2014 7th International Conference on BioMedical Engineering and Informatics (BMEI 2014)
Nonlinear Relationship Between Systolic Blood Pressure and Pulse Transit Time in Anesthetized Dogs Hong Tang, Jian Sun
Yongwan Park
Department of Biomedical Engineering, Dalian University of Technology, Dalian, China
Communication and Information Department, Yeungnam University, Dague, Korea
Abstract—Pulse wave transit time (PTT), as measured between the ECG R-wave and the arterial pulse wave at a distal site, has been previously reported to linearly correlate with blood pressure (BP). This study reinvestigated the relationship where various doses of epinephrine were administered to three anesthetized dogs to invoke a wide range of hypotension. The invasive systolic blood pressure in the left ventricle, the noninvasive photoplethysmogram pulse wave and the ECG of lead II were recorded synchronously. The results indicated that the relationship between the systolic BP and the PTT was nonlinear and logarithmic: P=b1-b2lnT, where b1 and b2 are coefficients. The estimated BP using the nonlinear relationship was highly correlated with the measured BP; the correlation coefficients were often greater than 0.96 in the 36 trials. The root mean square of the estimation error was less than 6.53 mmHg. However, the coefficients b1 and b2 varied between trials, doses, and dogs. An analysis of the error contribution revealed that the estimation error increased linearly with the coefficient errors, ǻb1 and ǻb2, and with the PTT error, ǻT. The definition of the pulse arrival time (PAT) also affected the performance of the estimation. The performance based on five PAT definitions was compared. This study shows that caution is necessary when using this relationship to monitor BP. Keywords-pulse wave transit time; photoplethysmogram; invasive systolic blood pressure; epinephrine; noninvasive measurement
I.
INTRODUCTION
Monitoring blood pressure (BP) is important in clinical diagnostics and home health care. However, a traditional sphygmomanometer cannot monitor the beat-to-beat variability in the BP, and invasive monitoring with a catheter inserted into the artery is limited to critically ill patients. A noninvasive beat-to-beat method of monitoring BP is desirable. The approach based on the relationship between the transit time of the pulse pressure wave and blood pressure has received much attention since the 1970s [1-6]. Previous studies concluded that a linear negative relationship exists between BP and pulse transit time (PTT) if the changes in the wall thickness, the interior diameter, and the elastic modulus of artery are negligible in the short term. The PTT can be measured by detecting the arrival of a pulse from a proximal site to a distal site. The ECG R wave is often used as a proximal timing point because it is easy to detect and is tolerant to artifacts created by motion. The noninvasive pulse wave was sampled at the distal site by using a piezoelectric sensor [2, 3], photop-
lethysmography [7, 8] or an intra-arterial pressure wave [4, 5]. However, there were no common criteria for measuring the pulse arrival time (PAT). Previous studies [2, 3, 9] have defined the PAT as the point at the maximum slope on the upstroke of the pulse wave. Ochiai et al [4] defined the PAT as the point where the slope reached 30% of the maximum. Chiu et al [3] defined the PAT as the maximum point of the first derivative, the maximum point of the second derivative, and the intersection of the tangent of the maximum slope to the time axis. Other researchers used the onset of the pulse wave to measure the PAT without giving a definition [7, 8]. The conclusions reached by the previous researchers were not in agreement: some determined that this approach was accurate enough, with correlation coefficients up to 0.97, whereas others concluded that this approach was unreliable and inconsistent. This study proposed a definition of PTT based on the onset of the upstroke pulse wave and investigated the relationship between systolic BP and PTT in anesthetized dogs given various doses of epinephrine to invoke a wide range of BP responses. The error contribution was analyzed. The performance of the BP estimation was compared after using various definitions of the PAT. II.
