Elsevier

Medical Engineering & Physics

Volume 48, October 2017, Pages 142-149
Medical Engineering & Physics

A new mathematical model of wrist pulse waveforms characterizes patients with cardiovascular disease – A pilot study

https://doi.org/10.1016/j.medengphy.2017.06.022Get rights and content

Abstract

The purpose of this study was to analyze and compare a series of measured radial pulse waves as a function of contact pressure for young and old healthy volunteers, and old patients with cardiovascular disease. The radial pulse waves were detected with a pressure sensor and the contact pressure of the sensor was incremented by 20 gf during the signal acquisition. A mathematical model of radial pulse waveform was developed by using two Gaussian functions modulated by radical functions and used to fit the pulse waveforms. Then, a ratio of area (rA) and a ratio of peak height (rPH) between percussion wave and dicrotic wave as a function of contact pressure were calculated based on fitted parameters. The results demonstrated that there was a maximum for waveform peak height, a minimum for rA (rAmin) and a minimum for rPH (rPHmin) appeared as contact pressure varied. On average, older patients had higher peak amplitude and a significantly smaller rAmin (p < 0.001) and rPHmin (p < 0.02) than the young and old volunteers. The rAmin and rPHmin calculated with the mathematical model had moderate to strong positive linear correlations (r = 0.66 to 0.84, p < 0.006) with those directly calculated without the model. The receiver operating characteristic (ROC) analysis showed that the rAmin calculated with the model and the contact pressure measured at the rAmin had good diagnostic accuracy to distinguish healthy volunteers vs. diseased patients. Therefore, using the mathematical model to quantitatively analyze the radial pulse waveforms as a function of contact pressure could be useful in the diagnosis of cardiovascular diseases.

Introduction

Radial pulse waves can be measured by a pressure sensor mounted on the wrist over the radial artery and provide important physiological information of a patient [1]. It is an innovative method to perform safe and fast physical testing without burden [2]. The characteristics of pulse waves could directly reflect the cardiovascular condition of patients [3] and are crucial for the development of novel tools for cardiovascular assessment. By using advanced electronic detectors, a series of pulse waves may be acquired and analyzed to obtain quantitative results regarding a patient's physiological and pathological information [4], [5], [6].

In 2000, Yoon et al. [7] characterized the relationship between the pulse peak amplitude and the contact pressure measured from the left radial artery demonstrating that there was a maximum pulse peak amplitude as contact pressure varied that could be used for diagnostic purposes. Similarly, Kim et al. [8] proposed an algorithm to classify the measurements of the floating pulse (a pulse potent when felt with no pressure applied but impotent when felt with pressure applied) and sunken pulse (a pulse impotent when felt with no pressure applied but potent when felt with pressure applied) versus contact pressure, and found that subjects in the sunken pulse group had a significantly higher body mass index than those in the floating pulse group. In contrast to varying the contact pressure, other techniques have been developed to assess the pulse depth (the depth of maximum pulse feeling with figures), based on, for example, the displacement of the skin's surface [9], [10], the width of the artery [11], and the effect of contact force in the context of pulse transit time measurements [12]. Moreover, the concept of contact pressure measurements is not limited to radial pulse measurements. In the work of Forouzanfar et al. [13], for example, the effect of external pressure applied with a cuff on non-invasive arterial pressure measurements was investigated. The influence of contact pressure on the variation of pulse morphology may provide new features that reflect the characteristics of cardiovascular system.

The radial pulse waves have been analyzed in many different ways to study heart disease and/or related problems [14], [15], [16], [17]. Some ideas for analyzing the radial pulse waves were adopted from the analysis of pressure waves [18], [19]. The sub-endocardial viability ratio and augmentation index calculated by the area ratio and peak height ratio of reflected wave and forward wave, respectively, were often used in radial pulse waves analysis to evaluate the cardiovascular conditions [20,21].

