Simulation of the cardiotocogram during labor : towards model-based understanding of fetal physiology
Citation for published version (APA): Jongen, G. J. L. M. (2016). Simulation of the cardiotocogram during labor : towards model-based understanding of fetal physiology. Technische Universiteit Eindhoven.
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Download date: 28. Sep. 2021 Simulation of the cardiotocogram during labor
Towards model-based understanding of fetal physiology
Germaine Jongen A catalogue record is available from the Eindhoven University of Technology Library. ISBN: 978-90-386-4123-2
Copyright © 2016 by G.J.L.M. Jongen All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronically, mechanically, by print, photo print, recording or any other means, without the prior written permission from the author.
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The research described in this thesis was funded by Stichting De Weijerhorst and performed within the IMPULS perinatology framework. Simulation of the cardiotocogram during labor
Towards model-based understanding of fetal physiology
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnicus prof.dr.ir. F.P.T. Baaijens, voor een commissie aangewezen door het College voor Promoties, in het openbaar te verdedigen op dinsdag 13 september 2016 om 16:00 uur
door
Germaine Josefa Lucienne Maria Jongen
geboren te Maastricht Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de promotiecom- missie is als volgt: voorzitter: prof.dr. P.A.J. Hilbers 1e promotor: prof.dr.ir. F.N. van de Vosse 2e promotor: prof.dr. S.G. Oei copromotor: dr.ir. P.H.M. Bovendeerd leden: prof.dr. M. Ursino (Università di Bologna) prof.dr. F.P.H.A. Vandenbussche (RUN) prof.dr.ir. J.W.M. Bergmans adviseur: dr.ir. M.B. van der Hout
Het onderzoek of ontwerp dat in dit proefschrift wordt beschreven is uitgevoerd in overeenstem- ming met de TU/e Gedragscode Wetenschapsbeoefening. Contents
Summary ix
1 Background and aim of the thesis 1 1.1 General introduction ...... 2 1.2 Mathematical models in a clinical setting ...... 3 1.3 The cardiotocogram ...... 4 1.3.1 Clinical evaluation of the CTG ...... 4 1.3.2 Physiological background ...... 5 1.3.3 Mathematical models for CTG simulation ...... 7 1.4 Outline of the thesis ...... 8
2 A mathematical model to simulate the cardiotocogram during labor Part A: Model setup and simulation of late decelerations 11 2.1 Introduction ...... 13 2.2 Material and methods ...... 14 2.2.1 Feto-maternal hemodynamics ...... 14 2.2.2 Oxygenation ...... 18 2.2.3 Regulation ...... 20 2.2.4 Model simulations ...... 23 2.3 Results ...... 24 2.4 Discussion ...... 27
v Contents
3 A mathematical model to simulate the cardiotocogram during labor Part B: Parameter estimation and simulation of variable decelerations 31 3.1 Introduction ...... 33 3.2 Material and methods ...... 33 3.2.1 Model extension ...... 33 3.2.2 Parameter estimation ...... 34 3.2.3 Model simulations ...... 38 3.3 Results ...... 38 3.4 Discussion ...... 42
4 Simulation of fetal heart rate variability with a mathematical model 45 4.1 Introduction ...... 47 4.2 Material and methods ...... 48 4.2.1 Mathematical model ...... 48 4.2.2 Model extension with FHRV ...... 50 4.2.3 Spectral analysis ...... 51 4.2.4 Model simulations ...... 51 4.3 Results ...... 52 4.4 Discussion ...... 58
5 Hypoxia-induced catecholamine feedback on fetal heart rate: A mathematical model study 63 5.1 Introduction ...... 65 5.2 Material and methods ...... 66 5.2.1 Physiological background ...... 66 5.2.2 Mathematical model ...... 67 5.2.3 Parameter estimation ...... 70 5.2.4 Model simulations ...... 71 5.3 Results ...... 72 5.4 Discussion ...... 77
6 General discussion 83 6.1 Introduction ...... 84 6.2 Main achievements ...... 84 6.3 Application of the CTG simulation model ...... 86 6.4 Future perspectives ...... 88
vi Bibliography 91
Samenvatting 105
Dankwoord 109
About the author 113
vii Contents
viii Summary
ix Summary
Simulation of the cardiotocogram during labor: towards model-based understanding of fetal physiology
During labor and delivery, it is important to monitor fetal well-being to enable timely and adequate intervention in case of fetal discomfort. Ideally, fetal monitoring should include assessment of oxygen status, but reliable oxygen measurements can only be performed during labor, after rupture of membranes, and then are only available at a limited number of time points. In current clinical practice, cardiotocography is therefore mainly used to estimate fetal well-being. The cardiotocogram (CTG) represents the simultaneous registration of the fetal heart rate (FHR) and uterine contractions. The underlying physiology, relating uterine contractions to the nal e ect on FHR, involves a complex chain of events. This chain includes the baro- and chemore ex, as a response to variations in blood and oxygen pressure. Humoral feedback is also thought to be part of this response. Due to the complexity of this system, assessment of fetal well-being on the basis of the CTG is a challenging task.
Mathematical models can be used to gain more insight into the complex chain through which uterine contractions lead to changes in fetal blood and oxygen pressure that nally result into changes in FHR. Previously, a mathematical model for simulation of the CTG was developed. This model describes feto-maternal hemodynamics, oxygenation, fetal regulation and uterine contraction generation, and can be used to simulate early, late and variable decelerations as caused by head compression, uterine blood ow reduction, and umbilical cord compression following uterine contractions.
The rst step of this work was to reduce model complexity of the submodels where pa- rameter estimation was complicated or where less detailed model output was su cient. In addition, the physical description of other submodels was improved. In the next step, fetal heart rate variability (FHRV), which is an important indicator of fetal distress, was added to the model. Finally, the contribution of humoral feedback in the cardiovascular response to repetitive severe episodes of hypoxia was investigated with the model.
The improved model, resulting from the rst step, was used to investigate the cascade from uterine contractions resulting in decreased uterine and/or umbilical blood ow, to FHR changes. Uterine contractions a ect fetal blood and oxygen pressures, which stimulate the baro- and chemoreceptor, and nally change FHR via the sympathetic and parasympathetic nervous system. The faster and more severe FHR decrease during uterine contractions caus- ing combined uterine and umbilical blood ow reduction, compared to contractions leading to uterine ow reduction alone, can be explained by the oxygen bu er function of the in- tervillous space. During the latter scenario, this oxygen bu er is still available for the fetus, resulting in a delayed and slower drop in fetal oxygen pressure. As a consequence, the chemoreceptor-mediated FHR reduction is also delayed and less severe. If the umbilical cord
x becomes occluded, this bu er is no longer available for the fetus. During both scenarios, fetal blood ow was redistributed from the peripheral to the cerebral circulation in order to maintain oxygen transport to the brain. The initial FHR increase, observed during umbilical cord occlusions, can be explained by a blood volume shift from the fetus to the fetal placenta. This results in a fetal blood pressure decrease and a baroreceptor-mediated increase in FHR. The volume shift can be attributed to the delay between the closure of the umbilical vein and arteries. The model was evaluated with data from sheep experiments: similar trends in blood pressure, oxygen pressure and FHR were obtained, showing the ability of the model to describe realistic decelerations.
Since the exact source of FHRV is not known, in the model we investigated the e ect of three possible sources of variability on FHRV: autoregulation of the peripheral blood vessels, in uence of higher brain centers on the processing of the baroreceptor output in the nucleus tractus solitarius of the medulla oblongata, and in uence of a erent systems, such as the heart, lungs and muscles, on the vagal center. Simulations were performed by superimposing either 1/f noise or white noise on the peripheral vascular resistance, baroreceptor output, and vagal e erent nervous system output. We evaluated FHR tracings by both visual inspection and spectral analysis. All power spectra showed a physiological 1/f character, irrespective of the noise source and type used. Since the clinically observed peak near 0.1 Hz was only obtained when white noise was superimposed on each of the di erent sources of variability, it is hypothesized that white noise is more likely to resemble physiological input. In accordance with clinical data, sympathetic control predominantly in uenced the low frequency power, while vagal control a ected both low and high frequency power. Addition of FHRV improved the capability of the model to generate realistic FHR signals, which is of importance if the model is used in clinical education.
During serious hypoxic episodes, induced by repeated severe contractions, secondary FHR re- sponses, such as FHR baseline increase and FHR overshoots, are often observed. Presumably, these FHR responses involve di erent mechanisms, including stress hormone feedback and attenuation of the vagal tone. We extended the model to describe secondary FHR responses via a simple catecholamine feedback submodel. Simulation results of repeated severe uterine blood ow reductions showed a similar trend as observed in sheep experiments: an initial decrease of inter-occlusion FHR, followed by a gradual increase. Simulations of repeated se- vere umbilical blood ow reductions showed FHR overshoots, following the FHR decelerations. However, these overshoots were less sharp than observed in sheep experiments. It is shown that catecholamines play a role in the origin of secondary FHR responses, however other mechanisms, such as vagal inhibition or hypoxic myocardial depression, cannot be excluded.
xi Summary
The improved and extended CTG simulation model is considered more suitable for use as a tool for hypothesis formation and testing and for educational purposes than our previous model. The new model contributes to understanding of the cascade of events between uterine contractions and FHR variations.
xii Chapter 1
Background and aim of the thesis Chapter 1
1.1 General introduction
Childbirth is a harzardous event for mother and child. Although fetal, neonatal, and infant mortality rates in Europe have declined between 2004 and 2010, these rates are still high [52]. In the 29 countries that participated in Euro-Peristat 2010 [52], fetal mortality rates ranged from 2.6 to 9.2 per 1000 total births. Neonatal mortality rates (until the 28th day after birth) ranged from 1.2 to 5.5 per 1000 live births. The infant mortality (0-364 days after birth) ranged from 2.3 to 9.8 per 1000 live births.
