Pulse wave velocity

<h2 id="relationship-with-arterial-stiffness">Relationship with arterial stiffness</h2>
The theory of the velocity of the transmission of the pulse through the circulation dates back to 1808 with the work of <a href="/facts/Thomas_Young_(scientist)/X4RtR47L">Thomas Young</a>.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The relationship between pulse wave velocity (PWV) and arterial wall stiffness can be derived from <a href="/facts/Newton%2527s_laws_of_motion/XKzGTXK1">Newton's second law of motion</a> (
 
 
 
 F
 =
 m
 a
 
 
 {\displaystyle F=ma}
 
) applied to a small fluid element, where the force on the element equals the product of <a href="/facts/Density/92p6hh9I">density</a> (the mass per unit volume; 
 
 
 
 ρ
 
 
 {\displaystyle \rho }
 
) and the <a href="/facts/Acceleration/UVDmjYvR">acceleration</a>.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> The approach for calculating PWV is similar to the calculation of the <a href="/facts/Speed_of_sound/dYtbt1nf">speed of sound</a>, 
 
 
 
 
 
 c
 
 0
 
 
 
 
 
 {\displaystyle {c_{0}}}
 
, in a <a href="/facts/Compressibility/eePznleN">compressible</a> <a href="/facts/Fluid/tMQ46Tmz">fluid</a> (e.g. <a href="/facts/Atmosphere_of_Earth/FV97Am25">air</a>):

 
 
 
 
 c
 
 0
 
 
 =
 
 
 
 B
 ρ
 
 
 
 
 
 {\displaystyle c_{0}={\sqrt {\frac {B}{\rho }}}}
 
,
where 
 
 
 
 
 B
 
 
 
 {\displaystyle {B}}
 
 is the <a href="/facts/Bulk_modulus/yCRFQonn">bulk modulus</a> and 
 
 
 
 
 ρ
 
 
 
 {\displaystyle {\rho }}
 
 is the density of the fluid.

<h3>The Frank / Bramwell-Hill equation</h3>
For an incompressible fluid (<a href="/facts/Blood/03zEulkj">blood</a>) in a compressible (elastic) tube (e.g. an artery):<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>

 
 
 
 P
 W
 V
 =
 
 
 
 
 V
 ⋅
 d
 P
 
 
 ρ
 ⋅
 d
 V
 
 
 
 
 
 
 {\displaystyle PWV={\sqrt {\frac {V\cdot dP}{\rho \cdot dV}}}}
 
,
where 
 
 
 
 V
 
 
 {\displaystyle V}
 
 is <a href="/facts/Volume/aeAXCBUd">volume</a> per unit <a href="/facts/Length/EwFyAqGH">length</a> and 
 
 
 
 P
 
 
 {\displaystyle P}
 
 is <a href="/facts/Pressure/eyc37GRG">pressure</a>. This is the <a href="/facts/Equation/pxFzLAVR">equation</a> derived by <a href="/facts/Otto_Frank_(physiologist)/k6Y6wuwW">Otto Frank</a>,<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> and John Crighton Bramwell and <a href="/facts/Archibald_Hill/ad0uLQWg">Archibald Hill</a>.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a>
Alternative forms of this equation are:

 
 
 
 P
 W
 V
 =
 
 
 
 
 r
 ⋅
 d
 P
 
 
 ρ
 ⋅
 2
 ⋅
 d
 r
 
 
 
 
 
 
 {\displaystyle PWV={\sqrt {\frac {r\cdot dP}{\rho \cdot 2\cdot dr}}}}
 
, or 
 
 
 
 P
 W
 V
 =
 
 
 1
 
 ρ
 ⋅
 D
 
 
 
 
 
 {\displaystyle PWV={\frac {1}{\sqrt {\rho \cdot D}}}}
 
,
where 
 
 
 
 r
 
 
 {\displaystyle r}
 
 is the <a href="/facts/Radius/9Gr9deYD">radius</a> of the tube and 
 
 
 
 D
 
 
 {\displaystyle D}
 
 is <a href="/facts/Distensibility/E676xwIa">distensibility</a>.

