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Non-invasive quantification of peripheral arterial volume distensibility and its non-linear relationship with arterial pressure
ARTICLE IN PRESS Journal of Biomechanics 42 (2009) 1032–1037
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Non-invasive quantification of peripheral arterial volume distensibility and its non-linear relationship with arterial pressure Dingchang Zheng , Alan Murray Medical Physics Department, Newcastle University, Freeman Hospital, Newcastle upon Tyne NE7 7DN, UK
a r t i c l e in f o
a b s t r a c t
Article history: Accepted 22 February 2009
Arterial wall function is associated with different physiological and clinical factors. Changes in arterial pressure cause major changes in the arterial wall. This study presents a simple non-invasive method to quantify arterial volume distensibility changes with different arterial pressures. The electrocardiogram, finger and ear photoplethysmogram were recorded from 15 subjects with the right arm at five different positions (901, 451, 01, 451 and 901 referred to the horizontal level). Arm pulse propagation time was determined by subtracting ear pulse transit time from finger pulse transit time, and was used to obtain arterial volume distensibility. The mean arterial blood pressure with the arm at the horizontal level was acquired, and changes with position were calculated using the hydrostatic principle that blood pressure in the arm is linearly related to its vertical distance from the horizontal level. The mean arm pulse propagation times for the five different positions were 88, 72, 57, 54 and 52 ms, with the corresponding mean arterial volume distensibility of 0.234%, 0.158%, 0.099%, 0.088% and 0.083% per mmHg. For all consecutive changes in arm position, arm pulse propagation time and arterial volume distensibility, were significantly different (all probability Po0.05). The slopes of arm pulse propagation time and arterial volume distensibility against arterial pressure decreased significantly between each consecutive arm position from 901 to 451 (all Po0.01), indicating significant nonlinearity. The experimental results fitted the physiological exponential model and Langewouters’ arctangent model well, and were also comparable to published data with arterial volume distensibility approximately tripling for transmural pressure changes from 101 to 58 mmHg. In conclusion, the inverse and non-linear relationship between arterial volume distensibility and arterial pressure has been quantified using a simple arm positioning procedure, with the greatest effect at low pressures. This work is an important step in developing a simple non-invasive technique for assessing peripheral arterial volume distensibility. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Arterial volume distensibility Photoplethysmography (PPG) Arm pulse propagation time
1. Introduction The arterial system is a major part of the overall circulatory system, playing an important role in cardiovascular physiology and pathophysiology (Glasser et al., 1997). Arteries expand and contract passively with arterial pulsations. This property is associated with different physiological (Joyner, 2000; Tanaka et al., 2000) and clinical factors (Arnett et al., 2000; Bortolotto et al., 1999; Lehmann et al., 1992), through alterations of the structure and properties of the arterial wall. Changes in arterial pressure cause major changes in arterial wall properties (Cox, 1975; Safar et al., 2003; Tardy et al., 1991). Therefore, the ability to
Corresponding author. Tel.: +44 0 191 2336161x26888.
E-mail address: [email protected] (D. Zheng). 0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.02.011
quantify changes in arterial wall properties with pressure is clinically important. Arterial volume compliance (C), defined as the change in arterial blood volume (DV) in response to a change in arterial pressure (DP) (C ¼ DV/DP), is a classic quantitative measure of arterial properties (O’Rourke et al., 2002). To obtain arterial volume compliance, in practice, both arterial pressure change and the simultaneous blood volume change are recorded by different invasive or non-invasive techniques (Buntin and Silver, 1990; Mackenzie et al., 2002; McVeigh et al., 2002; Pannier et al., 2002), but these techniques cannot yet give an accurate measurement of the blood volume (or artery radius) and arterial pressure changes in clinical use. Furthermore, most studies focused mainly on a relatively large single artery (Heerman et al., 2005; Laurent et al., 1994), rather than the total peripheral arterial system. Determining peripheral arterial properties can contribute to studying the development and progression of hypertension.
ARTICLE IN PRESS D. Zheng, A. Murray / Journal of Biomechanics 42 (2009) 1032–1037
In addition to arterial volume compliance, another terminology is commonly used, such as arterial volume distensibility (Dv) giving the relative change in blood volume with a known change in arterial pressure (Dv ¼ (DV/V)/DP) (McVeigh et al., 2002; Pannier et al., 2002). Substituting arterial radius for volume in the equation gives arterial radial distensibility. Arterial volume distensibility can be obtained directly and simply by measuring pulse wave velocity (PWV) (Asmar et al., 1995; Bank and Kaiser, 1998; Callaghan et al., 1986; Laogun and Gosling, 1982). To obtain PWV, analysis of pulse propagation time based on non-invasive photoplethysmography (PPG) has been commonly used because of its simplicity (Allen and Murray, 2002; Foo et al., 2005a, b). Recently we reported that when the pulse propagation time is measured simultaneously from fingertip and earlobe, the effect of pre-ejection time (time delay between the onset of electrical activity of the heart and the opening of the aortic valve) can be eliminated, providing a reliable tool for peripheral arterial property assessment (Zheng et al., 2007). Arterial wall property changes with pressure changes have been studied (Foran and Sheahan, 2004; Pannier et al., 2002), but in most studies, the pressure changes were measured between diastolic and systolic pressure of the cardiac cycle (MacWilliams et al., 1998; Tardy et al., 1991). Bank and Kaiser, 1998 and Bank et al. (1995, 1999) have also reported brachial artery elastic properties at different transmural pressures induced by external cuff pressure on the forearm. It is also known that arm position significantly influences arm blood pressure (Netea et al., 1998; Suzuki et al., 1994) and that by placing the arm at different positions, a range of arterial pressure changes can be easily induced. This study therefore presents a simple non-invasive method to determine a non-linear relationship between the arterial volume distensibility and the arterial pressure with the arm at different positions. The non-linearity could then be compared with results from the physiological exponential elastic model (Forster and Turney, 1986; Hardy and Collins, 1982) and Langewouters’ arctangent model (Langewouters et al., 1984), and with published data. Our hypothesis was that non-linear arterial properties could be quantified non-invasively using a simple arm positioning procedure.