One of the main concerns during labor and delivery is fetal oxygenation. If oxygen transport from mother to child is reduced, this may result in fetal acidosis, which is related to devel- opment of neonatal morbidity, including neurological, respiratory and cardiovascular compli- cations [99, 158, 176]. In order to reduce the number of complications and to enable timely intervention in case of fetal distress, it is important to monitor fetal well-being during labor and delivery. Ideally, assessment of fetal well-being is based on fetal oxygen status. However, since in current clinical practice reliable continuous oxygen measurement techniques are not available, the cardiotocogram (CTG) is used to estimate fetal condition. The CTG represents the simultaneous registration of fetal heart rate (FHR) and uterine contractions. The relation between uterine contractions and changes in FHR is rather complex. Apart from variations in oxygen pressure, also changes in e.g. blood pressure and stress hormone concentrations play a role. Although the CTG is widely used to monitor fetal well-being, the intra- and inter- observer variability is high [27, 110, 125]. Unfortunately, the use of cardiotocography has not lead to a reduction of perinatal death compared to intermittent auscultation, yet it is associ- ated with a reduction of neonatal seizures [7]. However, introduction of the CTG did result in an increased number of cesarean sections and instrumented vaginal births [7]. In addition to the CTG, fetal blood sampling, ST-waveform analysis, and pulse oximetry, can be used during delivery to gain more insight into the fetal condition. However, the added value of these techniques in the detection of fetal distress is limited [164]. Furthermore, these techniques will not replace the CTG and thus interpretation of the CTG still remains an important task of the clinician.
Due to the complex physiology involved in the cascade from uterine contractions to FHR variations, interpretation of the CTG is not an easy task. Mathematical models might help to gain insight into the di erent mechanisms involved in FHR regulation, and thus improve understanding of the CTG. Moreover, a CTG simulation model will not only provide the clinically measured signals –FHR and uterine contractions– but will also give an estimate of other clinically relevant signals such as fetal oxygenation and blood pressure. These models can be used for research and educational purposes, and in the longer term might be used to support clinical decision making.
2 Background and aim of the thesis
Aim of this thesis is to optimize and extend the existing CTG simulation model of Van der Hout-van der Jagt et al. [161–163] in order to enhance model applicability for research and education. As a rst step, model complexity of submodels was reduced where possible. In addition, the physical description of other submodels was improved. In subsequent steps, fetal heart rate variability (FHRV), which is an important indicator of fetal distress, as well as the contribution of humoral feedback in the cardiovascular response to repetitive severe episodes of hypoxia, were investigated with the model.
In this chapter, rst the use of mathematical models in clinic is discussed, whereafter two examples of such models are given. Thereafter, the CTG and the physiological aspects related to FHR changes are brie y explained. Furthermore, mathematical models available for CTG simulation are discussed. This chapter is concluded with an outline of the thesis.
1.2 Mathematical models in a clinical setting
In the clinic, many patient measurements are performed. However, the motto ‘the numbers tell the tale’ does not always hold for these kind of measurements. Often clinicians have to use data obtained via indirect measurements, since direct measurements usually are inva- sive or not possible at all. Besides, these measurements are often related to large measuring inaccuracies. Nevertheless, clinicians are expected to estimate patient well-being and deter- mine a treatment plan based on these data. This is where mathematical models come in. Mathematical models can be used to gain insight into the complex physiology and support hypothesis testing and formation. They can be made patient-specic in order to estimate the e ect of medical interventions and as such play a large role in clinical decision making.
An example is an existing model designed to support clinical decision-making concerning vascular access surgery in patients on hemodialysis therapy [18]. The model can help the clinician to choose the optimal location for creation of an arteriovenous stula (AVF), a direct connection between an artery and vein in the arm of patients su ering from kidney disease, by predicting the patient-specic postoperative blood ow for di erent AVF congurations. To be able to use the AVF-model in clinic, the model has rst been tested, both in vivo as experimentally. Presently, the feasibility of the model to support decision-making in AVF surgery is being investigated via a randomized controlled trial. Since the computer model is software specically designed for intervention planning, it will be considered a medical device by the medical ethics committee. Therefore, a computer model has to be certied like other medical devices.
3 Chapter 1
Another model, used to calculate the ‘virtual fractional ow reserve’ (vFFR) in patients with coronary artery disease based on coronary CT-angiography [111], has already obtained such certication [53]. The FFR assesses the ratio of ow across a stenosis to putative ow in the absence of a stenosis. It is an index of the physiological signicance of a coronary stenosis and an indication for percutaneous coronary intervention [151]. The FFR, which is normally assessed via invasive cardiac catheterization, can now be computed non-invasively by use of the vFFR-model on the basis of CT images, for a large patient population.
These examples show that the idea to use a model for simulation of human physiology is not new. Both models discussed are currently used, or will likely be used in future as a diagnostic modality. Inherently, these models only partly represent reality and can thus be used for decision support. Obviously, the nal decision-making is in hands of the clinician.
This section is based on publications in ‘Medisch Journaal’ [79] and ‘MT Integraal’ [80].
1.3 The cardiotocogram
1.3.1 Clinical evaluation of the CTG
The CTG contains the simultaneous registration of FHR and uterine contractions. An example is shown in gure 1.1. The clinical evaluation of the CTG is based on contraction strength, duration and frequency, in relation to FHR characteristics like FHR baseline, baseline variabil- ity, accelerations and decelerations. Fetal heart rate variability is described as uctuations in the FHR baseline, which are irregular in shape and frequency [115, 152]. Accelerations are dened as abrupt increases of more than 15 bpm above baseline, lasting longer than 15 s [100, 126], and are associated with fetal movements or may result from mild compression of the umbilical vein [109, 177]. Fetal asphyxia is unlikely in the presence of accelerations. Decelerations are FHR reductions, which often are related to contractions. There are three types of decelerations which have di erent shapes and vary in timing with respect to the uterine contraction: early, late and variable decelerations. Early decelerations, are gradual FHR reductions whose nadirs coincide with the uterine contraction peaks [100, 126]. They are caused by head compression, stimulating the vagal nerve via direct vagal hypoxia and/or stimulation of mechanoreceptors in the fetal head [102]. The clinical relevance of early de- celerations is limited. Late decelerations are also characterized by a gradual decrease in FHR, however, these decelerations are delayed with respect to the uterine contractions [100, 126]. They can be caused by a re ex pathway via the chemoreceptor, activated by low oxygen pressures caused by uterine contractions, or by hypoxic myocardial depression when oxygen delivery to the heart is not su cient [63, 103, 114]. The presence of late decelerations is in- dicative for fetal distress, hence clinical interventions to advance labor and delivery are often
4 Background and aim of the thesis
CTG
200 180 160 140 120 FHR[bpm] 100 80 60 0 1 2 3 4 5 6 7 8 9 10 11 12 13 time [min] 100 75 50 25 0 UP [mmHg] UP 0 1 2 3 4 5 6 7 8 9 10 11 12 13 time [min]
Figure 1.1: Example of a CTG. The upper signal represents fetal heart rate and the lower signal represents the uterine contractions. This gure is taken from [160] with permission from the author. indicated. Variable decelerations result from umbilical cord compression, which during labor mostly occur during uterine contractions [57]. This type of decelerations is characterized by an abrupt FHR decrease, and by a varying shape between successive contractions [100, 126]. A variable deceleration by itself is no indicator for fetal asphyxia. However, acidosis may develop if variable decelerations continue for a longer period. Additional information of fetal well-being is often needed in order to determine if intervention is required.
1.3.2 Physiological background
The cascade from uterine contractions to the nal e ect on FHR depends on several path- ways, with a prominent role for the chemore ex, barore ex, and humoral re exes, which will be discussed in this section.
The maternal and fetal cardiovascular systems are separated, meaning that the maternal blood will not be in contact with the fetal blood (see gure 1.2). Oxygen and nutrients are transported to the fetus via the placenta, while metabolic waste products are removed from the fetal circulation. In the mother, about 10% [55, 115, 171] of the cardiac output is directed to the uterine circulation, of which 70-90% [115, 131] enters the intervillous space to participate in gas exchange. Oxygen-rich blood enters the intervillous space via spiral arteries, branching from the uterine arteries. Oxygen-poor blood is collected in the uterine veins. On the fetal side, oxygen-poor blood enters the placenta via two umbilical arteries, which branch into the villous capillaries. The fetal placental villi actually bathe within the maternal blood in the
5 Chapter 1
fetal side
oxygen-poor blood from umbilical arteries oxygen-rich blood to umbilical vein placental membrane
villous capillaries with fetal blood
IVS with maternal blood
from uterine artery to uterine vein
maternal side
Figure 1.2: Schematic overview of the placenta. Maternal blood enters the placenta via the uterine artery and leaves the placenta via the uterine vein. Fetal blood enters the placenta via the umbilical arteries and leaves the placenta via the umbilical vein. Exchange of oxygen, waste products, and nutrients takes place between the maternal blood in the intervillous space (IVS) and the fetal blood in the villous capillaries. This illustration is taken from [160] with permission from the author.
intervillous space. Here oxygen di uses from the mother to the fetus. Oxygen-rich blood leaves the fetal placenta and enters the fetal circulation via the umbilical vein. Umbilical blood ow comprises about 25% of the fetal cardiac output [3, 87, 97, 115, 133].
During uterine contractions, the oxygen transport between mother and fetus might be dis- turbed. First of all, the vessels running through the uterine wall will be squeezed, resulting in reduced uterine blood ow [109]. Second, depending on its location, the umbilical cord might become compressed, reducing transport of oxygen-rich blood from the fetal placental villi to the fetus itself [109]. Both of these scenarios result in changes in fetal oxygen pressure and blood pressure [68, 69, 117], thus activating the chemo- and baroreceptor. Signals from these receptors are transmitted to the autonomic nervous system: the sympathetic nervous system is stimulated by the chemoreceptor and inhibited by the baroreceptor; the parasym- pathetic nervous system is stimulated by both chemo- and baroreceptor. Via the autonomic nervous system, several cardiovascular e ectors are a ected, including FHR, which is in- creased by activation of the sympathetic nervous system and decreased via the parasympa- thetic nervous system. As a net result, the FHR tracing shows decelerations. During hypoxia, the sympathetically-induced increase of the peripheral resistance results in a reduced per- fusion of the peripheral tissues. Concurrently, decreased cerebral vascular resistance results
6 Background and aim of the thesis in an increased blood ow to the fetal brain (cerebral autoregulation). Due to this blood ow redistribution, oxygen transport to the most vital organs is maintained at the expense of the peripheral circulation [115].
