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(Circulation. 1996;94:1870-1875.)
© 1996 American Heart Association, Inc.

Articles

Reconstruction of Brachial Artery Pressure From Noninvasive Finger Pressure Measurements

Willem Jan W. Bos, MD, PhD; Jeroen van Goudoever, PhD; Gert A. van Montfrans, MD, PhD; Anton H. van den Meiracker, MD, PhD; Karel H. Wesseling, MSc

the Department of Internal Medicine I (W.J.W.B., A.H.v.d.M.), University Hospital Rotterdam, Dijkzigt, Rotterdam, and TNO–Biomedical Instrumentation (J.v.G., K.H.W.) and Department of Internal Medicine (W.J.W.B., G.A.v.M.), Academic Medical Center, Amsterdam, The Netherlands.

Correspondence to Dr W.J.W. Bos, Department of Internal Medicine, Academic Medical Center, Meibergdreef 9, 1105 AZ Amsterdam, Netherlands.

	Abstract

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Background Pulse wave distortions, mainly caused by reflections, and pressure gradients, caused by flow in the resistive vascular tree, may cause differences between finger and brachial artery pressures. These differences may limit the use of finger pressure measurements. We investigated whether brachial artery pressure waves could be reconstructed from finger pressure measurements by correcting for the pressure gradient in addition to correction for pulse wave distortion with a previously described filter.

Methods and Results Finger artery pressure (with Finapres), intra-arterial brachial artery pressure (BAP), Riva-Rocci/Korotkoff (RRK), oscillometric, and return-to-flow (RTF) measurements were simultaneously performed in 57 healthy elderly subjects and patients with vascular disease and/or hypertension. A generalized waveform filter was used to correct for pulse wave distortions. Correction equations for the pressure gradient, based on finger pressure, RRK, RTF, or oscillometric measurements, were obtained in 28 randomly selected subjects and tested in 29. Before reconstruction, Finapres underestimated mean and diastolic BAP (finger pressure minus BAP: systolic, -3.2±16.9 mm Hg; mean, -13.0±10.5 mm Hg; diastolic, -8.4±9.0 mm Hg [mean±SD]). After filtering, reconstructed BAP waves were similar to actual BAP in shape but not in pressure level. Optimal correction for the pressure gradient with an equation based on RTF measurements reduced the pressure differences to meet American Association for the Advancement of Medical Instrumentation criteria (reconstructed finger pressure minus BAP: systolic, 3.7±7.0 mm Hg; mean, 0.7±4.6 mm Hg; and diastolic, 1.0±4.9 mm Hg).

Conclusions BAP waves can be reconstructed from noninvasive finger pressure registrations when finger pressure waves are corrected for pulse wave distortion and individual pressure gradients.

Key Words: pressure • arteries • waves • blood pressure

	Introduction

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Finger pressure measurement with Finapres is a well-accepted method to measure blood pressure continuously in a noninvasive way. It is now frequently being used as an alternative for invasive intra-arterial blood pressure registrations. Generally, finger pressure readings of systolic, mean, and diastolic pressures agree well with intra-arterial blood pressure measurements.^{1 2} However, in individual patients, pulse shape and pressure levels as measured at the finger may differ from those measured intra-arterially in the brachial artery.^{3 4 5 6} In elderly subjects and in patients with signs of arteriosclerotic vascular disease, systolic and diastolic finger pressures are lower than brachial artery pressure (BAP)^{4 6} because of a pressure gradient caused by flow in the resistive vascular tree. In contrast, systolic finger pressure overestimates systolic BAP in subjects of younger age.^{3 7} Furthermore, systolic finger pressure responses may deviate from those of systolic BAP during head-up tilt, standing up, exercise, the Valsalva maneuver, and infusion of vasoactive drugs.^{4 6 7 8 9 10} These systolic pressure deviations are caused by peripheral pulse wave distortion.^{3 4 7 11}

Such differences between finger pressure and BAP limit the usefulness of finger pressure registrations as a diagnostic tool. A frequency-dependent transfer function, or filter, recently has been described to correct for pulse wave distortions.¹² Although this filter corrects well for pulse wave distortion, it corrects insufficiently for a possible pressure gradient between brachial and finger artery in individuals. The aim of the present study was to reconstruct BAP from finger pressure registration by correcting both for pulse wave distortion, as previously described,¹² and for pressure gradient.

	Methods

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Patients
Continuous finger and intra-arterial BAP measurements obtained in 57 subjects, 34 to 83 years of age (Table 1) who participated in previously described studies,^{4 6 13 14} were used for this study. Blood pressure measurements were performed to rule out pseudohypertension in patients with therapy-resistant hypertension and signs of arteriosclerotic vascular disease (n=13, Reference 4), to validate Finapres blood pressure measurements in an elderly population (n=15, Reference 6), or to study the effect of cuff size on Riva-Rocci/Korotkoff (RRK) measurements (n=29, Reference 13). Subjects were excluded when left-to-right differences for either systolic or diastolic blood pressure were 10 mm Hg, as determined by six simultaneous RRK measurements on both arms. Thirty-nine subjects used antihypertensive medication at the time of blood pressure measurement. The studies as described were approved by the institutional review committees, and all participants had given informed consent.