A. Experimental settings This study was approved by the Animal Care Committee of Chongqing Medical University. The Principles of laboratory animal care were followed. Three healthy beagles, weighing 10-12 kg, were involved in the experiments. Each dog was anesthetized with xylazine (0.2 ml/kg). The dogs were in the supine position during the data collection. A catheter filled with a heparinized solution (500 units/ml) was inserted into the left ventricle via the carotid artery. The catheter was coupled to a pressure transducer (MLT0699, ADInstruments, Australia), which was calibrated at standard atmospheric pressure. An intravenous infusion of 0.9% saline was utilized to maintain a route for administering epinephrine at the required time. A photoplethysmogram sensor (MLT1020FC, ADInstruments, Australia) was noninvasively affixed to the femoral artery to record the pulse wave. The ECG signal of standard lead II, the blood pressure, and the pulse wave were simultaneously sampled at 1 KHz (MP150, BIOPAC, USA). The data collection was divided into three stages.
Corresponding author: Hong Tang Email:
[email protected]
978-1-4799-5838-2/14/$31.00 ©2014 IEEE
MATERIALS AND METHODS
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Stage 1: Epinephrine (0.5 g/kg) was injected. The data collection started from 10 seconds prior to the injection and ended when the systolic BP decreased to the normal. This stage was repeated four times. Stage 2: Epinephrine (1 g/kg) was injected. The remaining operations were the same as in stage 1. This stage was repeated five times.
Logarithmic model
P = b1 + b2 ln T D. Quality index to evaluate fitting
The quality index ( R 2 ) was used to evaluate the goodness of fit of the models (2) as defined by
Stage 3: Epinephrine (2 g/kg) was injected. The remaining operations were the same as in stage 1. This stage was repeated four times. The catheter, blood pressure transducer, ECG electrical node, photoplethysmogram sensor and all the electrical lines were immobilized during data collection to avoid motion artifacts. Thirteen recordings were collected for each subject. A total of 39 recordings were obtained for the three subjects. Unfortunately, 3 records were unusable because the pulse sensor came loose from the femoral site.
(2)
§ ¦ ( Pi − Pˆi ) 2 R 2 = ¨1 − ¨ ¦ (P − P )2 i i ©
· ¸ × 100% , ¸ ¹
(3)
where Pi was the observed amplitude, Pˆi was the amplitude predicted by the model, and Pi was the mean of Pi . The variable i was the cycle index. A greater quality index indicated a better fit. 300
BP R-wave
PTT (s)
BP (mmHg)
0.25 250
200
ECG
0.15
Pulse
150
PAT
0
100
200
300
0.1
0
(a) Time(s)
dP/dt
An illustration of the BP, ECG and pulse wave. The arrow indicates the PAT.
III.
B. signal preprocessing (1) The pulse wave was filtered using a high-pass filter with a low-cutoff frequency of 0.5 Hz to eliminate the DC component from the signal. (2) The ECG R waves were detected using a typical differential method. (3) The PTT was measured as the interval between the R wave and the PAT, which was determined based on the onset of the pulse wave (the zero crossing of the first derivative before the upstroke), which is denoted as PTT-zc in this paper. The timing relationship for the three signals and the determination of the PTT are illustrated in Fig. 1. C. Potential models Assume P is the systolic BP and T is the PTT. Based on the previous studies, it is known that P is negatively correlated to T. The potential models to fit the relationships are the follows. Linear model
P = a1 + a2T
100
200
300
(b) Time(s)
Figure 2. Dose responses. (a) and (b) The BP and PTT at a 1 μg/kg dose. The arrow indicates the timing of the injection.
PTT-zc
Figure 1.