<h3>The Moens–Korteweg equation</h3>
The <a href="/facts/Moens%25E2%2580%2593Korteweg_equation/CdBUPF0a">Moens–Korteweg equation</a>:

P
 W
 V
 
 =
 
 
 
 
 
 
 E
 
 
 i
 n
 c
 
 
 
 ⋅
 h
 
 
 2
 ⋅
 r
 ⋅
 ρ
 
 
 
 
 
 
 
 {\displaystyle \mathrm {PWV} ={\sqrt {\dfrac {E_{\mathrm {inc} }\cdot h}{2\cdot r\cdot \rho }}}}
 
,
characterises PWV in terms of the incremental elastic modulus 
 
 
 
 
 
 E
 
 
 i
 n
 c
 
 
 
 
 
 
 {\displaystyle {E_{\mathrm {inc} }}}
 
 of the vessel wall, the wall thickness 
 
 
 
 h
 
 
 {\displaystyle h}
 
, and the radius. It was derived independently by <a href="/facts/Adriaan_Isebree_Moens/TkF0WqTE">Adriaan Isebree Moens</a> and <a href="/facts/Diederik_Korteweg/CcvjHAcA">Diederik Korteweg</a> and is equivalent to the Frank / Bramwell Hill equation:<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a>: 64 
These equations assume that:

<ol><li>there is little or no change in vessel area.</li>
<li>there is little or no change in wall thickness.</li>
<li>there is little or no change in density (i.e. blood is assumed incompressible).</li>
<li>
 
 
 
 d
 
 v
 (
 d
 
 
 r
 
 −
 1
 
 
 )
 d
 
 x
 ⋅
 d
 
 t
 
 
 {\displaystyle \operatorname {d} \!v(\operatorname {d} \!r^{-1})\operatorname {d} \!x\cdot \operatorname {d} \!t}
 
 is negligible.</li></ol>
<h2 id="variation-in-the-circulatory-system">Variation in the circulatory system</h2>
Since the wall thickness, radius and incremental elastic modulus vary from blood vessel to blood vessel, PWV will also vary between vessels.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a> Most measurements of PWV represent an average velocity over a path length consisting of several vessels (e.g. from the <a href="/facts/Carotid/lndR9CgD">carotid</a> to the <a href="/facts/Femoral_artery/qL6wx3T9">femoral artery</a>).<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a>

<h2 id="dependence-on-blood-pressure">Dependence on blood pressure</h2>
PWV intrinsically varies with blood pressure.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a> PWV increases with pressure for two reasons:

<ol><li>Arterial <a href="/facts/Compliance_(physiology)/VRQbpfVt">compliance</a> (
 
 
 
 d
 
 V
 
 /
 
 d
 
 P
 
 
 {\displaystyle \operatorname {d} \!V/\operatorname {d} \!P}
 
) decreases with increasing pressure due to the curvilinear relationship between arterial pressure and volume.</li>
<li>Volume (
 
 
 
 V
 
 
 {\displaystyle V}
 
) increases with increasing pressure (the artery dilates), directly increasing PWV.</li></ol>
<h2 id="experimental-approaches-used-to-measure-pulse-wave-velocity">Experimental approaches used to measure pulse wave velocity</h2>
A range of invasive or non-invasive methods can be used to measure PWV. Some general approaches are:

<h3>Using two simultaneously measured pressure waveforms</h3>
PWV, by definition, is the distance traveled (
 
 
 
 Δ
 x
 
 
 {\displaystyle \Delta x}
 
) by the pulse wave divided by the time (
 
 
 
 Δ
 t
 
 
 {\displaystyle \Delta t}
 
) for the wave to travel that distance:

 
 
 
 
 P
 W
 V
 
 =
 
 
 
 
 Δ
 x
 
 
 Δ
 t
 
 
 
 
 
 
 {\displaystyle \mathrm {PWV} ={\dfrac {\Delta x}{\Delta t}}}
 
,
in practice this approach is complicated by the existence of reflected waves.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a> It is widely assumed that reflections are minimal during late <a href="/facts/Diastole/keHgaxbF">diastole</a> and early <a href="/facts/Systole/5KDbjw4B">systole</a>.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a> With this assumption, PWV can be measured using the `foot' of the pressure waveform as a <a href="/facts/Fiducial_marker/U2cjAwNU">fiducial marker</a> 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.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a> 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.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a>

<h3>Using pressure and volume, or pressure and diameter</h3>
This is based on the method described by Bramwell & Hill<a class="footnote-ref" id="fnref:22" href="#fn:22">22</a> who proposed modifications to the Moens-Kortweg equation. Quoting directly, these modifications were:
"A small rise 
 
 
 
 δ
 P
 
 
 {\displaystyle \delta P}
 
 in pressure may be shown to cause a small increase, 
 
 
 
 δ
 y
 =
 
 y
 
 2
 
 
 δ
 P
 
 /
 
 (
 E
 c
 )
 
 
 {\displaystyle \delta y=y^{2}\delta P/(Ec)}
 
, in the radius 
 
 
 
 y
 
 
 {\displaystyle y}
 
 of the artery, or a small increase, 
 
 
 