Progression of hypoxic insults often results in FHR baseline increase [115, 152], and develop- ment of FHR overshoots [138, 177]. Catecholamines are thought to at least partly play a role in the development of these secondary FHR variations [115, 136, 179]. Catecholamines enter the blood stream via over ow of neurotransmitters from the nervous system to the circu- lation, or via secretion by the adrenal medulla [49, 88]. In the fetus, adrenal catecholamine secretion can be increased by nervous stimulation or by a direct e ect of hypoxia on the adrenal medulla, known from several animal species [31–34, 141]. In adults, catecholamines are removed from the circulation via neuronal and extra-neuronal uptake [47]. In the fetus, the placenta also plays an important role in the elimination of catecholamines [23, 47, 119]. Catecholamines a ect the cardiovascular system by increasing heart rate and blood pressure [88, 109, 115]. However, many uncertainties concerning the catecholamine feedback system in the fetus remain.
1.3.3 Mathematical models for CTG simulation
In gure 1.3, an overview is given of the di erent subsystems contributing to the cascade between uterine contractions and FHR changes. Mathematical computer models do not only provide these two CTG signals, but also give an estimate of other clinically important, but immeasurable signals such as fetal oxygen pressure and blood pressure.
There are several submodels available that describe parts of the required model as shown in gure 1.3. For example, models focusing on uterine contractions [9, 14], circulation [21, 61, 66, 107, 134], oxygenation [67, 135], or regulation [154, 178]. However, models that describe all required submodels are scarce and most of these models are designed to simulate adult physiology and thus have to be adapted for the fetus.
At the start of the project, there was only one model available containing all submodels required to investigate the whole cascade from uterine contraction to FHR variations, namely the model of Van der Hout-van der Jagt et al. [161–163]. This model is designed to simulate non-asphyxiated fetuses and is used to investigate the in uence of caput compressions [162], uterine ow reductions [163] and umbilical cord compressions on FHR [161]. The model presented in this thesis is based on the model of Van der Hout-van der Jagt and describes fetal circulation, oxygenation, and regulation in a similar fashion. The model of Van der Hout-van der Jagt was critically evaluated and simplied, improved and extended in order to enhance applicability for educational and research purposes.
7 Chapter 1
cardiovascular system mother O2 distribution mother
contraction uterine pressure placenta generator O2 distribution oxygen pressure cardiovascular fetus system fetus blood pressure cardiovascular parameters Monitor NS fetus
contractions baroreflex
FHR chemoreflex
oxygen pressure
catecholamine feedback
Figure 1.3: Overview of all components of the CTG simulation model. The cardiovascular system of mother and fetus are separated and describe blood ows and volumes in di erent parts of the circulation. Changes of the cardiovascular parameters will lead to changes in the oxygen distribution models. In the placenta, oxygen di uses from mother to child. From the fetal cardiovascular model a blood pressure signal can be obtained. Oxygen pressures are obtained from the fetal oxygenation model. The blood and oxygen pressure variations are input for the baro- and chemoreceptors, which via the nervous system (NS) result into changes of several cardiovascular parameters, including FHR. A reduced oxygen pressure will also increase the production of catecholamines, which has an additional e ect on FHR. Uterine contractions are modeled via increases of uterine pressure, which a ect the fetal and maternal cardiovascular systems and so initiate the whole cascade from contractions to FHR changes. From the model, not only the two CTG signals can be obtained (FHR and uterine contractions), but it also gives an estimate of other clinically relevant signals such as oxygen pressure. Adapted from [160].
1.4 Outline of the thesis
In this thesis, the model of Van der Hout-van der Jagt [161–163] has been used as a starting point. Critical evaluation of the model setup showed room for improvement. In chapter 2, the updated model is introduced. In order to enhance model applicability for educational and research purposes, the complexity of some submodels is reduced, while the physical description of other submodels is improved. Furthermore, the model is used to investigate FHR variations induced by uterine contractions causing uterine blood ow reduction.
Parameter estimation remains di cult, despite a reduction in the number of model param- eters. Estimation of all model parameter values is extensively described in chapter 3. In addition, the model is used to gain insight into the mechanism through which umbilical cord
8 Background and aim of the thesis compressions lead to variable FHR decelerations.
Since fetal heart rate variability is an important indicator of fetal distress [181], this FHR feature is also included in the model. In chapter 4, three possible sources of variability are added to the model: autoregulation of the peripheral blood vessels, in uence of higher brain centers on the processing of the baroreceptor output in the nucleus tractus solitarius of the medulla oblongata, and in uence of other a erent systems on the vagal center. The e ect on the FHR tracings is investigated for each of these sources of variability, as well as for the type of noise applied to these sources.
During prolonged hypoxia, secondary FHR e ects might develop, such as increased FHR baseline and FHR overshoots. In chapter 5, a simple catecholamine model is proposed and added to the model in order to investigate the role of catecholamines in the development of these FHR e ects.
The thesis concludes with a general discussion in chapter 6 in which all ndings are put into a broader perspective. As chapter 2 to 5 are written to be self-contained, some overlap between these chapters will be present.
9 Chapter 1
10 Chapter 2
A mathematical model to simulate the cardiotocogram during labor Part A: Model setup and simulation of late decelerations
The contents of this chapter have been published in Journal of Biomechanics Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG and Bovendeerd PHM Available online: http://dx.doi.org/10.1016/j.jbiomech.2016.01.036 Chapter 2
Abstract
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 su cient (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 e ect of uterine contractions on FHR as initiated by reduction of uterine blood ow, mediated by changes in oxygen and blood pressure, and e ected by the chemore ex and barore ex. 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 ow, 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.
12 Uterine blood ow reduction
2.1 Introduction
In current clinical practice the cardiotocogram (CTG), the combined registration of fetal heart rate (FHR) and uterine contractions, is used to monitor fetal well-being during labor and de- livery. The CTG signals show the input (uterine contractions) and output (FHR) of a complex regulation mechanism, in which amongst others variations in fetal blood pressure and oxy- genation play a role. To better understand the underlying physiology, mathematical models can be used. Previously a model for CTG simulation was presented [161–163]. This model included feto-maternal hemodynamics, oxygen distribution, and regulation and was used to simulate di erent clinical scenarios following uterine ow reduction and umbilical cord com- pression as induced by uterine contractions. While model results were in line with clinical observations, critical evaluation of the model setup showed room for improvement. For example, since the description of regulation and cardiac function was very detailed while the availability of experimental data was limited, estimation of the many parameter values was ambiguous. Furthermore, the model of hemodynamics focused on the detailed change of arterial pressure during the cardiac cycle, whereas baroreceptor feedback was based on average arterial pressure only, allowing for a less complex model of cardiac function. Also, closure of the uterine and umbilical blood vessels due to uterine contractions was depen- dent on external vascular pressure, whereas it would be physically more realistic to make it dependent on vascular transmural pressure.
The aim of this study is to improve our previous model for simulation of the CTG, by reducing the complexity of some submodels (e.g. regulation and cardiac function) and thus reducing errors related to ambiguity in parameter estimation, and by improving the physical basis for the description of other submodels (e.g. vessel compression).
In this chapter an overview of the new CTG simulation model is given. Functionality of the model is tested by simulating the e ect of uterine ow reduction on FHR in term preg- nancy, resulting in FHR changes being known as late decelerations. Late decelerations are characterized as a gradual FHR decrease, meaning that it takes more than 30 s from onset of the deceleration to the FHR nadir, with the nadir of the deceleration occurring after the contraction peak [100, 126]. Two di erent mechanisms are known to be responsible for late decelerations: hypoxic myocardial depression, which plays a role when oxygen delivery to the heart is insu cient, and re ex feedback, which acts via activation of the chemo- and barore- ceptor as a result of reduced oxygen pressures induced by uterine contractions [63, 103, 114]. In this study we focus on the re ex induced late decelerations only. We tested the ability of the model to reproduce experimental data on arterial oxygen pressure, blood pressure and FHR from sheep experiments, in which late decelerations were evoked by means of in ation of a balloon catheter to reduce uterine blood ow [68, 117]. In chapter 3 we focus on the estimation of all model parameters and we investigate the e ect of combined uterine and
13 Chapter 2 umbilical ow reduction on FHR, resulting in so-called variable decelerations. Furthermore, in chapter 3 model limitations will be discussed.
2.2 Material and methods
The model consists of several submodels which describe feto-maternal hemodynamics, oxy- genation, fetal regulation, and uterine contractions. Although the general structure of the previous model is maintained [161–163], changes are applied to the di erent submodels in order to simplify and enhance the CTG simulation model. Below we describe the setup of the new model. A detailed description of the parameter estimation is given in chapter 3.
2.2.1 Feto-maternal hemodynamics
The model of hemodynamics is composed of compartments, representing the storage of blood and oxygen, which are connected via segments that represent convective transport. The fetal circulation consists of a combined ventricle (CV) from where blood ows into the cerebral, umbilical, and tissue circulation (gure 2.1). In the latter circulation, all tissues apart from the brain and fetal placenta (villi) are lumped. In the mother, the heart is represented by the left ventricle (LV) and the uterine circulation is modeled explicitly, while the remainder is lumped into the tissues.
2.2.1.1 Vascular function
To describe blood storage in the vascular system, we use a linear approximation of the pressure-volume relation around the working pressure of the blood vessel:
V – V0 p = (2.1) tm C where C represents the compliance of the vessel, V the actual volume, and V0 the unstressed volume of the vessel at zero transmural pressure. The transmural pressure ptm is dened as: ptm = p – pext (2.2) where p represents the absolute pressure in the compartment, and pext the external pressure acting on the outside. Fetal external pressure is equal to uterine pressure (put), while maternal external pressure is set to zero, except for the placental intervillous space (IVS) which is also subjected to put, see gure 2.1.