In addition to direct calculations, mathematical models are often used to fit the waveforms prior to any calculations. The sum of two Gaussian functions is a popular model used to fit the waveforms because of its bell shape that is similar to an individual pulse wave [22], [23]. Unfortunately, the sum of two Gaussian functions could not fit the waveform precisely. Goswami et al. [24] improved the fitting at the rising edge of waveform by using two Rayleigh functions. Furthermore, mathematical models using three or multi-Gaussian functions [15], [25], sums of sinusoids (with slowly varying amplitudes, phases, and frequencies) [26], [27], and piecewise Gaussian-cosine functions [28] were all proposed to fit the waveforms. Although the waveforms were fitted more accurately by using more functions with more parameters, it is hard to compare the parameters between experiments due to potential overfitting issues.

In this study, the radial pulse waveforms as a function of contact pressure were acquired from young and old healthy volunteers and old patients diagnosed with cardiovascular disease. A new mathematical model of radial pulse waveform was developed by using two Gaussian functions modulated by rational functions and then fitted to the pulse waveforms. The areas and peak heights of the percussion and dicrotic waves were calculated by using fitted parameters. The ratios of area and ratios of peak height between the percussion wave and dicrotic wave as a function of contact pressure were used to characterize the healthy volunteers and patients with cardiovascular disease.

Section snippets

Subjects

A total of 16 young healthy volunteers (mean age = 23.4 years, range 21-26 years), 15 old volunteers (mean age = 67.8 years, range 56–85 years) without known cardiovascular disease, and 14 old patients (mean age = 69.8 years, range 55–86 years) diagnosed with cardiovascular disease, participated in this study. All of the patients had cardiac insufficiency and five of these patients also had a myocardial infarction. All participants gave their informed consent, and were recruited from Northeastern

Results

Fig. 2(a)–(c) shows three typical examples of measured radial pulse waveforms (dots) and corresponding fits (red line) by our newly developed mathematical model. The areas governed by the two modulated Gaussians functions are representing the percussion wave (green line) and dicrotic wave (blue line), respectively. The pulse waveforms could be accurately fitted by the mathematical model, except for that it could not separate tidal wave from percussion wave due to a limited number of functions.

Discussion

The pulse waveforms were analyzed by using the newly developed mathematical model for young and old healthy volunteers without known heart problem, and old patients diagnosed with heart problems. By using the mathematical model, the peak heights and areas of percussion wave and dicrotic wave can be calculated more accurately. The preliminary results demonstrated that the ratio of area between percussion wave and dicrotic wave was the best parameter to separate between the three groups of

Conflicts of interest

None declared.

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 61374015 and 61202258), the Liaoning Natural Science Foundation (No. 20170540312), and the Fundamental Research Funds for the Central Universities (Nos. N161904002 and N130404016).

Ethical approval

The study was approved by the Institutional Review Board of Northeastern University in Shenyang, China.

Acknowledgments

One of the authors (DH) wishes to acknowledge the support of China Scholarship Council (CSC) for his scholarship to study abroad. We would like to thank Ms. Erica Markiewicz for carefully reading the manuscript.

References (35)

  • JeonY.J. et al.

    A clinical study of the pulse wave characteristics at the three pulse diagnosis positions of Chon, Gwan and Cheok

    Evid Based Complem Alternat Med

    (2011)
  • A.L. Pauca et al.

    Prospective evaluation of a method for estimating ascending aortic pressure from the radial artery pressure waveform

    Hypertension

    (2001)
  • WangP. et al.

    A compound pressure signal acquisition system for multichannel wrist pulse signal analysis

    IEEE Trans Instrum Meas

    (2014)
  • YoonY.Z. et al.

    Pulse type classification by varying contact pressure

    IEEE Eng Med Biol Mag

    (2000)
  • KimJ.U. et al.

    Novel diagnostic algorithm for the floating and sunken pulse qualities and its clinical test

    Evid Based Complem Alternat Med

    (2011)
  • BaeJ.H. et al.

    New assessment model of pulse depth based on sensor displacement in pulse diagnostic devices

    Evid Based Complem Alternat Med

    (2013)
  • LeeB.J. et al.

    Association of hypertension with physical factors of wrist pulse waves using a computational approach: a pilot study

    BMC Complem Altern Med

    (2015)
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