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Finger beat-to-beat blood pressure responses to successive hand elevations
Medical Engineering & Physics 31 (2009) 522–527
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Finger beat-to-beat blood pressure responses to successive hand elevations R. Raamat ∗ , K. Jagomägi, J. Talts, I. Mäger Department of Physiology, University of Tartu, 19 Ravila Street, 50411 Tartu, Estonia
a r t i c l e
i n f o
Article history: Received 28 March 2008 Received in revised form 21 July 2008 Accepted 5 October 2008 Keywords: Hand elevation Postural change Hydrostatic pressure Finger beat-to-beat blood pressure
a b s t r a c t We investigated finger beat-to-beat blood pressure responses to a series of successive hand elevations in 14 normal volunteers. By passive elevation of the hand by 40 cm and lowering it again after a minute, calibrated hydrostatic pressure changes were induced in the finger arteries of the subjects. Three successive procedures with a 2-min interval between them were performed. Transitions between positions were completed smoothly over a 10-s period. Non-invasive beat-to-beat mean arterial pressure (MAP) in the finger arteries was measured by applying the servo-oscillometric physiograph (University of Tartu, Estonia). A good agreement between the evoked MAP changes during all the three hand elevations (−31.2, −30.4 and −30.0 mmHg, respectively) and the calculated hydrostatic pressure change (−31.0 mmHg) was obtained. The height difference of approximately 40 cm and rate of 4–5 cm/s can be recommended for the hand elevation test, greater postural changes and higher rates may diminish agreement between the measured blood pressure response and the corresponding hydrostatic pressure change. The applied hydrostatic test may be helpful for assessing the accuracy of beat-to-beat finger blood pressure measurement. © 2008 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Continuous non-invasive blood pressure measurement in the finger arteries is increasingly used in clinical research. This involves the finger beat-to-beat blood pressure measurement with the help of the Finapres monitor (Ohmeda, Denver, USA) and its portable version Portapres (TNO, Amsterdam, Netherlands), as well as estimation by means of a few new developments—Finometer (Finapres Medical Systems, Arnhem, Netherlands) [1,2] and Task Force Monitor (CNSystems, Graz, Austria) [3]. All these devices are based on the ˜ volume-clamp method, first described by Penáz [4]. Some experimental servo-oscillometric monitors have also been applied to obtain beat-to-beat values of the finger arterial blood pressure [5]. It has been found that the accuracy of finger blood pressure measurement by Finapres is sensitive to cuff malapplication. This may be due to the position of the finger arteries relative to the infrared diodes situated on the inner surface of the pressure cuff [6]. Mean arterial pressure (MAP) underestimation in the case of application of tight finger cuffs on the one hand, and MAP overestimation in the case of application of loose finger cuffs on the other hand, was pointed out in [7]. Even when the cuffs are adjusted by an experienced operator, inaccuracies in the blood pressure measurement may appear due to individual peculiarities in the finger anatomy, preventing full transfer of the cuff pressure to the artery. The con-
∗ Corresponding author. E-mail address: [email protected] (R. Raamat).
tracted or stiffened wall of the artery also increases the uncertainty of measurement. Another type of measurement inaccuracies can be qualified as instrumental. Instrumental accuracy characterizes, first of all, the capacity of the servo-system of the finger monitor to ensure reliable closed-loop work of the instrument for the duration of a change of the vascular tone. As a rule, the overall gain factor change and setpoint shift affect readings of the volume-clamp monitors [8–10]. Although several innovations have been reported to partly overcome these limitations [11–12], the improvements have not yet been introduced into the manufactured monitors. The hand elevation test has been recommended by vendors of finger beat-to-beat blood pressure monitors for quickly checking the accuracy of operation of the instrument. However, although widely used and highly appreciated for rough assessment, the accuracy of such tests frequently remains questionable. From the physical point of view, a hydrostatic approach is attractive due to its simplicity and precision of calculating the hydrostatic pressure exerted by a column of blood. On the other hand, several physiological regulations accompanying hand postural change may interfere with the pure physical response [13]. There are only a few studies discussing the metrological aspects of the hydrostatic validation of the blood pressure measurement [14–16]. Beat-to-beat blood pressure responses to a series of hand elevations have not received satisfactory attention although successive hand elevations are usual in practical applications. As demonstrated by repeated blood pressure measurements on the brachial artery [17], the successive transmural pressure balance
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R. Raamat et al. / Medical Engineering & Physics 31 (2009) 522–527
Fig. 1. Schematic presentation of an experimental protocol. Beat-to-beat MAP in the fingers is continuously monitored by the servo-oscillometric UT9201 monitor. After a 10-min equilibrium period three successive hand elevation procedures were performed with a 2-min interval between them. The time periods chosen for data analysis are shown.
