# Pulse wave velocity

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Pulse wave velocity
Medical diagnostics

Pulse wave velocity (PWV) is the velocity at which the blood pressure pulse propagates through the circulatory system, usually an artery or a combined length of arteries. PWV is used clinically as a measure of arterial stiffness and can be readily measured non-invasively in humans, with measurement of carotid to femoral PWV (cfPWV) being the recommended method.[1][2][3] cfPWV is highly reproducible,[4] and predicts future cardiovascular events and all-cause mortality independent of conventional cardiovascular risk factors.[5][6] It has been recognized by the European Society of Hypertension as an indicator of target organ damage and a useful additional test in the investigation of hypertension.[7]

## Relationship between arterial stiffness and pulse wave velocity

The theory of the velocity of the transmission of the pulse through the circulation dates back to 1808 with the work of Thomas Young.[8] The relationship between pulse wave velocity (PWV) and arterial wall stiffness can be derived from Newton's second law of motion (${\displaystyle F=ma}$) applied to a small fluid element, where the force on the element equals the product of density (the mass per unit volume; ${\displaystyle \rho }$) and the acceleration.[9] The approach for calculating PWV is similar to the calculation of the speed of sound, ${\displaystyle {c_{0}}}$, in a compressible fluid (e.g. air):

${\displaystyle c_{0}={\sqrt {B/\rho }}}$,

where ${\displaystyle {B}}$ is the bulk modulus and ${\displaystyle {\rho }}$ is the density of the fluid.

### The Frank / Bramwell-Hill equation

For an incompressible fluid (blood) in a compressible (elastic) tube (e.g. an artery):[10]

${\displaystyle PWV={\sqrt {V\cdot dP/(\rho \cdot dV)}}}$,

where ${\displaystyle V}$ is volume per unit length and ${\displaystyle P}$is pressure. This is the equation derived by Otto Frank,[11] and John Crighton Bramwell and Archibald Hill.[12]

Alternative forms of this equation are:

${\displaystyle PWV={\sqrt {r\cdot dP/\rho \cdot 2\cdot dr}}}$, or ${\displaystyle PWV=1/{\sqrt {\rho \cdot D}}}$,

where ${\displaystyle r}$ is the radius of the tube and ${\displaystyle D}$ is distensibility.

### The Moens–Korteweg equation

This equation:

${\displaystyle \mathrm {PWV} ={\sqrt {\dfrac {E_{\mathrm {inc} }\cdot h}{2\cdot r\cdot \rho }}}}$,

characterises PWV in terms of the incremental elastic modulus ${\displaystyle {E_{\mathrm {inc} }}}$of the vessel wall, the wall thickness, ${\displaystyle h}$and the radius. It was derived independently by Adriaan Isebree Moens and Diederik Korteweg and is equivalent to the Frank / Bramwell Hill equation:[10]:64

These equations assume that:

1. there is little or no change in vessel area.
2. there is little or no change in wall thickness.
3. there is little or no change in density (i.e. blood is assumed incompressible).
4. ${\displaystyle \operatorname {d} \!v(\operatorname {d} \!r^{-1})\operatorname {d} \!x\cdot \operatorname {d} \!t}$ is negligible.

## Variation in pulse wave velocity in the circulatory system

Since the wall thickness, radius and incremental elastic modulus vary from blood vessel to blood vessel, PWV will also vary between vessels.[10] Most measurements of PWV represent an average velocity over several vessels (e.g. from the carotid to the femoral artery).

## Dependence of pulse wave velocity on blood pressure

PWV intrinsically varies with blood pressure.[13] PWV increases with pressure for two reasons:

1. Arterial compliance (${\displaystyle \operatorname {d} \!V/\operatorname {d} \!P}$) decreases with increasing pressure due to the curvilinear relationship between arterial pressure and volume.
2. Volume (${\displaystyle V}$) increases with increasing pressure (the artery dilates), directly increasing PWV.

