Fractional Calculus Pacemaker Control for Heart Rate Dynamics
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Solution Overview
Problem
Current pacemaker control algorithms rely on linear state equations, which fail to accurately model the fractal behavior of heart rate variability, leading to inadequate regulation of heart rate dynamics.
Innovation Solution
The use of fractional differential equations and constrained finite horizon optimal control theory to develop a fractal approach for pacemaker control, allowing for fine-grain optimization of pacemaker response to heart rate variations through the calculus of variations, reducing the problem to a linear program for hardware implementation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If linear state equations are used to model heart rate dynamics, then the control algorithm is simple and computationally efficient, but the modeling accuracy of heart rate variability is insufficient
Solution Approach 1:
The patent changes the mathematical parameters from integer-order derivatives to fractional-order derivatives, transforming the model from linear to fractal-based. This parameter change enables accurate modeling of heart rate variability's self-similar, scale-invariant characteristics while maintaining a manageable control structure through the fractional differential equation framework
Solution Approach 2:
The patent replaces the traditional linear mechanical control model with a fractal-based mathematical model that better represents the physiological complexity of heart rate dynamics. This substitution allows the system to capture the inherent variability and adaptability of cardiac control without requiring overly complex algorithms
2Manufacturing precision
If fractional differential equations are used to model fractal dynamics, then the precision of heart rate regulation is improved, but the computational complexity increases
Solution Approach 1:
The patent segments the continuous fractional differential equation into discrete-time difference equations that can be computed iteratively. This segmentation allows the complex fractal model to be implemented in real-time pacemaker hardware through step-by-step computation of the fractional derivative terms using measured heart rate intervals
Solution Approach 2:
The patent introduces intermediate computational variables and approximation methods to bridge the gap between the theoretical fractional calculus model and practical digital implementation. These intermediaries enable the precise fractal modeling to be computed efficiently using standard digital signal processing techniques
3Ease of manufacture
If conventional linear control algorithms are used, then the device is easier to implement in hardware, but the regulation of heart rate dynamics is inadequate
Solution Approach 1:
The patent transitions from static linear control parameters to dynamic fractional-order parameters that adapt to the changing fractal characteristics of heart rate variability. This dynamic approach maintains hardware feasibility while significantly improving regulation effectiveness by allowing the control algorithm to respond to the inherent non-stationary nature of cardiac dynamics
Data Source
AI summary
Method and system for non-linear modeling of physiological behavior, such as R-R intervals, in implantable devices, such as a rate responsive pacemakers, comprising a comprehensive modeling and optimization methodology based on fractional calculus and constrained finite horizon optimal control theory that allows for allows for fine-grain optimization of pacemaker response to heart rate variations; and the theoretical basis on which a hardware implementation of the fractional optimal controller that can respond to changes in the heart rate dynamics. Present invention describes a fractal approach to pacemaker control based on the constrained finite horizon optimal control problem. This is achieved by modeling the heart rate dynamics via fractional differential equations. Also, by using calculus of variations, the invention describes how the constrained finite horizon optimal control problem can be reduced to solving a linear system of equations. Finally, the invention describes the theoretical basis on which a hardware implementation become possible.