changes in the tissue may result in moderately different blood pressure responses compared to those of a single measurement. Due to viscoelastic properties of the arterial wall, the multiple hand elevations may cause more complicated reactions than those evoked by a single elevation. Besides the arterial viscous properties, the filling and empting of extra-arterial vessels surely play a significant role [18]. The filling and emptying of vessels of different size and function take place with different time constant and may affect sequential photoplethysmographic measurement [19]. Myogenic response [20], known to control blood flow to organs after acute pressure changes should be also considered. In the present study we investigate the effect of successive hand elevations on the beat-to-beat finger MAP measured by the differential servo-oscillometric method in healthy persons. A further aim of the study was to show that the applied hydrostatic test may be helpful for assessing the accuracy of non-invasive beat-to-beat blood pressure measurement. 2. Methods 2.1. Subjects The subjects were 14 volunteers, 8 females and 6 males, aged from 18 to 34. They had no history of vascular disease and gave their informed consent to participate in the study. The study was approved by the Ethics Committee of the University of Tartu. 2.2. Experimental design The subject rested in a supine position on a couch. After an initial equilibrium period (10 min) the subject’s right hand was passively raised with the help of a tilting support to the height of 40 cm from the initial level. It remained there for 1 min. Then the hand was brought back to the initial position. Transitions between two positions were completed smoothly over a 10-s period. Three successive hand elevation procedures were performed with a 2-min interval between them (Fig. 1). Finger beat-to-beat MAP, fingertip skin blood flow and respiratory movements were continuously recorded in every subject. The experiments were carried out at room temperature of 23–25 ◦ C. 3. Technique 3.1. Finger beat-to-beat mean arterial pressure Finger beat-to-beat MAP was measured by the UT9201 physiograph, University of Tartu, Estonia. This instrument applies the servo-oscillometric method for measuring finger beat-to-beat arte-
523
rial pressure [5,21]. Like Finapres this method needs a servo-system to control the counter pressure in the finger cuff. The difference is that the volume-clamp instrument tracks the instantaneous intraarterial pressure while the servo-oscillometric device tracks the mean intra-arterial pressure. By modulating the counter pressure level according to the criterion of getting maximum volume oscillations in the cuff in every cardiac cycle, the counter pressure in the cuff is kept equal to the MAP in finger arteries (Marey’s principle). For a higher reliability the control system is made differential, and it operates with two cuffs on adjacent fingers with pressures shifted from the mean pressure value in both directions for a constant difference (in other words, from the oscillometric maximum to the left and right). In this ‘differential’ version the principle of maximum oscillations becomes the principle of the equality of amplitudes of the simultaneous volume oscillations in the two adjacent finger cuffs. In every cardiac cycle the amplitudes of volume pulses in both cuffs are recorded and then the counter pressure level is changed according to the measured difference signal. Two cuffs of the UT9201 instrument were attached to the middle and ring fingers of the right hand. Special attention was paid to a proper attachment of finger cuffs to avoid tight or loose fixation. The UT9201 monitor has been compared to Finapres and Portapres in several clinical studies during various physiological tests and has demonstrated a good agreement with volumeclamp devices, except the episodes with intensive peripheral vasoconstriction [22–24]. Under these condition the volume-clamp instruments were found to underestimate blood pressure. Similar artifacts of Finapres have been reported by other researchers [25]. 3.2. Laser Doppler flowmetry (LDF) and respiratory movements Skin blood flow was recorded by a laser Doppler instrument (MBF3D, Moor Instruments, Axminster, Devon, UK). The bandwidth of the instrument was set at its highest level (21 kHz), the filter time constant on 0.5 s; the emitted wavelength was 820 nm. LDF flux signal was used to reveal single severe vasoconstrictions capable of affecting the accuracy of the finger blood pressure measurement. We have experienced that intensive alterations in the peripheral vasoactivity can affect both UT9201 and Finapres readings [21]. The laser Doppler probe was placed on the thumb pulp of the right hand. To detect single rapid and deep inspirations which result in arteriolar vasoconstriction, a perimetric pneumatic transducer was applied to record the respiratory movements of the chest during the whole experiment. 3.3. Signal processing and data analysis The analogue signals from the UT9201 and MBF3D instruments as well as from the perimetric transducer were digitised by an analog-to-digital converter (ADC) and transferred to the computer. The signal processing technique was analogous to that applied in our previous study [26]. Beat-to-beat MAP was obtained directly from the UT9201 servosystem. By elevation of the hand by 40 cm a controlled hydrostatic pressure drop of −31 mmHg was induced in the finger arteries of a subject (supposing that the blood density equals 1.05–1.06 g/cm3 ). The applied finger blood pressure monitor had no height level compensation unit. Three successive hand elevation procedures were conducted in each individual (Fig. 1). The data analysis session was split into two phases: (i) rest (reference) and (ii) measurement (hand elevated). During the first hand elevation procedure, the beat-to-beat MAP readings in the time period of 30 s (from 620 s to 650 s) were
Every procedure is presented with data recorded before the hand elevation (baseline) and after the hand elevation constituting changes from the baseline (dMAP, mmHg). Values in every subject are averaged over 30 s. a Significant (p < 0.001) calculated by Student’s paired t-test. b Not significant (p = 0.18), second procedure vs. first calculated by Student’s paired t-test. c Not significant (p = 0.12), third procedure vs. first calculated by Student’s paired t-test. d Not significant (p = 0.29) calculated by Student’s paired t-test.
0.5 (1.6)d −30.5 (1.6)a 81.5 (9.6) 81.2 (8.2) 81.8 (10.8) Group mean (S.D.)
−31.1 (2.1)a
−30.4 (1.9)a , b
−30.0 (2.2)a , c
−31.4 −30.6 −30.3 −31.0 −27.0 −27.7 −30.3 −30.6 −31.2 −33.6 −31.4 −29.8 −30.9 −31.6 −30.6 −29.9 −29.2 −31.0 −26.7 −25.9 −32.6 −26.8 −32.4 −33.0 −31.3 −30.6 −29.4 −31.0 77.4 91.8 93.1 93.8 94.6 67.4 90.6 84.2 77.4 72.8 72.8 77.8 77.5 69.6
Mean (mmHg)
77.5 89.3 95.6 93.2 88.4 71.6 84.4 84.2 76.7 72.6 73.5 73.0 82.7 73.7
−31.8 −30.6 −29.4 −28.6 −26.7 −27.6 −28.9 −33.0 −32.0 −32.7 −31.5 −30.1 −31.8 −31.2
Mean (mmHg)
−32.4 −31.2 −32.2 −33.3 −27.5 −29.5 −29.4 −32.0 −29.1 −35.1 −31.5 −28.6 −31.6 −32.6
Mean (mmHg)
77.8 90.3 97.4 99.7 91.9 70.3 84.1 94.3 74.7 72.1 72.2 73.2 77.3 70.0
Third procedure
Baseline
Change from baseline at elevated position Mean (mmHg) Second procedure
Baseline
Fig. 2 illustrates a typical time course of MAP, LDF and respiration movements during successive hand elevation procedures in one person (subject B). It can be seen that the MAP pattern entirely tracks the hydrostatic change regardless of moderate spontaneous fluctuations in the pressure. At about 680 s a deep inspiration can be detected resulting in a sharp fall of the skin blood flow signal. This may interfere with readings of the blood pressure measurement. Fortunately, this happened outside the data collection period (see Fig. 1) and thus did not influence results of the study. An averaged response for three hand elevations for subject B is shown in Fig. 3. The main finding of the study is that there was no significant difference between the MAP responses of the three successive elevations and the hydrostatic reference (Fig. 4 and Table 1). A good agreement between the evoked MAP changes during all the three hand elevations (−31.2, −30.4 and −30.0 mmHg, respectively) and the calculated hydrostatic pressure change (−31.0 mmHg) was measured. However, a slight “overshoot” can be noticed in the averaged MAP responses when the hand reached the upper level (Figs. 3 and 4). The lower transition rate in the present study (40 cm per 10 s instead of 40 cm per 5 s in our earlier measure-
First procedure
5. Discussion
Subject
The data of beat-to-beat MAP recordings during three successive hand elevation procedures in 14 subjects are listed in Table 1. Every procedure is presented with data recorded before the hand elevation (i.e. baseline value) and after the hand elevation constituting change from the baseline. Data in Table 1 show that the group-averaged changes from baseline to hand-elevated position in the case of the second procedure and in the case of the third procedure were not statistically significant versus the change for the first procedure. The levels of significance p were equal to 0.18 and 0.12, respectively. The group-averaged blood pressure changes over three procedures versus hydrostatic reference were also not statistically significant (p = 0.29). Fig. 2 is an example of an original recording in one individual (subject B). Responses in MAP, LDF and respiration during three successive hand elevation procedures are shown. Fig. 3 is a graphic illustration of the averaged three successive MAP responses to hand elevation in the observed subject. The group-averaged beat-to-beat MAP responses during the first, second and third hand elevation procedures are exposed in Fig. 4.
