Original Article

Application of the N-Point Moving Average Method for Brachial Pressure Waveform–Derived Estimation of Central Aortic Systolic PressureNovelty and Significance

Yuan-Ta Shih, Hao-Min Cheng, Shih-Hsien Sung, Wei-Chih Hu, Chen-Huan Chen
https://doi.org/10.1161/HYPERTENSIONAHA.113.02229
Hypertension. 2014;63:865-870
Originally published March 12, 2014

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Abstract

The N-point moving average (NPMA) is a mathematical low-pass filter that can smooth peaked noninvasively acquired radial pressure waveforms to estimate central aortic systolic pressure using a common denominator of N/4 (where N=the acquisition sampling frequency). The present study investigated whether the NPMA method can be applied to brachial pressure waveforms. In the derivation group, simultaneously recorded invasive high-fidelity brachial and central aortic pressure waveforms from 40 subjects were analyzed to identify the best common denominator. In the validation group, the NPMA method with the obtained common denominator was applied on noninvasive brachial pressure waveforms of 100 subjects. Validity was tested by comparing the noninvasive with the simultaneously recorded invasive central aortic systolic pressure. Noninvasive brachial pressure waveforms were calibrated to the cuff systolic and diastolic blood pressures. In the derivation study, an optimal denominator of N/6 was identified for NPMA to derive central aortic systolic pressure. The mean difference between the invasively/noninvasively estimated (N/6) and invasively measured central aortic systolic pressure was 0.1±3.5 and −0.6±7.6 mm Hg in the derivation and validation study, respectively. It satisfied the Association for the Advancement of Medical Instrumentation standard of 5±8 mm Hg. In conclusion, this method for estimating central aortic systolic pressure using either invasive or noninvasive brachial pressure waves requires a common denominator of N/6. By integrating the NPMA method into the ordinary oscillometric blood pressure determining process, convenient noninvasive central aortic systolic pressure values could be obtained with acceptable accuracy.

Introduction

See Editorial Commentary, pp 665–667

Although noninvasive blood pressure (BP) measured in the brachial artery (cuff BP) represents the basis for the present management of hypertension,1–3 it has long been recognized that waveform morphology4–6 and BP5,7–10 differ considerably between the central aorta and peripheral arterial system. These discernible differences vary among individuals because of variable timing and amplitude of arterial wave reflections.11 More importantly, central systolic and pulse pressure (CBP) may predict cardiovascular outcomes more accurately than cuff BP.12,13

The clinical application of CBP has been made possible by the advances in computational science and biomedical engineering. Noninvasive CBP is obtained using either tonometry-based5,14,15 or, more conveniently, cuff-based techniques.16–18 Recently, the capability of the N-point moving average (NPMA) method to estimate central aortic systolic BP (SBP-C) was demonstrated.19 Using a common denominator related to the sampling frequency, the NPMA is a mathematical low-pass filter that is frequently used in the engineering field for removing random noise from a time series. The high-frequency components, resulting primarily from arterial wave reflections,20 cause substantial transformations from central to peripheral aortic pressure waveforms and can be eliminated by the application of the NPMA.19 Applied on radial artery pressure waveforms obtained using arterial tonometry, the NPMA method with a common denominator of 4 (one quarter of the acquisition sampling frequency) has been shown to define SBP-C accurately.19 However, tonometry-based methods for estimating SBP-C are limited by the requirements of a sophisticated tonometric device and a certain level of operator skill. A cuff-based technique using the NPMA method would likely be more welcomed in clinical practice given the confirmation of its accuracy in measurement. In other words, this simple method can be seamlessly equipped into current oscillometric BP monitors and provide convenient SBP-C estimates for the management of hypertension. However, for brachial artery pressure (BAP) waveforms obtained either invasively or noninvasively with oscillometric BP monitors, the performance of the NPMA method for SBP-C estimation has yet to be evaluated. Therefore, the present study aimed to develop and validate the application of the NPMA method to noninvasively derive SBP-C values from the noninvasive BAP waveforms.

