshes. By substituting continuous differential operators with graph Laplacian and graph gradient operators, the method adapts the reconstruction algorithm to work naturally with the discrete topology of cardiac surface representations, thereby achieving high spatial resolution without requiring complex continuous formulations
2Manufacturing precision
If graph total variation regularization is used, then the spatial resolution and sharpness of R waves are improved, but the computational complexity increases due to iterative ADMM optimization
Solution Approach 1:
The patent segments the cardiac surface into discrete graph nodes and edges, allowing the reconstruction problem to be decomposed into localized operations. The graph structure enables independent computation at each node while maintaining global consistency through the optimization framework, which accelerates convergence compared to traditional methods
Solution Approach 2:
The patent introduces an intermediary graph structure that mediates between the measured body surface potentials and the reconstructed cardiac surface potentials. This graph-based intermediate representation facilitates efficient computation by providing a structured pathway for information flow and enabling the use of specialized graph algorithms that converge faster than general-purpose optimization methods
Data Source
AI summary
Systems and methods for graph total variation (GTV) based reconstruction of electrical potentials on a cardiac surface are disclosed. GTV-based systems and methods incorporate information about the graph structure of the heart surface as well as imposing sparsity constraints on neighboring nodes. To this end, the present disclosure uses a novel way of calculating derivatives on irregular meshes, and provides a fast solver to compute an inverse solution more efficiently than in previous systems and methods. Moreover, fast-changing signals can be recovered with less smoothing and thus greater fidelity to the original signals.