Table 1 Summary of individual and group mean MAP responses during three successive hand elevations by 40 cm in 14 subjects.
4. Results
Baseline
Change from baseline at elevated position Mean (mmHg)
To test for the presence of significant differences in the readings obtained by the UT9201 monitor, Student’s paired t-test was used. To test all the hypotheses, a level of significance of 0.05 was applied. Data are expressed as mean and standard deviation (in parentheses).
A B C D F G H I J K M N O P
3.4. Statistics
Change from baseline at elevated position Mean (mmHg)
Mean for 3 procedures
Difference from hydrostatic reference at elevated position Mean (S.D.) (mmHg)
included in the analysis. The readings of MAP over the control period of 30 s (from 570 s to 600 s) were defined as a baseline (reference). This baseline value was then subtracted from the measured blood pressure. In this way the signal dMAP was obtained, thus expressing a change from the baseline. The second and third hand elevation procedures were analysed in the same way. Then the mean dMAP for three procedures in every subject was calculated as an individual mean response to the hand elevation.
−0.4 (0.9) 0.4 (0.7) 0.7 (1.7) 0.0 (2.4) 4.0 (0.5) 3.3 (1.8) 0.7 (2.0) 0.4 (3.3) −0.2 (1.8) −2.6 (1.3) −0.4 (0.1) 1.2 (1.0) 0.1 (1.3) −0.6 (0.9)
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Change from baseline at elevated position Mean (mmHg)
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Fig. 2. Example of a multiparameter recording in subject B during a session of three successive hand elevation procedures. Finger beat-to-beat mean arterial pressure (MAP, mmHg), fingertip skin blood flow (LDF, arbitrary units, au) and respiratory movements (r, arbitrary units, au; upwards: inspiration, downwards: expiration) are shown.
ment [16]) seems to reduce the “overshoots”. This is consistent with the findings of Tschakovsky and Hughson [27] reporting transient vasodilatation as a result of venous emptying at arm elevation. It is our opinion that the supine position instead of sitting could also contribute to a smaller variance of readings in the present study (S.D. being 1.9–2.2 mmHg vs. 4.2 mmHg in the earlier investigation). Observing individual data in Table 1 one can notice that for each of the 14 subjects the individual mean differences (MAP minus hydrostatic reference) did not exceed 4 mmHg while the standard error of these differences was less than 3.5 mmHg. This allows concluding that the elevation-evoked local blood pressure changes in the finger arteries quite adequately responded in all the healthy subjects. Since physiological compensatory mechanisms were found not to affect the applied hand elevation test, data in the rightmost column of Table 1 can be used for the hydrostatic validation of the accuracy of individual measurements. For instance, subject F is characterized by a relatively large bias and small variance. Frequently this kind of systematic error can be reduced by slightly repositioning the cuff. The results in subject I show that the cuff was adjusted well, but a relatively high variance might have been caused by intensive spontaneous fluctuations in the blood pressure. To reduce the activity of MAP fluctuation, a lower room temperature can be recommended (21–22 ◦ C instead of 24–25 ◦ C in our experiment). At a lower ambient temperature thermoregulatory vasoconstrictions weaken considerably [28]. On the other hand, the fingers should be warm enough to ensure reliable work of a finger BP instrument [29]. Thus, by applying the described hand elevation test, it is possible to find out and remove inaccuracies which contribute to the differences between the intra-arterial and cuff pressure. Normally these pressures should be equal. It is our opinion that a
Fig. 3. An averaged over three hand elevations finger beat-to-beat MAP response in subject B. The signal is expressed as a change from the baseline (dMAP, mmHg).
recalibration of the instrument for work with incorrectly adjusted cuffs (distortions in pressure transfer) or with narrow volume pulses (arteries contracted) is not a good solution for the problem. A better way is to revise experimental conditions. Even when an attempt to improve the accuracy fails, the investigator will still get information on the reliability of the measurement. A question may be raised about the accuracy of measurement of the evoked blood pressure changes by UT9201. In our recent study [16] we compared responses of UT9201 and Finapres to
Fig. 4. Group-averaged finger beat-to-beat MAP responses during the first, second and third hand elevation procedures, calculated from corresponding individual responses in 14 subjects. The signals are expressed as changes from the baseline (dMAP, mmHg).
