Accuracy and precision of blood pressure determination with the Finapres: an overview using re-sampling statistics

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1 Journal of Human Hypertension (1998) 12, Stockton Press. All rights reserved /98 $ ORIGINAL ARTICLE Accuracy and precision of blood pressure determination with the Finapres: an overview using re-sampling statistics Therapeutics and Pharmacology, The Whitla Division of Medicine, The Queen s University of Belfast, Belfast, Northern Ireland The Finapres non-invasive blood pressure (BP) monitor uses the method of Penaz to indirectly record the arterial waveform; studies on its accuracy have suggested little systematic bias vs intra-arterial pressure (IAP) but substantial variability. Inconsistency between studies, in respect of the magnitude, direction and variance of bias, was described in the validation studies against the direct IAP. We have employed a novel resampling statistical method to combine the data from 20 published studies; a robust overall estimate of the accuracy and precision of the Finapres was thereby obtained. Based on 449 patients and 4490 re-samples, the average Finapres systolic bias (IAP - Finapres) was 2.2 mm Hg (s.d. ±12.4) with limits of agreement (bias ±2 s.d.) of 22.6 and 26.9 mm Hg. The average precision was 12.1 mm Hg (s.d. ±8.4). The Finapres diastolic bias was 0.3 mm Hg (s.d. ±7.9) with the limits of agreement of 16.1 and 15.5 mm Hg. The average precision was 7.6 mm Hg (s.d. ±5.3). The average Finapres mean arterial pressure bias was 2.1 mm Hg (s.d. ±8.6) with precision of 7.6 mm Hg (s.d. ±5.3). The calculated percentage of Finapres systolic values expected to fall within ±5 or±10 of the direct intra-arterial pressure was 35.9% and 73.1%, respectively. The calculated precision of the Finapres systolic pressure between 0 5 mm Hg was 1.6% and between 0 10 mm Hg 36.4%. The comparable values for Finapres diastolic BP for accuracy were 63.5% and 92.8% and for precision 23.1% and 79.2%. The Finapres device can provide an accurate estimate of diastolic and mean arterial pressure compared with the intra-arterial record; the apparent inaccuracy of the Finapres systolic pressure may have a physiological explanation. When the Finapres device is used in experimental or in clinical situations, then calibration against a reliable reference arterial pressure is desirable to obviate the possibility of an offset error. Keywords: blood pressure measurements; Finapres; validation Introduction The Finapres non-invasive blood pressure (BP) monitor uses the methodology of Penaz 1 to continuously display the arterial pressure waveform. The technique uses a small cuff to apply a volume clamp to the digit. 2,3 The total finger volume under an unloading cuff is determined by infra-red plethysmography and despite the changing arterial pressure, this volume is maintained at a set level by modulating the cuff pressure using a high speed electropneumatic servo-system. The continuously changing cuff pressure is measured electronically, and the signal displayed as the arterial pressure. This type of device has many potential experimental and clinical applications; the volume clamp principle offers an alternative method of arterial pressure monitoring to the invasive approach. Studies with the Finapres suggest small average bias but large variability 4 9 ; additionally the published data Correspondence: Dr B Silke, Therapeutics & Pharmacology, The Whitla Division of Medicine, The Queen s University of Belfast, 97 Lisburn Road, Belfast, BT9 7BL, N. Ireland Received 15 October 1997; revised and accepted 18 January 1998 show inconsistent magnitude, polarity and variance of discrepancies between the method and direct intra-arterial recordings. 10 Central and peripheral arterial pressures are dissimilar due to interaction of incident and reflected waveforms; 11 the distal arterial signal is amplified and therefore over-estimated compared with proximal pressure determinations. 12 Therefore any periheral BP method such as the Finapres requires rigorous validation to understand its strengths and limitations. The accuracy of the Finapres compared with intra-arterial reference pressure has now been assessed in many studies 3 10,13 23 without any clear consensus emerging on the average performance of the method; precision data has been infrequently reported. 20,24 This paper is a synthesis of these literature data; a novel statistical method of re-sampling allowed a global overview of the performance of the system to be derived. Materials and methods Finapres 2300 non-invasive monitor The Finapres is a non-invasive, automated system for the measurement of arterial BP. The BP, meas-

