A review study of fetal circulatory models to develop a digital twin of a fetus in a perinatal life support system

Abstract

Background: Preterm birth is the main cause of neonatal deaths with increasing mortality and morbidity rates with decreasing GA at time of birth. Currently, premature infants are treated in neonatal intensive care units to support further development. However, the organs of, especially, extremely premature infants (born before 28 weeks of GA) are not mature enough to function optimally outside the womb. This is seen as the main cause of the high morbidity and mortality rates in this group. A liquid-filled incubator, a so-called PLS system, could potentially improve these numbers for extremely premature infants, since this system is designed to mimic the environment of the natural womb. To support the development and implementation of such a complex system and to interpret vital signals of the fetus during a PLS system operation, a digital twin is proposed. This mathematical model is connected with a manikin representing the digital and physical twin of the real-life PLS system. Before developing a digital twin of a fetus in a PLS system, its functional and technical requirements are defined and existing mathematical models are evaluated.

Method and results: This review summarizes existing 0D and 1D fetal circulatory models that potentially could be (partly) adopted for integration in a digital twin of a fetus in a PLS system based on predefined requirements. The 0D models typically describe hemodynamics and/or oxygen transport during specific events, such as the transition from fetus to neonate. Furthermore, these models can be used to find hemodynamic differences between healthy and pathological physiological states. Rather than giving a global description of an entire cardiovascular system, some studies focus on specific organs or vessels. In order to analyze pressure and flow wave profiles in the cardiovascular system, transmission line or 1D models are used. As for now, these models do not include oxygen transport.

Conclusion: This study shows that none of the models identified in literature meet all the requirements relevant for a digital twin of a fetus in a PLS system. Nevertheless, it does show the potential to develop this digital twin by integrating (parts) of models into a single model.

Keywords: digital twin; fetal cardiovascular system; mathematical models; perinatal life support system; review.

Figure 1

An example of a modular arrangement. The numbers refer to the numbering of the technical requirements (Section Technical requirements). The first four requirements are applicable to the cardiovascular model. Metabolism is not included in this study (*) and the computational time applies to the entire model (not shown).

Figure 2

A simple schematic overview of the (A) fetal and (B) neonatal circulation with oxygen- and nutrient-rich (red), oxygen- and nutrient-poor (blue), and oxygen- and nutrient-rich and -poor mixed (purple) blood flow direction. AO, aorta; DA, ductus arteriosus; DV, ductus venosus; FO, foramen ovale; HV, hepatic veins; LA, left atrium; LV, left ventricle; PA, pulmonary arteries; PS, portal sinus; PV, pulmonary veins; RA, right atrium; RV, right ventricle; UA, umbilical arteries; UV, umbilical vein; VC, inferior and superior vena cava. The block “organs” represents all other organs, which are not separately mentioned in the figure.

Figure 3

Clinical scenario: cardiotocography (CTG) with variable decelerations and corresponding arterial oxygen (pO_{2, a}) and mean arterial pressure (MAP) signal. Each contraction evokes a different fetal heart rate (FHR) response, due to contraction-to-contraction changes in both uterine pressure level (UP) and duration, and in the compressibility of the umbilical cord. Overall, FHR corresponds well with changes in MAP and pO_{2, a}. This figure is obtained from the Ph.D. thesis of (73) with permission.

Figure 4

Proposed multiscale and multilevel approach with modules (white) organized on time scales (gray scale). Modules with the same time and length scale can have horizontal dependencies. Within a module, multilevel approach can be required (vertical dependencies). Over different time scales, modules influence each other (spatial dependencies).