0.2
(1)
RESULTS
A. Model selection An example of dose responses at the 1 g/kg dose is depicted in Fig. 2. The arrow in Fig. 2(a) indicates the timing of the epinephrine injection. The systolic BP increased rapidly and reached a maximum approximately 15 seconds after the injection. The BP gradually decreased while the animal metabolized the drug. The systolic BP typically approached baseline after 5 minutes. The linear and logarithmic models were used to fit the PTT and BP measurements from one trial, illustrated in Fig. 3. Clearly, the relationship between BP and PTT was not quite linear. The quality indexes of the two models were 0.9 and 0.95; the correlated coefficients were 0.91 and 0.98 with a confidence level of 0.05, respectively. The quality index and correlated coefficient are used to evaluate the goodness of model fitting, shown in Fig. 4. It can found that the quality index and correlated coefficient of the logarithmic model were higher than those of linear model. This revealed that the logarithmic model was better to fit the data. B. Parameter estimation of the logarithmic model Based on the above analysis, the logarithmic model is applied to fit the relationship. Table 1 includes the regression coefficients (b1 and b2), the correlation coefficients (CC), the root mean square of the estimation error (RMS), the arithmetic
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mean of the estimation error (Mean), and the key points (50% and 95%) in the error distributions for the 36 trials. 300
280
280
P =380 - 976T
220 200 180
80 Linear model logarithmic model
60 0
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(a) PTT (s)
40
1
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0.8
Linear model logarithmic model
0.6 0
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35
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30
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180
160 140 0.1
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CC
240
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P = - 90 - 170lnT
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Figure 3. Regression analysis of PTT and BP with 0.5 μg/kg epinephrine. (a) Linear fitting, (b) Logarithmic fitting.
Figure 4. Performance comparison between the two models. (a) Comparison of quality index, (b) Comparison of correlated coefficient. CC: correlated coefficient between measured BP and estimated BP.
Table 1 Parameter estimations for the 36 trials Agent
Dose 0.5 μg/kg
#1
1 μg/kg
2 μg/kg
0.5 μg/kg
#2
1 μg/kg
2 μg/kg
0.5 μg/kg
#3
1 μg/kg
2 μg/kg
Max Min Mean SD
b1a 18.76 -90.56 -40.84 -50.64 -73.27 -79.93 -90.07 -91.53 -91.33 -126.14 -128.24 -121.76 -124.89 41.02 32.82 136.35 126.36 -43.68 -54.09 -67.38 146.78 78.51 179.89 42.22 3.18 22.29 35.55 -33.19 -95.15 -79.60 -88.69 -86.71 -98.14 -127.78 -133.57 -178.56 179.89 -178.56 -37.00 89.56
b2b -102.37 -170.72 -137.19 -142.41 -154.03 -156.05 -159.66 -158.82 -156.85 -177.75 -178.03 -172.14 -172.07 -94.46 -113.17 -63.95 -74.46 -153.13 -155.56 -162.40 -35.19 -77.24 -18.05 -106.04 -137.12 -121.30 -111.68 -156.45 -186.92 -172.68 -177.20 -175.20 -186.54 -200.70 -200.38 -235.45 -18.05 -235.45 -143.15 47.54
a. b1 and b2: coefficients in the fitted equation b. correlation coefficient between the estimated BP and the invasively measured BP
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CCc 0.92 0.98 0.95 0.96 0.97 0.97 0.96 0.97 0.98 0.98 0.98 0.98 0.98 0.99 0.99 0.90 0.94 0.99 0.99 0.99 0.87 0.96 0.81 0.92 0.96 0.96 0.94 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.81 0.96 0.04
RMSd 4.31 4.44 4.75 4.14 4.27 4.08 4.14 4.30 3.88 4.17 3.98 3.85 3.73 3.65 3.71 3.66 5.18 4.93 4.13 3.70 6.53 5.53 6.51 5.51 4.90 5.81 5.91 4.73 4.74 5.06 5.07 5.20 4.80 4.41 4.25 3.72 6.53 3.65 4.60 0.79
Meane 3.52 3.70 3.99 3.48 3.56 3.38 3.36 3.57 3.16 3.32 3.04 3.08 2.90 2.72 2.84 3.37 4.20 4.04 3.12 2.84 5.77 4.79 5.70 4.75 4.16 4.96 5.15 3.87 3.89 4.26 4.22 4.42 4.08 3.68 3.59 2.86 5.77 2.72 3.81 0.79
50%f 2.98 3.27 3.71 3.15 3.21 3.02 2.85 3.13 2.55 2.68 2.13 2.46 2.15 1.12 1.82 2.02 2.91 3.38 2.39 2.03 6.14 3.52 3.63 4.44 3.90 4.70 5.16 3.20 3.25 3.76 3.71 4.20 3.75 3.42 3.34 2.12 6.14 1.12 3.20 0.98
95%g 8.09 8.23 8.38 7.57 7.82 7.49 7.41 7.84 7.66 8.14 8.19 7.42 7.48 7.33 7.98 3.88 9.25 8.69 7.13 7.73 9.28 8.88 8.27 8.97 8.27 9.96 8.86 8.21 8.32 8.45 8.62 8.76 8.16 8.04 7.88 6.89 9.96 3.88 8.04 0.97
c. RMS: root mean square of the estimation error d. Mean: arithmetic mean of estimation error e. 50%: estimation error with a cumulative distribution function of 0.5 f. 95%: estimation error with a cumulative distribution function of 0.95
IV.
