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

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.

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.

A mathematical model to investigate the effects of intravenous fluid administration and fluid loss

The optimal fluid administration protocol for critically ill perioperative patients is hard to estimate due to the lack of tools to directly measure the patient fluid status. This results in the suboptimal clinical outcome of interventions. Previously developed predictive mathematical models focus on describing the fluid exchange over time but they lack clinical applicability, since they do not allow prediction of clinically measurable indices. The aim of this study is to make a first step towards a model predictive clinical decision support system for fluid administration, by extending the current fluid exchange models with a regulated cardiovascular circulation, to allow prediction of these indices. The parameters of the model were tuned to correctly reproduce experimentally measured changes in arterial pressure and heart rate, observed during infusion of normal saline in healthy volunteers. With the resulting tuned model, a different experiment including blood loss and infusion could be reproduced as well. These results show the potential of using this model as a basis for a decision support tool in a clinical setting.

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 B: Parameter estimation and simulation of variable decelerations

During labor and delivery the cardiotocogram (CTG), the combined registration of fetal heart rate (FHR) and uterine contractions, is used to monitor fetal well-being. In part A of our study we introduced a new mathematical computer model for CTG simulation in order to gain insight into the complex relation between these signals. By reducing model complexity and by using physically more realistic descriptions, this model was improved with respect to our previous model. Aim of part B of this study is to gain insight into the cascade of events from uterine contractions causing combined uterine flow reduction and umbilical cord compression, resulting in blood and oxygen pressure variations, which lead to changes in FHR via the baro- and chemoreflex. In addition, we extensively describe and discuss the estimation of model parameter values. Simulation results are in good agreement with sheep data and show the ability of the model to describe variable decelerations. Despite reduced model complexity, parameter estimation still remains difficult due to limited clinical data.