## Experimental approaches used to measure pulse wave velocity

A range of invasive or non-invasive methods can be used to measure PWV. Some general approaches are:

### Using two simultaneously measured pressure waveforms

PWV, by definition, is the distance traveled (${\displaystyle \Delta x}$) by the pulse wave divided by the time (${\displaystyle \Delta t}$) for the wave to travel that distance:

${\displaystyle \mathrm {PWV} ={\dfrac {\Delta x}{\Delta t}}}$,

in practice this approach is complicated by the existence of reflected waves.[10] It is widely assumed that reflections are minimal during late diastole and early systole.[10] With this assumption, PWV can be measured using the `foot' of the pressure waveform as a fiducial marker from invasive or non-invasive measurements; the transit time corresponds to the delay in arrival of the foot between two locations a known distance apart. Locating the foot of the pressure waveform can be problematic.[14] The advantage of the foot-to-foot PWV measurement is the simplicity of measurement, requiring only two pressure wave forms recorded with invasive catheters, or non-invasively using pulse detection devices applied to the skin at two measurement sites, and a tape measure.[15]

### Using pressure and volume, or pressure and diameter

This is based on the method described by Bramwell & Hill[16] who proposed modifications to the Moens-Kortweg equation. Quoting directly, these modifications were:

"A small rise ${\displaystyle \delta P}$ in pressure may be shown to cause a small increase, ${\displaystyle \delta y=y^{2}\delta P/(Ec)}$, in the radius ${\displaystyle y}$ of the artery, or a small increase, ${\displaystyle \delta V=2\pi y^{3}\delta P/(Ec)}$, in its own volume ${\displaystyle V}$ per unit length. Hence ${\displaystyle 2y/Ec=\operatorname {d} \!V/(V\operatorname {d} \!P)}$"

where ${\displaystyle c}$ represents the wall thickness (defined as ${\displaystyle h}$above), ${\displaystyle E}$ the elastic modulus, and ${\displaystyle y}$ the vessel radius (defined as ${\displaystyle r}$above). This permits calculation of local PWV in terms of ${\displaystyle {\sqrt {V\cdot dP/(\rho \cdot dV)}}}$, or ${\displaystyle {\sqrt {r\cdot dP/\rho \cdot 2\cdot dr}}}$, as detailed above, and provides an alternative method of measuring PWV, if pressure and arterial dimensions are measured, for example by ultrasound [17][18] or magnetic resonance imaging (MRI).[19]

### Using pressure-flow velocity, pressure-volumetric flow relationships or characteristic impedance

The Water hammer equation expressed either in terms of pressure and flow velocity,[20] pressure and volumetric flow, or characteristic impedance[21] can be used to calculate local PWV:

${\displaystyle \mathrm {PWV} =P/\left(v\cdot \rho \right)=P/Q\cdot A/\rho =Z_{\mathrm {c} }\cdot A/\rho }$,

where ${\displaystyle v}$ is velocity, ${\displaystyle Q}$is volumetric flow, ${\displaystyle Z_{\mathrm {c} }}$ is characteristic impedance and ${\displaystyle A}$is the cross-sectional area of the vessel. This approach is only valid when wave reflections are absent or minimal, this is assumed to be the case in early systole.[22]

### Using diameter-flow velocity relationships

A related method to the pressure-flow velocity method uses vessel diameter and flow velocity to determine local PWV.[23] It is also based on the Water hammer equation:

${\displaystyle dP_{\pm }=\pm \rho \cdot PWV\cdot dv_{\pm }}$,

and since

${\displaystyle dP_{+}+dP_{-}={\frac {2\cdot \rho \cdot PWV^{2}}{S}}\cdot (dS_{+}+dS_{-})}$,

where ${\displaystyle S}$is diameter; then:

${\displaystyle PWV={\frac {S}{2}}\cdot {\frac {(dv_{+}+dv_{-})}{(dS_{+}+dS_{-})}}}$,

or using the incremental hoop strain, ${\displaystyle dS/S=d\ln S}$,

PWV can be expressed in terms of ${\displaystyle v}$and ${\displaystyle S}$

${\displaystyle PWV=\pm {\frac {1}{2}}\cdot {\frac {dv_{\pm }}{d\ln S_{\pm }}}}$,

therefore plotting ${\displaystyle \ln S}$against ${\displaystyle v}$gives a 'lnDU-loop', and the linear portion during early systole, when reflected waves are assumed to be minimal, can be used to calculate PWV.