denoted as ǻb1, ǻb2, and ǻT. The estimated BP based on equation (2) is
DISCUSSION
The association between BP and the PTT has been extensively studied since the 1970s in psychophysiology [1], in a clinical setting [7], and in healthy humans [8]. The present study simultaneously examined the effect of epinephrine on the PTT and invasively measured the systolic BP in anesthetized dogs. The systolic BP ranged from 130 to 290 mmHg, which has higher range of BP than has been commonly observed in previous studies. As presented in Table 1, the correlation coefficient for the estimated and the invasively measured BP was high (0.96). The standard deviation was low (0.04). In all 36 trials, 50% of the estimation errors were less than 6.14 mmHg, and 95% of the estimation errors were less than 9.96. The results proved that the relationship between systolic BP and the PTT was well described by equation (2), which performed well over a wide range of systolic BP. Therefore, systolic BP can be accurately estimated using equation (2) if the coefficients b1 and b2 can be determined in advance. Particular previous studies concluded that the relationship between PTT and systolic BP was linear [2-5, 8]. The authors believe that the previous linear relationship resulted from the narrower range of systolic BP that used in the studies of [2-5, 8]. Table 1 also highlights that the coefficients b1 and b2 varied significantly between doses and agents (see also Fig. 5). The coefficient b1 varied from -178 to 179 with a standard deviation of 89. The coefficient b2 varied from -18 to -235 with a standard deviation of 47. These data suggested that continuously estimating systolic BP based on this relationship should be performed cautiously because b1 and b2 varied significantly. 12
10
8
8
Occurence
Occurence
10
6 4
4
2
2 0 -200
6
-100
0
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Coefficient b1
200
0 -300
-200
-100
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Coefficient b2
Figure 5. Histograms of the coefficients b1 and b2 for the 36 trails.