2. Methods 2.1. Subjects Fifteen healthy volunteers with no history of cardiovascular disease from staff and students of Freeman Hospital and Newcastle University were studied. None
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was a smoker or under any medication. There were 8 male and 7 female subjects, with ages in the range 23–58 years. Each was studied again two weeks after the first study. The investigation conformed with the principles outlined in the Declaration of Helsinki (World Medical Association, 2000). The study received ethical permission, and all subjects gave their written informed consent.
2.2. Experimental procedure Each subject lay supine in a quiet environment at an ambient temperature of about 23 1C with a 5 min rest period before measurements to allow cardiovascular stabilization. For each study, a series of five separate tests were performed with the right arm at different positions (901, 451, 01, 451, and 901 to the horizontal level), as shown in Fig. 1. The arm was held in position by a mechanical support that kept it motionless and secured the desired muscular relaxation for a stable and repeatable recording. The subject was asked to breathe steadily. The electrocardiogram (ECG) and PPG were obtained from a dual-channel PPG measurement system designed and developed in the Department of Medical Physics, Freeman Hospital. After the arm had been maintained at the required position for approximately half a minute, with stable and high quality signals shown on the display screen, simultaneous finger and ear PPGs were recorded for 2 min from the right index finger and right earlobe along with the ECG at a sample rate of 2500 Hz. During recording, the right arm was kept as still as possible to reduce motion artifact. All measurements for the first and repeat studies were made by the same operator. The mean arterial blood pressure (MAP) was determined with the arm at the horizontal level at the beginning and end of each study using an automatic oscillometric monitor (Sirecust 732, Siemens, Erlangen, Germany). The oscillometric technique is known to give an accurate measure of MAP (Yamakoshi et al., 1982). Finally, the lengths between suprasternal notch and tip of index finger and mastoid were measured, and their difference was calculated to give a measure of the difference between propagation distance to finger and ear, and referred to below as arm length.
2.3. Pulse wave analysis The finger and ear pulse transit time (finger PTT and ear PTT) were calculated from the Q wave of the QRS complex to the corresponding pulse foot of the finger PPG and ear PPG using interactive software developed with Matlab 7.1 (MathWorks Inc). They were calculated from at least 60 consecutive heart beats. Arm pulse propagation time was calculated by subtracting the ear PTT from the finger PTT to remove the effect of the pre-ejection time on the computation of pulse wave transmission along the artery. The calculation methods are shown in Fig. 2. PWV was then calculated using arm length data.
2.4. Calculation of mean arterial pressure changes It has been reported that the arterial pressure change measured intra-arterially or non-invasively using a Finapres blood pressure monitor was linearly related to its vertical distance from the horizontal level, corresponding to the linear hydrostatic principle (Netea et al., 1998; Suzuki et al., 1994). Therefore, if the arm is raised to the perpendicular, for instance, with an arm length of 0.66 m, the average decrease of arterial pressure equal to the arterial pressure change at the arm mid point can be calculated as 26 mmHg. With the arm at 451 to the horizontal level, the decrease is 18 mmHg, and at 451 and 901 below the horizontal level the pressure increases by 18 and 26 mmHg. The actual changes in blood
ECG
90° 45°
ECG and PPG 0°
signal conditioning
Data capture computer
circuits -45°
Finger PPG
-90° Ear PPG Fig. 1. Schematic diagram of measurement system with the arm at different positions.
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D. Zheng, A. Murray / Journal of Biomechanics 42 (2009) 1032–1037 change with arterial pressure. The expressions for arterial volume distensibility as a function of arterial pressure (P) are Exponential elastic model : Dv ¼
a2 a3 expða3 PÞ ½a1 þ a2 ð1 expða3 PÞÞ
(4)
and Langewouters0 arctangent model : Dv ¼
½1=ðp b2 Þ=½1 þ ðP=b2 b1 =b2 Þ2 ½0:5 þ ð1=pÞtan1 ðP=b2 b1 =b2 Þ
(5)
where a1, a2, a3, b1, and b2, denote the unknown parameters of the models. The model parameters were calculated by employing the curve fitting toolbox in Matlab 7.1 (MathWorks Inc.). The least-square method was used to evaluate how well our data fitted the models.