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hand elevation by 40 cm. Both devices showed similar results in healthy subjects, the differences (MAP minus hydrostatic change) being −0.1 (4.2) mmHg for UT9201 and 1.2 (4.9) mmHg for Finapres, respectively. As mentioned afore, the servo-oscillometric device UT9201 has been compared to Finapres and Portapres in a number of clinical studies during various physiological tests and has demonstrated in general a good agreement with volume-clamp devices. Blood vessels respond to a transmural pressure increase with constriction, and to pressure reduction with dilation. This behaviour, termed ‘myogenic response’ was first described by Bayliss [20] and serves to control blood flow to organs after acute pressure changes. The regulatory processes accompanying hand lifting or lowering [13] may cause some differences between the actually recorded blood pressure change and the calculated hydrostatic reference signal. However, as shown above, we did not reveal a significant regulatory contribution to responses after 20 s from the beginning of each procedure during a 30-s period (i.e. when the data collection was performed). A problem that has to be addressed in hydrostatic validation is stability of the blood density. It is known that individual variations of several haematological factors may slightly change its value. However, an analysis provided by Sun and Jones [14] shows that a maximum 0.5 mmHg error may be introduced by the haematological variation among normal adults in the case of a 100 mmHg hydrostatic pressure change. In our experiments we used a hydrostatic pressure change of −31 mmHg, which covers about one third of the pressure scale needed for MAP registration. In principle, this number can be notably enlarged. In [15] the evoked hydrostatic pressure variations ranged from −40 to +40 mmHg, which was achieved by lifting and lowering a hand in a large range above and below the heart level. As a result, the pressure scale of the instrument was better verified by the controlled hydrostatic pressure. A drawback of this approach was the finding that blood pressure responses to hand postural movements above and below the heart level appeared to be asymmetrical: a statistically significant 8% difference in the corresponding slopes was detected (the slope being 1.06 for the hand above and 0.98 for the hand below the heart level). The asymmetry was explained by the displacement of extra-vascular liquids. Another experimental design was applied in [14] to validate oscillometric wrist monitors. Two oscillometric devices were used to provide simultaneous measurements of the pressures in the right and left wrists. To increase the hydrostatic pressure difference, one limb was placed vertically down while the other vertically up. Simultaneous blood pressure measurements were performed on each subject with the positions of the two limbs alternated for succeeding measurements. A disadvantage of the last set-up is that two similar blood pressure monitors are required. The study also revealed a statistically significant difference between left-arm-down/right-arm-up and left-arm-up/right-arm-down measurements. The asymmetry was remarkable for systolic pressures and less pronounced for MAP. This phenomenon was assumed to be related to the reflectance caused by intrathoracic vasculature asymmetry. In the present study as well as in most of the referred studies the hydrostatic pressure changes were introduced in healthy subjects. Limits of application of the proposed methodology in elderly subjects or in patients with cardiovascular pathology need further investigation. It should be mentioned that the hydrostatic principle is increasingly used in new developments for calibrating the cuffless blood pressure measurement or performing the cuffless transmural pressure scan in upper or lower limbs [30–33].
6. Conclusion Summarizing the study we can conclude that there was no significant difference between the mean arterial pressure responses to successive hand elevations in healthy subjects and the hydrostatic reference. The height difference of approximately 40 cm and rate of 4–5 cm/s can be recommended for the hand elevation test. The applied hydrostatic test may be useful for assessing the accuracy of beat-to-beat finger blood pressure measurement. Acknowledgment This work was supported by Grant 7723 from the Estonian Science Foundation. Conflict of interest None. References [1] Guelen I, Westerhof BE, van Der Sar GL, van Montfrans GA, Kiemeneij F, Wesseling KH, Bos WJ. Finometer, finger pressure measurements with the possibility to reconstruct brachial pressure. Blood Press Monit 2003;8:27–30. [2] Schutte AE, Huisman HW, van Rooyen JM, Oosthuizen W, Jerling JC. Sensitivity of the Finometer device in detecting acute and medium-term changes in cardiovascular function. Blood Press Monit 2003;8:195–201. [3] Parati G, Ongaro G, Bilo G, Glavina F, Castiglioni P, Di Rienzo M, Mancia G. Noninvasive beat-to-beat blood pressure monitoring: new developments. Blood Press Monit 2003;8:31–6. ˜ J. Photoelectric measurement of blood pressure, volume and flow in the [4] Penáz finger. In: Digest of the 10th International Conference on Medical and Biological Engineering. 1973. p. 104. [5] Reeben V, Epler M. Indirect Continuous Measurement of Mean Arterial Pressure. In: Ghista DN, editor. Advances in cardiovascular physics, cardiovascular engineering. Part II. Monitoring, 5. Basel: Karger; 1983. p. 90–118. [6] Jones RDM, Kornberg JP, Roulson CJ, Visram AR, Irwin MG. The Finapres 2300e finger cuff. Anaesthesia 1993;48:611–5. [7] Jagomägi K, Talts J, Raamat R, Länsimies E. Continuous non-invasive measurement of mean blood pressure in fingers by volume-clamp and differential oscillometric method. Clin Physiol 1996;16:551–60. [8] 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;1:17–29. [9] Wesseling KH. Finapres, continuous noninvasive finger arterial pressure based ˜ on the method of Penáz. In: Rüddel H, Curio I, editors. Non-invasive continuous blood pressure measurement. Bern, New York, Paris: Peter Lang, Frankfurt am Main; 1991. p. 9–17. [10] Imholz BPM, Parati G, Mancia G, Wesseling KH. Effects of graded vasoconstriction upon the measurement of finger arterial pressure. J Hypertens 1992;10:979–84. [11] Fortin J, Marte W, Grüllenberger R, Hacker A, Habenbacher W, Heller A, Wagner C, Wach P, Skrabal F. Continuous non-invasive blood pressure monitoring using concentrically interlocking control loops. Comput Biol Med 2006;36:941–57. ˜ J. Criteria for set point estimation in the volume clamp method of blood [12] Penáz pressure measurement. Physiol Res 1992;41:5–10. [13] Jepsen H, Gaehtgens P. Postural vascular response in human skin: passive and active reactions to alteration of transmural pressure. Am J Physiol Heart Circ Physiol 1993;265:H949–58. [14] Sun M, Jones R. A hydrostatic method assessing accuracy and reliability while revealing asymmetry in blood pressure measurements. Biomed Instrum Technol 1995;29:331–42. [15] Gizdulich P, Aschero G, Guerrisi M, Wesseling KH. Effect of hydrostatic pressure on finger pressure measured non-invasively by Finapres. Homeostasis 1995;36(2–3):120–9. [16] Raamat R, Talts J, Jagomägi K, Kivastik J, Länsimies E, Jurvelin J. Simultaneous application of differential servo-oscillometry and volume-clamp plethysmography for continuous non-invasive recording of the finger blood pressure response to a hand postural change. J Med Eng Technol 2006;30:139–44. [17] Ursino M, Cristalli C. A mathematical study of some biomechanical factors affecting the oscillometric blood pressure measurement. IEEE Trans Biomed Eng 1996;43:761–78. ˜ [18] Penáz J, Honzikova N, Jurak P. Vibration plethysmography: a method for studying the visco-elastic properties of finger arteries. Med Biol Eng Comput 1997;35:633–7. [19] Wesseling KH, de Wit B, van der Hoeven GMA, van Goudoever J, Settels JJ. Physiocal, calibrating finger vascular physiology for Finapres. Homeostasis 1995;36(2–3):67–82.