View this table: [in this window] [in a new window]   Table 1. Measurements Obtained in 57 Subjects in the Learn and Test Groups

Measurements
Intra-arterial BAP was used as the reference. A short Teflon cannula inserted in the brachial artery of the nondominant arm was connected to a Hewlett-Packard 1290A transducer (n=42) or a Gould DTX transducer (n=15) through 10- or 15-cm-long rigid tubing. Before and after each experiment, dynamic characteristics of the catheter-manometer system were checked by the flushing method.¹⁵ After the experiments, the response to a 100 mm Hg pressure square wave, applied at the tip of the cannula, was recorded. Natural frequency and damping coefficient were 25 Hz and .30.

RRK measurements were performed by a well-trained observer, using a 14x38-cm cuff on the dominant arm. The cuff was inflated rapidly and deflated at a fixed rate of 2.5 mm Hg/s. Cuff pressure was recorded with a strain gauge transducer (Motorola MPX 2050). At Korotkoff phases 1 and 5, a marker was given (Fig 1). Oscillometric mean pressure was obtained off-line by determination of the point of maximal oscillations (Fig 1). Brachial systolic pressure was additionally measured by a return-to-flow (RTF) method. The upper-arm cuff pressure was determined off-line at the moment that the first finger pressure pulsation became visible during cuff deflation (Fig 1).

View larger version (34K): [in this window] [in a new window]   Figure 1. Measurement cycle; cuff, finger, and brachial artery pressures. Cuff pressures at Korotkoff phases 1 and 5 (RRKsys, RRKdias), at return to flow (Pcuff RTF), and at the largest cuff pressure oscillations (Pmean Oscillometric) are indicated. Finger and brachial artery pressures were compared during a 30-second control period (bar).

Finger arterial pressure was measured on the index or middle finger of the dominant arm with a TNO model 5 Finapres.⁵ Recording started when a stable finger pressure signal was obtained. Finger pressure, BAP, cuff pressure, and marker signals were recorded on a strip chart (Gould TA 4000) and on an instrumentation tape recorder (Hewlett-Packard model 3964A).

Data Analysis
BAP, marker, finger, and cuff pressures were digitized at 100 Hz with a resolution of 0.25 mm Hg. BAP and finger pressure signals were subsequently analyzed with the BEATFAST program (BMI-TNO) to determine beat-to-beat systolic, diastolic, and mean pressures during a 30-second period preceding upper-arm cuff inflation (Fig 1). Finger pressure waves were run through BEATFAST twice, first unmodified and again with application of the filter.¹² With the use of a random number generator, the study population was divided into two groups. The data of one group (n=28, learn group) were used to develop (learn) level corrections, and the data of the second group (n=29, test group) were used to investigate (test) the corrections.

Method I: Correction for Pulse Wave Distortion
The frequency-dependent transfer function, or filter, correcting for pulse wave distortion, was derived from finger pressure and BAP measurements in a separate population,¹² enlarged with measurements of subjects from the learn group. The resulting waveform filter (Fig 2) differs slightly from the originally described waveform filter.¹² The filter amplifies frequencies to 2.5 Hz, compensating for the naturally occurring damping over this low-frequency range, and attenuates above 2.5 Hz, with a maximum at 8 Hz. This compensates for the natural pulse wave amplification over this frequency range. The effect of such filtering is a return of the finger pulse wave to a shape and pulse pressure close to that observed in the brachial artery. The filter amplifies at 0 Hz, which means that the mean pressure level increases by 19% with the use of this filter.

View larger version (10K): [in this window] [in a new window]   Figure 2. Frequency-dependent amplification characteristics of the filter. Low-frequency oscillations are amplified; high-frequency oscillations are attenuated.

Method II: Correction for Pressure Gradient
To correct for an individual's gradient, six different correction methods were developed and evaluated. For the first three correction methods, individual differences between diastolic, mean, and systolic indirect upper-arm blood pressure measurements and filtered finger pressures were added to the filtered finger pressure (Table 2). For correction method a, diastolic finger pressure during the 30 seconds preceding cuff inflation was subtracted from diastolic RRK pressure. For correction method b, mean finger pressure was subtracted from oscillometrically measured mean BAP; for correction method c, systolic finger pressure was subtracted from systolic BAP, as measured with RTF (Fig 1).

