Vascular graft compliance mismatch

Vascular graft compliance mismatch is a difference between the pressure-dependent deformation of a vascular graft and that of the adjoining blood vessel, compared under specified loading conditions. Equal unloaded diameters do not imply equal diameter changes during a pressure pulse. The comparison must specify both the geometric observable and the pressure interval.

For the diameter compliance of a vascular graft, one useful definition isBoth have inverse-pressure units; the second is an interval estimate referenced to $D_1$. This differs from the volume-based vascular compliance $C_V=dV/dp$. For a cylindrical segment of fixed length, $V=\pi D^{2}L/4$, so differentiation gives $C_V/V=2C_D$. A diameter convention and a volume convention cannot be compared merely because both are called compliance.

Suppose two stipulated segments each have diameter $4.0\mathrm{mm}$ at $80\mathrm{mmHg}$. At $120\mathrm{mmHg}$ their diameters are $4.4$ and $4.1\mathrm{mm}$. The fractional diameter increases are 10 percent and 2.5 percent, givingOne interval compliance is four times the other despite equal initial diameters. Attaching these segments constrains their deformation near the join; this calculation alone does not determine the resulting local stress or biological response.

In a primary experiment on engineered bovine arteries, a video motion analyzer tracked vessel edges while a pressure transducer recorded loading. A bellows pump supplied pulsatile loading; static loading was assessed separately. The authors observed lower dynamic than static compliance overall, illustrating that the loading history and analysis method belong in the measured property.^[ref] Their diameter-based values expressed as percent per 100 millimeters of mercury require a factor of $10^4$ relative to fractional change per millimeter of mercury.

A mismatch assessment should therefore compare like observables at comparable pressure, frequency and reference diameter. It is distinct from vascular graft burst pressure, which concerns rupture, and from graft patency, which concerns whether the conduit remains open.

Diameter compliance of a vascular graft quantifies how the measured diameter of a vascular graft changes with distending pressure. A fractional differential convention isThis logarithmic diameter compliance has inverse-pressure units. State whether $D$ is an internal or external diameter and use the same convention throughout a comparison. The distending pressure is lumen pressure minus surrounding pressure.

An interval estimate often uses the lower-pressure diameter as reference:For constructed external diameters $D(80\mathrm{mmHg})=4.00\mathrm{mm}$ and $D(120\mathrm{mmHg})=4.16\mathrm{mm}$, this gives $0.0010\mathrm{mmH}{\mathrm{g}}^{-1}$. Expressed as percent diameter change per 100 millimeters of mercury, its numerical value is $10^4{\overline{C}}_D=10$. The factor $10^4$ combines percent conversion and the 100-millimeter pressure interval; it is not a change in the measured deformation.

A logarithmic interval average instead givesIt differs slightly because its normalization follows the changing diameter. Neither interval value is automatically the local derivative at every pressure.

A primary apparatus measured external vessel-edge motion with video and paired it with transducer measurements of static or pulsatile pressure. The published compliance equation uses systolic and diastolic diameters and pressures, expressed as percent per 100 millimeters of mercury.^[ref] Thus loading frequency, pressure interval and the chosen diameter observable belong to the reported result.

This fractional diameter response differs from volume-based vascular compliance $dV/dp$. For a cylindrical segment with fixed length, $V=\pi D^{2}L/4$ implies $(1/V)dV/dp=2C_D$. Comparisons of vascular graft compliance mismatch should therefore identify both the observable and normalization before comparing numbers.