Methods

Study Population

All study protocols were approved by the Institutional Review Board of Taipei Veterans General Hospital and adhered to the principles of the Declaration of Helsinki.

Two independent groups were studied, the derivation group (n=40) and the validation group (n=100). The characteristics of the subjects in both groups have been presented in our previous studies (Table S1 in the online-only Data Supplement).21

Data Acquisition

The study procedures have been described elsewhere.21 Briefly, in the derivation group, simultaneous invasive central aortic and BAP waveforms were obtained for 20 to 30 consecutive beats to cover ≥2 respiratory cycles.

To illustrate the contributions of different frequency components (hertz) to the construction of the BAP and aortic pressure waveforms, the discrete Fourier transformations of the individual invasive brachial and aortic waveforms were evaluated to yield the average moduli and phase angles ≤9 Hz.

Although we derived the denominator from the derivation group by investigating the relationship between invasive BAP and central aortic pressure waveforms, only noninvasive BAP waveforms could be obtained in the routine clinical practice. Therefore, we chose to examine the accuracy of the NPMA method for the noninvasive BAP waveforms and compared the estimates with the invasively measured SBP-C. In the validation group, invasive aortic pressure waveforms were recorded simultaneously with noninvasive BAP waveforms for 20 to 30 consecutive beats. The noninvasive BAP waveform was obtained at a cuff pressure of 60 mm Hg in the left arm using a commercially available oscillometric cuff-based device (VP-2000, Colin Corporation, Komaki, Japan).17

Study Protocol

In the derivation group, by applying the NPMA method to the invasive brachial BP waveforms, we attempted to identify the optimal denominator from N=2 to 10 for defining the SBP-C. The accuracy of these different denominators to obtain NPMA method–derived waveforms and corresponding maximal values, the predicted SBP-C, was investigated. In the derivation group, we determined the optimal denominator from which the most accurate estimates could be rendered.

In the validation group with another 100 independent subjects, the accuracy of the NPMA method with the optimal denominator was examined.

Statistical Analyses

Data were presented as the mean±SD to assess differences between NPMA method–derived and measured SBP-C values. Furthermore, paired samples t tests and the Bland–Altman analysis were used to examine the agreement between measurements. Statistical significance was set at the 2-tailed P<0.05 level.

Results

Based on the time domain (Figure 1A) and frequency domain (Figure 1B) analyses for the ensemble average pressure waveforms, noticeable differences between the aortic and BAP waveforms were illustrated. As demonstrated in Figure 1B, frequency components >3 Hz contributed trivially to defining the SBP-C. In comparison, more high-frequency components were required to define the brachial SBP.

Figure 1.
Figure 1.

Comparisons of ensemble average pressure waveforms in the time domain (A) and frequency domain (B) between invasively measured central aortic and brachial pressure waveforms in the derivation group. SBP-B indicates brachial systolic blood pressure; and SBP-C, central aortic systolic blood pressure.

When applied on the BAP waveforms, the NPMA with the common denominator related to the sampling frequency could differ from that proposed by Williams et al19 for radial pressure waveforms. Applying NPMA with a denominator of N/4, as previously proposed, to the invasively obtained BAP waveforms in the derivation group, we observed a difference between the NPMA method–derived and invasively measured SBP-C values of −4.6±4.1 mm Hg. Therefore, the optimal denominator from N/2 to N/10 in the derivation group should be re-evaluated. As shown in Figure 2, acting as a low-pass filter, the NPMA exerted stronger filtering effects on BAP waveforms with a smaller denominator. With the denominators of N/6 and N/4, frequency components >4 Hz and >3 Hz, respectively, were eliminated.

Figure 2.
Figure 2.

Effects of the application of the N-point moving average method on brachial pressure waveforms to define central aortic systolic blood pressure (SBP-C) by exploiting different denominators with reference to invasively measured SBP-C (dotted line).