3. Results 3.1. Pulse propagation time with different arm positions and their repeatability
pressure elicited by rotating the arm were calculated individually for each subject by using the individual arm length. 2.5. Data and statistical analysis The mean values of PTTs (finger PTT, ear PTT and arm pulse propagation time) with the arm at different positions were firstly calculated individually for the first and repeat studies, and the overall means, changes in mean and their standard deviations (SDs) then calculated from both studies. SPSS software package (SPSS Inc.) was employed to perform analysis of variance (ANOVA) for determining the effect of arm position on finger PTT, ear PTT and arm pulse propagation time. The arm pulse propagation time differences for all consecutive changes in arm position were calculated. Comparisons were then performed to determine whether their differences were significant. A value of Po0.05 was considered statistically significant. The between-study repeatability was also analysed by comparing paired differences. Finally, measurements and calculated properties were analysed for nonlinearity against the mean arterial pressure. 2.6. Quantification of arterial properties The speed with which the wave propagates down an artery depends on the elasticity of the artery. If the effects of viscosity are neglected, the PWV is approximated by the Bramwell and Hill equation (Nichols and O’Rourke, 2005) sffiffiffiffiffiffiffi V (1) PWV ¼ rC where V is blood volume in a unit length of artery, r is blood density 1050 kg/m3, and C is arterial volume compliance. From Eq. (1), it is known that the absolute arterial volume compliance cannot be calculated from PWV without knowing the blood volume or artery radius. However, with the definition of arterial volume compliance, the Bramwell and Hill equation gives sffiffiffiffiffiffiffiffiffiffiffi V DP (2) PWV ¼ r DV From Eq. (2) and the definition of arterial volume distensibility (Dv), the following equation can be obtained: Dv ¼
1
r PWV 2
(3)
Arterial volume distensibility with the arm at different positions was then calculated using Eq. (3) and analysed against the mean arterial pressure.
3.2. Non-linear relationship between arm pulse propagation time and arterial pressure Fig. 4(A) and (B) shows the overall means and SDs of arm pulse propagation time and PWV against the overall mean arterial pressure for each arm position. Mean arterial pressure with the arm positioning at 901, 451, 01, 451 and 901 referred to the horizontal level were 58, 65, 83, 101 and 109 mmHg. The corresponding mean arm pulse propagation times were 88, 72, 57, 54 and 52 ms. The mean PWV obtained with the arm at the horizontal level (11.6 m/s) is in close agreement with results for the arm artery reported by Avolio et al. (1985) and summarized by Nichols and O’Rourke (2005), where arm arterial PWV is derived as a function with age and expressed as: Arm
300
Pulse propagation times (ms)
Fig. 2. Arm pulse propagation time measurement.
Fig. 3 gives the overall means and SDs of finger PTT, ear PTT and arm pulse propagation time with the arm at different positions. Variance analysis showed that arm position caused significant effects on the measured finger PTT and arm pulse propagation time (both Po0.01), but not the ear PTT. The repeat measurements were not significantly different (all P40.1). The paired differences between the first and repeat study in finger PTT, ear PTT and arm pulse propagation time are shown in Table 1. The overall SD of differences between both studies for all arm positions was 9.0 ms. The mean absolute repeat differences were small and were 5.9, 8.1 and 6.1 ms for overall finger PTT, ear PTT and arm pulse propagation time, respectively.
250 Finger PTT 200 Ear PTT 150 100 Arm pulse propagation time 50 0 90°
2.7. Comparison with exponential model and Langewouters’ arctangent model The physiological exponential elastic model proposed by Hardy and Collins (1982) and Forster and Turney (1986) and the Langewouters’ arctangent model (Langewouters et al., 1984) are commonly used to describe how arterial properties
45° 0° -45° -90° Arm position from horizontal level
Fig. 3. The means and SDs of finger PTT, ear PTT and arm pulse propagation time with the arm at different positions. SDs are population values relating to betweensubject variability.
ARTICLE IN PRESS D. Zheng, A. Murray / Journal of Biomechanics 42 (2009) 1032–1037
Table 1 The means and SDs of paired differences between the first and repeat study in finger PTT, ear PTT and arm pulse propagation time with the arm at different positions.
Finger PTT (ms)
Ear PTT (ms)
Arm pulse propagation time (ms)
90 45 0 45 90
3712 378 177 1710 179
1710 0710 1710 2710 1710
378 376 178 177 277
PWV ¼ 0.048 Age+9.98 (m/s), giving 11.9 m/s for a mean age of 40 years. For all consecutive changes in arm position, the arm pulse propagation times were significantly different (all Po0.05). The slope of arm pulse propagation time against arterial pressure for consecutive arm positions were 2.0, 0.8, 0.2 and 0.2 ms/ mmHg, with the consecutive slopes decreasing significantly with the arm from 901 to 451 (all Po0.01). Therefore, with the increase of arterial blood pressure, the arm pulse propagation time decreased non-linearly, with the greatest changes at the lowest pressures. 3.3. Non-linear relationship between arterial volume distensibility and arterial pressure
Arm pulse propagation time (ms)
Paired difference between first and repeat study
45°
0°
-45°
-90°
100 90 80 70 60 50 40 30 50
60
70
80
90
100
110
120
16 14 Pulse wave velocity (m/s)
Arm position from horizontal level (deg.)