2 404 Accuracy and precision of the Finapres ured at the digit using servo-plethysmomanometry, employs the volume clamp technique. 2,3 The finger artery is unloaded such that its arterial volume is held constant (or clamped) at any given instant. A servo-controller compares the arterial diameter with a reference value (the set point) that has been chosen to ensure a near-zero transmural digital artery presure. The continuously changing cuff pressure is measured electronically, and the signal displayed, thus indirectly providing an estimate of the arterial pressure. Clearly the accuracy of the method is very dependent on the finger positioning within the cuff and the extent to which the device has been correctly calibrated during the initial set up. 10,23 In 50 coronary patients undergoing diagnostic angiography, we previously accessed its accuracy and variability; the Finapres systolic pressure was higher than the aortic pressure (mean difference +7.2 mm Hg (s.d. 13.7), but the diastolic 1.0 mm Hg (s.d. 5.9) and mean +1.7 mm Hg (s.d. 6.8) pressures were comparable. 23 The reproducibility of the Finapres and direct arterial pressure method was not significantly different; the respective coefficients of variation were 4.6 and 4.0% for systolic, 2.8 and 2.7% for diastolic, and 3.3 and 3.0% for the mean arterial pressure. Re-sampling statistics and data simulations It is possible to take the numerical data generated during different validation studies and re-sample these data to derive a global estimate of the accuracy and precision of the method. Re-sampling statistics is a relatively new science where the power of computers is used to simulate complex situations, where conventional statistics is often at a loss or simply unable to supply answers. 25 The re-sampling method simulates or models the physical process; based on the observed data a universe is postulated and the data are used to produce new hypothetical samples whose properties are examined. The behaviour outcome then can be compared with some criterion. The operational definition of the re-sampling process is to use the entire set of data available to produce samples of data from a hypothetical population, that embodies all that is known about the parent population. This hypothetical population is in theory the sample itself replicated many times; in practice the hypothetical population is constructed by repeatedly re-sampling the data-set with replacement. Unlike conventional or formulaic statistics, where the complex abstractions and the mathematical assumptions of the test are not transparent, resampling is a much easier process to comprehend; it does not require detailed familiarity with the conduct of statistical procedures and the methodology is intuitively obvious. The conventional formulaic and the re-sampling method both seek an estimate of the sample and its partitions; however, when the nature of the problem is complex and cannot be simply expressed in a form allowing conventional statistical methods to be applied, then re-sampling methodology can often, by modelling the physical process, provide an acceptable problem-solving solution. Thus conventional statistics produces estimates of probability based on formulae; re-sampling estimates the same probabilities from numerical experiments by working directly with a model of the physical process. Re-sample 1: re-sampling of individual patient accuracy data: A total of 148 individual patient data (50 radial; 98 brachial or aorta) was available from four publications. 16,23,24,26 Five thousand re-samples of this data-set were used for the computation. Each re-sample selected one of the patients at random and used that subject s IAP - Finapres difference to generate 10 re-sampled values (by taking a normally distributed sample using the mean difference and s.d. of the difference). These new re-sampled data are hypothetical data, that faithfully represent the characteristics of the parent population; thus if for example 1000 points were normally re-sampled from a population of mean 5 and s.d. 10, reversing the process and calculating the mean of these points would yield an approximate average of 5 with a s.d. of 10. It is therefore possible to combine the individual re-sampled data (each derived from one individual) and calculate the overall population statistics of the entire data-set. The mean bias and s.d. was calculated from the 5000 re-samples together with the precision and its s.d. to provide the population statistics of the data-set. Re-sample 2: re-sampling of 20 studies and 449 patients: A total of 449 patients grouped data, with average and s.d. of difference, was available from 20 publications; 3 10,13 24 the radial (56%) rather than the brachial artery site was more commonly employed. A total of 4490 re-samples of these datasets were used for the computation. Each group was consecutively re-sampled; the numbers of resamples being the numbers of individuals in each group. Thus for a group of 38 patients, 38 re-samples were made using the average difference between the intra-arterial and Finapres pressure determinations to generate the 10 values for each re-sample (normally distributed using the mean and s.d. of the difference of the group sample). The mean difference and precision for each re-sample and their respective deviations were calculated and stored; by repeating the procedure 10 times, a total of 4490 values were obtained from which the overall population statistics of the data-base were determined. Re-sample 3: re-sampling of eight robust studies and 186 patients: Of the various studies reported, only nine documented the frequency response and damping ratio of the IABP system; 3,8 10,16,17,22,23 one was an exercise study and was therefore excluded. 27 A total of 186 patient-grouped data, with average IAP - Finapres bias and s.d. of the difference, was available from these publications. The reference catheter site was brachial in 116 and radial in 70. A total of 5580 re-samples of these data-sets were used for the computation. Each group was consecutively resampled; the number of patients in the group being the basis of the re-sample. By repeating the procedure 30 times, a total of 5580 re-samples were available from which the population statistics were calculated.