## Clinical measurement of pulse wave velocity

### Clinical methods

Clinically, PWV can be measured in several ways and in different locations. The 'gold standard' for arterial stiffness assessment in clinical practice is cfPWV,[2][3] and validation guidelines have been proposed.[24] Other measures such as brachial-ankle PWV and cardio-ankle vascular index (CAVI) are also popular.[25] For cfPWV, it is recommended that the arrival time of the pulse wave measured simultaneously at both locations, and the distance travelled by the pulse wave calculated as 80% of the direct distance between the common carotid artery in the neck and the femoral artery in the groin.[2] Numerous devices exist to measure cfPWV;[26][27] some techniques include:

• use of a transducer to record the time of arrival of the pulse wave at the carotid and femoral arteries.
• use of cuffs placed around the limbs and neck to record the time of arrival of the pulse wave oscillometrically.
• use of Doppler ultrasound or magnetic resonance imaging to record the time of arrival of the pulse wave based on the flow velocity waveform.

Newer devices that employ an arm cuff,[28] fingertip sensors[29] or special weighing scales[30] have been described, but their clinical utility remains to be fully established.

### Interpretation

Current guidelines by the European Society of Hypertension state that a measured PWV larger than 10 m/s can be considered an independent marker of end-organ damage.[7] However, the use of a fixed PWV threshold value is debated, as PWV is dependent on blood pressure .[13] A high pulse wave velocity (PWV) has also been associated with poor lung function.[31]

