AbstractâBlood pressure measurement is performed ei- ther invasively by an intra arterial catheter or noninvasively by cuff sphygmomanometry. The invasive ...
Proceedings of the 26th Annual International Conference of the IEEE EMBS San Francisco, CA, USA • September 1-5, 2004
Continuous Noninvasive Blood Pressure Measurement by Pulse Transit Time Parry Fung1 , Guy Dumont1 , Craig Ries2 , Chris Mott1 , Mark Ansermino2 1 Department
of Electrical and Computer Engineering, The University of British Columbia, Canada 2 Department
of Anesthesia, The University of British Columbia, Canada
Abstract—Blood pressure measurement is performed either invasively by an intra arterial catheter or noninvasively by cuff sphygmomanometry. The invasive method is continuous and accurate but has increased risk; the cuff is safe but less reliable and infrequent. A reliable continuous noninvasive blood pressure measurement is highly desirable. While the possibility of using pulse transit time to monitor blood pressure has previously been investigated, most studies were limited to calculating the correlation of the pulse transit time and blood pressure under rather static conditions. The relationship between the pulse transit time and blood pressure is yet to be clearly identified. This paper focuses on the modeling between the two values and presents results on cases where dramatic variation in blood pressure of the patient was induced by drug administration or surgical stimulation. Index Terms—Continuous, Noninvasive, Blood Pressure, Pulse transit time, Pulse Oximetry
I. Introduction A continuous measurement of blood pressure (BP) is desirable for consistent patient care and monitoring. Although BP can be measured continuously by an intra arterial catheter, this costly and invasive method introduces risk to the patient and workload for physicians. Risks of arterial injury and skin infection does not justify its use in many circumstances. Moreover, the rather complex setup procedure for arterial catheter insertion may take up to 30 minutes. Expensive disposable equipment adds to the cost of direct arterial measurement. Therefore, a noninvasive method of measuring BP is desirable for patients without significant organ dysfunction during short duration surgery, especially patients with expected fluctuation in BP, e.g. undergoing Cesarean Section. Conventional noninvasive BP measured by cuff sphygmomanometry updates a BP reading at most every minute (usually 3 minutes), which is not frequent enough for certain clinical situations, e.g. hypotension treatment during a Cesarean Section. Here, an algorithm of inferring BP by pulse transit time (PTT) was developed for an advisory system which aims to treat maternal hypotension induced by spinal anesthesia performed for Cesarean Section. It is commonly accepted that PTT is correlated with BP [1] and a number of commercial BP monitors use PTT to infer BP. However, the details of the actual algorithms have not been disclosed by the manufacturers. A human model of BP and PTT is first presented. The model simplifies the body structure and relates BP to PTT by fundamental physics, the conservation of energy. To reduce inter-patient variability, the model customizes parameters by using an easily accessible physical property of the pa-
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tient, height. The practicality of the model is retained by ignoring or approximating a few unavailable parameters such as the elasticity of arterial wall, heart pre-ejection period (PEP) and blood density. The paper also includes a method for computing PTT from the ECG and plethysmogram (PPG). While ECG and PPG are two standard signals in most anesthesia monitors, the PTT-BP model in conjunction with the PTT computation algorithm provides a low cost alternative to continuous invasive BP monitoring. II. PTT-BP Model The model assumes laminar blood flow from the heart chamber to the fingertip through a rigid pipe, the artery. While it is well known that artery wall expands and contracts, its small compliance of 0.0018 liter/mmHg on average [2] justifies this assumption. The model estimates the pressure difference between the two sites, the heart and the fingertip, by the pulse wave velocity. A pulse wave travels from the heart to the fingertip, along the artery and its velocity can be calculated from the distance travelled divided by the PTT. The relationship between the PTT and BP is demonstrated in the following postulate. The work done by the pulse wave can be expressed in terms of the kinetic energy of the wave and the gravitational potential energy: F ·d where F d m v g h
= = = = = = =
1 mv 2 + mgh 2 f orce exerted on blood distance f rom heart to f ingertip mass of blood pulse wave velocity 9.81m/s2 height dif f erence between two sites
(1)
The force can also be written in terms of pressure difference: F = BP · a
(2)
where a is defined as the cross section area of the artery. Substitute equation (2) into (1) and after rearrangement: BP =
as
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m a·d = d PTT ,
m 1 m 2 gh v + a·d 2a·d
(3)
ρ is the density of blood and v can be expressed so BP =
d2 1 + ρgh ρ 2 PTT2
(4)
PTT from ECG and PPG
The distance d can be approximated from patient’s height. PTT is the pulse transit time in seconds. The average blood density ρ is 1035 kg/m3 [3]. The pressure drop in the arterial side of circulation accounts for roughly 70% of the total pressure drop in the body [2], therefore the patient’s overall BP is approximately: BP