A. The contribution of measurement errors Because the coefficients b1 and b2 varied significantly, an erroneous estimation of BP was unavoidable if any errors occurred in determining the coefficients. To analyze the contribution of such errors, the errors for b1, b2 and T were
P + ΔP = (b1 + Δb1 ) − (b2 + Δb2 ) ln(T + ΔT ) ,
(4)
where P is the accurate estimation and ǻP is the estimation error. The function ln(1+x) can be expanded as a Taylor series: (−1) k x k . k k =1 ∞
ln(1 + x) = ¦
(5)
To simplify the analysis, the first three terms were considered: ln(1 + x − 1) = ( x − 1) −
( x − 1) 2 ( x − 1) 3 . + 2 3
(6)
The equation ln(T+ǻT)=ln(1+ T +ǻT -1) can be written as ln(1 + T + ΔT − 1) = (T + ΔT − 1) −
(T + ΔT − 1) 2 (T + ΔT − 1) 3 + 2 3 (7)
It was experimentally determined that T was a small number, between 0.1 and 0.3, and that ǻT was an even smaller number. The multiplied items in equation (7), such as T3, T2, (ǻT)3, (ǻT)2, T(ǻT)2, T2(ǻT), and T(ǻT), could be neglected. The estimation error ǻP was obtained by subtracting (2) from (4):
ΔP = (b1 + Δb1 ) − (b2 + Δb2 ) ln(T + ΔT ) - [b1 − b2 ln T ] . (8) The subtraction was simplified to
ΔP ≈ Δb1 + 11(Δb2 ) / 6 − 3T ( Δb2 ) − 3b2 (ΔT ) − 3(Δb2 )(ΔT ) (9) The first two terms on the right hand of equation (9) contributed the most, the third and fourth items contributed less, and the last item could be neglected. The primary difficulty in utilizing this method to continuously monitor systolic BP is the fact that the coefficients b1 and b2 are not constants. The BP estimation error increased linearly with ǻb1, ǻb2, and ǻT. To reduce the estimation error, the coefficients b1 and b2 must be intermittently calibrated. B. Various definitions of the PAT at a distal site There are various definitions of the PAT. Lane and Chiu defined the PAT based on the peak of the first derivative of the pulse wave [2, 3, 9]. Ochiai defined the PAT as the time point that approached 0.3 times the peak valve of the first derivative [4]. Chiu et al [3] defined the PAT as the peak of the second derivative. Payne et al [5] and Chiu et al [3] defined the PAT based on the intersection of the tangent of the peak of the first derivative and the time axis [3, 5]. The authors of this paper defined the PAT as the onset of the pulse wave (the zero crossing of the first derivative before the pulse peak). The PTTs based on the five definitions were denoted as PTT-1d, PTT-1d30, PTT-2d, PTT-int, and PTT-zc (Fig. 6). Some previous studies used the onset of the pulse wave [7, 8] without providing a definition for the onset. It was necessary to
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compare their performances. The correlation coefficients and RMS values for the five definitions are presented in Fig. 7; trials 1 to 13 were for agent #1, trials 14 to 23 were for agent #2 and trials 24 to 36 were for agent #3. The five definitions performed similarly (Fig. 6), but the differences could not be neglected. PTT-1d, PTT-int and PTT-zc performed similarly, but PTT-1d30 and PTT-2d performed worse. R ECG PTT-zc Pulse wave PTT-1d3030%
dP/dt
PTT-1d
dP/dt
variation. The results from the statistics of 36 trials demonstrated that the relationship was best described as in logarithmic terms. The correlation coefficient was typically greater than 0.96. The average root mean square of the estimation error was 4.6 mmHg with a standard deviation of 0.76. The 95% estimation error was generally less than 9.96 mmHg. However, the coefficients b1 and b2 varied between trials, doses, and dogs. Therefore, the primary difficulty in continuously monitoring systolic BP was determining b1 and b2, which were inconsistent. An analysis of the error contribution revealed that the BP estimation error increased linearly with ǻb1, ǻb2, and ǻT. The definition of the PAT also affected the estimation performance. The performances based on the five definitions were compared. The results indicated that PTT-1d, PTT-int, and PTT-zc had the best performance, whereas PTT-1d30 and PTT-2d were the worst. ACKNOWLEDGMENTS
PTT-int
Pulse wave
This work was supported in part by the National Natural Science Foundation of China (grant 81000643, 61471081), and the National Key Technology Support Program (grant 2012BAJ18B06).
dP2/dt2 PTT-2d
REFERENCES
Figure 6. Five definitions of the PAT 1.5 PTT-1d
PTT-1d30
PTT-2d
PTT-int
PTT-zc
CC
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PTT-int
PTT-zc
6 4 2 0
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Figure 7. A comparison of the performance based on the five definitions of the PAT
V. CONCLUSIONS This study investigated the relationship between systolic BP and PTT in anesthetized dogs. Various doses of epinephrine were used to invoke significant hemodynamic
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