Placenta Previa: 2D Margin Shear-Field Model

Placental Position

Edge-to-os distance 20 mm (low-lying)

Lower-segment stretch (gestational age) 32%

Uterine contraction intensity 0%

Clinical Readout

Low-lying placenta

Edge 20 mm from internal os.

Hemorrhage risk0%

Intervillous flow

0 mL/min

Peak margin shear

0.0 Pa

Bleed rate (field-avg)

0 mL/min

Os coverage

How this 2D field model works

The 3D version treats the placental margin as a single point and assigns it one shear-stress scalar. This 2D cross-section instead samples the margin as a genuine curved arc: the placenta is a disc of radius R sitting against the uterine wall, and every point on its os-facing rim has its own true geometric distance to the internal os,

d(θ) = edge + R·(1 − cos θ),   θ ∈ [−90°, +90°] measured from the closest point

so only the single closest point (θ=0) equals the "edge-to-os distance" slider value exactly — every other point on the rim recedes from the os purely from the disc's own curvature, with no extra assumption. Feeding d(θ) through the same piecewise coverage rule as the 3D model, then the same shear formula, produces a full 1D shear-stress field τ(θ) along the margin rather than one number:

ov(d)  = 1                 if d ≤ 0 (covers os)
       = 1 − d/20          if 0 < d < 20 mm
       = 0                 if d ≥ 20 mm
τ(θ)   = ov(d(θ)) × (0.3+0.7·stretch) × (0.2+0.8·contraction) × 12   [Pa-ish]

Bleeding is the field-average excess over the venous-sinus tolerance (3.2 Pa), integrated across the whole sampled arc by the trapezoid rule rather than read off one point — so a placenta whose closest point just grazes the 20 mm cutoff can still show a little marginal bleeding if enough of its curved rim sits closer than that, a behavior the single-point 3D model cannot show at all. Spiral-artery inflow on the far (fundal) hemisphere still follows the same Poiseuille Q ∝ r⁴ relation as the 3D model, with contractions transiently compressing the feeding vessels.

Edge-to-os distance — repositions the placental disc's closest point to the os; negative values mean it overlaps.
Lower-segment stretch — third-trimester elongation of the lower uterine segment, raising baseline shear everywhere on the field.
Contraction intensity / pulse — transiently raises shear across the whole margin field, the same way a real contraction stretches the entire lower segment at once, not just one spot.

Placenta (disc) Bleeding (local shear field) Spiral-artery inflow

Placenta Previa — 2D Margin Shear-Field Model