View this table: [in this window] [in a new window]   Table 2. Methods to Reconstruct Brachial Artery Pressure From Finger Pressure Waves: An Overview of All Methods Described

Another way to correct for the pressure gradient was the addition of a correction factor obtained with various formulas, estimating the individual difference between mean intra-arterial BAP and mean filtered finger pressure, to the filtered finger pressure measurements. These formulas were derived from the learn group. The difference between mean BAP and mean waveform-filtered finger pressure over the 30-second period preceding cuff inflation was explained by means of stepwise regression analyses. As independent variables for the stepwise regression analysis we used finger pressures, alone or in combination with oscillometric or RTF upper-arm pressures: formula d, waveform-filtered Finapres data (systolic, mean, and finger pressures and heart rate); formula e, waveform-filtered Finapres data and oscillometrically determined mean BAP; and formula f, waveform-filtered Finapres data and systolic BAP as determined with RTF measurements (Table 2).

Uncorrected finger pressure and reconstructed BAP were compared with the intra-arterially measured BAP during the 30-second period preceding cuff inflation. For methods II, a through f, the individual correction factor for the pressure gradient was calculated once for each subject. The waveform filter was applied to the entire 30-second registration.

Statistics
All data are the average of two measurements in each subject. Data were distributed normally and are presented as mean±SD. The accuracy of a correction method was defined as the mean difference between reconstructed and actual BAP. The precision was defined as the standard deviation of the differences (SDD). Accuracies were compared with the use of paired Student's t tests and the Bonferroni method for multiple comparisons. Precisions were compared with the F test for variance ratios.

	Results

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Age, heart rate, and blood pressure levels of the learn and test groups did not differ (Table 1).

As shown in Table 3, uncorrected finger systolic pressure was almost equal to systolic BAP, but precision was low in this relatively old population, as reflected by a high SDD. Mean (P<.01) and diastolic finger pressures (P<.01) were lower than mean and diastolic BAP, but with a smaller SDD (Table 3).

View this table: [in this window] [in a new window]   Table 3. Comparison With BAP: Mean (Accuracy) and SDD (Precision) of Differences Between Finger Pressure, Reconstructed Brachial Artery Pressure, and Actual BAP in the Test Group

Application of the filter produced pressure waves almost shaped as brachial artery pulsations (Fig 3). The pulse pressure was closer to the brachial artery pulse pressure. However, filtered finger pressures overestimated the BAP, and precision did not improve (Table 3).

View larger version (26K): [in this window] [in a new window]   Figure 3. Finger pressure and reconstructed and actual brachial artery pressure (BAP) waves in 6 subjects. Original finger artery pressure waves (top) and BAP waves reconstructed from finger pressure registrations, with the use of the general waveform filter and the return-to-flow multiple regression formula f to correct for pulse wave distortion and individual pressure gradient (bottom), as compared with actual BAP.

Correction with the individual difference between diastolic RRK and finger measurements (correction method a) improved accuracy and precision of diastolic and mean pressures and the precision of systolic pressures (Table 3). Correction methods b and c only improved the precision of systolic pressures (Table 3). Correction methods d, e, and f, derived from the learn group and evaluated in the test group, are given in Table 2. These equations explained 57%, 66%, and 85% of variance in differences between mean BAP and mean filtered finger pressure in the learn group and 55%, 71%, and 88% of variance in these differences in the test group. Differences between mean BAP and mean filtered finger pressure as actually observed and as predicted with method f are depicted in Fig 4. The use of these formulas resulted in an improved accuracy of reconstructed BAPs (Table 3, d through f). The best precision and accuracy were obtained with equation f. (Table 3 and Fig 5).

View larger version (16K): [in this window] [in a new window]   Figure 4. Predicted and actual differences between mean waveform-filtered finger pressure (FP) and mean brachial artery pressure (BAP), using correction method f (n=29, r2=.88).

View larger version (33K): [in this window] [in a new window]   Figure 5. Bland Altman graphs. Uncorrected finger pressure (FP) and reconstructed brachial artery pressure (RBAP) compared with actual brachial artery pressure (BAP). RBAP was obtained by filtering and the return-to-flow correction formula (formula f). Mean difference and 95% confidence interval (2 standard deviations of the differences) are indicated by dashed lines.

In the test group, systolic RRK-BAP differences were -3.5±7.0 mm Hg; mean RRK (diastolic + 1/3 pulse pressure)-BAP differences were -4.8±4.6 mm Hg; and diastolic RRK-BAP differences were 2.2±6.3 mm Hg.