## References

1. ^ Laurent S, Cockcroft J, Van Bortel L, Boutouyrie P, Giannattasio C, Hayoz D, et al. (November 2006). "Expert consensus document on arterial stiffness: methodological issues and clinical applications". European Heart Journal. 27 (21): 2588–605. doi:10.1093/eurheartj/ehl254. PMID 17000623.
2. ^ a b c Van Bortel LM, Laurent S, Boutouyrie P, Chowienczyk P, Cruickshank JK, De Backer T, et al. (March 2012). "Expert consensus document on the measurement of aortic stiffness in daily practice using carotid-femoral pulse wave velocity". Journal of Hypertension. 30 (3): 445–8. doi:10.1097/HJH.0b013e32834fa8b0. PMID 22278144.
3. ^ a b Townsend RR, Wilkinson IB, Schiffrin EL, Avolio AP, Chirinos JA, Cockcroft JR, et al. (September 2015). "Recommendations for Improving and Standardizing Vascular Research on Arterial Stiffness: A Scientific Statement From the American Heart Association". Hypertension. 66 (3): 698–722. doi:10.1161/HYP.0000000000000033. PMC 4587661. PMID 26160955.
4. ^ Wilkinson IB, Fuchs SA, Jansen IM, Spratt JC, Murray GD, Cockcroft JR, Webb DJ (December 1998). "Reproducibility of pulse wave velocity and augmentation index measured by pulse wave analysis". Journal of Hypertension. 16 (12 Pt 2): 2079–84. doi:10.1097/00004872-199816121-00033. PMID 9886900.
5. ^ Vlachopoulos C, Aznaouridis K, Stefanadis C (March 2010). "Prediction of cardiovascular events and all-cause mortality with arterial stiffness: a systematic review and meta-analysis". Journal of the American College of Cardiology. 55 (13): 1318–27. doi:10.1016/j.jacc.2009.10.061. PMID 20338492.
6. ^ Ben-Shlomo Y, Spears M, Boustred C, May M, Anderson SG, Benjamin EJ, et al. (February 2014). "Aortic pulse wave velocity improves cardiovascular event prediction: an individual participant meta-analysis of prospective observational data from 17,635 subjects". Journal of the American College of Cardiology. 63 (7): 636–646. doi:10.1016/j.jacc.2013.09.063. PMC 4401072. PMID 24239664.
7. ^ a b Mancia G, Fagard R, Narkiewicz K, Redón J, Zanchetti A, Böhm M, et al. (July 2013). "2013 ESH/ESC Guidelines for the management of arterial hypertension: the Task Force for the management of arterial hypertension of the European Society of Hypertension (ESH) and of the European Society of Cardiology (ESC)". Journal of Hypertension. 31 (7): 1281–357. doi:10.1097/01.hjh.0000431740.32696.cc. PMID 23817082.
8. ^ Young T (1809). "The Croonian Lecture: On the functions of the heart and arteries". Philosophical Transactions of the Royal Society of London. 99: 1–31. doi:10.1098/rstl.1809.0001.
9. ^ Sir., Lighthill, M. J. (1978). Waves in fluids. Cambridge [England]: Cambridge University Press. ISBN 978-0521216890. OCLC 2966533.
10. McDonald DA, Nichols WW, O'Rourke MJ, Hartley C (1998). McDonald's Blood Flow in Arteries, Theoretical, experimental and clinical principles (4th ed.). London: Arnold. ISBN 978-0-340-64614-4.
11. ^ Frank, Otto (1920). "Die Elastizitat der Blutegefasse". Zeitschrift für Biologie. 71: 255–272.
12. ^ Bramwell JC, Hill AV (1922). "Velocity transmission of the pulse wave and elasticity of arteries". Lancet. 199 (5149): 891–2. doi:10.1016/S0140-6736(00)95580-6.
13. ^ a b Spronck B, Heusinkveld MH, Vanmolkot FH, Roodt JO, Hermeling E, Delhaas T, et al. (February 2015). "Pressure-dependence of arterial stiffness: potential clinical implications". Journal of Hypertension. 33 (2): 330–8. doi:10.1097/HJH.0000000000000407. PMID 25380150.
14. ^ Milnor WR (1982). Hemodynamics. Baltimore: Williams & Wilkins. ISBN 978-0-683-06050-8.
15. ^ Boutouyrie P, Briet M, Collin C, Vermeersch S, Pannier B (February 2009). "Assessment of pulse wave velocity". Artery Research. 3 (1): 3–8. doi:10.1016/j.artres.2008.11.002.
16. ^ Bramwell JC, Hill AV (1922). "The velocity of the pulse wave in man". Proceedings of the Royal Society of London. Series B. 93 (652): 298–306. doi:10.1098/rspb.1922.0022. JSTOR 81045.
