Stiffness indices
Compliance coefficient of a vessel wall is defined as [138]\(C=\frac{\text{ΔA}}{\text{Δp}}=\left[\pi D_{d}\left(D_{s}-D_{d}\right)/2\right]/\text{ΔP}\)where ΔA is change in cross-sectional area\(;\ \text{ΔP}\) is pulse pressure;\(\ D_{s},\) \(D_{d}\ \)are arterial diameter in systole and diastole respectively. The distensibility coefficient is described as [138]:
\(D=\frac{\text{ΔA}}{\text{A\ .\ \ Δp}}=2\left[\left(D_{s}-D_{d}\right)/D_{d}\right]\text{ΔP}\)
Pulse wave velocity (PWV) as explained by Bramwell and Hill is [138]:
\begin{equation} \text{PWV}=\sqrt{\frac{\,\text{ΔP}}{\text{ρ\ .\ ΔV}}}=\frac{1}{\sqrt{\text{ρ\ .\ D}}}=\sqrt{\frac{{D_{d}}^{2}\,\text{ΔP}}{\rho\left(2.D_{d}\text{.Δ}D+\Delta D^{2}\right)}}\nonumber \\ \end{equation}
A significant version applied for the analysis of PWV is using the Moens-Korteweg equation:
\begin{equation} \text{PWV}=\sqrt{\frac{\,\text{E\ .h\ }}{2\ .r.\rho\ }}\nonumber \\ \end{equation}
where \(\Delta D\) is the alteration in artery diameter, \(\rho\) is the density of blood. E is the young’s modulus, h is the IMT and \(r\) is the radius of the artery. The stiffness-index \(\beta\) is stated as [139]:
\begin{equation} \beta=\frac{\text{ΔP}}{\left(D_{s}-D_{d}\right)/D_{d}}\nonumber \\ \end{equation}
Augmentation index is the difference between first and second systolic peaks in pressure waveform relative to PP. AIx is analysed from pressure waveform and is stated as [139]:
\begin{equation} \text{AIx}=\frac{\left(P_{1}-P_{2}\right)}{\text{PP}}.100\%\nonumber \\ \end{equation}\begin{equation} \beta=\frac{\ln\left(P_{s}/P_{d}\right)}{\left(D_{s}-D_{d}\right)/D_{d}}\nonumber \\ \end{equation}
Cardio-ankle vascular index (CAVI) is an indicator of stiffness from the aorta to ankle [140]. CAVI is defined as:
\begin{equation} \text{CAVI}=a\left[\frac{2\,\rho\,}{\text{ΔP}}\ln\left(P_{s}/P_{d}\right)\text{.PW}V^{2}\right]+b\nonumber \\ \end{equation}
where \(a\) and \(b\) are adjustable constants.