3 Accuracy and precision of the Finapres 405 Figure 1 Individual data from four Finapres validation studies in 148 patients. Data is IAP - Finapres average bias for systolic BP in each subject. The calculated limits of agreement (bias ±2 s.d.) for the group are displayed. Statistical methods Data is presented as mean ±s.d.. For both systolic and diastolic pressures, bias (mean error) and precision (mean absolute value of error) relative to the directly measured intra-arterial pressure (IAP) were calculated. The bias was calculated as (IAP i Finapres I )/n and the precision as IAP i Finapres i /n. The bias and precision values of the re-sampled data were then averaged to give the mean bias and mean precision for the Finapres device. Results Re-sampling of individual patient data (n=148) (Figures 1 and 2) Five thousand re-samples (of 148 individual patient data) were used for the computation. The resampled data did not suggest systematic bias between the IAP and the Finapres device but the precision of the systolic BP measurement was poor. The average bias (IAP-Finapres SBP) was 0.8 mm Hg (s.d. ±16.0); the limits of the agreement (bias ±2 s.d.) were 32.8 and 31.1 mm Hg. The average Figure 3 The predicted bias of IAP - Finapres measurements for a future patient, based on the re-sample of all 20 studies. The curves illustrate the distribution of probability of bias for systolic and diastolic BP. The probability that the bias for a future patient will be in the range 5 to+5 mm Hg is 0.36 for systolic and 0.64 for diastolic BP. precision of Finapres systolic BP was 13.5 mm Hg (s.d. ±9.6). The accuracy and precision of Finapres diastolic BP was better. The average bias was 1.6 mm Hg (s.d. ±9.2) with limits of agreement of 20 and 16.8 mm Hg. The average precision was 7.4 mm Hg (s.d. ±6.0). Re-sampling of grouped data (n=449) (Figures 3 5) A total of 449 patients had been reported in 20 publications. A total of 4490 re-samples (ie, 10 resamples of each patient) were used for the calculations. The re-sampled data demonstrated no great systematic bias between the IAP and Finapres systolic values but considerable variability. The average bias for systolic BP was 2.2 mm Hg (s.d. ±12.4) with limits of the agreement of 22.6 and 26.9 mm Hg. The average precision was 12.1 mm Hg (s.d. ±8.4). The corresponding Finapres diastolic bias was 0.3 mm Hg (s.d. ±7.9) with limits of agreement of 16.1 and 15.5 mm Hg. The average precision was 7.6 Figure 2 Individual data from four Finapres validation studies in 148 patients. Data is IAP - Finapres average bias for diastolic BP in each subject. The calculated limits of agreement (bias ±2 s.d.) for the group are displayed. Figure 4 The predicted precision if IAP - Finapres measurements for a future patient, based on the re-sample of all 20 studies. The curves illustrate the distribution of probability of precision for systolic and diastolic BP. The probability that the precision for a future patient will be in the range 0 to 10 mm Hg is 0.36 for systolic and 0.93 for diastolic BP.