90°
110
1035
12 10 8 6
3.4. Comparison with physiological models and published data
4 50
60
50
60
70
80
90
100
110
120
110
120
0.35
Arterial volume distensibility (% per mmHg)
Fig. 4(C) shows the overall means and SDs of arterial volume distensibility against mean arterial pressure. Mean arterial volume distensibilities for the five different positions were 0.234%, 0.158%, 0.099%, 0.088% and 0.083% per mmHg. Again, for all consecutive changes in arm position, arterial volume distensibilities were significantly different (all Po0.05). From the slope of arterial volume distensibility against arterial pressure for consecutive arm positions, the arterial volume distensibility change associated with a 10 mmHg fall in arterial pressure was 0.10%, 0.03%, 0.006% and 0.006% per mmHg, with the consecutive slopes decreasing significantly with the arm from 901 to 451 (all Po0.001). The relationship between arterial volume distensibility and arterial pressure was therefore significantly different from linear.
0.30 0.25 0.20 0.15 0.10 0.05
Table 2 shows the arterial volume distensibility computed from the physiological exponential model (with a1 ¼ 0.564, a2 ¼ 0.004, a3 ¼ 0.092) and Langewouters’ arctangent model (with b1 ¼ 5.9 and b2 ¼ 14.0). Our experimental data fitted the two models well with the square of the correlation coefficients of 0.95 and 0.94, respectively. Although the arterial volume distensibility calculated in the present study were approximately 33–66% greater than those measured by Bank et al. (1999), similar relative changes were observed in both studies, with the arterial volume distensibility approximately tripling with transmural pressure ranging from 101 to 58 mmHg.
4. Discussion and conclusions We have described a simple non-invasive PPG technique for directly measuring in vivo peripheral arterial volume distensibility over a range of pressures. The changes in arterial volume
0.00 70 80 90 100 Mean arterial perssure (mmHg)
Fig. 4. Relationship between mean arterial pressure and arm pulse propagation time (A), PWV (B), and arterial volume distensibility (C). SDs are population values relating to between-subject variability.
distensibility with different arm positions have been experimentally detected by arm pulse propagation time, with correction for the effect of pre-ejection time. The repeatability was also assessed over a period of two weeks, with no significant difference. The relationship between arterial blood pressure and arm pulse propagation time and arterial volume distensibility were inverse and non-linear. We also showed that our experimental data matched the physiological exponential model and Langewouters’ arctangent
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Table 2 Comparison of arterial volume distensibility experimental results with accepted physiological models and published data.
have made an important step in developing a simple non-invasive technique for this important clinical measurement.
Arterial volume distensibility (% per mmHg) At mean arterial pressure (mmHg) 58
65
83
101
Conflict of interest statement None
Experimental and published data Experimental data Exponential model Langewouters’ arctangent model Bank et al’s published dataa
0.234 0.238 0.220 0.176
0.158 0.133 0.178 0.120
0.099 0.098 0.113 0.067
0.088 0.094 0.078 0.053
Relative to experimental data Exponential model Langewouters’ arctangent model Bank et al’s published dataa
0.004 0.014 0.058
0.025 0.020 0.038
0.001 0.014 0.031
0.006 0.010 0.035
a
109
0.083 0.093 0.068 –
Acknowledgments
0.010 0.015 –
This study was supported by an Overseas Research Studentship (Universities UK) and an International Research Studentship (Newcastle University) to Dingchang Zheng, and funding from Newcastle Hospitals Trustees.
Measured from Fig. 4 and 5 published by Bank et al. (1999).
References model. These are the two commonly used physiological models for describing arterial wall behaviour with arterial pressure (Tardy et al., 1991). The modeled information computed from the experimental data may provide the opportunity to estimate the arterial properties outside the range of arterial pressures induced in this present study. Our experimental data were comparable with in vivo data from the work of Bank et al. (1999) using an ultrasound technique for measuring brachial artery elastic properties, with similar relative arterial volume distensibility changes for transmural pressures between 101 and 58 mmHg. However, approximately 33–66% greater arterial volume distensibilities were calculated in the present study, with better agreement found at lower pressures. In addition, the arm positioning procedure proposed in our study is much simpler than using an ultrasound technique providing the potential for application in clinical research contexts. This work is an important step in quantifying arterial volume distensibility changes with pressure non-invasively and easily at physiological distending pressures. One limitation of our study is that we cannot assess characteristics with non-physiological pressures. However, the range of mean pressure between approximately 60 and 110 mmHg is of value in assessing clinical performance. Another limitation of this study is that we obtained MAP from the measured pressure with the arm at the horizontal level and calculated the changes induced by different arm positions using the hydrostatic principle. This is supported by Netea et al. (1998) and Suzuki et al. (1994) who have shown that the changes in measured blood pressure were in strong agreement with the theoretical linear hydrostatic effect. Their experimental maximum differences were 29% and 17%, respectively, for the arm lowered in comparison with the arm elevated by an equal vertical distance. However, this tendency for the actual pressure change to be greater with the arm in the lower position would increase, rather than decrease, the non-linearity of the curve. In addition, these figures contrast with our results for change in distensibility referred to the horizontal level, which was 840% greater (0.135 compared with 0.016% per mmHg) for raising the arm compared with lowering it. It should also be noted that there are inaccuracies in estimating the arterial distance from external body measurements, and that findings were limited to healthy subjects. However, the simple method presented here makes it possible to perform evaluation of arterial properties non-invasively in different haemodynamic conditions caused by various cardiovascular diseases or ageing. Further research is required to study different clinical populations and ethnic groups. Nevertheless we
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Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Non-invasive quantification of peripheral arterial volume distensibility and its non-linear relationship with arterial pressure Dingchang Zheng , Alan Murray Medical Physics Department, Newcastle University, Freeman Hospital, Newcastle upon Tyne NE7 7DN, UK
