Intrinsic Frequency Analysis and Fast Algorithms

TL;DR

This paper provides a mathematical derivation of the Intrinsic Frequency (IF) method, introduces a significantly faster algorithm for its computation, and demonstrates its practical application in analyzing cardiovascular data and drug effects.

Contribution

It derives the IF method from fundamental equations and develops a fast algorithm that improves computation speed by over 100 times, with validation on real datasets.

Findings

The fast algorithm matches the accuracy of the brute-force method.

The new method significantly reduces computation time.

Correlations between IF features and drug infusion are observed.

Abstract

Intrinsic Frequency (IF) has recently been introduced as an ample signal processing method for analyzing carotid and aortic pulse pressure tracings. The IF method has also been introduced as an effective approach for the analysis of cardiovascular system dynamics. The physiological significance, convergence and accuracy of the IF algorithm has been established in prior works. In this paper, we show that the IF method could be derived by appropriate mathematical approximations from the Navier-Stokes and elasticity equations. We further introduce a fast algorithm for the IF method based on the mathematical analysis of this method. In particular, we demonstrate that the IF algorithm can be made faster, by a factor or more than 100 times, using a proper set of initial guesses based on the topology of the problem, fast analytical solution at each point iteration, and substituting the brute force algorithm with a pattern search method. Statistically, we observe that the algorithm presented in this article complies well with its brute-force counterpart. Furthermore, we will show that on a real dataset, the fast IF method can draw correlations between the extracted intrinsic frequency features and the infusion of certain drugs. In general, this paper aims at a mathematical analysis of the IF method to show its possible origins and also to present faster algorithms.