 δ
 V
 =
 2
 π
 
 y
 
 3
 
 
 δ
 P
 
 /
 
 (
 E
 c
 )
 
 
 {\displaystyle \delta V=2\pi y^{3}\delta P/(Ec)}
 
, in its own volume 
 
 
 
 V
 
 
 {\displaystyle V}
 
 per unit length. Hence 
 
 
 
 2
 y
 
 /
 
 E
 c
 =
 d
 
 V
 
 /
 
 (
 V
 d
 
 P
 )
 
 
 {\displaystyle 2y/Ec=\operatorname {d} \!V/(V\operatorname {d} \!P)}
 
"
where 
 
 
 
 c
 
 
 {\displaystyle c}
 
 represents the wall thickness (defined as 
 
 
 
 h
 
 
 {\displaystyle h}
 
 above), 
 
 
 
 E
 
 
 {\displaystyle E}
 
 the elastic modulus, and 
 
 
 
 y
 
 
 {\displaystyle y}
 
 the vessel radius (defined as 
 
 
 
 r
 
 
 {\displaystyle r}
 
 above). This permits calculation of local PWV in terms of 
 
 
 
 
 
 V
 ⋅
 d
 P
 
 /
 
 (
 ρ
 ⋅
 d
 V
 )
 
 
 
 
 {\displaystyle {\sqrt {V\cdot dP/(\rho \cdot dV)}}}
 
, or 
 
 
 
 
 
 r
 ⋅
 d
 P
 
 /
 
 ρ
 ⋅
 2
 ⋅
 d
 r
 
 
 
 
 {\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 <a href="/facts/Ultrasound/31Pa5IH9">ultrasound</a><a class="footnote-ref" id="fnref:23" href="#fn:23">23</a><a class="footnote-ref" id="fnref:24" href="#fn:24">24</a> or <a href="/facts/Magnetic_resonance_imaging/Vh9yG9qq">magnetic resonance imaging (MRI)</a>.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a>

<h3>Using pressure-flow velocity, pressure-volumetric flow relationships or characteristic impedance</h3>
The <a href="/facts/Water_hammer/z4coe4cN">Water hammer</a> equation expressed either in terms of pressure and flow velocity,<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a> pressure and volumetric flow, or characteristic impedance<a class="footnote-ref" id="fnref:27" href="#fn:27">27</a> can be used to calculate local PWV:

 
 
 
 
 P
 W
 V
 
 =
 P
 
 /
 
 
 (
 
 v
 ⋅
 ρ
 
 )
 
 =
 P
 
 /
 
 Q
 ⋅
 A
 
 /
 
 ρ
 =
 
 Z
 
 
 c
 
 
 
 ⋅
 A
 
 /
 
 ρ
 
 
 {\displaystyle \mathrm {PWV} =P/\left(v\cdot \rho \right)=P/Q\cdot A/\rho =Z_{\mathrm {c} }\cdot A/\rho }
 
,
where 
 
 
 
 v
 
 
 {\displaystyle v}
 
 is velocity, 
 
 
 
 Q
 
 
 {\displaystyle Q}
 
 is <a href="/facts/Volumetric_flow_rate/X5KI7zzH">volumetric flow</a>, 
 
 
 
 
 Z
 
 
 c
 
 
 
 
 
 {\displaystyle Z_{\mathrm {c} }}
 
 is characteristic impedance and 
 
 
 
 A
 
 
 {\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.<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a>

<h3>Using diameter-flow velocity relationships</h3>
A related method to the pressure-flow velocity method uses vessel diameter and flow velocity to determine local PWV.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a> It is also based on the Water hammer equation:

 
 
 
 d
 
 P
 
 ±
 
 
 =
 ±
 ρ
 ⋅
 P
 W
 V
 ⋅
 d
 
 v
 
 ±
 
 
 
 
 {\displaystyle dP_{\pm }=\pm \rho \cdot PWV\cdot dv_{\pm }}
 
,
and since

 
 
 
 d
 
 P
 
 +
 
 
 +
 d
 
 P
 
 −
 
 
 =
 
 
 
 2
 ⋅
 ρ
 ⋅
 P
 W
 
 V
 
 2
 
 
 
 S
 
 
 ⋅
 (
 d
 
 S
 
 +
 
 
 +
 d
 
 S
 
 −
 
 
 )
 
 
 {\displaystyle dP_{+}+dP_{-}={\frac {2\cdot \rho \cdot PWV^{2}}{S}}\cdot (dS_{+}+dS_{-})}
 
,
where 
 
 
 