a r t i c l e in f o
a b s t r a c t
Article history: Accepted 22 February 2009
Arterial wall function is associated with different physiological and clinical factors. Changes in arterial pressure cause major changes in the arterial wall. This study presents a simple non-invasive method to quantify arterial volume distensibility changes with different arterial pressures. The electrocardiogram, finger and ear photoplethysmogram were recorded from 15 subjects with the right arm at five different positions (901, 451, 01, 451 and 901 referred to the horizontal level). Arm pulse propagation time was determined by subtracting ear pulse transit time from finger pulse transit time, and was used to obtain arterial volume distensibility. The mean arterial blood pressure with the arm at the horizontal level was acquired, and changes with position were calculated using the hydrostatic principle that blood pressure in the arm is linearly related to its vertical distance from the horizontal level. The mean arm pulse propagation times for the five different positions were 88, 72, 57, 54 and 52 ms, with the corresponding mean arterial volume distensibility of 0.234%, 0.158%, 0.099%, 0.088% and 0.083% per mmHg. For all consecutive changes in arm position, arm pulse propagation time and arterial volume distensibility, were significantly different (all probability Po0.05). The slopes of arm pulse propagation time and arterial volume distensibility against arterial pressure decreased significantly between each consecutive arm position from 901 to 451 (all Po0.01), indicating significant nonlinearity. The experimental results fitted the physiological exponential model and Langewouters’ arctangent model well, and were also comparable to published data with arterial volume distensibility approximately tripling for transmural pressure changes from 101 to 58 mmHg. In conclusion, the inverse and non-linear relationship between arterial volume distensibility and arterial pressure has been quantified using a simple arm positioning procedure, with the greatest effect at low pressures. This work is an important step in developing a simple non-invasive technique for assessing peripheral arterial volume distensibility. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Arterial volume distensibility Photoplethysmography (PPG) Arm pulse propagation time
1. Introduction The arterial system is a major part of the overall circulatory system, playing an important role in cardiovascular physiology and pathophysiology (Glasser et al., 1997). Arteries expand and contract passively with arterial pulsations. This property is associated with different physiological (Joyner, 2000; Tanaka et al., 2000) and clinical factors (Arnett et al., 2000; Bortolotto et al., 1999; Lehmann et al., 1992), through alterations of the structure and properties of the arterial wall. Changes in arterial pressure cause major changes in arterial wall properties (Cox, 1975; Safar et al., 2003; Tardy et al., 1991). Therefore, the ability to
Corresponding author. Tel.: +44 0 191 2336161x26888.
E-mail address: [email protected] (D. Zheng). 0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.02.011
quantify changes in arterial wall properties with pressure is clinically important. Arterial volume compliance (C), defined as the change in arterial blood volume (DV) in response to a change in arterial pressure (DP) (C ¼ DV/DP), is a classic quantitative measure of arterial properties (O’Rourke et al., 2002). To obtain arterial volume compliance, in practice, both arterial pressure change and the simultaneous blood volume change are recorded by different invasive or non-invasive techniques (Buntin and Silver, 1990; Mackenzie et al., 2002; McVeigh et al., 2002; Pannier et al., 2002), but these techniques cannot yet give an accurate measurement of the blood volume (or artery radius) and arterial pressure changes in clinical use. Furthermore, most studies focused mainly on a relatively large single artery (Heerman et al., 2005; Laurent et al., 1994), rather than the total peripheral arterial system. Determining peripheral arterial properties can contribute to studying the development and progression of hypertension.
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In addition to arterial volume compliance, another terminology is commonly used, such as arterial volume distensibility (Dv) giving the relative change in blood volume with a known change in arterial pressure (Dv ¼ (DV/V)/DP) (McVeigh et al., 2002; Pannier et al., 2002). Substituting arterial radius for volume in the equation gives arterial radial distensibility. Arterial volume distensibility can be obtained directly and simply by measuring pulse wave velocity (PWV) (Asmar et al., 1995; Bank and Kaiser, 1998; Callaghan et al., 1986; Laogun and Gosling, 1982). To obtain PWV, analysis of pulse propagation time based on non-invasive photoplethysmography (PPG) has been commonly used because of its simplicity (Allen and Murray, 2002; Foo et al., 2005a, b). Recently we reported that when the pulse propagation time is measured simultaneously from fingertip and earlobe, the effect of pre-ejection time (time delay between the onset of electrical activity of the heart and the opening of the aortic valve) can be eliminated, providing a reliable tool for peripheral arterial property assessment (Zheng et al., 2007). Arterial wall property changes with pressure changes have been studied (Foran and Sheahan, 2004; Pannier et al., 2002), but in most studies, the pressure changes were measured between diastolic and systolic pressure of the cardiac cycle (MacWilliams et al., 1998; Tardy et al., 1991). Bank and Kaiser, 1998 and Bank et al. (1995, 1999) have also reported brachial artery elastic properties at different transmural pressures induced by external cuff pressure on the forearm. It is also known that arm position significantly influences arm blood pressure (Netea et al., 1998; Suzuki et al., 1994) and that by placing the arm at different positions, a range of arterial pressure changes can be easily induced. This study therefore presents a simple non-invasive method to determine a non-linear relationship between the arterial volume distensibility and the arterial pressure with the arm at different positions. The non-linearity could then be compared with results from the physiological exponential elastic model (Forster and Turney, 1986; Hardy and Collins, 1982) and Langewouters’ arctangent model (Langewouters et al., 1984), and with published data. Our hypothesis was that non-linear arterial properties could be quantified non-invasively using a simple arm positioning procedure.