Based on the results presented in Figure 3, we identified N/6 to be the optimal denominator for BAP waveforms, which provided the most accurate SBP-C estimates characterized by minimal systematic and random error (mean difference, 0.1±3.5 mm Hg) as compared with other denominators. In addition, the results of the Bland–Altman analysis shown in Figure 4 confirmed that no significant proportional systematic bias was noted for the denominator N/6.

Figure 3.
Figure 3.

Effects of different denominators on the mean difference (A) and SD of the differences (B) between noninvasive N-point moving average–derived central aortic systolic blood pressure (SBP-C) vs invasively measured SBP-C in the derivation group (n=40).

Figure 4.
Figure 4.

Bland–Altman analysis. Central aortic systolic blood pressure (SBP-C) estimated by N-point moving average method with N/6 (N6 SBP-C) using invasively obtained brachial pressure waves vs invasively measured SBP-C in the derivation group (n=40). CI indicates confidence interval.

Subsequently, the NPMA with the denominator N/6 was applied to noninvasive BAP waveforms in the validation group for estimating SBP-C. As shown in the Table and Figure 5, compared with the invasively measured SBP-C, the denominator N/6 provided SBP-C estimates with a mean difference of −0.6±7.6 mm Hg and without significant proportional systematic bias. In comparison with other denominators (Table), the SBP-C estimated with N/6 had minimal systematic and random error. When applying the NPMA N/6 method to derive noninvasive SBP-C, the 95% limits of agreement (mean difference±1.96×SD of differences) against the invasively measured SBP-C ranged from −15.6 to 14.2 mm Hg. In a supplementary analysis (Table S3), we also provided the absolute band errors between the various noninvasive BPs and the invasively measured SBP-C. The accuracy of SBP-C estimated with the NPMA N/6 clearly surpassed that of cuff SBP.

View this table:
Table.

Comparison of NPMA Method–Derived SBP-C With Different Denominators Between Noninvasive Brachial Pressure Waves and Invasively Measured SBP-C in the Validation Group

Figure 5.
Figure 5.

Bland–Altman analysis. N-point moving average method–derived central aortic systolic blood pressure (SBP-C) with N/6 (N6 SBP-C) using noninvasive brachial pressure waves vs invasively measured SBP-C in the validation group (n=100). CI indicates confidence interval.

Discussion

The NPMA method is a new and simple addition to the existing armamentarium for estimating SBP-C values. After its introduction in 2011 by Williams et al,19 the present study further investigated the validity of this application on BAP waveforms and extended the use to the noninvasively obtained BAP waveforms, which could be acquired during routine BP measurement using an automatic sphygmomanometer.

Williams et al19 demonstrated that the optimal denominator of NPMA method to derive SBP-C noninvasively using radial pressure waveform was N/4. As shown in Figure 2, the low-pass filtering effect of the NPMA increases with decreases in the denominator. The present study demonstrated that the NPMA filter mainly acts to remove the high-frequency components of the BAP waveforms resulting from the impact of wave reflections in the upper limbs. There has been an argument about the importance of amplification of pressure waveform in the forearm between the brachial and radial arteries.22 If the brachial-to-radial amplification is negligible, the denominator N/4 of NPMA method for the radial pressure waveforms may also work for the BAP waveforms. However, direct application of the denominator N/4 to the invasively measured BAP waveforms to derive SBP-C values produced a large systematic bias in the present study. On the contrary, in 10 subjects who had received sequential invasive measurements of BAP and radial pressure waveforms using the high-fidelity Millar catheters (online-only Data Supplement and Table S2), we found that radial SBP was significantly higher than brachial SBP by 4.4±3.8 mm Hg (P=0.005; Figure S1A). The averaged foot-to-foot interval between the BAP and radial pressure waveforms was 26.8±18.2 ms (P=0.005). Moreover, the difference between the radial and brachial SBPs was likely attributable to the higher energy content in the high-frequency harmonics of the radial pressure waveforms (Figure S1B). Thus, local wave reflections in the upper limb exert greater impact on the radial than the BAP waveforms, so the radial pressure waveform is characterized by a sharper rise during systole and a higher peak (SBP) and larger pulse wave amplitude (pulse pressure).6,22 Therefore, to derive noninvasive SBP-C values by filtering out the influences of local reflection waves, the NPMA with a lesser low-pass filtering effect should be implemented for BAP waveforms in comparison with that for radial pressure waveforms. In the first part of this study, we then determined that N/6 represents the optimal denominator for estimating SBP-C using the invasive BAP waveforms.