4 Accuracy and precision of the Finapres 406 thousand re-samples of these original data were used; the average Finapres mean bias was 2.1 mm Hg (s.d. ±8.6) with limits of agreement of 15.3 and 19.3 mm Hg. The average precision was 7.6 mm Hg (s.d. ±5.3). The calculated percentage of Finapres observations expected to fall within ±5, ±10 and ±15 mm Hg of the direct IAP was 48.2%, 72.9% and 90.4%. The calculated precision of the Finapres mean pressure between 0 5, 0 10 and 0 15 mm Hg was 39.0%, 71.4% and 90.1%. Figure 5 Bar chart indicating the average bias (± s.d.) compared with the IAP in the three re-sampled data-sets. These re-samples were based on original data for each of 148 patients in four papers, or grouped data for all 20 papers with reported bias and its s.d. for both systolic and diastolic pressure (n = 449), or eight studies whose arterial frequency response data indicated a highquality recording system (n = 186). mm Hg (s.d. ±5.3) The calculated percentage of Finapres systolic observations that would fall within ±5, ±10 and ±15 mm Hg of the direct IAP was 35.9%, 73.1% and 90.8%. The calculated precision of the Finapres systolic pressure between 0 5, 0 10 and 0 15 mm Hg was 1.6%, 36.4% and 75.4%. The comparable values for diastolic BP for accuracy were 63.5%, 92.8% and 98.6% and for precision 23.1%, 79.2% and 97.1%. Re-sampling of high quality studies (n = 186, eight studies) A total of 186 patients were included in eight studies, that reported the frequency and damping characteristics of the IAP method. Of these resamples 5580 data-sets were used for the computation; each group sample was based on its sample size. The re-sampled data demonstrated systematic bias between the IAP and Finapres systolic values and poor precision. The average Finapres systolic bias was 3.6 mm Hg (s.d. ±3.5) with limits of the agreement of 23.5 and 30.7 mm Hg. The average precision was 12.9 mm Hg (s.d. ±9.2). The corresponding Finapres diastolic bias was 1.6 mm Hg (s.d. ±8.1) with limits of agreement of 14.6 and 17.8 mm Hg. The average precision was 7.5 mm Hg (s.d. ±5.3). Finapres accuracy/precision of Finapres mean arterial pressure Individual Finapres and mean arterial data was available for 175 patients from five publications (reference brachial 98: radial 77). 16,23,24,26,28 Five Discussion This study examined BP accuracy and precision, using the non-invasive volume clamp method, as implemented in the Finapres. It measured the accuracy and precision of the technique using three sets of literature data; firstly the published individual data-sets, second the entire literature validation studies, and third only those studies with high fidelity for the arterial reference system. These data were re-sampled and subsequently combined to allow detailed estimates of the accuracy and precision of the device. Overall the three different approaches yielded remarkably similar estimates for the accuracy and precision of the Finapres. There was little systematic bias compared with the directly determined intra-arterial pressure, the precision of the Finapres device was considerably better for the diastolic and mean compared with the systolic BP. One of the fundamental methodological problems for comparisons of the Finapres and intra-arterial pressure arises due to sampling of the arterial pressure at different points in the circulation. The physiological principles governing the shape of the peripheral arterial pressure waveform are complex; but depend to a considerable extent on the heart rate, pulse wave velocity together with the phenomenon of waveform reflection and dispersion. As the pulse wave travels distally the wave form is dispersed and subsequently reflected at the peripheral circulatory resistance; this amplifies the systolic peak resulting in an increased systolic BP without appreciable changes in the diastolic or mean pressure. The waveform dispersion occurs as a consequence of the higher pressure points on the pulse wave travelling faster, tending to produce a steeper wave of higher amplitude. Importantly the peripheral BP may not bear a constant relationship to the central pressure, as it is disproportionately influenced by changes in the physiological variables. Thus, changes in the heart rate or in the arterial compliance may result in a disproportionate amplification of the distal arterial waveform during exercise. 23 However, under resting conditions the relationship between the central and peripheral estimates of arterial pressure is sufficiently robust under most conditions for the Finapres to be useful in tracking pressure changes in man under a variety of clinical conditions and physiological circumstances. 10,26,29 There are no defined standards against which a continuous non-invasive BP monitor, such as the Finapres, can be assessed. Suggested evaluation protocols, such as those of AAMI and subsequent revision, 30,31 are intended to cover the situations

