A Multiscale Mathematical Model for the Fetal Blood Circulation of the Second Half of Pregnancy

Doppler ultrasound is a commonly used method to assess hemodynamics of the fetal cardiovascular system and to monitor the well-being of the fetus. Indices based on the velocity profile are often used for diagnosis. However, precisely linking these indices to specific underlying physiology factors is challenging. Several influences, including wave reflections, fetal growth, vessel stiffness, and resistance distal to the vessel, contribute to these indices. Understanding these data is essential for making informed clinical decisions. Mathematical models can be used to investigate the relation between velocity profiles and physiological properties. This study presents a mathematical model designed to simulate velocity wave propagation throughout the fetal cardiovascular system, facilitating the assessment of factors influencing velocity-based indices. The model combines a one-fiber model of the heart with a 1D wave propagation model describing the larger vessels of the circulatory system and a lumped parameter model for the microcirculation. Fetal growth from 20 to 40 weeks of gestational age is incorporated by adjusting cardiac and circulatory parameter settings according to scaling laws. The model's results, including cardiac function, cardiac output distribution, and volume distribution, show a good agreement with literature studies for a growing healthy fetus from 20 to 40 weeks. In addition, Doppler indices are simulated in various vessels and agree with literature as well. In conclusion, this study introduces a novel closed-loop 0D-1D mathematical model that has been verified against literature studies. This model offers a valuable platform for analyzing factors influencing velocity-based indices in the fetal cardiovascular system.