Subsequently, we investigated the accuracy of the application of the NPMA with this new denominator on the noninvasive BAP waveform in the independent validation group. Although the noninvasive BAP waveform is only a surrogate BAP waveform, its usefulness has been confirmed in numerous studies.16–18,23 Currently, all international standards, including European Society of Hypertension International Protocol,24 Association for the Advancement of Medical Instrumentation,25 and British Hypertension Society,26 require that the measurement error (mean differences against standards) of tested automatic BP monitors should surpass the minimal requirement of <5±8 mm Hg in validation studies for all BP parameters. The former number refers to systematic bias, which is the group average result for the validity evaluation, and the latter refers to random error, which suggests the scatter of the error. With the random error <8 mm Hg, the BP monitors could be regarded as a reliable tool for BP assessment. Exemplified by the standards of automatic BP monitors, we demonstrated (Table and Figure 5) that the NPMA method could derive noninvasive SBP-C values within the required standards using the BAP waveforms (mean difference, −0.6±7.6 mm Hg).

The clinical usefulness of the noninvasive SBP-C in individual cases could be appreciated by the analysis of absolute band errors with reference to the invasive SBP-C (Table S3). The NPMA N/6–derived noninvasive SBP-C surpassed the cuff SBP with higher percentages of absolute error within the criteria of ≤5, 10, and 15 mm Hg. The filter of NPMA N/6 was also better than the NPMA N/4 filter because the latter yielded lower percentages of absolute error within the criteria of ≤10 and ≤15 mm Hg (Table S3).

In the validation group, the random error (SD of the differences) of the NPMA method–derived SBP-C increased from 3.5 (in the derivation group) to 7.6 mm Hg. Similar to other noninvasive methods, the major source of errors arises from the decreased accuracy of sphygmomanometer-measured brachial BP.27 The improvement in the measurement accuracy of brachial BP by automatic BP monitors would be beneficial for risk assessment not only in current management of hypertension, but also in the clinical application of central BP concepts in the near future.

In a previous study that tested the validity of 2 noninvasive SBP-C measurement devices,28 large systematic bias and random error proportional to the magnitudes of measured SBP-C values were noted with the NPMA method (mean difference, 0.9±13 mm Hg), which was not evident in our study (Figure 5). The major source of error of such disappointing results may primarily arise from inaccurate cuff BP values used for calibration, as discussed in our previous study.27 Further studies should be performed to investigate and quantify the effects of calibration errors on different methods for estimating SBP-C and central aortic pulse pressure.

The effect of measurement error on the dilution of the prognostic value has been clearly delineated.29 Therefore, there is always a need for more accurate BP measurement devices. The prognostic value of conventional office BP readings has been outweighed by home BP and ambulatory BP measurement devices,3 mainly because of the regression toward the mean phenomenon,30 which likely could reduce the random error if a consistent relation exists, and also by avoiding the white-coat effect. Our study supports that brachial BP should be regarded as a surrogate for CBP blended with high-frequency noise resulting from local wave reflections. Thus, CBP is naturally a more accurate BP value and a better predictor of future cardiovascular events. Therefore, the development of a more user-friendly device with more accurate BP estimates, such as a cuff-based NPMA method–derived SBP-C BP monitor, is justified.

