Journal of Medical Engineering & Technology
ISSN: 0309-1902 (Print) 1464-522X (Online) Journal homepage: http://www.tandfonline.com/loi/ijmt20
Cardiac cycle phase uncertainty: another source of error in indirect blood pressure measurement C. P. Hatsell To cite this article: C. P. Hatsell (1992) Cardiac cycle phase uncertainty: another source of error in indirect blood pressure measurement, Journal of Medical Engineering & Technology, 16:4, 157-158 To link to this article: http://dx.doi.org/10.3109/03091909209030219
Published online: 09 Jul 2009.
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Date: 19 September 2015, At: 21:17
Journal of Medical Engineering 8c Technology, Volume 16, Number 4 Uuly/August 1992), pages 157-158
Downloaded by [University of Otago] at 21:17 19 September 2015
Cardiac cycle phase uncertainty: another source of error in indirect blood pressure measurement C. P. Hatsell
Measurement bias
Aerospace Medicine Directorate, Amstrong Laboratory, Brooks AFB, TX 78235, USA
Let T be the cardiac cycle period and P , the BP-cuff pressure at the first Korotkoff sound if the BP-cuff were allowed to deflate arbitrarily slowly (i.e. P, is free of bias due to cardiac cycle phase uncertainty). Then, if the BP-cuff deflates at a finite rate according to a pressure function P c ( t ) , and if 7 is defined by
Cardiac cycle phase uncertainty causes a small error in indirect estimation of arterial blood pressure by sphygmomanometry . A simple analysis yields a statistical description of the error and a rule for its reduction: correct bias b~ adding to the systolic estimate and subtracting from the diastolic estimate one-half of the per-cardiac-cycle cuff defration decrement. If several measurements are taken, the least-square estimate is approximately the arithmetic mean of the greatest and least of the bias corrected estimates.
Pc(I) = Pc,
(1) then Po, the observed blood pressure, is a random variable distributed on the interval [Pc(j+T ) , Pc(t)]. A specific case of practical importance is that of a constant BP-cuff deflation rate r and, therefore, a uniform uncertainty in cardiac cycle phase. For this case Po is uniformly distributed with probability density function
Introduction
r
Ascultatory estimation of arterial blood pressure (BP) using standard BP-cuff techniques is subject to many sources of error. Digit preference can be largely eliminated by using random-zero, zero-muddler, or automatic devices [I]. Clinically significant errors persist, however, as these devices exhibit their own peculiarities [ 2 ] .Other factors such as cuff size can also contribute to indirect BP estimation error, especially if the cuff is too small [3]. A review of the literature for another purpose revealed to this author a common characteristic error which is manifest in those studies which compare direct intra-arterial BP measurements with various indirect BP estimation methods: systolic estimates are low, and diastolic estimates are high [4-81. Auscultation when compared with oscillometry has also shown this effect ~91. It will be shown in this paper that this estimation bias is due to the a priori ignorance of the observer about the time of occurrcnce of the Korotkov sounds (uiz. cardiac cycle phase uncertainty), and that bias magnitude is a function of cuff deflation rate. A method for correcting this bias will be described, and the proper method for averaging indirect BP estimates will be presented.
Analysis First, the estimate bias due to cardiac cycle phase Uncertainty will be calculated, and then the proper method for averaging several indirect BP estimates will be presented. The major results are given by equations (4), (8) and (9), along with the attendant discussion.
[O
otherwise
where x a n d y represent values of the random variables,
Po and P,, respectively. Using ( 2 ) the BP estimate bias B is
B so
B
=
=
I
(x-PcclfPolPc ( X l P J dx.
(3)
- R / 2 , where R = r‘ T.
Note that R is cuff-pressure decrement per cardiac cycle, which can be determined by noting the cuff pressure decrease between two successive Korotkoff sounds. A similar analysis yields a diastolic pressure bias of equal magnitude but opposite sign; therefore, an unbiased estimator for indirect BP is
P=
Po 2 R/2
(4) with the negative sign chosen for systolic pressure. Hence, bias in the indirect estimation of arterial blood pressure due to cardiac cycle phase uncertainty can be corrected by adding to the systolic estimate and subtracting from the diastolic estimate one-half the cuffpressure decrement per cardiac cycle.