14 Uterine blood ow reduction
For the IVS, that may undergo large volume changes during uterine contractions, a nonlinear pressure-volume relation is used: 1 1 –1 ptm–p0 V (ptm) = Vmax · f (ptm) with f (ptm) = + · tan (2.3) ivs 2 π p1 where Vivs represents the IVS blood volume, Vmax the maximal IVS blood volume, and ptm the transmural blood pressure of the compartment, while p0 and p1 are constants. The function f (ptm) was based on a relation between vessel cross-sectional area and transmural pressure [92].
In each compartment, the change in blood volume in time is determined by:
dV = q – q (2.4) dt in out where qin and qout represent in ow and out ow, respectively.
Blood ow q in between compartments is generally described by:
∆p q = (2.5) R where R represents the resistance of the segment and ∆p the (absolute) pressure di erence over a segment. The resistance Rutv of the uterine vein, which is exposed to large changes in transmural pressure during uterine contractions, is modeled as function of transmural pressure. Assuming as a rst approximation that the ow in this segment follows Poiseuille’s law, we model the resistance to be inversely proportional to the square of the vessel area:
2 R(p ) = max R · 1 ,R tm 0 f (ptm) ref (2.6) where Rref is the resistance in steady state, R0 is a constant, and f (ptm) is dened by eq. 2.3. The transmural pressure of the uterine veins (ptm,utv) is determined as the mean absolute pressure of the two neighboring blood compartments (see gure 2.1) minus the external uterine pressure put: pivs+pven ptm,utv = 2 – put (2.7)
During uterine contractions, uterine pressure put increases above the resting pressure prest [162]: ( 2 π(t–tcon) pcon · sin T , tcon < t < tcon + Tcon put = prest + con (2.8) 0, else with pcon peak pressure, tcon moment of contraction initiation, and Tcon contraction duration. See section 2.2.4 for parameter values.
15 Chapter 2
QD,lung qin qout ven LV art
QM,tis,m
tisv tis tisa mother
utv ivs uta
put QD,plac
umv villi uma
put q qin out p put ven CV art ut
put QM,tis,f fetus
tisv tis tisa
put QM,cer,f
cerv cer cera
put
Figure 2.1: Schematic overview of the model of feto-maternal hemodynamics and oxygen distribution. The circles represent compartments where storage of blood and oxygen can take place, while rectangles represent segments where blood ows from one compartment to the next. Metabolic and di usional oxygen ows are indicated with dashed arrows. In the mother, blood ows from the left ventricle (LV), via the systemic arteries (art) and the tissue microcirculation arteries (tisa) into the tissue microcirculation (tis). Blood ow into the inter- villous space (ivs) takes place via the uterine spiral arteries (uta). Via the microcirculation veins (tisv) and the intramural veins in the uterus (utv) blood ows into the systemic veins (ven), back to the heart. In the fetus, blood ows from the combined ventricle (CV) into the systemic arteries (art). Via the microcirculation arteries (tisa and cera) blood reaches the tissue and cerebral microcirculation (tis and cer, respectively), while blood leaves the mi- crocirculation compartments via the microcirculation veins (tisv and cerv). Via the umbilical arteries (uma) blood ows into the placental villi (villi), and via the umbilical vein (umv) back into the systemic veins (ven). From the veins, blood ows back into the heart. Uterine vein resistance (utv), and umbilical artery and vein resistance (uma and umv, respectively) are variable and change as function of transmural blood pressure as described in eq. 2.6. In both mother and fetus, qin represents in ow of blood into the heart, while qout represents car- diac out ow. The intervillous space and all fetal compartments experience external uterine pressure put. In the mother, oxygen di uses from the air into the lungs (QD,lung) (modeled as oxygen di usion into the systemic veins), while oxygen metabolism takes place in the tissues (QM,tis,m). In the placenta, oxygen di uses from the mother to the fetus (QD,plac). In the fetus, oxygen is consumed in the tissues (QM,tis,f ) and the brain (QM,cer,f ).
16 Uterine blood ow reduction
Table 2.1: Cardiovascular parameters. Parameter estimation and sources are extensively described in chapter 3.
Fetal parameters Parameter Value Unit Parameter Value Unit T* 60/135 s EF 0.67 - Vart,0 35.2 ml Rtisa* 2.81 mmHg·s/ml Vven,0* 153.4 ml Rtisv 0.15 mmHg·s/ml Vtis,0 15.9 ml Rcera* 7.24 mmHg·s/ml Vcer,0 2.6 ml Rcerv 0.38 mmHg·s/ml Vvilli,0 35.9 ml Ruma 3.84 mmHg·s/ml Cart 0.33 ml/mmHg Rumv 2.56 mmHg·s/ml Cven 21.91 ml/mmHg Emax* 7.71 mmHg/ml Ctis 0.35 ml/mmHg Emin 0.26 mmHg/ml Ccer 0.06 ml/mmHg V0,max 0 ml Cvilli 2.40 ml/mmHg V0,min 5.8 ml
Maternal parameters Parameter Value Unit Parameter Value Unit T 60/80 s Rtisv 0.04 mmHg·s/ml Vart,0 721 ml Ruta 5.71 mmHg·s/ml Vven,0 3604 ml Rutv 1.43 mmHg·s/ml Vtis,0 504 ml R0,utv 0.358 mmHg·s/ml Vivs,0 163 ml p0,utv -2.5 mmHg Cart 3.9 ml/mmHg p1,utv 25 mmHg Cven 308.9 ml/mmHg Emax 1.83 mmHg/ml Ctis 6.4 ml/mmHg Emin 0.06 mmHg/ml Civs,max 2.4 ml/mmHg V0,max 0 ml EF 0.67 - V0,min 44 ml Rtisa 0.67 mmHg·s/ml
*Denotes a reference parameter for the regulation submodel.
2.2.1.2 Cardiac function
Since only mean blood pressure values are used as input for the regulation submodel, we replaced the dynamic one-ber model of cardiac function [11, 20] by a two-state elastance model [65, 148]. This model relates the end diastolic volume Ved and the end ejection volume Vee to the transmural end diastolic pressure ptm,ed and end ejection pressure ptm,ee according to: ptm,ed = Emin(Ved – Vmin,0); ptm,ee = Emax(Vee – Vmax,0) (2.9) where the elastances Emin and Emax represent the slopes of the pressure-volume relations, and Vmin,0 and Vmax,0 the intercepts at zero pressure. We assume that the ventricle lls at the average venous blood pressure pv and ejects at the average arterial blood pressure pa. The average ow from the heart, the cardiac output qCO, is described by:
Vstroke Ved – Vee qCO = = (2.10) Tcycle Tcycle
17 Chapter 2
with stroke volume Vstroke and cardiac cycle time Tcycle.
The variation of the cycle-averaged cardiac volume with time is accounted for by: d Ved+Vee qout = qCO ; qin = qCO + qV with qV = dt 2 (2.11) where qout and qin represent cardiac out ow and in ow, respectively. Parameter values for the hemodynamic model can be found in table 2.1.
2.2.2 Oxygenation
For a schematic representation of the oxygen model see gure 2.1. While we adopted the structure of our previous model [162], we modied several details. For completeness, we describe the new model below.
2.2.2.1 Oxygen content
In each compartment, oxygen concentration cO2 is determined by the sum of the oxygen bound to hemoglobin and the oxygen dissolved in blood:
αHb · sO2 cO = + βpO (2.12) 2 100 2
Here α represents the maximum binding capacity of hemoglobin, Hb the hemoglobin con- centration and β the content of dissolved oxygen per unit of partial pressure pO2. Oxygen saturation sO2 is related to oxygen partial pressure by:
100 sO 2 = 3 (2.13) 1 + c1/(pO2 + c2 · pO2) where c1 and c2 are constants. Since fetal blood has a higher oxygen a nity than maternal blood, for the fetus this curve is steeper and shifted to the left compared to an adult [108], as determined by a lower value of c1 (see table 2.2).
2.2.2.2 Oxygen transport
In each compartment the rate of change of oxygen amount (oxygen concentration cO2 mul- tiplied by compartment blood volume V) is determined by the sum of convective transport QC, di usive exchange QD and metabolic uptake QM:
d(cO2V) = Q + Q – Q (2.14) dt C D M
18 Uterine blood ow reduction where the change in volume is determined from the hemodynamic model. Whereas the actual sign of the di usive and convective transport may vary depending on the compartment, metabolic uptake always leads to a reduction of oxygen content.
Table 2.2: Oxygen distribution parameters. See chapter 3 for estimation and sources.
Parameter Value Unit Parameter Value Unit Dplac 0.082 ml O2/(s·mmHg) α 1.34 ml O2/g Hb –5 Dlung 0.169 ml O2/(s·mmHg) β 3.1 · 10 ml O2/(ml blood·mmHg) –1 –2 QM,0,tis,f 3.36·10 ml O2/s Hbf 17 · 10 g Hb/ml blood –1 –2 QM,0,cer,f 1.31·10 ml O2/s Hbm 12 · 10 g Hb/ml blood 4 3 QM,0,tis,m 10 ml O2/s c1f 1.04 · 10 mmHg 4 3 pO2,th,cer,f 5 mmHg c1m 2.34 · 10 mmHg 2 pO2,th,tis,f 10 mmHg c2f 150 mmHg 2 pO2,air 160 mmHg c2m 150 mmHg f indicates a fetal parameter, and m indicates a maternal parameter.
Convection describes the blood ow related transport of oxygen through the cardiovascular system. For each compartment convection is described by:
i i j QC = ∑qincO2,in – ∑qoutcO2 (2.15) i j
The rst term represents the sum of all oxygen in ows of the current compartment, where i i runs across all segments with a blood in ow qin into the compartment, with oxygen concen- i tration of the in ow compartment cO2,in. The second term represents the sum of all oxygen out ows with oxygen concentration of the current compartment cO2, where j runs across j all segments with a blood out ow qout from the compartment.
In the model, oxygen di usion takes place both in the placenta (QD,plac) from the maternal IVS into the fetal placental villi, and in the maternal lungs (QD,lung) from the air into the maternal veins (see gure 2.1):
QD,plac = Dplac(pO2,ivs – pO2,villi); QD,lung = Dlung(pO2,air – pO2,mat,ven) (2.16) with Dplac and Dlung the di usion coe cient in the placenta and the lung, respectively, and pO2 the partial oxygen pressure in a compartment. Since we did not explicitly model the maternal pulmonary circulation, we introduced pulmonary oxygen uptake at the in ow of the LV, in the maternal veins.
