A mathematical model of umbilical venous pulsation

Pulsations in the fetal heart propagate through the precordial vein and the ductus venosus but are normally not transmitted into the umbilical vein. P ulsations in the umbilical vein do occur, however, in early pregnancy and i n pathological conditions. Such transmission into the umbilical vein is poo rly understood. In this paper we hypothesize that the mechanical properties and the dimensions of the vessels do influence the umbilical venous pulsat ions, in addition to the magnitude of the pressure and flow waves generated in the fetal atria. To support this hypothesis we established a mathematic al model of the umbilical vein/ductus venosus bifurcation. The umbilical ve in was modeled as a compliant reservoir and the umbilical vein pressure was assumed to be equal to the stagnation pressure at the ductus venosus inlet . We calculated the index of pulsation of the umbilical Vein pressure ((max -min)/mean), the reflection and transmission factors at the ductus venosus inlet, numerically and with estimates. Typical dimensions in the physiologi cal range for the human fetus were used, while stiffness parameters were ta ken from fetal sheep. We found that wave transmission and reflection in the umbilical vein ductus venosus bifurcation depend on the impedance ratio be tween the umbilical vein and the ductus venosus, as well as the ratio of th e mean velocity and the pulse wave velocity in the ductus venosus. Accordin gly, the pulsations initiated by the fetal heart are transmitted upstream a nd may arrive in the umbilical vein with amplitudes depending on the impeda nce ratio and the ratio between the mean velocity and the pulse wave veloci ty in the ductus venosus. (C) 2000 Elsevier Science Ltd. All rights reserve d.