Limitations

There were some limitations in this study. We evaluated the performance of the NPMA in subjects who were referred for diagnostic catheterization. As with all invasive validation studies, whether our study population represents the general population remains questionable. Therefore, the accuracy of the NPMA in subjects with different characteristics should be investigated further. However, as shown in the previous report by William et al,19 the accuracy seemed robust when applying the NPMA method in the large ASCOT-CAFÉ cohort.31 We used the high-fidelity invasive brachial BP waveforms instead of the low-fidelity noninvasive BAP waveforms to identify the optimal NPMA common denominator in the derivation group. This may explain why it appears from the Table that N/7 may be preferable for noninvasive use than N/6. On the contrary, the use of high-fidelity brachial BP waveforms allowed for the detailed time domain and frequency domain analyses for the understanding and application of the NPMA method. Last, the NPMA method provides only SBP-C estimates. No other waveform characteristics can be obtained from the NPMA method–filtered brachial BP waveforms.

In conclusion, our study demonstrated that the NPMA method could be applied to derive SBP-C estimates using invasive and noninvasive brachial pulse waveforms, which was achieved principally by eliminating the aortic-to-BAP amplification phenomenon. After comparison of the denominator used for radial pressure waveforms (N/4), we further determined and validated that the optimal denominator for BAP waveforms was N/6. By integrating the NPMA method into ordinary oscillometric BP measurement, convenient noninvasive SBP-C values could be obtained with acceptable accuracy.

Perspectives

Central BP has been shown to provide better prognostic value than conventionally measured brachial cuff BP.12,13 The NPMA method, a simple mathematical low-pass filter, can be added to the existing armamentarium for estimating SBP-C using tonometry-derived radial pressure waveforms.19 The present study further confirmed the validity of this application on BAP waveforms and extended the use to the noninvasively obtained BAP waveforms, which could be acquired during routine BP measurement using an automatic sphygmomanometer. The convenient CBP values obtained with automatic BP monitors, if its superior prognostic value could be further confirmed prospectively, will make the CBP concept successfully translated from research into clinical practice.

Sources of Funding

This study was supported by the National Science Council (NSC 96–2314-B-010-035-MY3), Ministry of Education, Aim for the Top University Plan (96A-D-D131), and a research grant from an Industry-Academia Cooperation between Microlife Co., Ltd., and National Yang-Ming University.

Disclosures

None.

Footnotes

  • Received August 12, 2013.
  • Revision received September 5, 2013.
  • Accepted November 27, 2013.

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Novelty and Significance

What Is New?

  • Central blood pressure (BP) has been shown to provide better prognostic value than conventionally measured brachial cuff BP.

  • The N-point moving average method is a new and simple addition to the existing armamentarium for estimating central aortic systolic BP using tonometry-derived radial pressure waveforms.

  • The present study further investigated the validity of this application on brachial pressure waveforms and extended its use to the noninvasive brachial pressure waveforms, which could be acquired during routine BP measurement using an automatic sphygmomanometer.

What Is Relevant?

  • The present study demonstrated that by integrating the N-point moving average method into ordinary oscillometric BP measurement, convenient noninvasive central aortic systolic BP values could be obtained with acceptable accuracy.

Summary

The N-point moving average method was able to obtain a central aortic systolic pressure from the noninvasively recorded brachial pressure waveforms, which was obtained from ordinary oscillometric BP monitors.

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  • Application of the N-Point Moving Average Method for Brachial Pressure Waveform–Derived Estimation of Central Aortic Systolic PressureNovelty and Significance
    Yuan-Ta Shih, Hao-Min Cheng, Shih-Hsien Sung, Wei-Chih Hu and Chen-Huan Chen
    Hypertension. 2014;63:865-870, originally published March 12, 2014
    https://doi.org/10.1161/HYPERTENSIONAHA.113.02229
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