Table 1.

Commonly used Indices of arterial stiffness

Index	Definition	Formula	Comments
Volume compliance	Change in arterial volume relative to the change in arterial pressure	$\frac{\Delta V}{\Delta P}$	Expressed in m1/mmHg (or equivalent volume/pressure units). Influenced by wall stiffness, arterial size and wall thickness (and thus also by body size). Most often used to quantify the total arterial compliance. The latter is virtually impossible to measure directly in vivo, but can be approximated as the ratio of stroke volume to pulse pressure (SV/PP) or estimated from the diastolic decay time or fitting a windkessel model to measured pressure and flow (with different models yielding slightly different values).
Area compliance	Absolute change in cross-sectional area relative to the change in arterial pressure	$\frac{\text{d}A}{\text{d}p}$; mostly calculated as $\frac{\Delta A}{\Delta P}$	Expressed in mn2/mmHg (or equivalent area/pressure units). Estimation of compliance based on cross-sectional (rather than volume) measurements. In case of availability of pressure and area waveforms as a function of time, area compliance can be calculated at any pressure level as the local tangent to the pressure-area relation (dA/dP). In practice, it is often calculated from systolic-diastolic differences in area (ΔA) and pressure (ΔP), ignoring the pressure-dependency of compliance and yielding one single value. It relates linearly to volume compliance under the assumption of a perfectly homogeneous arterial segment and no changes in segmental arterial length. The dependence on vessel caliber makes area compliance less useful for clinical studies.
		Assuming circular cross-section, $\frac{\Delta A}{\Delta P}$ equals $\frac{D_{max}{}^2-D_{min}{}^2}{\Delta P}\times \frac{\pi }{4}$
Distensibility and distensibility coefficient (DC)	Fractional change in cross-sectional area relative to the change in arterial pressure	$\frac{\raisebox{1ex}{$\text{d}A$}\!\left/ \!\raisebox{-1ex}{$A$}\right.}{\text{d}P}$, mostly calculated as $DC=\frac{\raisebox{1ex}{$\Delta \text{A}$}\!\left/ \!\raisebox{-1ex}{$\text{A}$}\right.}{\Delta P}$	Area compliance normalized for arterial caliper, and thus expressed in 1/mmHg or %/mmHg (relative change in lumen cross-sectional area per unit increase in pressure). Just like area compliance, the distensibility can be calculated at any given pressure level, but is most often derived using diastolic-systolic pressure and area differences, and normalized to diastolic lumen area and is known as the distensibility coefficient DC.
		Assuming circular cross-section, $\frac{\Delta A/P}{\Delta P}$ equals $\frac{2D_{min}\times \Delta D+\Delta D^2}{D^2\Delta P}$
Pulse Wave Velocity	Speed at which the arterial pulse propagates within the arteries	Bramwell-Hill equation: $\text{PWV=}\sqrt{\frac{AdP}{\rho dA}}\approx \sqrt{\frac{1}{\rho DC}}$	Pulse Wave Velocity (PWV) is typically expressed in m/s. For a uniform tube, PWV relates to distensibility via the Bramwell-Hill equation, demonstrating the inverse relation between both. The Bramwell-Hill equation is an elegant way to convert distensibility into PWV, which then expresses the local wave propagation speed at that specific point in the circulation. PWV is easily measured as the ratio of the distance Ax between two measuring sites, and the time delay Δx of the arterial pulse between these sites. The clinical reference method is carotid-femoral pulse wave velocity, measured from these 2 easily accessible measuring sites, but several other variants exist.
		PWV = distance/time

ΔP is the difference between maximum and minimum pressure. ΔV is the difference between the corresponding maximum and minimum volume. ΔA is the difference between maximum and minimum cross-sectional vessel area. D_max is the maximum lumen diameter, D_min is the minimum lumen diameter.