For example, suppose the unbiased blood pressure estimate is Pc = 120 mmHg, the heart rate is 72 beats per min, and the cuff deflation rate is a uniform 10 mmHg per three cardiac cycles; then the indirect blood pressure estimate would be biased by only 1.5 mmHg, confirming that this commonly taught ruleof-thumb is quite conservative. The standard deviation 157
0309-1902/92 53.00
0 1992 7’a)Iur
& Francis Ltd
C.
P. Hatsell Cardiac cycle phase uncertainty
for this single measurement, ignoring sources of error other than cardic cycle phase uncertainty, would be 1.5 mmHg; however, accounting multiple measurements requires special consideration. Averaging multiple measurements
A common clinical practice is to take several BP measurements with the patient quiescent and use the sample average as a BP estimate. This would reduce the measurement variance due to cardiac phase uncertainty by 1/N, where N is the number of measurements taken; however, such a n estimate is not least square. The non-linear least square estimator is the conditional mean [ 101
Downloaded by [University of Otago] at 21:17 19 September 2015
4,
where, by Bayes’ rule,
From equations (2), (3), a n d the conditional independence of the observations, f p l P c [ ~ ( l L..., P(N)lVl =
(-)R rI w w m - y l ) , 1”
Discussion Excessively slow BP-cuff deflation rates can be quite uncomfortable to the patient. Common practice has the technician inflate the cuff to a t least 160 mmHg; so at the recommended deflation rate of 10 m m H g per threc cardiac cycles, a person with a heart rate of 60 beats per min and a normal blood pressure of 120 m m H g will have 12 s of arterial occlusion before the first Korotkoff sound. For some, this is long enough to produce pain. Slow cuff deflation rates can also lead to distal venous engorgement a n d inaccuracies in diastolic pressure estimation. If the patient can be kept reasonably quiescent, the estimation technique described in this paper can allow faster cuff deflation if the rate can be held constant. Many patients are using commercially available automated BP measuring devices a t home to monitor their BP on a frequent basis. These devices could be designed to correct for measurement bias through simple computational procedures incorporated in contained hardware. Such a control mechanism is certainly feasible and should be considered as part of any BP device employing sphygmomanometry.
References 1. CANNER, P. L., BORHANI, N. O., OBERMAN, A., CUTLER,
J., PRINEAS, R. J., LANCFORD, H. and HOOPER,F. J.
j=l
(7) where U(-) is the unit step function. Combining equations (5), (6), and (7), the minimum variance estimator for large N is approximately
2. 3. 4.
5. Equation (9) is a n interesting result as it prescribes that only the minimum and maximum BP readin s be used in computing the estimate. T h e variance of follows from an elementary result in order statistics [ 111 which is stated here as a theorem.
%,,
Let xI, random and let Ify =
x2, ..., x, be n independent, identically distributed, variables w i t h unform probability density on (a,b], x: 5 xf S x$ 6 ... S x*, be their order statistics. (x*,+x*,)/2, then the variance of y i s varCy) =
6.
7.
8.
(b-a)‘ 2(n+ l)(n+2)’
Applying this theorem to (8) gives var(Pl,) =
2(N+ 1)(N+2)
which shows the estimator given by performs better than the sample mean thercforc, even though equation (8) minimum variance estimator only for always better than the sample mean. 158
9.
R2
equation (8) for all N > 2; approaches a large N , it is
10. 11.