2. Methods 2.1. Subjects Fifteen healthy volunteers with no history of cardiovascular disease from staff and students of Freeman Hospital and Newcastle University were studied. None
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was a smoker or under any medication. There were 8 male and 7 female subjects, with ages in the range 23–58 years. Each was studied again two weeks after the first study. The investigation conformed with the principles outlined in the Declaration of Helsinki (World Medical Association, 2000). The study received ethical permission, and all subjects gave their written informed consent.
2.2. Experimental procedure Each subject lay supine in a quiet environment at an ambient temperature of about 23 1C with a 5 min rest period before measurements to allow cardiovascular stabilization. For each study, a series of five separate tests were performed with the right arm at different positions (901, 451, 01, 451, and 901 to the horizontal level), as shown in Fig. 1. The arm was held in position by a mechanical support that kept it motionless and secured the desired muscular relaxation for a stable and repeatable recording. The subject was asked to breathe steadily. The electrocardiogram (ECG) and PPG were obtained from a dual-channel PPG measurement system designed and developed in the Department of Medical Physics, Freeman Hospital. After the arm had been maintained at the required position for approximately half a minute, with stable and high quality signals shown on the display screen, simultaneous finger and ear PPGs were recorded for 2 min from the right index finger and right earlobe along with the ECG at a sample rate of 2500 Hz. During recording, the right arm was kept as still as possible to reduce motion artifact. All measurements for the first and repeat studies were made by the same operator. The mean arterial blood pressure (MAP) was determined with the arm at the horizontal level at the beginning and end of each study using an automatic oscillometric monitor (Sirecust 732, Siemens, Erlangen, Germany). The oscillometric technique is known to give an accurate measure of MAP (Yamakoshi et al., 1982). Finally, the lengths between suprasternal notch and tip of index finger and mastoid were measured, and their difference was calculated to give a measure of the difference between propagation distance to finger and ear, and referred to below as arm length.
2.3. Pulse wave analysis The finger and ear pulse transit time (finger PTT and ear PTT) were calculated from the Q wave of the QRS complex to the corresponding pulse foot of the finger PPG and ear PPG using interactive software developed with Matlab 7.1 (MathWorks Inc). They were calculated from at least 60 consecutive heart beats. Arm pulse propagation time was calculated by subtracting the ear PTT from the finger PTT to remove the effect of the pre-ejection time on the computation of pulse wave transmission along the artery. The calculation methods are shown in Fig. 2. PWV was then calculated using arm length data.
2.4. Calculation of mean arterial pressure changes It has been reported that the arterial pressure change measured intra-arterially or non-invasively using a Finapres blood pressure monitor was linearly related to its vertical distance from the horizontal level, corresponding to the linear hydrostatic principle (Netea et al., 1998; Suzuki et al., 1994). Therefore, if the arm is raised to the perpendicular, for instance, with an arm length of 0.66 m, the average decrease of arterial pressure equal to the arterial pressure change at the arm mid point can be calculated as 26 mmHg. With the arm at 451 to the horizontal level, the decrease is 18 mmHg, and at 451 and 901 below the horizontal level the pressure increases by 18 and 26 mmHg. The actual changes in blood
ECG
90° 45°
ECG and PPG 0°
signal conditioning
Data capture computer
circuits -45°
Finger PPG
-90° Ear PPG Fig. 1. Schematic diagram of measurement system with the arm at different positions.
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D. Zheng, A. Murray / Journal of Biomechanics 42 (2009) 1032–1037 change with arterial pressure. The expressions for arterial volume distensibility as a function of arterial pressure (P) are Exponential elastic model : Dv ¼
a2 a3 expða3 PÞ ½a1 þ a2 ð1 expða3 PÞÞ
(4)
and Langewouters0 arctangent model : Dv ¼
½1=ðp b2 Þ=½1 þ ðP=b2 b1 =b2 Þ2 ½0:5 þ ð1=pÞtan1 ðP=b2 b1 =b2 Þ
(5)
where a1, a2, a3, b1, and b2, denote the unknown parameters of the models. The model parameters were calculated by employing the curve fitting toolbox in Matlab 7.1 (MathWorks Inc.). The least-square method was used to evaluate how well our data fitted the models.