Oxygen metabolism is modeled in the fetal and maternal tissues and fetal brain. Metabolic uptake is constant (QM,0) as long as the oxygen level in the compartment is above a certain
19 Chapter 2
threshold pO2,th and will decrease linearly if the oxygen level becomes lower: ( QM,0, pO2 ≥ pO2,th QM = Q (2.17) Q + M,0 · (pO – pO ), else M,0 pO2,th 2 2,th
Parameter values of the oxygen model can be found in table 2.2.
2.2.3 Regulation
The cardiovascular regulation submodel describes cerebral autoregulation as well as central regulation in the fetus.
2.2.3.1 Cerebral autoregulation
The model for cerebral autoregulation increases oxygen transport to the brain in case of hypoxemia. It is adapted with respect to Van der Hout-van der Jagt [163], to better re ect the limited capability of the cerebral autoregulation submodel to completely compensate for a reduced oxygen supply, via parameter γ in eq. 2.19. Cerebral autoregulation is included via decrease of cerebral artery resistance Rcera if oxygen levels drop. The limited ability of ∗ the actual resistance Rcera to instantaneously follow a desired resistance Rcera is described through a low pass lter with time constant τRcera :
dRcera 1 ∗ = (Rcera – Rcera) (2.18) dt τRcera
∗ The value of the desired resistance Rcera is based on [120], who found a hyperbolic relation between arterial oxygen content and cerebral blood ow in fetal lambs:
∗ Rcera,ref Rcera = cO (2.19) (1 – γ) + γ · 2,a,ref cO2,a where cO2,a represents the oxygen concentration in the fetal arteries, and Rcera,ref and cO2,a,ref represent the reference value of Rcera and cO2,a respectively (table 2.1 and 2.3). The term γ [-] determines how well Rcera can adapt to variations in arterial oxygen concentration cO2,a. A value of 1 means that a decrease in cO2,a is completely compensated by an increase ∗ of blood ow (modeled via a decrease of Rcera) to keep up oxygen delivery to the brain. In ∗ our model a value of 0.5 is chosen for γ based on Peeters [120]. The minimal value of Rcera was set to half of its reference value.
20 Uterine blood ow reduction
uterine and umbilical flow reduction R Δput utv
Rumv & Ruma receptors NS effectors
+1 + ev z + D x k + + x T T + ref ptm,a,ref p Δ tm,a rb - - + rb D x k G z z D x k x Emax,ref Emax - es +1 + + pO ΔpO r 2,a,ref 2,a c + z x V + D x k ven,0,ref Vven,0 - G rc +1 z D x k x R R +1 tisa,ref tisa
cO2,a,ref ÷ Rcera x Rcera,ref Rcera cerebral autoregulation cO2,a p pO tm,a 2,a cardiovascular and oxygen model
Figure 2.2: Schematic overview of the e ect of uterine contractions on the cardiovascular e ectors via the regulation submodel. Uterine contractions result in changes in uterine pressure put, and a ect uterine vein resistance (Rutv) and possibly umbilical vein and artery resistance (Rumv and Ruma, respectively). This will lead to changes in mean transmural arterial blood pressure ptm,a and oxygen pressure pO2,a. Via a Gompertz relation G and a low pass lter τ, these variations are translated into the normalized baro- and chemoreceptor outputs, rb and rc respectively, which in turn in the nervous system (NS) are combined into a normalized vagal ev, and sympathetic es e erent output. Via a delay D, another low pass lter, and a multiplication factor k, these outputs lead to relative changes z of the four cardiovascular e ectors: heart period T (composed of a sympathetic and a vagal heart rate response), cardiac contractility Emax, venous unstressed volume Vven,0, and peripheral vascular resistance Rtisa. Addition of the value 1, followed by multiplication with the reference value of each e ector, results into the nal e ector values. For the cerebral autoregulation, arterial oxygen content cO2,a is derived from pO2,a by use of the fetal saturation curve. A nonlinear function, a low pass lter, and multiplication with the reference resistance value, determine the relation between cO2,a and cerebral resistance Rcera.
2.2.3.2 Central regulation
The model for central regulation describes the e ect of baro- and chemoreceptor regulation on four cardiovascular e ectors: heart period T, cardiac contractility Emax, peripheral vascu- lar resistance Rtisa, and venous unstressed volume Vven,0. We replaced our previous model based on Ursino [154] by a simpler model based on Wesseling [178]. Our new regulation model only contains a baro- and chemoreceptor and does no longer include the responses of vagal nerve hypoxia or central nervous system (CNS) hypoxia. Furthermore, the two sympathetic pathways (α and β) were combined into one sympathetic e erent signal (see gure 2.2).
21 Chapter 2
In the receptor model, deviations of transmural arterial blood pressure ptm,a and oxygen pressure pO2,a are translated into normalized deviations of the baroreceptor output rb and chemoreceptor output rc, with respect to their steady-state value of 0. The actual receptor output r (where r may represent rb or rc) responds to variations in input y (representing ptm,a or pO2,a) via a low pass lter with time constant τr:
dr(y) 1 = (r∗(y)– r(y)) (2.20) dt τr
Here r∗ represents the desired output, which is described by an asymmetric sigmoid relation (Gompertz function): ∗ η ·eη2·(y–yref ) r (y) = rmin + (rmax – rmin) · e 1 (2.21) with yref a reference value for ptm,a or pO2,a, and rmin [-] and rmax [-] the minimum and maximum receptor value, respectively (table 2.3). Derivation of η1 and η2 is described in chapter 3.
The e erent pathways e in the model consist of a vagal and a sympathetic signal (ev and es, respectively), which both are a function of the a erent information from the baro- and chemoreceptor. The e erent pathways also represent normalized deviations from steady state in which ev = es = 0:
ev = wb,v · rb + wc,v · rc, with wb,v + wc,v = 1 (2.22) es = –wb,s · rb + wc,s · rc, with wb,s + wc,s = 1
The weighting parameters w are all positive (table 2.3). Since an increase in transmural arterial blood pressure has an inhibiting e ect on the sympathetic output, the contribution of the baroreceptor output rb to the sympathetic signal es is taken negative.
The e erent vagal and sympathetic signal determine the setting of the four cardiovascular e ectors. The e ectors Rtisa, Vven,0, and Emax are sympathetically-mediated. For T we distinguish between a vagally- and sympathetically-induced change in heart period. In general, for each e ector rst the corresponding e erent signal (ev or es) is delayed with a time delay D. The resulting intermediate output x∗(t) passes a low pass lter characterized by its specic time constant τ to yield a signal x(t), that in turn is multiplied by an e ector gain k [-] to obtain an e ector signal z(t):
dx(t) 1 x∗(t) = e(t – D); = (x∗(t)– x(t)) ; z(t) = kx(t) (2.23) dt τ
22 Uterine blood ow reduction
Table 2.3: Regulation parameters. See chapter 3 for estimation and sources.
Model component Parameter Value Unit Parameter Value Unit Cerebral cO2,a,ref 0.107 ml O2/ml blood γ 0.5 - autoregulation τRcera 10 s η1,b -0.69 - η1,c -6.91 - –1 –1 η2,b -0.06 mmHg η2,c 0.52 mmHg rb,min -1 - rc,min -0.001 - Central regulation: rb,max 1 - rc,max 1 -
receptors τrb 8 s τrc 2 s yref ,b 45 mmHg yref ,c 18.1 mmHg wb,s 1/4 - wc,s 3/4 - wb,v 1/4 - wc,v 3/4 -
DTv 0.2 s kEmax 1.2 - τTv 1.5 s DRtisa 2 s kTv 2.4 - τRtisa 6 s Central regulation: DTs 2 s kRtisa 4.2 - e ectors τTs 2 s DVven,0 5 s kTs 1.2 - τVven,0 20 s DEmax 2 s kVven,0 -1.2 - τEmax 8 s
The signal z(t) represents the relative change of the e ector value. For Rtisa, Vven,0, and Emax the new e ector values are computed via:
Rtisa(t) = Rtisa,ref · (1 + zRtisa (t))
Vven,0(t) = Vven,0,ref · (1 + zVven,0 (t)) (2.24)
Emax(t) = Emax,ref · (1 + zEmax (t)) where Rtisa,ref , Vven,0,ref , and Emax,ref represent the reference e ector values (table 2.1). For T the e ector value is computed through:
T(t) = Tref · (1 + zTv (t)– zTs (t)) (2.25)
where zTv and zTs represent the vagally- and sympathetically-induced relative change in heart period and are determined using eq. 2.23 and Tref represents the reference heart period. The minus sign in eq. 2.25 indicates the inhibitory e ect of the sympathetic feedback on T(t). Parameter values for the regulation model can be found in table 2.3.
2.2.4 Model simulations
The model was implemented in MATLAB R2013a (The MathWorks, Inc., USA). Di erential equations were evaluated by forward Euler time integration with a time step of 0.02 s. Sce- narios described below were initiated from a steady-state situation at which variation of ptm,a –4 and pO2,a was less than 1 · 10 mmHg/s, respectively.
23 Chapter 2
We simulated uterine ow reduction in term pregnancy (full term fetus of 3.5 kg) during a reference contraction dened by a duration (Tcon) of 60 s and a uterine pressure amplitude (pcon) of 70 mmHg with respect to the reference pressure (prest), which was set at 15 mmHg [109, 115], (i.e. a maximum uterine pressure of 85 mmHg is reached). Furthermore, more severe contractions, with a contraction amplitude of 110 mmHg or a contraction duration of 120 s, were simulated.
We also simulated sheep experiments in which uterine blood ow was blocked for 20 s by use of a balloon catheter in the descending aorta [68, 117]. We assumed that the balloon catheter was in ated and de ated over a time span of 5 s [69]. We linearly increased uterine artery resistance Ruta over 5 s to a maximum value of 100 times the reference resistance, then kept the resistance at maximum level for 20 s, and subsequently decreased the resistance back to steady-state level over another 5 s. To investigate the e ect of compression duration, simulations of 30 s compression were performed as well.
Simulation results of combined uterine and umbilical ow reduction are presented in chapter 3 of this paper.