(1991) The Hypertension Prevention Trial: assessment of the quality of blood pressure measurements. American Journal of Epidemiology, 134, 379-392. O’BRIEN, E., MEE, F., ATKINS,N. and O’MALLEY, K. (1990) Inaccuracy of the Hawksley random zero sphygmomanometer. Lancet, 337, 556. J. K. (1990) Blood CROFT,P. R. and CRUICKSHANK, pressure measurement in adults: large cuffs for all?Journal of Epidemiology and Community Health, 44, 170-1 7 3 . REBENSON-PIANO, M., HOLM,K., FORMAN, M. D. and K. T. (1989) An evaluation of two indirect KIRCHHOFF, methods of blood pressure measurement in ill patients. Nursing Research, 38, 42-45. SALAITA, K., WHELTON, P. K. and SEIDLER, A. J. (1990) A community-based evaluation of the Vita-Stat automatic blood pressure recorder. American Journal of Hypertension, 3, 366-72. RUSSELL, A. E., WING,L. M., SMITH,S. A., AYLWARD, P. E., MCRITCHIE, R. J., HASSAM, R. M., WEST,M. J. and CHALMERS, J. P. (1989) Optimal size of cuff bladder for indirect measurement of arterial pressure in adults. Journal of Hypertension, 7, 607-613. DAVIS,R. F. (1985) Clinical comparison of automated auscultatory and oscillometric and catheter-transducer measurements of arterial pressure. Journal of Clinical Monitoring, 1, 1 14- 1 19. MAHESWARAN, R., ZEZULKA, A. V., GILL,J. S., BEEVERS, G. (1988) Clinical evaluation M., DAVIES, P. and BEEVERS, of the Copal UA-251 and the Dinamap 1848 automatic blood-pressure monitors. Journal of Medical Engineering and Technology, 12, 160-163. PESSENHOFER, H. (1986) Single cuff comparison of two methods for indirect measurement of arterial blood pressure: standard auscultatory method versus automatic oscillometric method. Basic Research in Cardiology, 81, 101- 109. VANTREES, H. L. (1968) Detection, Estimation, and Modulation Theory (John Wiley and Sons, New York), p. 56. KARLIN,S. (1965) A First Course in Stochastic Processes (Academic Press, New York), p. 236.
ISSN: 0309-1902 (Print) 1464-522X (Online) Journal homepage: http://www.tandfonline.com/loi/ijmt20
Cardiac cycle phase uncertainty: another source of error in indirect blood pressure measurement C. P. Hatsell To cite this article: C. P. Hatsell (1992) Cardiac cycle phase uncertainty: another source of error in indirect blood pressure measurement, Journal of Medical Engineering & Technology, 16:4, 157-158 To link to this article: http://dx.doi.org/10.3109/03091909209030219
Published online: 09 Jul 2009.
Submit your article to this journal
Article views: 2
View related articles
Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=ijmt20 Download by: [University of Otago]
Date: 19 September 2015, At: 21:17
Journal of Medical Engineering 8c Technology, Volume 16, Number 4 Uuly/August 1992), pages 157-158
Downloaded by [University of Otago] at 21:17 19 September 2015
Cardiac cycle phase uncertainty: another source of error in indirect blood pressure measurement C. P. Hatsell
Measurement bias
Aerospace Medicine Directorate, Amstrong Laboratory, Brooks AFB, TX 78235, USA
Let T be the cardiac cycle period and P , the BP-cuff pressure at the first Korotkoff sound if the BP-cuff were allowed to deflate arbitrarily slowly (i.e. P, is free of bias due to cardiac cycle phase uncertainty). Then, if the BP-cuff deflates at a finite rate according to a pressure function P c ( t ) , and if 7 is defined by
Cardiac cycle phase uncertainty causes a small error in indirect estimation of arterial blood pressure by sphygmomanometry . A simple analysis yields a statistical description of the error and a rule for its reduction: correct bias b~ adding to the systolic estimate and subtracting from the diastolic estimate one-half of the per-cardiac-cycle cuff defration decrement. If several measurements are taken, the least-square estimate is approximately the arithmetic mean of the greatest and least of the bias corrected estimates.