= = =
BP/0.7 2 1 1 + ρgh) ( ρ d 0.7 2 P T T 2 A + B 2 PTT
=
(0.6 × height)2 ×
ρ 1.4
PPG PPG max Slope ECG ECG R peak
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50
PTT
PTT
0
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1550.2
1550.4
1550.6
1550.8 Seconds
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Fig. 1. The definition of PTT. (5)
In summary, the BP can be written in terms of PTT, with two variables namely A and B. A can be estimated from the subject height. A
200
(6)
From the above calculations, BP can be estimated from PTT and few average empirical values. Recursive calibration between the estimated BP and the BP measured by a cuff is necessary in order to obtain the absolute BP of the patient using estimated values. Calibration is performed by using total least squares as it is an optimum method for reducing the uncertainty of two noisy signals [4]. Since A does not vary significantly between subjects and performing adaptation on A may lead to unstable estimation, the calibration will adapt B only. The adaptation of B may still absorb some of the mismatch in A. Nonetheless, according to the results in Section V, A and B are time invariant so the adaptation should converge to a single set of values. The BP in equation (5) describes the mean BP assuming laminar and non-pulsatile flow. The cuff measurement of diastolic blood pressure, and hence the estimation of mean blood pressure, may be impossible in pregnancy due to the changes induced in the arterial wall by gestational hormones. When the BP cuff operates in continuous mode during the treatment of hypotension induced by spinal anesthesia for Cesarean Section, the constraint of measuring mean blood pressure would result in a significant reduction in data points. Therefore, based on the assumption that systolic BP is highly correlated with mean BP, PTT is used to infer systolic BP.
real-time implementation was desired. A wavelet implementation based upon the techniques described in [6] was implemented. The ECG signal was decomposed into 512 sample segments, and a five level stationary wavelet transform (SWT) [7] was performed. The highest frequency decomposition captures much of the noise, and the lowest frequency decomposition captures baseline trends. The intermediate frequency bands thus contain most of the energy of the QRS waveform and a recursive, rule-based pattern recognition algorithm identifies the locations of the Rpeak patterns. These are primarily characterized by a local minimum followed by a local maximum. One of the significant modifications made from the approach suggested in [6] is that upsampling is used to improve the accuracy of the peak location measurement. After an R-peak has been identified by its pattern in the wavelet decompositions, a segment of the original ECG’s samples surrounding that location is upsampled by a factor of ten, and the point of the local maximum is recorded. With an original sampling rate of 300Hz the resolution after upsampling is 0.33 ms. The sequence of R-peak locations is provided continuously to the PTT algorithm. The detection of the location of the maximum slope of the PPG signal is accomplished using a wavelet decomposition as well. Since the PPG is a relatively simple signal, a 2-level SWT with ‘db3’ wavelet was used to smoothen out and filter out the noise in the differentiated PPG. The rule-based system, as displayed by a flow chart in Figure 2, processes the low frequency wavelet components and detects all the maximum slopes of the PPG. The flow chart is an infinite loop as it simulates a real-time application. Initialize dPPG by filtering differentiated PPG by SWT up_slope_counter =0; down_slope_counter =0; flat_counter =0; look_forward_counter =0; temp_max = null; temp_max_index= null;
III. PTT Detection from ECG and PPG PTT in this paper is defined as the time between the ECG R peak and the corresponding maximum inclination in the PPG, as illustrated in Figure 1. The detection of PTT involves the peak detection in both ECG and the differentiated PPG. A wavelet-based approach was taken to decompose the signals into different frequency bands and a rule-based expert system was used to analyze the wavelet components. The detection of the Q, R, and S characteristic peaks in ECG signals has been extensively covered by previous authors. Numerous approaches have proven successful and a good review of the software-based algorithms is provided in [5]. For this application an algorithm providing efficient
Store temporary maximum temp_max = dPPG(i); temp_max_index = i; up_slope_counter++; flat_counter - -; look_forward_counter=0;
i++;
If dPPG(i) > temp_max & dPPG(i) < MAX & dPPG(i) > MIN
Yes
No
If up_slope_counter > UPSLOPEMIN & down_slope_counter > DOWNSLOPEMIN & flat_counter < FLATMAX & look_forward_counter > HORIZON
Yes
Store temp_max_index as Peak
No If temp_max==null
Reset Set up_slope_counter =0; down_slope_counter =0; flat_counter =0; look_forward_counter =0; temp_max = null; temp_max_index= null;
No
look_forward_counter++;
Yes
Yes
Yes
If dPPG(i)==0
flat_counter++;
If flat_counter >= FLATMAX
No If dPPG(i)>0
No down_slope_counter++;
Yes up_slope_counter++;
Fig. 2. The flow chart of maximum slope detection in PPG.