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Finger beat-to-beat blood pressure responses to successive hand elevations R. Raamat ∗ , K. Jagomägi, J. Talts, I. Mäger Department of Physiology, University of Tartu, 19 Ravila Street, 50411 Tartu, Estonia
a r t i c l e
i n f o
Article history: Received 28 March 2008 Received in revised form 21 July 2008 Accepted 5 October 2008 Keywords: Hand elevation Postural change Hydrostatic pressure Finger beat-to-beat blood pressure
a b s t r a c t We investigated finger beat-to-beat blood pressure responses to a series of successive hand elevations in 14 normal volunteers. By passive elevation of the hand by 40 cm and lowering it again after a minute, calibrated hydrostatic pressure changes were induced in the finger arteries of the subjects. Three successive procedures with a 2-min interval between them were performed. Transitions between positions were completed smoothly over a 10-s period. Non-invasive beat-to-beat mean arterial pressure (MAP) in the finger arteries was measured by applying the servo-oscillometric physiograph (University of Tartu, Estonia). A good agreement between the evoked MAP changes during all the three hand elevations (−31.2, −30.4 and −30.0 mmHg, respectively) and the calculated hydrostatic pressure change (−31.0 mmHg) was obtained. The height difference of approximately 40 cm and rate of 4–5 cm/s can be recommended for the hand elevation test, greater postural changes and higher rates may diminish agreement between the measured blood pressure response and the corresponding hydrostatic pressure change. The applied hydrostatic test may be helpful for assessing the accuracy of beat-to-beat finger blood pressure measurement. © 2008 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Continuous non-invasive blood pressure measurement in the finger arteries is increasingly used in clinical research. This involves the finger beat-to-beat blood pressure measurement with the help of the Finapres monitor (Ohmeda, Denver, USA) and its portable version Portapres (TNO, Amsterdam, Netherlands), as well as estimation by means of a few new developments—Finometer (Finapres Medical Systems, Arnhem, Netherlands) [1,2] and Task Force Monitor (CNSystems, Graz, Austria) [3]. All these devices are based on the ˜ volume-clamp method, first described by Penáz [4]. Some experimental servo-oscillometric monitors have also been applied to obtain beat-to-beat values of the finger arterial blood pressure [5]. It has been found that the accuracy of finger blood pressure measurement by Finapres is sensitive to cuff malapplication. This may be due to the position of the finger arteries relative to the infrared diodes situated on the inner surface of the pressure cuff [6]. Mean arterial pressure (MAP) underestimation in the case of application of tight finger cuffs on the one hand, and MAP overestimation in the case of application of loose finger cuffs on the other hand, was pointed out in [7]. Even when the cuffs are adjusted by an experienced operator, inaccuracies in the blood pressure measurement may appear due to individual peculiarities in the finger anatomy, preventing full transfer of the cuff pressure to the artery. The con-
∗ Corresponding author. E-mail address: [email protected] (R. Raamat).
tracted or stiffened wall of the artery also increases the uncertainty of measurement. Another type of measurement inaccuracies can be qualified as instrumental. Instrumental accuracy characterizes, first of all, the capacity of the servo-system of the finger monitor to ensure reliable closed-loop work of the instrument for the duration of a change of the vascular tone. As a rule, the overall gain factor change and setpoint shift affect readings of the volume-clamp monitors [8–10]. Although several innovations have been reported to partly overcome these limitations [11–12], the improvements have not yet been introduced into the manufactured monitors. The hand elevation test has been recommended by vendors of finger beat-to-beat blood pressure monitors for quickly checking the accuracy of operation of the instrument. However, although widely used and highly appreciated for rough assessment, the accuracy of such tests frequently remains questionable. From the physical point of view, a hydrostatic approach is attractive due to its simplicity and precision of calculating the hydrostatic pressure exerted by a column of blood. On the other hand, several physiological regulations accompanying hand postural change may interfere with the pure physical response [13]. There are only a few studies discussing the metrological aspects of the hydrostatic validation of the blood pressure measurement [14–16]. Beat-to-beat blood pressure responses to a series of hand elevations have not received satisfactory attention although successive hand elevations are usual in practical applications. As demonstrated by repeated blood pressure measurements on the brachial artery [17], the successive transmural pressure balance
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R. Raamat et al. / Medical Engineering & Physics 31 (2009) 522–527
Fig. 1. Schematic presentation of an experimental protocol. Beat-to-beat MAP in the fingers is continuously monitored by the servo-oscillometric UT9201 monitor. After a 10-min equilibrium period three successive hand elevation procedures were performed with a 2-min interval between them. The time periods chosen for data analysis are shown.