2.3 Results
Figure 2.3 shows simulation results of isolated uterine ow reduction caused by a reference uterine contraction of 60 s with a pressure amplitude of 70 mmHg. In steady state, uterine pressure (panel A1) is equal to the resting pressure of 15 mmHg. Fetal arterial blood pressure is 45 mmHg (panel A2), arterial oxygen pressure is 18.5 mmHg (panel A3), and fetal heart rate is about 135 bpm (panel A4). Uterine blood ow is about 630 ml/min (panel B1) and IVS blood volume is 175 ml (panel B2). Oxygen pressure both in fetal tissues and brain is 15.4 mmHg (panel B3). Blood ow through the fetal tissues and brain equals 850 and 330 ml/min, respectively (panel B4). Note that blood pressures mentioned in this section represent transmural blood pressures.
Column A shows the CTG signals (uterine pressure and FHR) and vital signals (arterial blood pressure and oxygen pressure). During a standard uterine contraction, modeled via an in- crease in uterine pressure (panel A1), only a slight increase in arterial blood pressure is ob- served (panel A2), while arterial oxygen pressure is reduced by about 1.5 mmHg (panel A3). FHR only shows a small deceleration of 3 bpm (panel A4). If we look into more detail (col- umn B) we observe an initial increase of IVS out ow and decrease of IVS in ow (panel B1), due to compression of the IVS. As uterine pressure increases, IVS venous out ow decreases because the uterine veins become compressed. Due to the pressure build-up in the IVS, the pressure di erence between the maternal arteries and IVS reduces, decreasing IVS in ow via
24 Uterine blood ow reduction
qutv 100 1000 quta 100 [ml/min] [mmHg] 50 500 [mmHg] 50 ut ut ut q p p A1 B1 C1 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 50 200 50
150 [mmHg] [mmHg] ivs
45 V [ml] 45 tm,a tm,a p A2 B2 p C2 100 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 20 20 20 pO2,tis pO2,cer [mmHg] [mmHg] 15 [mmHg] 15 15 2 2,a 2,a pO pO A3 B3 pO C3 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 1000 150 150
qtis
100 600 100
qcer FHR [bpm] FHR [bpm]
A4 fetal q [ml/min] B4 C4 50 200 50 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 time [min] time [min] time [min]
Figure 2.3: Simulation results for a standard uterine contraction of 60 s with an amplitude of 70 mmHg and for contraction variations. From top to bottom, signals in column A repre- sent: uterine pressure (put); mean arterial transmural blood pressure (ptm,a); arterial oxygen pressure (pO2,a); and FHR. In column B, signals represent: blood ow through the uterine intramural veins and uterine spiral arteries (qutv and quta, respectively); IVS blood volume (Vivs); tissue and cerebral oxygen pressure (pO2,tis and pO2,cer, respectively); and fetal tissue and cerebral blood ow (qtis and qcer, respectively). In column C, similar signals as in column A are shown for the standard contraction (light gray), for a contraction with an increased amplitude of 110 mmHg (dark gray), and for a contraction with an increased duration of 120 s (black). Signals are described brie y in the main text. the uterine arteries. Since IVS out ow is larger than IVS in ow, IVS blood volume drops (panel B2). When uterine pressure decreases, the uterine veins open again, causing an increase of venous out ow. IVS pressure decreases as well, causing an increase in arterial in ow. Finally, IVS blood volume is restored. During the contractions fetal oxygen levels drop (panel B3), the drop in the brain being less deep than that in the tissues. This di erence is caused by the redistribution of fetal blood ow from the tissues to the brain, since peripheral resistance increases due to central re ex regulation, and cerebral resistance decreases due to cerebral autoregulation (panel B4). As shown in column C, more severe contractions result in a larger reduction of oxygen pressure, a larger increase of blood pressure, and a larger deceleration of FHR.
25 Chapter 2
20 [mmHg] 15
2,a 20 pO 10 0 1 2 3 4 ns 50 Parer 20 s Itskovitz 20 s
[mmHg] Model 20 s 45 -20 Model 30 s tm,a p
0 1 2 3 4
150 [%] state steady from Variation pO2,a [mmHg] ptm,a [mmHg] FHR [bpm]
100 FHR [bpm]
50 0 1 2 3 4 time [min] A: Simulation results. B: Comparison with sheep data.
Figure 2.4: Results from simulations of uterine artery block. A) Model response to uterine artery occlusions of 20 (gray) and 30 s (black). From top to bottom: arterial oxygen pressure (pO2,a); transmural arterial blood pressure (ptm,a); and FHR. The rectangles in the bottom indicate the uterine artery occlusion times. B) Comparison of model results to experimental results from sheep studies [68, 117]. From left to right: relative maximum variations in arterial oxygen pressure (pO2,a), transmural arterial blood pressure (ptm,a), and FHR. N.B.: ‘ns’ indicates that uterine artery block does not result in a signicant variation with respect to the steady-state value.
Figure 2.4 shows the simulation results of uterine artery block of 20 and 30 s. From these signals the relative changes of arterial oxygen pressure, blood pressure and FHR were ob- tained and compared to relative changes as obtained from sheep experiments [68, 117]. In both sheep experiments uterine blood ow was blocked for 20 s. In the model, 20 s of uter- ine ow reduction caused qualitatively correct changes in oxygen pressure, blood pressure and FHR, although these changes were quantitatively reduced as compared to those obtained from the sheep experiments. A ow block of 30 s was required to obtain results more similar to sheep data.
26 Uterine blood ow reduction
2.4 Discussion
Mathematical model. In comparison to our previous model [161–163], we replaced the dy- namic one-ber model [11, 20], that enabled computation of the change of blood pressures and blood ows during a heart beat, by a two-state elastance model [65, 148] that gener- ates average blood ows and pressures. This simplication did reduce the number of model parameters, but did not a ect input for the regulation model: the baroreceptor only uses average blood pressure as input, and computed oxygen concentrations vary at a time scale that exceeds that of one cardiac cycle.
The central regulation submodel used in our previous model [161, 163] was based on an adult model [154], extended with the e ect of vagal nerve hypoxia. While the model could be used to simulate early, late and variable decelerations in FHR, critical review showed several shortcomings. Parameter estimation in the complex model was di cult because of lack of experimental data. Furthermore, model response in simulations of contraction-induced uterine and umbilical ow reductions was dominated by the response to vagal nerve hypoxia, and a reference contraction of 60 s with a pressure amplitude of 70 mmHg causing uterine ow reduction alone, would lead to an FHR deceleration of 15 bpm. This response was considered not representative for an uncompromised fetus.
In the current study, we drastically reduced the complexity of the central regulation model to reduce the number of input parameters and facilitate interpretation of the model results. The central regulation submodel was based on Wesseling [178], while still maintaining some aspects of Ursino [154]. The new model only contains the baro- and chemore ex and does not describe the response to vagal nerve and CNS hypoxia. Whereas literature data suggest a hyperbolic relation between arterial oxygen pressure and chemoreceptor discharge frequency [17, 90], we used a Gompertz relation (an asymmetrical S-curve) to prevent chemoreceptor output to go to innity at very low oxygen pressures. The baroreceptor response was also modeled through a Gompertz relation. The description of the central regulation, in which a erent baro- and chemoreceptor signals are combined into e erent vagal and sympathetic signals, was simplied as well by replacing the nonlinear transfer functions in the previous model by constant weighting factors. We also chose not to di erentiate between sympathetic e erent signals to the blood vessels and to the heart (α- and β-sympathetic pathways, re- spectively), because of lack of experimental data on these pathways in the fetus. This implies that it is impossible in the model to activate α- and β-sympathetic pathways separately. As shown in the results, these simplications did not limit the ability of the model to describe variation of FHR or clinically vital signals such as blood and oxygen pressure.
As in the previous model, uterine contractions are implemented through a transient increase of uterine pressure. However, we now model the e ect of the changes in uterine pressure on vessel volume and resistance in terms of vascular transmural pressure instead of external
27 Chapter 2 uterine pressure. This is physically more realistic, since it is the pressure di erence across the vessel wall that determines the cross sectional area of the vessel lumen, and thereby vessel volume and resistance. Also, compression of the uterine circulation leads to closure of the uterine veins rather than of the uterine artery, which is more realistic as well.
Results. In the scenario of contraction-induced uterine ow reduction, the FHR deceleration is delayed with respect to the contraction peak. This can be explained from the fact that during uterine ow reduction, oxygen in the IVS is still available to the fetus. Consequently it will take some time before fetal oxygen pressure, and accordingly FHR will drop (gure 2.3). Therefore these decelerations are referred to as ‘late’ decelerations. In our model the delay between the onset of the FHR deceleration and FHR nadir is about 40 s, which is in accordance with the guidelines of late decelerations, stating that the delay should be at least 30 s [100, 126]. The decelerations, however, are not symmetrical as is usually observed in the clinic [100, 126]. Presumably this is caused by the relative slow return of arterial oxygen pressure to baseline levels. The primary cardiovascular response is chemoreceptor-mediated. As a secondary response the mean arterial blood pressure will increase, thereby activating the baroreceptor. The steady-state values correspond with values found in literature as indicated in chapter 3.
If we compare predicted variations in FHR for the current and the previous model [163], we observe that for uterine ow reduction more realistic FHR decelerations of 3 bpm are ob- tained, even though the oxygen and blood pressure signals show the same characteristics. We think that this response is more realistic, since a standard contraction in an uncompro- mised full term fetus does not lead to fetal distress that is considered clinically signicant. Simulations of increased contraction amplitude (110 mmHg) or duration (120 s) showed that larger FHR deceleration depths (about 14 bpm and 21 bpm, respectively) can be obtained during severe contractions, see gure 2.3.
Due to the limited measurements that can be performed in a human fetus, sheep exper- iments from literature were simulated in order to test our model. Trends in variation of arterial oxygen pressure, blood pressure and FHR were similar to the trends obtained from sheep experiments. To obtain results quantitatively similar to sheep data, occlusion time had to be prolonged with 10 s (gure 2.4). The temporal variations in gure 2.4 show a delayed response with respect to experimental data [68, 117]. The drop in fetal oxygen levels could be accelerated by increasing fetal oxygen metabolism or decreasing IVS blood volume. This would also lead to a better correspondence of the results of the 20 s occlusion with the experimental data in gure 2.4. However, we did not perform such model adaptations since then values for these parameters would no longer be consistent with values found in litera- ture. Moreover, it is unclear whether the response of the sheep fetus would quantitatively match that of the human fetus described in our model.
