Modeling carotid and radial artery pulse pressure waveforms by curve fitting with Gaussian functions

doi:10.1016/j.bspc.2013.01.003

Biomedical Signal Processing and Control

Volume 8, Issue 5, September 2013, Pages 449-454

https://doi.org/10.1016/j.bspc.2013.01.003 Get rights and content

Abstract

Modeling arterial pressure waveforms holds the potential for identifying physiological changes. There is a clinical need for a simple waveform analysis method with a high accuracy in reproducing the original waveforms. The aim of this study was to determine the accuracy of modeling carotid and radial pulses using Gaussian functions, making no physiological assumptions. Carotid and radial pulses were recorded from 20 normal volunteers. Ten consecutive beats from each volunteer were analyzed to determine beat-to-beat variability. Each pulse was decomposed using seven combinations of up to three Gaussian functions. The first function was always positive, but the second or third could be either positive or negative. Three positive Gaussian functions reproduced the original waveforms best with a mean absolute error (MAE) of 1.2% and 1.3% for the carotid and radial pulses respectively, and a maximum residual error of only 4.1% for both. This model had significantly smaller errors than any of the other six (all P < 0.001). Four positive Gaussian functions were then used to test the stability of this model. An insignificant change of the mean MAE (1.2% for both carotid and radial pulses) was obtained, showing that the stability has been reached with three positive Gaussian functions. The variability of MAE calculated as the standard deviation (SD) over the 10 beats was small at 0.2% for both pulses confirming the repeatability of using three positive Gaussian functions.

Highlights

► Optimum combination of Gaussian functions for pulse waveforms was determined. ► Three positive Gaussian functions accurately model both carotid and radial pulses. ► The mean absolute errors for carotid and radial pulses are both at the level of 1%. ► The maximum residual error for carotid and radial pulses are both only 4.1%.

Introduction

Developments in arterial hemodynamics have indicated that arterial pressure waveform contains more information than is visually available from peripheral measured sites (wrist, ear, finger, or toe) [1], [2], [3]. Due to the complicated arterial topology, arterial pressure waveforms vary between different measured sites. However, all sites contain information about the general function of the cardiovascular system. This includes indices describing left ventricular systolic function [4], arterial stiffness [5], dynamics of the autonomic nervous system and heart–vasculature interaction [6]. Therefore, contour analysis of the arterial pressure waveform could be an important tool to explore and assess changes in cardiovascular system function.

Many researchers have used various waveform analysis techniques to identify specific features of the arterial pressure waveform. The most common are by derivative methods, which use the first [7], second [8] or third derivatives [9] of the arterial pressure waveform, or by wave intensity analysis [10], [11], which analyzes vascular hemodynamics in terms of traveling energy waves. These techniques are simple and can be used in real-time analysis. However, none of these techniques analyzed the features of the complete arterial pressure waveform.

Researchers have also modeled the complete arterial pressure pulse using the Windkessel model from which compliance of the artery can be derived [12], [13], or used distributed models of the systemic arterial tree to reproduce pressure waveforms at various locations [14], [15], [16], or used waveform fitting techniques, which decompose the arterial pressure waveform into several independent sub-waveforms. Published waveform fitting approaches include Rubins’ method for analyzing simultaneously measured ear and finger blood volume pulse signals using four Gaussian functions [2], and Huotari's method for analyzing finger and toe photoplethysmographic (PPG) pulses using five logarithmic normal functions [17], [18]. Both studies have demonstrated that the Gaussian function parameters were highly related to cardiac hemodynamic parameters, including the augmentation index, the reflection index, arterial elasticity and vascular aging. In terms of the effectiveness of modeling, Rubins reported that the residual error between the measured pulse and the fitted function did not exceed 10%. Huotari's study provided only some examples with an average maximum residual error of 4%. However, none of those studies attempted to specifically evaluate the accuracy of model fitting. Furthermore, when component separation methods are used for contour analysis of the arterial pressure waveform, it is important to determine the best combination of fitting functions.

The aim of this study was to investigate the optimum combination of Gaussian functions that make up the arterial pressure waveform without any assumption about incident and reflection waves or any other physiological factor. Gaussian functions were used in this study because ventricular pressure induced by cardiac output has been shown to contain some Gaussian features [2]. We tested this modeling approach for both carotid artery pressure waveforms (CAPW) and radial artery pressure waveforms (RAPW) using between one and three Gaussian functions with different polarities.

Section snippets

Data acquisition

Twenty normal volunteers were enrolled in this study at Qilu Hospital of Shandong University (8 female and 12 male, mean age 51 years, range 32–73 years). The volunteers had not participated in any other ‘clinical trial’ within the previous three months. The basic clinical characteristics including age, height and weight were measured by an experienced operator. Manual auscultatory systolic and diastolic blood pressures (SBP and DBP) were also recorded from the right upper arm at the beginning

Results

Fig. 3 shows a waveform fitting example for the CAPW and RAPW from one volunteer. For each pulse waveform, the left panel shows the seven sets of Gaussian functions. The middle panel shows the original normalized pulse F(n) (bold dotted line) and the curve fitting result f(n) (solid line) obtained by summating the Gaussian functions, and the residual error is presented in the right panel. It is clearly shown that using 3 Gaussian functions was better than 2, which was better than only one. It

Discussion

The major finding of this study was that it was possible to accurately and reliably model both carotid and radial pulses using only three positive Gaussian functions. Previous studies of the contour analysis of the arterial pressure waveform have mainly employed the first derivative [7], second derivative [8], third derivative [9], wave intensity analysis [10], [11] and Windkessel model [12], [13] and distributed model [14], [15], [16]. Results from these studies are conflicting, such as for

Acknowledgements

We gratefully acknowledge the support of research grants from the National Natural Science Foundation of China (No. 61201049) and the China Postdoctoral Science Foundation funded project (No. 20110491593). The authors also would like to thank all of the volunteers for participating in this study.

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¹: Joint first authors: these authors contributed equally to this work.

View full text

Modeling carotid and radial artery pulse pressure waveforms by curve fitting with Gaussian functions

Abstract

Highlights

Introduction

Section snippets

Data acquisition

Results

Discussion

Acknowledgements

Artery Research

American Journal of Hypertension

Computers and Biomedical Research

Journal of Biomechanics

Contour analysis of the photoplethysmographic pulse measured at the finger

Journal of Hypertension

Finger and ear photoplethysmogram waveform analysis by fitting with Gaussians

Medical and Biological Engineering and Computing

Distal shift of arterial pressure wave reflection sites with aging

Hypertension

Pulse wave analysis of the aortic pressure waveform in severe left ventricular systolic dysfunction

Circulation: Heart Failure

The variability of the photoplethysmographic signal—a potential method for the evaluation of the autonomic nervous system

Physiological Measurement

Determination of age-related increases in large artery stiffness by digital pulse contour analysis

Clinical Science

Reduced systolic wave generation and increased peripheral wave reflection in chronic heart failure

American Journal of Physiology – Heart and Circulatory Physiology