A mathematical model to simulate the cardiotocogram during labor. Part B: Parameter estimation and simulation of variable decelerations

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

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.

Simulation of fetal heart rate variability with a mathematical model

In the clinic, the cardiotocogram (CTG), the combined registration of fetal heart rate (FHR) and uterine contractions, is used to predict fetal well-being. Amongst others, fetal heart rate variability (FHRV) is an important indicator of fetal distress. In this study we add FHRV to our previously developed CTG simulation model, in order to improve its use as a research and educational tool. We implemented three sources of variability by applying either 1/f or white noise to the peripheral vascular resistance, baroreceptor output, or efferent vagal signal. Simulated FHR tracings were evaluated by visual inspection and spectral analysis. All power spectra showed a 1/f character, irrespective of noise type and source. The clinically observed peak near 0.1 Hz was only obtained by applying white noise to the different sources of variability. Similar power spectra were found when peripheral vascular resistance or baroreceptor output was used as source of variability. Sympathetic control predominantly influenced the low frequency power, while vagal control influenced both low and high frequency power. In contrast to clinical data, model results did not show an increase of FHRV during FHR decelerations. Still, addition of FHRV improves the applicability of the model as an educational and research tool.

A mathematical model to simulate the cardiotocogram during labor. Part A: Model setup and simulation of late decelerations

The cardiotocogram (CTG) is commonly used to monitor fetal well-being during labor and delivery. It shows the input (uterine contractions) and output (fetal heart rate, FHR) of a complex chain of events including hemodynamics, oxygenation and regulation. Previously we developed a mathematical model to obtain better understanding of the relation between CTG signals and vital, but clinically unavailable signals such as fetal blood pressure and oxygenation. The aim of this study is to improve this model by reducing complexity of submodels where parameter estimation is complicated (e.g. regulation) or where less detailed model output is sufficient (e.g. cardiac function), and by using a more realistic physical basis for the description of other submodels (e.g. vessel compression). Evaluation of the new model is performed by simulating the effect of uterine contractions on FHR as initiated by reduction of uterine blood flow, mediated by changes in oxygen and blood pressure, and effected by the chemoreflex and baroreflex. Furthermore the ability of the model to simulate uterine artery occlusion experiments in sheep is investigated. With the new model a more realistic FHR decrease is obtained during contraction-induced reduction of uterine blood flow, while the reduced complexity and improved physical basis facilitate interpretation of model results and thereby make the model more suitable for use as a research and educational tool.