3. Results 3.1. Pulse propagation time with different arm positions and their repeatability
pressure elicited by rotating the arm were calculated individually for each subject by using the individual arm length. 2.5. Data and statistical analysis The mean values of PTTs (finger PTT, ear PTT and arm pulse propagation time) with the arm at different positions were firstly calculated individually for the first and repeat studies, and the overall means, changes in mean and their standard deviations (SDs) then calculated from both studies. SPSS software package (SPSS Inc.) was employed to perform analysis of variance (ANOVA) for determining the effect of arm position on finger PTT, ear PTT and arm pulse propagation time. The arm pulse propagation time differences for all consecutive changes in arm position were calculated. Comparisons were then performed to determine whether their differences were significant. A value of Po0.05 was considered statistically significant. The between-study repeatability was also analysed by comparing paired differences. Finally, measurements and calculated properties were analysed for nonlinearity against the mean arterial pressure. 2.6. Quantification of arterial properties The speed with which the wave propagates down an artery depends on the elasticity of the artery. If the effects of viscosity are neglected, the PWV is approximated by the Bramwell and Hill equation (Nichols and O’Rourke, 2005) sffiffiffiffiffiffiffi V (1) PWV ¼ rC where V is blood volume in a unit length of artery, r is blood density 1050 kg/m3, and C is arterial volume compliance. From Eq. (1), it is known that the absolute arterial volume compliance cannot be calculated from PWV without knowing the blood volume or artery radius. However, with the definition of arterial volume compliance, the Bramwell and Hill equation gives sffiffiffiffiffiffiffiffiffiffiffi V DP (2) PWV ¼ r DV From Eq. (2) and the definition of arterial volume distensibility (Dv), the following equation can be obtained: Dv ¼
1
r PWV 2
(3)
Arterial volume distensibility with the arm at different positions was then calculated using Eq. (3) and analysed against the mean arterial pressure.
3.2. Non-linear relationship between arm pulse propagation time and arterial pressure Fig. 4(A) and (B) shows the overall means and SDs of arm pulse propagation time and PWV against the overall mean arterial pressure for each arm position. Mean arterial pressure with the arm positioning at 901, 451, 01, 451 and 901 referred to the horizontal level were 58, 65, 83, 101 and 109 mmHg. The corresponding mean arm pulse propagation times were 88, 72, 57, 54 and 52 ms. The mean PWV obtained with the arm at the horizontal level (11.6 m/s) is in close agreement with results for the arm artery reported by Avolio et al. (1985) and summarized by Nichols and O’Rourke (2005), where arm arterial PWV is derived as a function with age and expressed as: Arm
300
Pulse propagation times (ms)
Fig. 2. Arm pulse propagation time measurement.
Fig. 3 gives the overall means and SDs of finger PTT, ear PTT and arm pulse propagation time with the arm at different positions. Variance analysis showed that arm position caused significant effects on the measured finger PTT and arm pulse propagation time (both Po0.01), but not the ear PTT. The repeat measurements were not significantly different (all P40.1). The paired differences between the first and repeat study in finger PTT, ear PTT and arm pulse propagation time are shown in Table 1. The overall SD of differences between both studies for all arm positions was 9.0 ms. The mean absolute repeat differences were small and were 5.9, 8.1 and 6.1 ms for overall finger PTT, ear PTT and arm pulse propagation time, respectively.
250 Finger PTT 200 Ear PTT 150 100 Arm pulse propagation time 50 0 90°
2.7. Comparison with exponential model and Langewouters’ arctangent model The physiological exponential elastic model proposed by Hardy and Collins (1982) and Forster and Turney (1986) and the Langewouters’ arctangent model (Langewouters et al., 1984) are commonly used to describe how arterial properties
45° 0° -45° -90° Arm position from horizontal level
Fig. 3. The means and SDs of finger PTT, ear PTT and arm pulse propagation time with the arm at different positions. SDs are population values relating to betweensubject variability.
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Table 1 The means and SDs of paired differences between the first and repeat study in finger PTT, ear PTT and arm pulse propagation time with the arm at different positions.
Finger PTT (ms)
Ear PTT (ms)
Arm pulse propagation time (ms)
90 45 0 45 90
3712 378 177 1710 179
1710 0710 1710 2710 1710
378 376 178 177 277
PWV ¼ 0.048 Age+9.98 (m/s), giving 11.9 m/s for a mean age of 40 years. For all consecutive changes in arm position, the arm pulse propagation times were significantly different (all Po0.05). The slope of arm pulse propagation time against arterial pressure for consecutive arm positions were 2.0, 0.8, 0.2 and 0.2 ms/ mmHg, with the consecutive slopes decreasing significantly with the arm from 901 to 451 (all Po0.01). Therefore, with the increase of arterial blood pressure, the arm pulse propagation time decreased non-linearly, with the greatest changes at the lowest pressures. 3.3. Non-linear relationship between arterial volume distensibility and arterial pressure
Arm pulse propagation time (ms)
Paired difference between first and repeat study
45°
0°
-45°
-90°
100 90 80 70 60 50 40 30 50
60
70
80
90
100
110
120
16 14 Pulse wave velocity (m/s)
Arm position from horizontal level (deg.)