changes in the tissue may result in moderately different blood pressure responses compared to those of a single measurement. Due to viscoelastic properties of the arterial wall, the multiple hand elevations may cause more complicated reactions than those evoked by a single elevation. Besides the arterial viscous properties, the filling and empting of extra-arterial vessels surely play a significant role [18]. The filling and emptying of vessels of different size and function take place with different time constant and may affect sequential photoplethysmographic measurement [19]. Myogenic response [20], known to control blood flow to organs after acute pressure changes should be also considered. In the present study we investigate the effect of successive hand elevations on the beat-to-beat finger MAP measured by the differential servo-oscillometric method in healthy persons. A further aim of the study was to show that the applied hydrostatic test may be helpful for assessing the accuracy of non-invasive beat-to-beat blood pressure measurement. 2. Methods 2.1. Subjects The subjects were 14 volunteers, 8 females and 6 males, aged from 18 to 34. They had no history of vascular disease and gave their informed consent to participate in the study. The study was approved by the Ethics Committee of the University of Tartu. 2.2. Experimental design The subject rested in a supine position on a couch. After an initial equilibrium period (10 min) the subject’s right hand was passively raised with the help of a tilting support to the height of 40 cm from the initial level. It remained there for 1 min. Then the hand was brought back to the initial position. Transitions between two positions were completed smoothly over a 10-s period. Three successive hand elevation procedures were performed with a 2-min interval between them (Fig. 1). Finger beat-to-beat MAP, fingertip skin blood flow and respiratory movements were continuously recorded in every subject. The experiments were carried out at room temperature of 23–25 ◦ C. 3. Technique 3.1. Finger beat-to-beat mean arterial pressure Finger beat-to-beat MAP was measured by the UT9201 physiograph, University of Tartu, Estonia. This instrument applies the servo-oscillometric method for measuring finger beat-to-beat arte-
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rial pressure [5,21]. Like Finapres this method needs a servo-system to control the counter pressure in the finger cuff. The difference is that the volume-clamp instrument tracks the instantaneous intraarterial pressure while the servo-oscillometric device tracks the mean intra-arterial pressure. By modulating the counter pressure level according to the criterion of getting maximum volume oscillations in the cuff in every cardiac cycle, the counter pressure in the cuff is kept equal to the MAP in finger arteries (Marey’s principle). For a higher reliability the control system is made differential, and it operates with two cuffs on adjacent fingers with pressures shifted from the mean pressure value in both directions for a constant difference (in other words, from the oscillometric maximum to the left and right). In this ‘differential’ version the principle of maximum oscillations becomes the principle of the equality of amplitudes of the simultaneous volume oscillations in the two adjacent finger cuffs. In every cardiac cycle the amplitudes of volume pulses in both cuffs are recorded and then the counter pressure level is changed according to the measured difference signal. Two cuffs of the UT9201 instrument were attached to the middle and ring fingers of the right hand. Special attention was paid to a proper attachment of finger cuffs to avoid tight or loose fixation. The UT9201 monitor has been compared to Finapres and Portapres in several clinical studies during various physiological tests and has demonstrated a good agreement with volumeclamp devices, except the episodes with intensive peripheral vasoconstriction [22–24]. Under these condition the volume-clamp instruments were found to underestimate blood pressure. Similar artifacts of Finapres have been reported by other researchers [25]. 3.2. Laser Doppler flowmetry (LDF) and respiratory movements Skin blood flow was recorded by a laser Doppler instrument (MBF3D, Moor Instruments, Axminster, Devon, UK). The bandwidth of the instrument was set at its highest level (21 kHz), the filter time constant on 0.5 s; the emitted wavelength was 820 nm. LDF flux signal was used to reveal single severe vasoconstrictions capable of affecting the accuracy of the finger blood pressure measurement. We have experienced that intensive alterations in the peripheral vasoactivity can affect both UT9201 and Finapres readings [21]. The laser Doppler probe was placed on the thumb pulp of the right hand. To detect single rapid and deep inspirations which result in arteriolar vasoconstriction, a perimetric pneumatic transducer was applied to record the respiratory movements of the chest during the whole experiment. 3.3. Signal processing and data analysis The analogue signals from the UT9201 and MBF3D instruments as well as from the perimetric transducer were digitised by an analog-to-digital converter (ADC) and transferred to the computer. The signal processing technique was analogous to that applied in our previous study [26]. Beat-to-beat MAP was obtained directly from the UT9201 servosystem. By elevation of the hand by 40 cm a controlled hydrostatic pressure drop of −31 mmHg was induced in the finger arteries of a subject (supposing that the blood density equals 1.05–1.06 g/cm3 ). The applied finger blood pressure monitor had no height level compensation unit. Three successive hand elevation procedures were conducted in each individual (Fig. 1). The data analysis session was split into two phases: (i) rest (reference) and (ii) measurement (hand elevated). During the first hand elevation procedure, the beat-to-beat MAP readings in the time period of 30 s (from 620 s to 650 s) were
Every procedure is presented with data recorded before the hand elevation (baseline) and after the hand elevation constituting changes from the baseline (dMAP, mmHg). Values in every subject are averaged over 30 s. a Significant (p < 0.001) calculated by Student’s paired t-test. b Not significant (p = 0.18), second procedure vs. first calculated by Student’s paired t-test. c Not significant (p = 0.12), third procedure vs. first calculated by Student’s paired t-test. d Not significant (p = 0.29) calculated by Student’s paired t-test.
0.5 (1.6)d −30.5 (1.6)a 81.5 (9.6) 81.2 (8.2) 81.8 (10.8) Group mean (S.D.)
−31.1 (2.1)a
−30.4 (1.9)a , b
−30.0 (2.2)a , c
−31.4 −30.6 −30.3 −31.0 −27.0 −27.7 −30.3 −30.6 −31.2 −33.6 −31.4 −29.8 −30.9 −31.6 −30.6 −29.9 −29.2 −31.0 −26.7 −25.9 −32.6 −26.8 −32.4 −33.0 −31.3 −30.6 −29.4 −31.0 77.4 91.8 93.1 93.8 94.6 67.4 90.6 84.2 77.4 72.8 72.8 77.8 77.5 69.6
Mean (mmHg)
77.5 89.3 95.6 93.2 88.4 71.6 84.4 84.2 76.7 72.6 73.5 73.0 82.7 73.7
−31.8 −30.6 −29.4 −28.6 −26.7 −27.6 −28.9 −33.0 −32.0 −32.7 −31.5 −30.1 −31.8 −31.2
Mean (mmHg)
−32.4 −31.2 −32.2 −33.3 −27.5 −29.5 −29.4 −32.0 −29.1 −35.1 −31.5 −28.6 −31.6 −32.6
Mean (mmHg)
77.8 90.3 97.4 99.7 91.9 70.3 84.1 94.3 74.7 72.1 72.2 73.2 77.3 70.0
Third procedure
Baseline
Change from baseline at elevated position Mean (mmHg) Second procedure
Baseline
Fig. 2 illustrates a typical time course of MAP, LDF and respiration movements during successive hand elevation procedures in one person (subject B). It can be seen that the MAP pattern entirely tracks the hydrostatic change regardless of moderate spontaneous fluctuations in the pressure. At about 680 s a deep inspiration can be detected resulting in a sharp fall of the skin blood flow signal. This may interfere with readings of the blood pressure measurement. Fortunately, this happened outside the data collection period (see Fig. 1) and thus did not influence results of the study. An averaged response for three hand elevations for subject B is shown in Fig. 3. The main finding of the study is that there was no significant difference between the MAP responses of the three successive elevations and the hydrostatic reference (Fig. 4 and Table 1). A good agreement between the evoked MAP changes during all the three hand elevations (−31.2, −30.4 and −30.0 mmHg, respectively) and the calculated hydrostatic pressure change (−31.0 mmHg) was measured. However, a slight “overshoot” can be noticed in the averaged MAP responses when the hand reached the upper level (Figs. 3 and 4). The lower transition rate in the present study (40 cm per 10 s instead of 40 cm per 5 s in our earlier measure-
First procedure
5. Discussion
Subject
The data of beat-to-beat MAP recordings during three successive hand elevation procedures in 14 subjects are listed in Table 1. Every procedure is presented with data recorded before the hand elevation (i.e. baseline value) and after the hand elevation constituting change from the baseline. Data in Table 1 show that the group-averaged changes from baseline to hand-elevated position in the case of the second procedure and in the case of the third procedure were not statistically significant versus the change for the first procedure. The levels of significance p were equal to 0.18 and 0.12, respectively. The group-averaged blood pressure changes over three procedures versus hydrostatic reference were also not statistically significant (p = 0.29). Fig. 2 is an example of an original recording in one individual (subject B). Responses in MAP, LDF and respiration during three successive hand elevation procedures are shown. Fig. 3 is a graphic illustration of the averaged three successive MAP responses to hand elevation in the observed subject. The group-averaged beat-to-beat MAP responses during the first, second and third hand elevation procedures are exposed in Fig. 4.
