Table 2 Summary of 4D flow-derived metrics

Geometry &

Stiffness

PA volume, V (ml)

Temporally averaged volume of the MPA, LPA, RPA branches over a cardiac cycle

Internal diameters potentially influenced by proximal thrombus

PA area, A (cm²)

Centerline-based cross-sectional slice located 50% down the length of the MPA, LPA, and RPA branches

Relative area change (Pulsatility)

\(\frac{{A}_{\text{m}\text{a}\text{x}}-{A}_{\text{m}\text{i}\text{n}}}{{A}_{\text{m}\text{i}\text{n}}}\)

Compliance (cm²/mmHg)

\(\frac{{A}_{\text{m}\text{a}\text{x}}-{A}_{\text{m}\text{i}\text{n}}}{SPAP-DPAP}\)

Healthy PA compliance = 0.15 cm²/mmHg^§

Distensibility (%/mmHg)

\(\frac{Relative Area Change}{SPAP-DPAP}\times 100\)

Healthy PA distensibility = 3.1%/mmHg^§

Velocity Flow Profile

Centerline velocity (cm/s)

Maximum velocity in the center 30% radius of a cross-sectional slice located 50% down the length of each branch.

Flow rate (L/min)

\(\int \left(\overrightarrow{u}\cdot \overrightarrow{n}\right)dA\)

\(\overrightarrow{u}\) is the velocity vector, \(\overrightarrow{n}\) is the surface normal vector, A is the area of the cross-sectional slice located 10% down the length of the MPA, LPA, and RPA

Acceleration ime ratio

\(\frac{{t}_{end-diastole}-{t}_{peak systolic flow}}{{t}_{systole}}\)

\({t}_{systole}\) is the time between the end-systolic and end-diastolic timepoint

Secondary Flow Profile

Fractional area of reverse flow

Areas where velocity is perpendicular or negative to the forward flow direction.

\(\frac{{{A_{\vec u \cdot \vec n \leqslant 0}}}}{{{A_{total}}}}\)

Taken at a cross-sectional slice 50% down the length of the branch

Quantifies areas of recirculation, may correspond to large visual vortices

Vorticity, \(\overrightarrow{\omega }\) (1/s)

\(\frac{1}{\text{V}}\int \nabla \times \overrightarrow{u} dV\)

\(\nabla\) is the spatial gradient, \(\overrightarrow{u}\) is the velocity vector, V is the volume of the branch; spatially averaged over the volume of the branch

Local rotation in a fluid flow including local shearing in space

Helicity density, H_d (m/s²)

\({H_d} = \vec u \cdot \vec \omega\)

Amount of rotation parallel to the local velocity vector

Clockwise rotation when \({H}_{d}\)>0, counterclockwise rotation when \({H}_{d}\)<0

Volume fraction of positive helicity

\(\frac{{V}_{{H}_{d}>0}}{{V}_{total}}\)

V is the volume of the branch

Helical flow index, HFI

\(\frac{1}{V}\int {\left( {\left| {\frac{{\vec u \cdot \vec \omega }}{{\left| {\vec u} \right|\left| {\vec \omega } \right|}}} \right|} \right)} dV\)

Absolute value of the cosine of the angle between the vorticity and velocity vector, measure of helicity intensity

Limit from 0 to 1

Dean number, De

\(\frac{\rho \stackrel{-}{u}D}{\mu }\sqrt{\frac{D}{2{R}_{c}}}\)

D is the diameter of the vessel, \(\stackrel{-}{u}\) is the mean velocity (computed at a cross-sectional slice 50% down the length of the pulmonary trunk), \(\rho\) is the density of blood (1.06 g/cm³), \(\mu\) is the viscosity of blood (0.04 Poise), and \({R}_{c}\) is the radius of curvature of the vessel defined from the centerlines in the MPA, LPA, or RPA

Non-dimensional parameter of the inertial, centripetal, and viscous forces; tendency of Dean vortices to form in a curved vessel

Q-criterion

\(\frac{1}{2}\left[ {\parallel \Omega {\parallel ^2} - \parallel S{\parallel ^2}} \right] > 0\)

Defines a vortex as a connected fluid region where the norm of the vorticity tensor, \({\Omega }\), outweighs the norm of the strain rate tensor, \(S\).

May not uniquely detect visual vortical regions

RV Function^§§

% Predicted RV metrics

\(\frac{RV metric}{m\cdot Ag{e}^{a}\cdot H{t}^{b}\cdot W{t}^{c}}\)

Adjusted for differences in sex, age, weight, height

RVEF: a = 0.0706, b=-0.00771, c=-0.0782

 m = 75.19 (female), 71.52 (male)

RVEDV: a=-0.258, b = 1.582, c = 0.382

 m = 27.94 (female), 31.50 (male)

RVESV: a=-0.417, b = 1.501, c = 0.617

 m = 5.58 (female), 7.24 (male)

RVSV: a=-0.187, b = 1.574, c = 0.304

 m = 21.12 (female), 22.42 (male)