First-generation hemodynamic model

TTTS. First-generation hemodynamic model

The blood volumes of the twins are the primary model parameters because the anastomoses transport blood volume from one twin to the other. Our model relates overall growth of the blood volumes of donor and recipient twins to a linear combination of their natural growth, i.e. the anticipated normal physiological growth of their blood volume, and the net fetofetal transfusion from donor to recipient, eqn (1). Here, the NetFetofetalTransf is assumed to directly affect fetal growth of both twins. 

This is an approximation that neglects possible control mechanisms that try to maintain normal growth. The following two growth equations of the fetal blood volumes constitute our first-generation model: 

The plus sign denotes the equation for the recipient and the minus sign for the donor. 

NaturalBloodVolGrowth was taken proportional to the fetal arterial minus venous pressure gradient. Through Poiseuille’s law, eqn (2), the anastomotic resistances at 40 weeks can be calculated, and because we used that the length and radii increase linearly with gestation, their resistances at any gestational age t (weeks), denoted as XY-Resist(t), XY = AVDR, AVRD, AA, or VV, relate to the resistances at t = 40 weeks as 

We assumed that placental anastomoses become functional at 4 weeks – hence the term (t–4). Growth eqns (5) translate mathematically as first-order differential equations. They can be solved numerically, combined with eqns (1), (2) and (6), assessing blood pressures from pressure–volume curves, and using as initial condition that blood volumes of both twins are zero at t = 0, the moment of embryonic splitting. 

The numerical solution, from 0 to 40 weeks, is by a standard forward finite-difference method using a time step of about 1 minute, and using type and size of anastomoses and degree of placental sharing as input parameters.