17. ^ Meinders JM, Kornet L, Brands PJ, Hoeks AP (October 2001). "Assessment of local pulse wave velocity in arteries using 2D distension waveforms". Ultrasonic Imaging. 23 (4): 199–215. doi:10.1177/016173460102300401. PMID 12051275.
18. ^ Rabben SI, Stergiopulos N, Hellevik LR, Smiseth OA, Slørdahl S, Urheim S, et al. (October 2004). "An ultrasound-based method for determining pulse wave velocity in superficial arteries". Journal of Biomechanics. 37 (10): 1615–22. doi:10.1016/j.jbiomech.2003.12.031. PMID 15336937.
19. ^ Westenberg JJ, van Poelgeest EP, Steendijk P, Grotenhuis HB, Jukema JW, de Roos A (January 2012). "Bramwell-Hill modeling for local aortic pulse wave velocity estimation: a validation study with velocity-encoded cardiovascular magnetic resonance and invasive pressure assessment". Journal of Cardiovascular Magnetic Resonance. 14 (1): 2. doi:10.1186/1532-429x-14-2. PMC 3312851. PMID 22230116.
20. ^ Khir AW, O'Brien A, Gibbs JS, Parker KH (September 2001). "Determination of wave speed and wave separation in the arteries". Journal of Biomechanics. 34 (9): 1145–55. doi:10.1016/S0021-9290(01)00076-8. PMID 11506785.
21. ^ Murgo JP, Westerhof N, Giolma JP, Altobelli SA (July 1980). "Aortic input impedance in normal man: relationship to pressure wave forms". Circulation. 62 (1): 105–16. doi:10.1161/01.CIR.62.1.105. PMID 7379273.
22. ^ Hughes AD, Parker KH (February 2009). "Forward and backward waves in the arterial system: impedance or wave intensity analysis?". Medical & Biological Engineering & Computing. 47 (2): 207–10. doi:10.1007/s11517-009-0444-1. PMID 19198913.
23. ^ Feng J, Khir AW (February 2010). "Determination of wave speed and wave separation in the arteries using diameter and velocity". Journal of Biomechanics. 43 (3): 455–62. doi:10.1016/j.jbiomech.2009.09.046. PMID 19892359.
24. ^ Wilkinson IB, McEniery CM, Schillaci G, Boutouyrie P, Segers P, Donald A, Chowienczyk PJ (2010). "ARTERY Society guidelines for validation of non-invasive haemodynamic measurement devices: Part 1, arterial pulse wave velocity". Artery Research. 4 (2): 34–40. doi:10.1016/j.artres.2010.03.001. ISSN 1872-9312.
25. ^ Park JB, Kario K (January 2017). "New Epoch for Arterial Stiffness Measurement in the Clinic". Pulse. 4 (Suppl 1): 1–2. doi:10.1159/000448497. PMC 5319595. PMID 28275587.
26. ^ Davies JM, Bailey MA, Griffin KJ, Scott DJ (December 2012). "Pulse wave velocity and the non-invasive methods used to assess it: Complior, SphygmoCor, Arteriograph and Vicorder". Vascular. 20 (6): 342–9. doi:10.1258/vasc.2011.ra0054. PMID 22962046.
27. ^ Pereira T, Correia C, Cardoso J (2015). "Novel Methods for Pulse Wave Velocity Measurement". Journal of Medical and Biological Engineering. 35 (5): 555–565. doi:10.1007/s40846-015-0086-8. PMC 4609308. PMID 26500469.
28. ^ Horváth IG, Németh A, Lenkey Z, Alessandri N, Tufano F, Kis P, Gaszner B, Cziráki A (October 2010). "Invasive validation of a new oscillometric device (Arteriograph) for measuring augmentation index, central blood pressure and aortic pulse wave velocity". Journal of Hypertension. 28 (10): 2068–75. doi:10.1097/HJH.0b013e32833c8a1a. PMID 20651604.
29. ^ Nabeel PM, Jayaraj J, Mohanasankar S (November 2017). "Single-source PPG-based local pulse wave velocity measurement: a potential cuffless blood pressure estimation technique". Physiological Measurement. 38 (12): 2122–2140. doi:10.1088/1361-6579/aa9550. PMID 29058686.
30. ^ Campo D, Khettab H, Yu R, Genain N, Edouard P, Buard N, Boutouyrie P (September 2017). "Measurement of Aortic Pulse Wave Velocity With a Connected Bathroom Scale". American Journal of Hypertension. 30 (9): 876–883. doi:10.1093/ajh/hpx059. PMC 5861589. PMID 28520843.
31. ^ Amaral AF, Patel J, Gnatiuc L, Jones M, Burney PG (December 2015). "Association of pulse wave velocity with total lung capacity: A cross-sectional analysis of the BOLD London study". Respiratory Medicine. 109 (12): 1569–75. doi:10.1016/j.rmed.2015.10.016. PMC 4687496. PMID 26553156.