A mathematical model of maternal vascular growth and remodeling and changes in maternal hemodynamics in uncomplicated pregnancy.

The maternal vasculature undergoes tremendous growth and remodeling (G&R) that enables a > 15-fold increase in blood flow through the uterine vasculature from conception to term. Hemodynamic metrics (e.g., uterine artery pulsatility index, UA-PI) are useful for the prognosis of pregnancy complications; however, improved characterization of the maternal hemodynamics is necessary to improve prognosis. The goal of this paper is to develop a mathematical framework to characterize maternal vascular G&R and hemodynamics in uncomplicated human pregnancies. A validated 1D model of the human vascular tree from the literature was adapted and inlet blood flow waveforms at the ascending aorta at 4 week increments from 0 to 40 weeks of gestation were prescribed. Peripheral resistances of each terminal vessel were adjusted to achieve target flow rates and mean arterial pressure at each gestational age. Vessel growth was governed by wall shear stress (and axial lengthening in uterine vessels), and changes in vessel distensibility were related to vessel growth. Uterine artery velocity waveforms generated from this model closely resembled ultrasound results from the literature. The literature UA-PI values changed significantly across gestation, increasing in the first month of gestation, then dramatically decreasing from 4 to 20 weeks. Our results captured well the time-course of vessel geometry, material properties, and UA-PI. This 1D fluid-G&R model captured the salient hemodynamic features across a broad range of clinical reports and across gestation for uncomplicated human pregnancy. While results capture available data well, this study highlights significant gaps in available data required to better understand vascular remodeling in pregnancy.