90°
110
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12 10 8 6
3.4. Comparison with physiological models and published data
4 50
60
50
60
70
80
90
100
110
120
110
120
0.35
Arterial volume distensibility (% per mmHg)
Fig. 4(C) shows the overall means and SDs of arterial volume distensibility against mean arterial pressure. Mean arterial volume distensibilities for the five different positions were 0.234%, 0.158%, 0.099%, 0.088% and 0.083% per mmHg. Again, for all consecutive changes in arm position, arterial volume distensibilities were significantly different (all Po0.05). From the slope of arterial volume distensibility against arterial pressure for consecutive arm positions, the arterial volume distensibility change associated with a 10 mmHg fall in arterial pressure was 0.10%, 0.03%, 0.006% and 0.006% per mmHg, with the consecutive slopes decreasing significantly with the arm from 901 to 451 (all Po0.001). The relationship between arterial volume distensibility and arterial pressure was therefore significantly different from linear.
0.30 0.25 0.20 0.15 0.10 0.05
Table 2 shows the arterial volume distensibility computed from the physiological exponential model (with a1 ¼ 0.564, a2 ¼ 0.004, a3 ¼ 0.092) and Langewouters’ arctangent model (with b1 ¼ 5.9 and b2 ¼ 14.0). Our experimental data fitted the two models well with the square of the correlation coefficients of 0.95 and 0.94, respectively. Although the arterial volume distensibility calculated in the present study were approximately 33–66% greater than those measured by Bank et al. (1999), similar relative changes were observed in both studies, with the arterial volume distensibility approximately tripling with transmural pressure ranging from 101 to 58 mmHg.
4. Discussion and conclusions We have described a simple non-invasive PPG technique for directly measuring in vivo peripheral arterial volume distensibility over a range of pressures. The changes in arterial volume
0.00 70 80 90 100 Mean arterial perssure (mmHg)
Fig. 4. Relationship between mean arterial pressure and arm pulse propagation time (A), PWV (B), and arterial volume distensibility (C). SDs are population values relating to between-subject variability.
distensibility with different arm positions have been experimentally detected by arm pulse propagation time, with correction for the effect of pre-ejection time. The repeatability was also assessed over a period of two weeks, with no significant difference. The relationship between arterial blood pressure and arm pulse propagation time and arterial volume distensibility were inverse and non-linear. We also showed that our experimental data matched the physiological exponential model and Langewouters’ arctangent
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Table 2 Comparison of arterial volume distensibility experimental results with accepted physiological models and published data.
have made an important step in developing a simple non-invasive technique for this important clinical measurement.
Arterial volume distensibility (% per mmHg) At mean arterial pressure (mmHg) 58
65
83
101
Conflict of interest statement None
Experimental and published data Experimental data Exponential model Langewouters’ arctangent model Bank et al’s published dataa
0.234 0.238 0.220 0.176
0.158 0.133 0.178 0.120
0.099 0.098 0.113 0.067
0.088 0.094 0.078 0.053
Relative to experimental data Exponential model Langewouters’ arctangent model Bank et al’s published dataa
0.004 0.014 0.058
0.025 0.020 0.038
0.001 0.014 0.031
0.006 0.010 0.035
a
109
0.083 0.093 0.068 –
Acknowledgments
0.010 0.015 –
This study was supported by an Overseas Research Studentship (Universities UK) and an International Research Studentship (Newcastle University) to Dingchang Zheng, and funding from Newcastle Hospitals Trustees.
Measured from Fig. 4 and 5 published by Bank et al. (1999).
References model. These are the two commonly used physiological models for describing arterial wall behaviour with arterial pressure (Tardy et al., 1991). The modeled information computed from the experimental data may provide the opportunity to estimate the arterial properties outside the range of arterial pressures induced in this present study. Our experimental data were comparable with in vivo data from the work of Bank et al. (1999) using an ultrasound technique for measuring brachial artery elastic properties, with similar relative arterial volume distensibility changes for transmural pressures between 101 and 58 mmHg. However, approximately 33–66% greater arterial volume distensibilities were calculated in the present study, with better agreement found at lower pressures. In addition, the arm positioning procedure proposed in our study is much simpler than using an ultrasound technique providing the potential for application in clinical research contexts. This work is an important step in quantifying arterial volume distensibility changes with pressure non-invasively and easily at physiological distending pressures. One limitation of our study is that we cannot assess characteristics with non-physiological pressures. However, the range of mean pressure between approximately 60 and 110 mmHg is of value in assessing clinical performance. Another limitation of this study is that we obtained MAP from the measured pressure with the arm at the horizontal level and calculated the changes induced by different arm positions using the hydrostatic principle. This is supported by Netea et al. (1998) and Suzuki et al. (1994) who have shown that the changes in measured blood pressure were in strong agreement with the theoretical linear hydrostatic effect. Their experimental maximum differences were 29% and 17%, respectively, for the arm lowered in comparison with the arm elevated by an equal vertical distance. However, this tendency for the actual pressure change to be greater with the arm in the lower position would increase, rather than decrease, the non-linearity of the curve. In addition, these figures contrast with our results for change in distensibility referred to the horizontal level, which was 840% greater (0.135 compared with 0.016% per mmHg) for raising the arm compared with lowering it. It should also be noted that there are inaccuracies in estimating the arterial distance from external body measurements, and that findings were limited to healthy subjects. However, the simple method presented here makes it possible to perform evaluation of arterial properties non-invasively in different haemodynamic conditions caused by various cardiovascular diseases or ageing. Further research is required to study different clinical populations and ethnic groups. Nevertheless we
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