New Cardiovascular Indices Based on a Nonlinear Spectral Analysis of Arterial Blood Pressure Waveforms

A new method for analyzing arterial blood pressure is presented in this report. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schr\"odinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which includes negative eigenvalues and corresponds to the interacting components of an N-soliton. The approach is similar to a nonlinear Fourier transform where the solitons play the role of sine and cosine components. The method provides new cardiovascular indices that seem to contain relevant physiological information. We first show how to use this approach to decompose the arterial blood pressure pulse into elementary waves and to reconstruct it or to separate its systolic and diastolic phases. Then we analyse the parameters computed from this technique in two physiological conditions, the head-up 60 degrees tilt test and the isometric handgrip test, widely used for studying short term cardiovascular control. Promising results are obtained

Arterial blood pressure analysis based on scattering transform I

This article presents a new method for analyzing arterial blood pressure waves. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which includes negative eigenvalues and corresponds to the interacting components of an N-soliton. The approach is analogous to the Fourier transform where the solitons play the role of sinus and cosinus components. The proposed method seems to have interesting clinical applications. It can be used for example to separate the fast and slow parts of the blood pressure that correspond to the systolic (pulse transit time) and diastolic phases (low velocity flow) respectively

Input Impedance of the Arterial System Using Parametric Models

In this work, we propose to use parametric models for the estimation of arterial tree input impedance. The results of this new method are compared with those of the standard method based on the Fast Fourier Transform (FFT). The comparison is first made with pressure and flow measurements on a calf, then with human blood pressure measurements completed by blood flow data simulated from a soliton+windkessel model. The input impedance is calculated both at aorta and finger. As illustrated by the numerical results, the advantage of the proposed parametric method is its smooth impedance estimations, whereas the standard FFT method yields more disturbed results

New cardiovascular indices based on nonlinear spectral analysis of arterial blood pressure waveforms

A new method for analyzing arterial blood pressure is presented in this article. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which includes negative eigenvalues and corresponds to the interacting components of an N-soliton. The approach is similar to a nonlinear Fourier transform where the solitons play the role of sine and cosine components. The method provides new cardiovascular indices that seem to have meaningful physiological information, especially about the stroke volume and the ventricular contractility. We first show how to reconstruct the arterial blood pressure waves and separate its systolic and diastolic phases using this approach. Then we analyse the parameters computed from this technique in two physiological conditions, the head-up 60 degrees tilt test and the isometric handgrip test, widely used for studying short term cardiovascular control. Promising results are obtained

Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations

A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line / on-line strategy. Numerical examples are shown for the linear advection, KdV and FKPP equations, in one and two dimensions

Travelling-wave analysis and identification. A scattering theory framework

This article presents a new travelling waves analysis and identification method based on scattering theory. This inverse scattering technique consists in solving the spectral problem associated to a one-dimensional Schrödinger operator perturbed by a potential depending upon the wave to analyze, and optimized in order to approximate this wave by an isospectral flow in the sense of Lax. In this method, the interacting components of an N-soliton are the elementary travelling waves for the approximation. These N solitons play an analogous role to linear superpositions of sinus and cosinus in the Fourier analysis of standing waves. In the proposed analysis of travelling waves, low and high frequency components are replaced by low and high velocity components. Two applications of the method are presented. The first one concerns the identification of an N-soliton and is illustrated with N=3. The second one consists in the analysis of the arterial blood pressure waves during the systolic phase (pulse transit time) and the diastolic phase (low velocity flow)

Reduced-Order Modeling based on Approximated Lax Pairs

A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where the solution is searched for evolves according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive waves or front propagation. Numerical examples are shown for the KdV and FKPP (nonlinear reaction diffusion) equations, in one and two dimensions

Development, Validation, and Clinical Application of a Numerical Model for Pulse Wave Velocity Propagation in a Cardiovascular System with Application to Noninvasive Blood Pressure Measurements

High blood pressure blood pressure is an important risk factor for cardiovascular disease and affects almost one-third of the U.S. adult population. Historical cuff-less non-invasive techniques used to monitor blood pressure are not accurate and highlight the need for first principal models. The first model is a one-dimensional model for pulse wave velocity (PWV) propagation in compliant arteries that accounts for nonlinear fluids in a linear elastic thin walled vessel. The results indicate an inverse quadratic relationship (R^2=.99) between ejection time and PWV, with ejection time dominating the PWV shifts (12%). The second model predicts the general relationship between PWV and blood pressure with a rigorous account of nonlinearities in the fluid dynamics, blood vessel elasticity, and finite dynamic deformation of a membrane type thin anisotropic wall. The nonlinear model achieves the best match with the experimental data. To retrieve individual vascular information of a patient, the inverse problem of hemodynamics is presented, calculating local orthotropic hyperelastic properties of the arterial wall. The final model examines the impact of the thick arterial wall with different material properties in the radial direction. For a hypertensive subject the thick wall model provides improved accuracy up to 8.4% in PWV prediction over its thin wall counterpart. This translates to nearly 20% improvement in blood pressure prediction based on a PWV measure. The models highlight flow velocity is additive to the classic pressure wave, suggesting flow velocity correction may be important for cuff-less, non-invasive blood pressure measures. Systolic flow correction of the measured PWV improves the R2 correlation to systolic blood pressure from 0.81 to 0.92 for the mongrel dog study, and 0.34 to 0.88 for the human subjects study. The algorithms and insight resulting from this work can enable the development of an integrated microsystem for cuff-less, non-invasive blood pressure monitoring