Pc(I) = Pc,
(1) then Po, the observed blood pressure, is a random variable distributed on the interval [Pc(j+T ) , Pc(t)]. A specific case of practical importance is that of a constant BP-cuff deflation rate r and, therefore, a uniform uncertainty in cardiac cycle phase. For this case Po is uniformly distributed with probability density function
Introduction
r
Ascultatory estimation of arterial blood pressure (BP) using standard BP-cuff techniques is subject to many sources of error. Digit preference can be largely eliminated by using random-zero, zero-muddler, or automatic devices [I]. Clinically significant errors persist, however, as these devices exhibit their own peculiarities [ 2 ] .Other factors such as cuff size can also contribute to indirect BP estimation error, especially if the cuff is too small [3]. A review of the literature for another purpose revealed to this author a common characteristic error which is manifest in those studies which compare direct intra-arterial BP measurements with various indirect BP estimation methods: systolic estimates are low, and diastolic estimates are high [4-81. Auscultation when compared with oscillometry has also shown this effect ~91. It will be shown in this paper that this estimation bias is due to the a priori ignorance of the observer about the time of occurrcnce of the Korotkov sounds (uiz. cardiac cycle phase uncertainty), and that bias magnitude is a function of cuff deflation rate. A method for correcting this bias will be described, and the proper method for averaging indirect BP estimates will be presented.
Analysis First, the estimate bias due to cardiac cycle phase Uncertainty will be calculated, and then the proper method for averaging several indirect BP estimates will be presented. The major results are given by equations (4), (8) and (9), along with the attendant discussion.
[O
otherwise
where x a n d y represent values of the random variables,
Po and P,, respectively. Using ( 2 ) the BP estimate bias B is
B so
B
=
=
I
(x-PcclfPolPc ( X l P J dx.
(3)
- R / 2 , where R = r‘ T.
Note that R is cuff-pressure decrement per cardiac cycle, which can be determined by noting the cuff pressure decrease between two successive Korotkoff sounds. A similar analysis yields a diastolic pressure bias of equal magnitude but opposite sign; therefore, an unbiased estimator for indirect BP is
P=
Po 2 R/2
(4) with the negative sign chosen for systolic pressure. Hence, bias in the indirect estimation of arterial blood pressure due to cardiac cycle phase uncertainty can be corrected by adding to the systolic estimate and subtracting from the diastolic estimate one-half the cuffpressure decrement per cardiac cycle.
For example, suppose the unbiased blood pressure estimate is Pc = 120 mmHg, the heart rate is 72 beats per min, and the cuff deflation rate is a uniform 10 mmHg per three cardiac cycles; then the indirect blood pressure estimate would be biased by only 1.5 mmHg, confirming that this commonly taught ruleof-thumb is quite conservative. The standard deviation 157
0309-1902/92 53.00
0 1992 7’a)Iur
& Francis Ltd
C.
P. Hatsell Cardiac cycle phase uncertainty
for this single measurement, ignoring sources of error other than cardic cycle phase uncertainty, would be 1.5 mmHg; however, accounting multiple measurements requires special consideration. Averaging multiple measurements
A common clinical practice is to take several BP measurements with the patient quiescent and use the sample average as a BP estimate. This would reduce the measurement variance due to cardiac phase uncertainty by 1/N, where N is the number of measurements taken; however, such a n estimate is not least square. The non-linear least square estimator is the conditional mean [ 101
Downloaded by [University of Otago] at 21:17 19 September 2015
4,
where, by Bayes’ rule,
From equations (2), (3), a n d the conditional independence of the observations, f p l P c [ ~ ( l L..., P(N)lVl =
(-)R rI w w m - y l ) , 1”
Discussion Excessively slow BP-cuff deflation rates can be quite uncomfortable to the patient. Common practice has the technician inflate the cuff to a t least 160 mmHg; so at the recommended deflation rate of 10 m m H g per threc cardiac cycles, a person with a heart rate of 60 beats per min and a normal blood pressure of 120 m m H g will have 12 s of arterial occlusion before the first Korotkoff sound. For some, this is long enough to produce pain. Slow cuff deflation rates can also lead to distal venous engorgement a n d inaccuracies in diastolic pressure estimation. If the patient can be kept reasonably quiescent, the estimation technique described in this paper can allow faster cuff deflation if the rate can be held constant. Many patients are using commercially available automated BP measuring devices a t home to monitor their BP on a frequent basis. These devices could be designed to correct for measurement bias through simple computational procedures incorporated in contained hardware. Such a control mechanism is certainly feasible and should be considered as part of any BP device employing sphygmomanometry.