	Discussion

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Pulse wave shape and pressure levels of finger artery pressure differ from pulse wave shape and pressure levels of BAP due to pulse wave distortion and pressure gradients. Correction for the individual pressure gradient with the described formulas, in addition to correction for pulse wave distortion with a digital filter, allowed reconstruction of BAP waves, closely resembling actual intra-arterially measured brachial pressure waves in shape and pressure level from noninvasive finger pressure measurements. With the use of the formula based on Finapres and RTF measurements (Table 3, f, and Figs 4 and 5), BAPs could be reconstructed from finger pressure measurements that are within the criteria for the evaluation of automated sphygmomanometers (accuracy, <5 mm Hg; precision, <8 mm Hg) developed by the American Association for the Advancement of Medical Instrumentation.¹⁶ Accuracy and precision of reconstructed BAPs are as good as those of traditional RRK measurements; accuracy of reconstructed mean BAPs and precision of reconstructed diastolic pressures are even better. The fact that the precision of reconstructed systolic pressures is not as good as that of diastolic and mean pressures (Table 3 and Fig 5) might be due to the fact that systolic pressures are much more affected by the high-frequency characteristics of the generalized waveform filter, which might slightly undercorrect or overcorrect in individual subjects. Furthermore, differences in diastolic and mean pressure resulting from a possible stenotic lesion between brachial and finger arteries are annulled by the correction factor for the pressure gradient, whereas reconstructed systolic pressures might underestimate the actual BAP when the stenosis attenuates high-frequency components¹⁷ stronger than our waveform filter.

Previously, aortic^{18 19} and brachial¹² pressure waves have been constructed from peripheral pressure waves with the use of frequency-dependent filters. These filters correct for pulse wave distortions, which primarily affect systolic pressure levels,^{12 18} but do not correct for pressure gradients. Epstein et al²⁰ suggested estimation of the size of the pressure gradient by comparing mean finger and oscillometric Dinamap readings. In the present study, correction with the individual difference between indirect upper-arm pressure measurements and unfiltered (results not shown) or filtered finger pressure measurements resulted in improved but not optimal correction (Table 3, a through c). The remaining difference between thus reconstructed and actual BAP waves might in part be explained by the difference between direct and indirect (RRK, oscillometric, or RTF) measurements of BAP^{13 14} and by the fact that finger pressures were obtained during the control period preceding cuff inflation, while blood pressure has been shown to rise slightly during measurements with an upper-arm cuff.¹³ The latter error could be prevented by performing RRK or oscillometric measurements on the contralateral arm. This solution is not possible for RTF measurements, since finger pressure measurements are used to detect the first pulse passing underneath the cuff.

The remaining differences between reconstructed and actual BAP could be reduced when individual finger pressure, oscillometric, or RTF values were used in regression formulas derived from the learn group (Table 3, d, e, and f). Formula d has the advantage that only data available from Finapres are used as input, but the best precision was obtained with formula f, on the basis of Finapres data and RTF measurements (Table 3, f, and Figs 4 and 5).

The availability of optimally corrected finger pressure measurements will be especially helpful during experiments that require continuous knowledge of the exact blood pressure level and in circumstances or populations in which finger pressure measurements have been shown to represent BAP with reduced accuracy. The methods correcting for the pressure gradient were developed in such a population, including elderly patients and patients with signs of arteriosclerotic disease. In these subjects, a pressure gradient between uncorrected finger and BAP measurements might be expected²¹ and was indeed observed (Table 3). Although no overcorrection was observed in the younger part of our population, additional studies are needed to investigate the reliability of the proposed correction methods in young and healthy subjects, in whom a smaller pressure gradient^{1 2 7} and a larger pulse wave amplification might be expected.¹¹ The reliability of the correction methods also remains to be tested in situations with changing blood pressure and pulse wave amplification, such as the Valsalva maneuver, standing up, head-up tilt, or infusion of vasoactive drugs.^{4 6 7 8 9}

Since the waveform filter is generally applicable, it can be incorporated in future models of finger pressure–measuring devices. Once an upper-arm cuff and an algorithm to detect the moment of return to flow are incorporated as well, one would only have to wrap an upper-arm cuff around the arm at which the finger cuff is located. All further steps can be automated.

Another issue is the frequency with which the correction for pressure gradient should be performed. During systemic infusions of vasoactive drugs, the pressure gradient did not change⁷ ; one calibration would suffice. The pressure gradient between brachial and finger arteries has also been shown to be quite stable during 24-hour measurements.²² However, the pressure gradient between brachial and finger arteries has been observed to change slightly during head-up tilt,⁶ standing,⁴ and walking.²² The gradient might also be expected to change as the result of changes in blood flow, especially in patients with stenotic lesions between the brachial and finger arteries.²³ For optimal correction, repeated calibration might therefore be necessary.

Conclusions
BAP waves, closely resembling intrabrachial pressure waves in shape and pressure level, can be constructed from noninvasive finger pressure measurements when both a frequency-dependent filter and an additional level correction method are applied to correct for pulse wave distortion and pressure gradient between brachial and finger arteries, respectively.

Received February 22, 1996; revision received April 24, 1996; accepted May 1, 1996.

	References

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