Illustrations of the calculation of curvature, branching angle, and ostia position.
a: Curvature at P
i was defined as the inverse of the radius, R, of a circumscribed circle around three points P
a, P
i, and P
b on the centerline path. The arclength between P
a to P
i and P
b to P
i was defined as the vessel radius, averaged over the length of the vessel.
b: Curve angle, Φ, was defined as the angle between two vectors,
, connecting P
a to P
i, and
, connecting P
i to P
b along the path of the renal artery.
c: Branching angle, θ, was defined as the angle between two vectors,
d⃗a, along the centerline path of the abdominal aorta, and
d⃗b, along the path of the renal artery, each the length of the average renal artery diameter.
d: Ostia 1 and ostia 2 were defined as the renal ostium centroid and the point of the first renal artery bifurcation, respectively.