References 1. CANNER, P. L., BORHANI, N. O., OBERMAN, A., CUTLER,
J., PRINEAS, R. J., LANCFORD, H. and HOOPER,F. J.
j=l
(7) where U(-) is the unit step function. Combining equations (5), (6), and (7), the minimum variance estimator for large N is approximately
2. 3. 4.
5. Equation (9) is a n interesting result as it prescribes that only the minimum and maximum BP readin s be used in computing the estimate. T h e variance of follows from an elementary result in order statistics [ 111 which is stated here as a theorem.
%,,
Let xI, random and let Ify =
x2, ..., x, be n independent, identically distributed, variables w i t h unform probability density on (a,b], x: 5 xf S x$ 6 ... S x*, be their order statistics. (x*,+x*,)/2, then the variance of y i s varCy) =
6.
7.
8.
(b-a)‘ 2(n+ l)(n+2)’
Applying this theorem to (8) gives var(Pl,) =
2(N+ 1)(N+2)
which shows the estimator given by performs better than the sample mean thercforc, even though equation (8) minimum variance estimator only for always better than the sample mean. 158
9.
R2
equation (8) for all N > 2; approaches a large N , it is
10. 11.
(1991) The Hypertension Prevention Trial: assessment of the quality of blood pressure measurements. American Journal of Epidemiology, 134, 379-392. O’BRIEN, E., MEE, F., ATKINS,N. and O’MALLEY, K. (1990) Inaccuracy of the Hawksley random zero sphygmomanometer. Lancet, 337, 556. J. K. (1990) Blood CROFT,P. R. and CRUICKSHANK, pressure measurement in adults: large cuffs for all?Journal of Epidemiology and Community Health, 44, 170-1 7 3 . REBENSON-PIANO, M., HOLM,K., FORMAN, M. D. and K. T. (1989) An evaluation of two indirect KIRCHHOFF, methods of blood pressure measurement in ill patients. Nursing Research, 38, 42-45. SALAITA, K., WHELTON, P. K. and SEIDLER, A. J. (1990) A community-based evaluation of the Vita-Stat automatic blood pressure recorder. American Journal of Hypertension, 3, 366-72. RUSSELL, A. E., WING,L. M., SMITH,S. A., AYLWARD, P. E., MCRITCHIE, R. J., HASSAM, R. M., WEST,M. J. and CHALMERS, J. P. (1989) Optimal size of cuff bladder for indirect measurement of arterial pressure in adults. Journal of Hypertension, 7, 607-613. DAVIS,R. F. (1985) Clinical comparison of automated auscultatory and oscillometric and catheter-transducer measurements of arterial pressure. Journal of Clinical Monitoring, 1, 1 14- 1 19. MAHESWARAN, R., ZEZULKA, A. V., GILL,J. S., BEEVERS, G. (1988) Clinical evaluation M., DAVIES, P. and BEEVERS, of the Copal UA-251 and the Dinamap 1848 automatic blood-pressure monitors. Journal of Medical Engineering and Technology, 12, 160-163. PESSENHOFER, H. (1986) Single cuff comparison of two methods for indirect measurement of arterial blood pressure: standard auscultatory method versus automatic oscillometric method. Basic Research in Cardiology, 81, 101- 109. VANTREES, H. L. (1968) Detection, Estimation, and Modulation Theory (John Wiley and Sons, New York), p. 56. KARLIN,S. (1965) A First Course in Stochastic Processes (Academic Press, New York), p. 236.