5 Accuracy and precision of the Finapres when a non-invasive BP monitor (NIBM) is assessed either using a standard mercury reference sphygmomanometer (measuring at the same level in the circulation), or against the directly recorded arterial pressure. In these circumstances it is likely that the pressures recorded by the NIBM and reference can be considered essentially similar. However, although the peripheral mean and diastolic arterial pressures are relatively unaffected by the arterial sampling site (ie, distance along the arterial system at which the pressure is recorded), the waveform amplification at distal sites of systolic BP is problematic. One may not conclude that the inability of the Finapres systolic reading to satisfy the AAMI criteria for agreement (average bias 5/s.d 8 mm Hg) is due to inaccuracy of the device. The fact that these agreement criteria may be met for Finapres mean and diastolic, unlike systolic observations, suggests an alternative possibility that the extent to which the peripheral systolic pressure is amplified, relative to the central pressures, is not constant but depends on physiological conditions. Certainly a variable relationship between central and peripheral pressures has been recognised on exercise 32 and during certain physiological stressors. 29 The re-sampling method of performing this metaanalysis is novel. Essentially using this methodology one constructs a hypothetical population, that retains the essential numerical characteristics of the parent population; the properties of this population can be examined. In the examples of this review, we have employed the literature data to obtain robust accuracy and precision estimates for the Finapres. There are conventional statistical approaches to handle even the most complex numerical problem and to derive probability estimates of the likelihood of a particular outcome; the advantage of the re-sampling approach is that the methodology is straightforward and errors less likely to be introduced, due to the transparency of the approach. The assumption, in combining the results of all the published studies, is that this is the best estimate of the results likely to be obtained on average by the device. In our previous study we demonstrated systematic bias (+7.2 mm Hg) for Finapres systolic pressure compared with the intra-arterial reference. This was comparable to other reports. Bos 22 found the Finapres peripheral systolic pressure was 15.7 mm Hg higher than the intra-brachial level, Dorlas 13 reported Finapres systolic bias of 7.0 mm Hg. However, the meta-analysis of the 20 studies does not support such a consistent over-estimate of systolic arterial pressure by the Finapres compared with the intra-arterial reference. This is surprising as it is generally accepted that amplification of the systolic BP occurs distally, due to a combination of physiological events including waveform dispersion and reflection. 11,12,33 We have previously noted 23 that the bulk of validation studies on the Finapres suggested that the systolic and diastolic pressures were underrecorded compared with that directly assessed; 3,14,18,24,26,28 physiologically one would expect an accurate peripheral device to record a higher systolic but a lower diastolic pressure compared with that recorded at a more proximal recording site. However, the extent to which the systolic pressure is amplified may be variable, depending both on biological (age and extent of arterial pathology) and technical factors. The method of cuff application may be critical; 20,34 on the one hand anatomic variations may be such that incomplete transfer of the cuff pressure to the digital artery requires a greater cuff pressure to maintain the zero transmural pressure. Alternatively, with a cuff application that is too tight, the cuff inflation pressure will be lower than would otherwise be the case with a correctly applied cuff. In either case a constant offset or calibration error would result. Our meta-analysis provides information on the accuracy and precision of the Finapres, making the not unreasonable assumption that this represents the best estimate of the average performance of the system. It cannot provide information as to what the results would have been had the device been invariably correctly calibrated (much less how this might have been achieved). Clearly the inclusion of studies where the device may have been incorrectly calibrated would be expected to reduce any systematic bias of the Finapres device while at the same time increasing the observed variability. For this reason we attempted to examine different subsets of the publications (investigators with or without high fidelity arterial measurement systems; studies with at least 20 patients etc) with the expectation that these might have produced a more reliable estimate of the accuracy and precision of the Finapres. The fact that none of these sub-sets provided a materially different outcome to that derived from the composite literature, argues strongly against the likelihood of any user achieving consistently better than these average results with the Finapres. The Finapres diastolic pressure did not show systematic bias compared with the directly recorded arterial pressure; the s.d. of the bias at 7.9 mm Hg was within the AAMI standard. 