Table 1 Summary of individual and group mean MAP responses during three successive hand elevations by 40 cm in 14 subjects.
4. Results
Baseline
Change from baseline at elevated position Mean (mmHg)
To test for the presence of significant differences in the readings obtained by the UT9201 monitor, Student’s paired t-test was used. To test all the hypotheses, a level of significance of 0.05 was applied. Data are expressed as mean and standard deviation (in parentheses).
A B C D F G H I J K M N O P
3.4. Statistics
Change from baseline at elevated position Mean (mmHg)
Mean for 3 procedures
Difference from hydrostatic reference at elevated position Mean (S.D.) (mmHg)
included in the analysis. The readings of MAP over the control period of 30 s (from 570 s to 600 s) were defined as a baseline (reference). This baseline value was then subtracted from the measured blood pressure. In this way the signal dMAP was obtained, thus expressing a change from the baseline. The second and third hand elevation procedures were analysed in the same way. Then the mean dMAP for three procedures in every subject was calculated as an individual mean response to the hand elevation.
−0.4 (0.9) 0.4 (0.7) 0.7 (1.7) 0.0 (2.4) 4.0 (0.5) 3.3 (1.8) 0.7 (2.0) 0.4 (3.3) −0.2 (1.8) −2.6 (1.3) −0.4 (0.1) 1.2 (1.0) 0.1 (1.3) −0.6 (0.9)
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Change from baseline at elevated position Mean (mmHg)
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Fig. 2. Example of a multiparameter recording in subject B during a session of three successive hand elevation procedures. Finger beat-to-beat mean arterial pressure (MAP, mmHg), fingertip skin blood flow (LDF, arbitrary units, au) and respiratory movements (r, arbitrary units, au; upwards: inspiration, downwards: expiration) are shown.
ment [16]) seems to reduce the “overshoots”. This is consistent with the findings of Tschakovsky and Hughson [27] reporting transient vasodilatation as a result of venous emptying at arm elevation. It is our opinion that the supine position instead of sitting could also contribute to a smaller variance of readings in the present study (S.D. being 1.9–2.2 mmHg vs. 4.2 mmHg in the earlier investigation). Observing individual data in Table 1 one can notice that for each of the 14 subjects the individual mean differences (MAP minus hydrostatic reference) did not exceed 4 mmHg while the standard error of these differences was less than 3.5 mmHg. This allows concluding that the elevation-evoked local blood pressure changes in the finger arteries quite adequately responded in all the healthy subjects. Since physiological compensatory mechanisms were found not to affect the applied hand elevation test, data in the rightmost column of Table 1 can be used for the hydrostatic validation of the accuracy of individual measurements. For instance, subject F is characterized by a relatively large bias and small variance. Frequently this kind of systematic error can be reduced by slightly repositioning the cuff. The results in subject I show that the cuff was adjusted well, but a relatively high variance might have been caused by intensive spontaneous fluctuations in the blood pressure. To reduce the activity of MAP fluctuation, a lower room temperature can be recommended (21–22 ◦ C instead of 24–25 ◦ C in our experiment). At a lower ambient temperature thermoregulatory vasoconstrictions weaken considerably [28]. On the other hand, the fingers should be warm enough to ensure reliable work of a finger BP instrument [29]. Thus, by applying the described hand elevation test, it is possible to find out and remove inaccuracies which contribute to the differences between the intra-arterial and cuff pressure. Normally these pressures should be equal. It is our opinion that a
Fig. 3. An averaged over three hand elevations finger beat-to-beat MAP response in subject B. The signal is expressed as a change from the baseline (dMAP, mmHg).
recalibration of the instrument for work with incorrectly adjusted cuffs (distortions in pressure transfer) or with narrow volume pulses (arteries contracted) is not a good solution for the problem. A better way is to revise experimental conditions. Even when an attempt to improve the accuracy fails, the investigator will still get information on the reliability of the measurement. A question may be raised about the accuracy of measurement of the evoked blood pressure changes by UT9201. In our recent study [16] we compared responses of UT9201 and Finapres to
Fig. 4. Group-averaged finger beat-to-beat MAP responses during the first, second and third hand elevation procedures, calculated from corresponding individual responses in 14 subjects. The signals are expressed as changes from the baseline (dMAP, mmHg).