28 Uterine blood ow reduction
Conclusion. A new CTG model was presented, which in comparison to our previous model was improved by reducing complexity of some submodels and by using a better physical basis for the description of other submodels. The model shows a more realistic FHR response during uterine ow reduction. Due to the reduced complexity and improved physical basis, the model is more suitable for use as a research and educational tool.
29 Chapter 2
30 Chapter 3
A mathematical model to simulate the cardiotocogram during labor Part B: Parameter estimation and simulation of variable decelerations
The contents of this chapter have been published in Journal of Biomechanics Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG and Bovendeerd PHM Available online: http://dx.doi.org/10.1016/j.jbiomech.2016.01.046 Chapter 3
Abstract
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 chapter 2 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 this chapter is to gain insight into the cascade of events from uterine contractions causing combined uterine ow reduction and umbilical cord compression, resulting in blood and oxygen pressure variations, which lead to changes in FHR via the baro- and chemore ex. 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 di cult due to limited clinical data.
32 Umbilical blood ow reduction
3.1 Introduction
In chapter 2, we gave an overview of a new cardiotocogram (CTG) simulation model. Com- pared to our previous model [161–163] the complexity of some submodels was reduced and the physical basis for the description of other submodels was enhanced. It was shown that the model was able to simulate realistic FHR decrease in response to uterine ow reduction as induced by uterine contractions.
In this chapter the model is used to gain insight into the mechanism of variable FHR decel- erations which are caused by umbilical cord compressions, that mostly occur during uterine contractions during labor [57]. Variable decelerations are dened as an abrupt FHR decrease of more than 15 bpm, with a maximum time delay of 30 s between onset of the deceleration and FHR nadir, and a duration of less than 2 min [100, 126]. In addition, the e ect of varying amplitude and duration of uterine contractions on the CTG is investigated. We also compare model output with data of sheep experiments in which the umbilical cord was temporarily blocked by use of an occluder [69]. Although model complexity is reduced, parameter esti- mation is di cult due to the limited clinical data. Therefore, we will extensively describe and discuss estimation of these parameter values.
The new model is intended to be used to gain insight into the regulation of FHR during labor and delivery. For use as a clinical decision support tool, the model should be made patient- specic. This is a challenging task in view of the limited availability of clinical data and the limited time span for model analysis during labor. Use as an educational tool would be a more realistic next step.
3.2 Material and methods
The model is extensively described in chapter 2. In this chapter we extend the model in order to simulate combined uterine blood ow reduction and umbilical cord compression induced by contractions. Besides, an overview of model parameter estimation is given.
3.2.1 Model extension
Since during cord compression the umbilical vein and arteries are exposed to large changes in transmural pressure, the corresponding resistances, Rumv and Ruma respectively, are modeled as function of transmural pressure ptm, as described in eq. 2.6. Parameter values are chosen such that rst the umbilical vein will be closed, followed by the umbilical arteries at higher external umbilical pressures, see table 3.1.
33 Chapter 3
Table 3.1: Umbilical vein and artery resistance parameters.
Parameter Value Unit R0,umv 2.05 mmHg·s/ml p0,umv -17 mmHg p1,umv 10 mmHg R0,uma 2.34 mmHg·s/ml p0,uma -27 mmHg p1,uma 16 mmHg
The transmural pressure of the umbilical vein ptm,umv and umbilical arteries ptm,uma is deter- mined as the mean absolute pressure of the two neighboring blood compartments minus the external pressure: pvilli+pven ptm,umv = 2 –(put + pum) pvilli+part (3.1) ptm,uma = 2 –(put + pum) where the external pressure consists of the uterine pressure put, that acts on the whole fetus, plus an extra pressure pum, caused by umbilical cord compression.
The degree of cord compression depends on the contraction intensity, fetal position, stage of labor, etc. The e ect of these random variables is modeled through a weighting factor wum [-], relating put to the external pressure on the umbilical cord pum:
pum = wum(put – prest), wum ≥ 0 (3.2) with prest uterine resting pressure.
3.2.2 Parameter estimation
Due to the limited available human fetal data, parameter estimation is di cult. For this reason parameter estimation is extensively described. Fetal cardiovascular parameters were obtained from literature and set to values of a 3.5 kg term human fetus. If human data were not available, fetal sheep data were used to derive the parameters. Some parameter values were set to obtain the desired model responses. Parameter choices are brie y explained below, all parameter values can be found in table 2.1 to 2.3.
3.2.2.1 Feto-maternal hemodynamics
Fetal combined ventricular output qCO was aimed at 450 ml/min/kg [87, 115, 133, 168], ejec- tion fraction EF at 0.67 [137], and heart rate at 135 bpm (table 2.1). Mean arterial transmu- ral blood pressure ptm,a and mean transmural venous blood pressure ptm,v were set to 45 mmHg [69, 147, 150, 153] and 3 mmHg [74, 133, 150] respectively. Fetal blood volume was reported to be about 75 ml/kg [96, 156, 182], which is about two third of total feto-placental
34 Umbilical blood ow reduction blood volume [182]. Therefore, the latter volume was set to 110 ml/kg, which is in accordance with Schwarz [139]. Total microcirculation blood volume was computed from Guyton et al. [62] and set to 8% of fetal body blood volume, which was distributed over cerebral (14%) [26, 64] and tissue microcirculation (86%). Average cardiac cavity volume follows from qCO, EF and FHR and equals 11.7 ml. The remainder of the body blood volume was distributed over the systemic fetal arteries (1/6) and veins (5/6). Based on geometric considerations [43, 97, 172], blood volume of the umbilical circulation was divided between the placental villi (65%), umbilical arteries (10%) and vein (25%). Since for the umbilical arteries and vein no separate compartments were included in the model, these blood volumes were added to the systemic arteries and veins respectively.
Maternal cardiovascular parameters were based on pregnancy-related changes as described in literature (table 2.1). Target values for ptm,a and ptm,v were set to 80 mmHg [29, 59, 84] and 5 mmHg [109] respectively. During pregnancy, heart rate HR increases up to a target value of 80 bpm [29, 59, 84, 132], while the cardiac output [1, 29, 84, 98] and blood volume [1, 98] both increase by 40%. In our model cardiac output and total blood volume were set to 7 l/min and 7 l, respectively. EF was set to a value of 0.67 [29, 59, 84]. Intervillous space (IVS) volume was chosen to be 175 ml [15, 105, 123], while the volume of the tissue microcirculation was chosen to be 8% of total maternal blood volume [62]. Average left ventricular blood volume follows from qCO, EF and HR and equals 87.5 ml. Like in the fetus, the remainder of the blood volume was distributed over systemic arteries (1/6) and veins (5/6). Parameters p1 and Vmax, dening the relation between IVS volume Vivs and transmural blood pressure as described by eq. 2.3, were determined by assuming that p0 = pref , where pref is the reference transmural IVS blood pressure in steady state. Then it follows that:
Vmax = 2 · Vivs(pref )
Finally p1 was determined by assuming that IVS compliance is maximal at pref , meaning that:
Vmax p1 = π · Civs,max
For Civs,max we chose a similar value as for the placental villi (2.4 ml/mmHg).
For both fetus and mother, target values of blood ows and pressures were used to estimate resistances and compliances. We chose umbilical cord ow to be 25% of qCO, in agreement with literature data that range from 15 to 34% of qCO [3, 87, 97, 115, 133]. The fraction of cardiac output going to the fetal brain was estimated by use of a fractional brain mass of 14% [26, 64] and by the estimation that oxygen metabolism per gram tissue, and thus also blood ow per gram tissue, should be twice as high in brain tissue compared to peripheral tissues. This means that 21% of total cardiac output goes to the brain and 54% to the fetal tissues, which is in accordance with Rudolph [133]. In the mother about 10% of the cardiac
35 Chapter 3 output is directed to the uterine circulation [55, 115, 171], of which 70-90% is directed to the IVS [115, 131, 174]. Hence we chose 9% of qCO to be directed to the IVS, while 91% is directed to the other maternal tissues.
For the fetal and maternal tissues and fetal brain, 95% of the total resistance was assigned to the microcirculation arteries, while 5% was assigned to the microcirculation veins. In the umbilical circulation, the arterial resistance fraction was set to 60%, to obtain a blood pressure of about 20 mmHg in the placental villi [66]. In the uterine circulation this fraction was set to 80%, in order to obtain an IVS pressure of about 60-70 mmHg below mean arterial pressure [124]. Except for the placental villi and IVS, compliances were estimated assuming that 70% of the volume in the reference state contributes to the unstressed volume. For the cerebral and tissue microcirculation, unstressed volume fraction was set to 90%. The compliance in the placental villi was set to 2.4 ml/mmHg [12, 66].
Initial values of Ved and Vee were calculated from target values of qCO, EF and FHR. Vmin,0 was chosen to be equal to Vee, while Vmax,0 was set to 0. Finally, Emax could be calculated as the slope of a line through the data points (Vee, ptm,a) and (Vmax,0, 0), while Emin was calculated as the slope of a line through (Ved, ptm,v) and (Vmin,0, 0).
3.2.2.2 Oxygen distribution
The oxygen di usion coe cient in the placenta was set to 0.082 ml O2/(s·mmHg) (table 2.2) such that in steady state a fetal umbilical arterial oxygen pressure of 18.5 mmHg was obtained [2, 97, 140]. Fetal oxygen metabolism was set to be 8 ml O2/(min·kg) [2, 19] and divided over cerebral metabolism (28%) and tissue metabolism (72%). We chose a threshold value of 5 mmHg for cerebral oxygen metabolism (pO2,th,cer,f ) [77] and 10 mmHg for the peripheral tissues (pO2,th,tis,f ), where the latter value corresponds to about 50% of the steady- state oxygen concentration, based on Sá Couto [135].