30,31 The probability of the diastolic BP being within 5 mm Hg of the IAP was 0.64 and within 10 mm Hg of IAP The systolic BP did not show any systematic bias; however, its s.d. of difference from the IAP was higher (12.4 mm Hg); this in comparison would ensure that the probability of similar accuracy would be respectively 0.36 and Expressed in terms of probability, 50% of the time the accuracy of systolic BP would be beyond the 5.1 to +8.1 mm Hg range, with diastolic BP 50% of the time beyond 4.1 to +3.2 mm Hg. Kermode 24 concluded that the Finapres device displayed too great a variability in BP estimations when compared with intra-arterial monitoring to be used as an alternative method of monitoring the BP. Gibbs 35 supported a cautious approach to the use of the Finapres as a substitute for IAP monitoring; the concern was with the occasional situation where large discrepancies would occur. Imholz 26 stressed the low within subject variability and the value of the method for following pressure changes within individuals; however, the Finapres did not guarantee a true assessment of the arterial pressure, to the AAMI standard. The results of this meta-analysis does not lead us to modify the conclusions of our 407

6 408 Accuracy and precision of the Finapres earlier investigation. 23 The Finapres fulfilled the AAMI accuracy requirements 30,31 for the mean and diastolic mean difference (+1.7 mm Hg (s.d. 6.8); 1.0 mm Hg (s.d. 5.9) respectively) but not for the systolic pressure (+7.2 mm Hg (s.d. 13.7)). The Finapres accurately tracked the dynamic changes in pressure and was not different in this respect from the results derived from the direct arterial record. 23 There is no precise method of determining when the finger cuff is correctly applied; a pragmatic approach to ensure correct calibration is to initially check the reported values of Finapres diastolic pressure against a reliable non-invasive method (a standard mercury sphygmomanometer). If the measurements do not agree within ±5 mm Hg (this should be achieved 60% of the time), then the cuff should be repositioned or its tightness adjusted until the indicated diastolic pressure approximates to that determined by the reference method. If the cuff is moved then the calibration should be rechecked. When considering the results of our meta-analysis it is worth noting that none of the publications have suggested that the Finapres be treated as a relative signal, requiring calibration against a reliable standard to assure accuracy. However, this would merely appear to be a matter of common sense. With experience, one can achieve a high success rate with this approach, although some patients whose anatomy is unfavourable or with poor peripheral perfusion may not permit the device to be used successfully. There are many clinical and research situations where, if correctly calibrated, the device will correctly indicate the diastolic and mean arterial pressure in the underlying digital artery. However, due to the variable amplification of the systolic pressure, as the arterial waveform travels distally, the Finapres systolic pressure may indicate quite large differences to the systolic pressure recorded more proximally in the circulation. Acknowledgements The authors wish to acknowledge the statistical advice of Peter Bruce of Re-sampling Statistics, Inc. and Keith Wilson-Davies, statistician of the Drug Utilization Research Unit, The Queen s University of Belfast. References 1 Penaz J. Photoelectric measurement of blood pressure, volume and flow in the finger. In: Albert A, Vogt W, Hellig W (eds). Digest of the 10th International Conference on Medical and Biological Engineering, Dresden: International Federation for Medical and Biological Engineering, 1973, p Penaz J, Voight A, Teichmann W. Beitrag zur fortlaufenden indirekten Blutdruckmessung. Zschr Inn Med 1976; 31: Molhoek GP et al. 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7 25 Simon JL. Resampling: The New Statistics. Arlington, VA 22201: Resampling Stats, Inc., Imholz BPM, Wieling W, Langewouters GJ, van Montfrans GA. Continuous finger arterial pressure: utility in the cardiovascular laboratory. Clin Autonom Res 1991; 1: Idema RN et al. Comparison of Finapres non-invasive beat-to-beat finger blood pressure with intrabrachial artery pressure during and after bicycle ergometry. J Hypertens 1989; 7(6): S58 S Smith NT, Wesseling KH, de Wit B. Evaluation of two prototype devices producing noninvasive, pulsatile, calibrated blood pressure measurement from a finger. J Clin Monit 1985; 1: McAuley D, Silke B, Farrell S. Reliability of blood pressure determination with the Finapres with altered physiological states or pharmacodynamic conditions. Clin Autonom Res 1997; 7: Association for the Advancement of Medical Instrumentation. American National Standard for electronic Accuracy and precision of the Finapres or automated sphygmomanometers. Washington DC, USA: AAMI, Association for the Advancement of Medical Instrumentation. American National Standards for electronic or automated sphygmomanometers. Arlington, VA: AAMI, Rowell LB et al. Disparities between aortic and peripheral pulse pressures induced by upright exercise and vasomotor changes in man. Circulation 1968; 37: O Rourke MF. The arterial pulse in health and disease. Am Heart J 1971; 82: Lal SKL et al. Continuous, non-invasive volume-clamp blood pressure: determinants of performance. J Hypertens 1993; 12: Gibbs NM, Larach DR, Derr JA. The accuracy of Finapres non-invasive mean arterial pressure measurements in anaesthetized patients. Anaesthesiology 1991; 74(4):