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No
toe. According to the model, the parameter A of those different sites should be directly proportional to the square of its distance from heart. The Nellcor PPG sensor was used in this case and it was observed that its filter produces a constant phase lag compared to the Datex sensor. That delay, estimated as 0.087 seconds, was subtracted from the PTT for BP calculation. Then, an attempt was made to estimate PEP of the subject because the PTT of the ear is much shorter and is more sensitive to PEP. PEP must be excluded in the BP calculation for PTT of the ear. PEP was approximated to be around 7% of the RR interval and it was subtracted from all PTT (finger, ear, toe) for BP calculation in Figure 3. Assuming the ratio of the distance from the heart to the fingertip is 1, the ear 0.5 and the toe 1.6, we substitute the ratios into equation (6) to calculate A. The BP estimated by PTT is plotted at the bottom of Figure 3. The consistent results reinforce the value of the model and the assumptions made. PTT of right finger, ear, left finger and toe PTT 0.5 Seconds
In our current set of data, ECG and PPG were collected at 300Hz though the PPG was interpolated by the monitor from 100Hz data; the threshold constants described in the flow chart are UPSLOPEMIN=30, DOWNSLOPEMIN=5, FLATMAX = 15 and HORIZON = 100. MAX and MIN are 25% and 5% of the saturation of the PPG signal. The dPPG is the filtered discrete differentiated PPG and i is a dPPG array counter. After R peaks of ECG and maximum slopes of PPG were detected, the corresponding pairs are mapped together to compute PTT. For each R peak, the algorithm checks the next maximum slope and validates whether the PTT lies within 20% to 70% of the RR interval. The confirmed PTT is then stored for BP computation in equation (5). Theoretically, the pulse to pulse BP can be computed. However practically, a sampling interval of 5-10 seconds for BP is clinically adequate. Extreme values (noises) are filtered out by a probability density filter. A weighted average filter emphasizing the most recent readings is employed to combine several PTT readings in that time interval into one BP index. The variable B in equation (5) has to be calibrated consistently whenever a new cuff measurement is available. Recursive total least square calibration is performed.
Left finger
Right finger
0.4 0.3
Toe
Ear
0.2 0.1
IV. Limitations of the PTT-BP Model
100
200
300 Seconds
400
500
600
Pulse Transit Time to SBP 100
V. Results In this section, the PTT model is validated by measuring PPG at different sites. Then the PTT technique is compared with existing invasive and noninvasive BP measurements. First, to validate the relationship described in equation (6), a test case with PPG measured at different sites was recorded, as shown in Figure 3. On the same subject, the PPG was measured at his right finger, ear, left finger and
SBP by PPT SBP by Cuff 90 mmHg
There are several limitations to the model. Firstly the three signals, ECG, PPG and cuff BP have to be relatively noise free. Since the PPG is sensitive to subject movement, the BP index from PTT can be inaccurate or missing at the times of vigorous muscle activity. Body movement also affects the height differential between the two sites hence the potential energy in equation (1). The recursive calibration can only adapt slowly to the change in height. In addition, it is mandatory that all three signals, especially the ECG and PPG, are synchronized correctly. It was observed that some PPG sensor units have a built-in filter. The filter generates an artificial phase lag between the ECG and PPG, which inadvertently lengthens the PTT and distorts the BP index. Lastly, as the R peak marks the electric excitation of the heart contraction, there is a small delay before mechanical contraction. This delay is the PEP. As we cannot noninvasively measure PEP, the PTT detected includes the PEP, which is negligibly short compared to the actual PTT. It is speculated that for subjects with low heart rate, the PEP may become more significant. Therefore the model may have to estimate the PEP based on the RR interval for these subjects.
80
70
60
100
200
300 Seconds
400
500
600
Fig. 3. PTT and its BP measured at different sites from a single subject.
During surgery, the invasive and noninvasive systolic BP’s were recorded every 5 seconds and the ECG and PPG were sampled at 300Hz from a Datex AS5 monitor (Datex, Finland). The variable B in equation (5) was kept constant for the entire case after it was estimated once offline, as we intended to demonstrate the ability of the algorithm to capture the change in BP. The variable B in Figure 4 is a constant offset and the variations in BP by PTT are not affected by the calibration. The case is over 100 minutes long but the cuff was cycled every 10 minutes, while its inflation produces the dips in the invasive BP due to the fact that the cuff was on the same arm as the arterial catheter. The results displayed in Figure 4 illustrate how effectively the algorithm can trace changes in BP. If the arterial BP signal is unavailable, the sudden increase or decrease of BP can be detected much earlier than using the cuff alone and appropriate procedures can be carried out to correct BP. The constraint on the PTT-BP algorithm is that it can only be as accurate as its calibration standard, the cuff measurement. As a result, there is a -5mmHg bias between the cuff and PTT measurement and the direct arterial measurement, though the mean difference between the two is less than 0.001mmHg. Another 22 cases of noninvasive BP data were collected
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Pulse Transit Time to SBP
Cesarean Section Case SBP by PPT SBP by Cuff Invasive SBP
SBP by PTT SBP by Cuff Spinal Anesthetic Phenylephrine
140
mmHg | % of Spinal Anesthetic | ug of PE
140
120
mmHg
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60
40
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100
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60
40
1000
2000
3000 Seconds
4000
5000
6000
0
500
1000 Seconds
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Fig. 4. Comparison between systolic BP by PTT and invasive systolic BP from a single patient.