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hand elevation by 40 cm. Both devices showed similar results in healthy subjects, the differences (MAP minus hydrostatic change) being −0.1 (4.2) mmHg for UT9201 and 1.2 (4.9) mmHg for Finapres, respectively. As mentioned afore, the servo-oscillometric device UT9201 has been compared to Finapres and Portapres in a number of clinical studies during various physiological tests and has demonstrated in general a good agreement with volume-clamp devices. Blood vessels respond to a transmural pressure increase with constriction, and to pressure reduction with dilation. This behaviour, termed ‘myogenic response’ was first described by Bayliss [20] and serves to control blood flow to organs after acute pressure changes. The regulatory processes accompanying hand lifting or lowering [13] may cause some differences between the actually recorded blood pressure change and the calculated hydrostatic reference signal. However, as shown above, we did not reveal a significant regulatory contribution to responses after 20 s from the beginning of each procedure during a 30-s period (i.e. when the data collection was performed). A problem that has to be addressed in hydrostatic validation is stability of the blood density. It is known that individual variations of several haematological factors may slightly change its value. However, an analysis provided by Sun and Jones [14] shows that a maximum 0.5 mmHg error may be introduced by the haematological variation among normal adults in the case of a 100 mmHg hydrostatic pressure change. In our experiments we used a hydrostatic pressure change of −31 mmHg, which covers about one third of the pressure scale needed for MAP registration. In principle, this number can be notably enlarged. In [15] the evoked hydrostatic pressure variations ranged from −40 to +40 mmHg, which was achieved by lifting and lowering a hand in a large range above and below the heart level. As a result, the pressure scale of the instrument was better verified by the controlled hydrostatic pressure. A drawback of this approach was the finding that blood pressure responses to hand postural movements above and below the heart level appeared to be asymmetrical: a statistically significant 8% difference in the corresponding slopes was detected (the slope being 1.06 for the hand above and 0.98 for the hand below the heart level). The asymmetry was explained by the displacement of extra-vascular liquids. Another experimental design was applied in [14] to validate oscillometric wrist monitors. Two oscillometric devices were used to provide simultaneous measurements of the pressures in the right and left wrists. To increase the hydrostatic pressure difference, one limb was placed vertically down while the other vertically up. Simultaneous blood pressure measurements were performed on each subject with the positions of the two limbs alternated for succeeding measurements. A disadvantage of the last set-up is that two similar blood pressure monitors are required. The study also revealed a statistically significant difference between left-arm-down/right-arm-up and left-arm-up/right-arm-down measurements. The asymmetry was remarkable for systolic pressures and less pronounced for MAP. This phenomenon was assumed to be related to the reflectance caused by intrathoracic vasculature asymmetry. In the present study as well as in most of the referred studies the hydrostatic pressure changes were introduced in healthy subjects. Limits of application of the proposed methodology in elderly subjects or in patients with cardiovascular pathology need further investigation. It should be mentioned that the hydrostatic principle is increasingly used in new developments for calibrating the cuffless blood pressure measurement or performing the cuffless transmural pressure scan in upper or lower limbs [30–33].
6. Conclusion Summarizing the study we can conclude that there was no significant difference between the mean arterial pressure responses to successive hand elevations in healthy subjects and the hydrostatic reference. The height difference of approximately 40 cm and rate of 4–5 cm/s can be recommended for the hand elevation test. The applied hydrostatic test may be useful for assessing the accuracy of beat-to-beat finger blood pressure measurement. Acknowledgment This work was supported by Grant 7723 from the Estonian Science Foundation. Conflict of interest None. References [1] Guelen I, Westerhof BE, van Der Sar GL, van Montfrans GA, Kiemeneij F, Wesseling KH, Bos WJ. Finometer, finger pressure measurements with the possibility to reconstruct brachial pressure. Blood Press Monit 2003;8:27–30. [2] Schutte AE, Huisman HW, van Rooyen JM, Oosthuizen W, Jerling JC. Sensitivity of the Finometer device in detecting acute and medium-term changes in cardiovascular function. Blood Press Monit 2003;8:195–201. [3] Parati G, Ongaro G, Bilo G, Glavina F, Castiglioni P, Di Rienzo M, Mancia G. Noninvasive beat-to-beat blood pressure monitoring: new developments. Blood Press Monit 2003;8:31–6. ˜ J. Photoelectric measurement of blood pressure, volume and flow in the [4] Penáz finger. In: Digest of the 10th International Conference on Medical and Biological Engineering. 1973. p. 104. [5] Reeben V, Epler M. Indirect Continuous Measurement of Mean Arterial Pressure. In: Ghista DN, editor. Advances in cardiovascular physics, cardiovascular engineering. Part II. Monitoring, 5. Basel: Karger; 1983. p. 90–118. [6] Jones RDM, Kornberg JP, Roulson CJ, Visram AR, Irwin MG. The Finapres 2300e finger cuff. Anaesthesia 1993;48:611–5. [7] Jagomägi K, Talts J, Raamat R, Länsimies E. Continuous non-invasive measurement of mean blood pressure in fingers by volume-clamp and differential oscillometric method. Clin Physiol 1996;16:551–60. [8] 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;1:17–29. [9] Wesseling KH. Finapres, continuous noninvasive finger arterial pressure based ˜ on the method of Penáz. In: Rüddel H, Curio I, editors. Non-invasive continuous blood pressure measurement. Bern, New York, Paris: Peter Lang, Frankfurt am Main; 1991. p. 9–17. [10] Imholz BPM, Parati G, Mancia G, Wesseling KH. Effects of graded vasoconstriction upon the measurement of finger arterial pressure. J Hypertens 1992;10:979–84. [11] Fortin J, Marte W, Grüllenberger R, Hacker A, Habenbacher W, Heller A, Wagner C, Wach P, Skrabal F. Continuous non-invasive blood pressure monitoring using concentrically interlocking control loops. Comput Biol Med 2006;36:941–57. ˜ J. Criteria for set point estimation in the volume clamp method of blood [12] Penáz pressure measurement. Physiol Res 1992;41:5–10. [13] Jepsen H, Gaehtgens P. Postural vascular response in human skin: passive and active reactions to alteration of transmural pressure. Am J Physiol Heart Circ Physiol 1993;265:H949–58. [14] Sun M, Jones R. A hydrostatic method assessing accuracy and reliability while revealing asymmetry in blood pressure measurements. Biomed Instrum Technol 1995;29:331–42. [15] Gizdulich P, Aschero G, Guerrisi M, Wesseling KH. Effect of hydrostatic pressure on finger pressure measured non-invasively by Finapres. Homeostasis 1995;36(2–3):120–9. [16] Raamat R, Talts J, Jagomägi K, Kivastik J, Länsimies E, Jurvelin J. Simultaneous application of differential servo-oscillometry and volume-clamp plethysmography for continuous non-invasive recording of the finger blood pressure response to a hand postural change. J Med Eng Technol 2006;30:139–44. [17] Ursino M, Cristalli C. A mathematical study of some biomechanical factors affecting the oscillometric blood pressure measurement. IEEE Trans Biomed Eng 1996;43:761–78. ˜ [18] Penáz J, Honzikova N, Jurak P. Vibration plethysmography: a method for studying the visco-elastic properties of finger arteries. Med Biol Eng Comput 1997;35:633–7. [19] Wesseling KH, de Wit B, van der Hoeven GMA, van Goudoever J, Settels JJ. Physiocal, calibrating finger vascular physiology for Finapres. Homeostasis 1995;36(2–3):67–82.
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