 S
 
 
 {\displaystyle S}
 
 is diameter; then:

 
 
 
 P
 W
 V
 =
 
 
 S
 2
 
 
 ⋅
 
 
 
 (
 d
 
 v
 
 +
 
 
 +
 d
 
 v
 
 −
 
 
 )
 
 
 (
 d
 
 S
 
 +
 
 
 +
 d
 
 S
 
 −
 
 
 )
 
 
 
 
 
 {\displaystyle PWV={\frac {S}{2}}\cdot {\frac {(dv_{+}+dv_{-})}{(dS_{+}+dS_{-})}}}
 
,
or using the incremental hoop strain, 
 
 
 
 d
 S
 
 /
 
 S
 =
 d
 ln
 ⁡
 S
 
 
 {\displaystyle dS/S=d\ln S}
 
,
PWV can be expressed in terms of 
 
 
 
 v
 
 
 {\displaystyle v}
 
 and 
 
 
 
 S
 
 
 {\displaystyle S}

P
 W
 V
 =
 ±
 
 
 1
 2
 
 
 ⋅
 
 
 
 d
 
 v
 
 ±
 
 
 
 
 d
 ln
 ⁡
 
 S
 
 ±
 
 
 
 
 
 
 
 {\displaystyle PWV=\pm {\frac {1}{2}}\cdot {\frac {dv_{\pm }}{d\ln S_{\pm }}}}
 
,
therefore plotting 
 
 
 
 ln
 ⁡
 S
 
 
 {\displaystyle \ln S}
 
 against 
 
 
 
 v
 
 
 {\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.

<h2 id="clinical-measurement">Clinical measurement</h2>
<h3>Clinical methods</h3>
Clinically, PWV can be measured in several ways and in different locations. The 'gold standard' for arterial stiffness assessment in clinical practice is cfPWV,<a class="footnote-ref" id="fnref:30" href="#fn:30">30</a><a class="footnote-ref" id="fnref:31" href="#fn:31">31</a> and validation guidelines have been proposed.<a class="footnote-ref" id="fnref:32" href="#fn:32">32</a> Other measures such as brachial-ankle PWV and cardio-ankle vascular index (CAVI) are also popular.<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a> 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.<a class="footnote-ref" id="fnref:34" href="#fn:34">34</a> Numerous devices exist to measure cfPWV;<a class="footnote-ref" id="fnref:35" href="#fn:35">35</a><a class="footnote-ref" id="fnref:36" href="#fn:36">36</a> some techniques include:

<ul><li>use of a <a href="/facts/Transducer/YS7zfv9d">transducer</a> to record the time of arrival of the pulse wave at the carotid and femoral arteries.</li>
<li>use of cuffs placed around the limbs and neck to record the time of arrival of the pulse wave oscillometrically.</li>
<li>use of <a href="/facts/Doppler_ultrasound/SFn4tBkY">Doppler ultrasound</a> or <a href="/facts/Magnetic_resonance_imaging/Vh9yG9qq">magnetic resonance imaging</a> to record the time of arrival of the pulse wave based on the flow velocity waveform.</li></ul>
Newer devices that employ an arm cuff,<a class="footnote-ref" id="fnref:37" href="#fn:37">37</a> fingertip sensors<a class="footnote-ref" id="fnref:38" href="#fn:38">38</a> or special weighing scales<a class="footnote-ref" id="fnref:39" href="#fn:39">39</a> have been described, but their clinical utility remains to be fully established.

<h3>Interpretation</h3>
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.<a class="footnote-ref" id="fnref:40" href="#fn:40">40</a> However, the use of a fixed PWV threshold value is debated, as PWV is dependent on blood pressure.<a class="footnote-ref" id="fnref:41" href="#fn:41">41</a> A high pulse wave velocity (PWV) has also been associated with poor lung function.<a class="footnote-ref" id="fnref:42" href="#fn:42">42</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Arterial_stiffness/GlSgeYzJ">Arterial stiffness</a></li>
<li><a href="/facts/Blood_pressure/VtqqSM2J">Blood pressure</a></li>
<li><a href="/facts/Compliance_(physiology)/VRQbpfVt">Compliance (physiology)</a></li></ul>

<h2 id="references">References</h2>

<ol>
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<li id="fn:2">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. <a href="https://doi.org/10.1093%2Feurheartj%2Fehl254" target="_blank">https://doi.org/10.1093%2Feurheartj%2Fehl254</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
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<li id="fn:14">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. <a href="978-0-340-64614-4" target="_blank">978-0-340-64614-4</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
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</ol>

Pulse wave velocity open-in-new

Pulse wave velocity