Fig. 6. Comparison between systolic BP by PTT and BP by cuff sphygmomanometry during a Cesarean Section.
from a study of Cesarean Section hypotension treatment with phenylephrine [8]. The ECG and PPG were sampled at 300Hz and the cuff sphygmomanometry systolic BP were recorded every 10 seconds. Even though the cuff BP was sampled every 10 seconds, the cuff inflates either every minute in normal mode or as frequent as it is able to in continuous inflation mode. In normal mode, BP data remains unchanged until the next inflation. In continuous inflation mode, BP data recorded between inflations come from interpolation by the monitor. During the cases, spinal anesthesia and phenylephrine were administered, causing sudden but significant fluctuations in BP. The 22 cases form a total of 4660 data points where both the cuff systolic BP and the new noninvasive BP by PTT are available. Figure 5 displays the histogram of the difference and the limits of agreements [9] on the two BP measurements. The mean difference is -0.0790 mmHg with a standard deviation of 11.32 mmHg. The offset parameter B was recursively calibrated by the total least squares, instead of being kept constant.
with the data. It is clear that the BP estimated by PTT is capable of capturing the hypotension and hypertension caused by spinal anesthesia and phenylephrine respectively. Continuous monitoring of blood pressure will result in earlier treatment of induced hypotension and avoidance of hypertension due to by careful titrated administration of phenylephrine . VI. Conclusion A simplistic yet practical model was developed to relate PTT and BP. With a more sophisticated calibration and noise filtering method, the algorithm can easily be converted into a real time application. Preliminary results suggest that the algorithm should be an integral part of all anesthesia monitors as it requires no extra sensors but improves the quality and sampling rate of noninvasive BP measurement. The algorithm can also trigger the recycling of the noninvasive cuff measurement when major BP fluctuation is detected. References
Limits of Agreement on SBP by cuff and SBP by PTT
Histogram of SBP by cuff minus SBP from PTT
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data mean 95% confidence interval 40
SBP by cuff − SBP by PTT (mmHg)
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count
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Fig. 5. Histogram on the difference and limits of agreement between systolic BP by cuff and by PTT from 22 patients undergoing Cesarean Section.
The limits of agreement in Figure 5 can be misleading because, operating in the normal mode, the cuff only updates the BP reading immediately after an inflation. In continuous inflation mode, the monitor interpolates the systolic BP between cuff inflation, at each sampling interval. Figure 6 best describes the phenomenon. Before the spinal anesthetic is injected, the monitor was in normal mode, updating the BP every minute, so there is a delay between the two measurements. The injections of drugs were marked by the snapshot function of the Datex monitor so they are synchronized
[1] X. Teng and Y. Zhang, “Continuous and noninvasive estimation of arterial blood pressure using photoplethysmographic approach,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2003. [2] J. Keener and J. Sneyd, Mathmatical Physiology. New York, USA: Springer-Verlag, 1998. [3] G. Elert, “Density,” The Physics Hypertextbook, 1998. http://hypertextbook.com/physics/matter/density/. [4] D. Boley and K. Sutherland, “Recursive total least squares: An alternative to the discrete Kalman filter,” 1993. [5] B. Kohler, C. Hennig, and R. Orglmeister, “The principles of software QRS detection,” IEEE Engineering in Medecine and Biology, vol. 21, no. 1, pp. 42–57, 2002. [6] L. Cuiwei, Z. Chongxun, and T. Changfeng, “Detection of ECG characteristic points using wavelet transforms,” IEEE Transactions on Biomedical Engineering, vol. 42, pp. 21–28, Jan. 1995. [7] The Mathworks Inc., MA, Matlab user’s guide. Wavelet toolbox, 1997. [8] P. Fung, G. Dumont, M. Ansermino, M. Huzmezan, and A. Kamani, “Toward an advisory system for Cesarean Section spinal anesthesia,” in Proceedings of the American Control Conference, 2004. [9] J. Bland and D. Altman, “Measuring agreement in method comparison studies,” Statistical Methods om Medical Research, vol. 8, pp. 135–160, 1999.
Acknowledgment We would like to thank Datex Ohmeda for assistance with the data collection.
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