Maternal oxygen consumption was set to 600 ml O2/min. The oxygen pressure in the air was set to 160 mmHg, while target maternal arterial oxygen pressure was set to 98 mmHg. Combination of this oxygen pressure di erence and total feto-maternal oxygen metabolism yielded a pulmonary oxygen di usion coe cient of 0.169 ml O2/(s·mmHg). Since in the current study maternal oxygenation was kept constant, an oxygen metabolism threshold was irrelevant for the maternal model.
Fetal and maternal parameter values dening the relation between cO2 and pO2 were chosen as described by Sá Couto [135].
36 Umbilical blood ow reduction
3.2.2.3 Regulation
Cerebral autoregulation For the cerebral autoregulation the value of γ, indicating how well the cerebral resistance can adapt to variations in arterial oxygen content, was estimated by use of Peeters [120] and set to a value of 0.5. The cerebral resistance can maximally decrease by 50%, which means that cerebral blood ow can increase with a factor of 2. Finally, the time constant τRcera was chosen to be 10 s according to Ursino [154].
Central regulation For the baroreceptor and chemoreceptor outputs, as described in eq. 2.21, the parameters η1 and η2 follow from the condition that r(y = yref ) = 0 and from the (desired) slope at the reference point (y = yref ): –rmin η1 = ln( ) (3.3) rmax – rmin ∗ dr (y) η = η · η e 1 (rmax – rmin) (3.4) dy 2 1 y=yref Baroreceptor parameters were obtained by scaling the relation as described by Ursino [154] to fetal values and normalizing it to a range between -1 and 1 (table 2.3). Baroreceptor sensitivity in the fetus is reduced by a factor two as compared to the adult [38]. Parameter values of the Gompertz function were chosen such that the relation between baroreceptor input ptm,a and output rb closely resembled the scaled response of Ursino. Parameter values for the chemoreceptor response were chosen such that a reference contraction of 60 s with a pressure amplitude of 70 mmHg would lead to a maximum FHR deceleration of about 3 bpm for uterine ow reduction alone and about 50 bpm for combined uterine ow reduction and umbilical cord compression. The values of the e ector gains k and e erent weighting factors w were also chosen to obtain the desired e ects in FHR (table 2.3). For all e ectors time delays D and low pass lter time constants τ were obtained from Ursino [154] (table 2.3).
3.2.2.4 Uterine and umbilical blood vessel compressions
In the relation between transmural blood pressure and vessel resistance, as described in eq. 2.6, R0 was chosen such that R(pth) = Rref , with pth the transmural pressure below which the blood vessel resistance starts to increase and Rref the reference resistance in steady state. For the uterine vein p0 and p1 were chosen such that a contraction with a uterine pressure amplitude of 60 mmHg and a duration of 60 s would result in a 60% blood ow reduction through the uterine artery [70] (table 2.1). In our model, the uterine arteries are not subjected to increasing uterine pressure. Parameter settings for the umbilical cord resistances were found by simulating the sheep experiments in which initial fetal blood volume changes were
37 Chapter 3 measured during umbilical cord compressions with increasing external pressures [35]. The umbilical vein is totally closed if the external pressure exceeds 40 mmHg, while the umbilical arteries are compressed over a pressure range of 40 to 90 mmHg (see table 3.1).
3.2.3 Model simulations
We simulated combined uterine ow reduction and umbilical cord compression in term preg- nancy by setting wum = 1 in eq. 3.2. A reference contraction with a duration (Tcon) of 60 s and a pressure amplitude (pcon) of 70 mmHg with respect to the reference pressure (prest) of 15 mmHg was used. To illustrate the e ect of regulation, simulations with and without central regulation and autoregulation were performed. In addition, the e ect of contraction intensity was investigated by changing contraction amplitude from 70 mmHg to 30 and 110 mmHg respectively, or contraction duration from 60 s to 30 and 120 s respectively.
The model was evaluated by use of sheep experiments in which umbilical cord blood ow was temporarily reduced by use of an occluder [69]. The sheep experiments were simulated by linearly increasing the external pressure (pum) on the cord over 5 s to a maximum level, which was maintained for 35 s, and reduced to zero over another 5 s, while keeping put at the resting level. In order to obtain umbilical ow reductions of 25%, 50%, 75% or 100%, as presented by Itskovitz, maximum external pressure was set to a value of 25, 33, 41, or 90 mmHg, respectively. Umbilical vein and artery resistance, Rumv and Ruma respectively, were calculated by use of eq. 2.6.
3.3 Results
Figure 3.1 shows the scenario of combined uterine ow reduction and umbilical cord com- pression induced by a reference contraction of 60 s with a pressure amplitude of 70 mmHg. Initial values for this scenario are the same as for the scenario of uterine ow reduction alone, as described in chapter 2. In addition, gure 3.1 shows that umbilical blood ow is about 394 ml/min (panel B1) and that villous volume is 83 ml (panel B2). Note that blood pressures described in this section represent transmural blood pressures.
We rst consider the simulation without regulation, indicated by the gray lines. During cord compression the external umbilical pressure rises (panel A1) and fetal blood pressure (panel A2) and arterial oxygen pressure (panel A3) decrease. Without regulation, FHR will not be a ected (panel A4). If we now look into more detail (column B), we observe that rst umbilical venous ow reduces to near zero (panel B1) and that the placental villi are lled via the umbilical arteries (panel B2). Once the umbilical arteries are compressed as well, villous volume remains more or less constant. This blood volume shift from fetus to placenta
38 Umbilical blood ow reduction
800 0.8 100
0.4 400 [mmHg] [ml/min] um um
p q 0 0 0 signals afferent
0 1 2 3 0 1 2 3 afferent CNS signals 0 1 2 3 75
0.4
[ml] 120 55 [mmHg] villi V
tm,a 0 p
35 80 signals efferent
0 1 2 3 0 1 2 3 efferent CNS signals 0 1 2 3 20 20 ZRtisa ZVven,0 15 15 ZEmax auto [mmHg] [mmHg]
10 2 10 2,a pO pO 5 5 0 1 2 3 0 1 2 3 1000 ZTv Z 150 Ts ZTv-ZTs
100 FHR [bpm] fetal q [ml/min] 50 200 0 1 2 3 0 1 2 3 time [min]
Figure 3.1: Simulation results for a standard uterine contraction of 60 s with an amplitude of 70 mmHg. Results for the simulation with regulation are indicated in black, results for the simulation without regulation are indicated in gray. From top to bottom signals in column A represent external umbilical pressure (pum); mean arterial transmural blood pressure (ptm,a); arterial oxygen pressure (pO2,a); and FHR. In column B, signals represent blood ow through the umbilical vein and arteries (qumv and quma, respectively); villous blood volume (Vvilli); tissue and cerebral oxygen pressure (pO2,tis and pO2,cer, respectively); and fetal tissue and cerebral blood ow (qtis and qcer, respectively). Dimensionless signals in column C represent baro- and chemoreceptor outputs (rb and rc, respectively); sympathetic and vagal e erent signals (es and ev, respectively); relative e ector changes z for peripheral vascular resistance (Rtisa), venous unstressed volume (Vven,0), and cardiac contractility (Emax), while the ‘auto’ signal represents the relative change of the autoregulated cerebral resistance (Rcera); and
nally relative vagally- and sympathetically-induced heart period changes (zTv and zTs , re-
spectively), and the di erence between both (zTv – zTs ). (Note the change in axes compared to gure 2.3.)
39 Chapter 3 explains the drop in blood pressure (panel A2) that in turn causes a drop of blood ow through the fetal tissues and brain (panel B4). The reduction of umbilical blood ow decreases arterial, cerebral, and tissue oxygen levels (panel A3 and B3). Initially, no di erence is observed between the cerebral and tissue oxygen pressures. Later, cerebral oxygen pressure drops deeper than tissue oxygen pressure, which is due to the lower oxygen metabolism threshold value in the brain, as described in eq. 2.17. At the end of the occlusion umbilical cord vessels open again and all values will return back to normal levels. The regulation signals, as shown in column C, do not change if regulation is switched o .
In the situation with cardiovascular regulation, indicated by the black lines, the initial decrease in arterial blood pressure results in a decreased baroreceptor output (panel C1) that in turn causes an increase of the sympathetic, and decrease of the vagal e erent signal. This change is modied by the chemoreceptor-mediated increase of both e erent signals. The resulting e erent signals (panel C2) cause an initial drop of heart period (panel C4) and consequently an initial increase in FHR (panel A4). The ongoing decrease in oxygen pressure further increases chemoreceptor output (panel C1), stimulating both e erent signals (panel C2). The increased sympathetic response results in an increase of peripheral vascular resistance and cardiac contractility, while venous unstressed volume is reduced (panel C3). This leads to an increase of arterial blood pressure (panel A2) and baroreceptor output (panel C1). The weighted average of the chemoreceptor and baroreceptor outputs now results in a similar time course of the vagal and sympathetic e erent signal (panel C2). Since vagal feedback on heart period is twice as strong as sympathetic feedback, FHR responds with a deceleration (panel A4). Comparison of panels A4 and C1 shows that the timing of the minimum FHR at about 1.3 min is dominated by the chemoreceptor response, while the timing of the second dip at 1.6 min is caused by the baroreceptor response. Finally, cerebral autoregulation decreases cerebral vascular resistance (panel C3), thereby increasing cerebral blood ow (panel B4). Together with ow reduction in the tissues caused by the increased peripheral resistance, this results in ow redistribution in favor of the fetal brain. As a consequence, the drop in cerebral oxygen pressure is reduced compared to the unregulated case (panel B3).
In gure 3.2 the e ect of variation in contraction amplitude and duration is shown. In gen- eral an increased or decreased contraction duration has a similar but opposite e ect on pressures and FHR, while variation of amplitude has a nonlinear e ect. When contraction amplitude is increased to 110 mmHg (column A), only minor changes are seen compared to the reference contraction. When contraction amplitude is reduced to 30 mmHg (column B), umbilical vessels do not become fully blocked, hence less blood is stored in the villi, and thus the drop of arterial blood pressure is reduced. The drop of oxygen pressure is reduced since oxygen supply through venous umbilical ow continues. FHR remains rather constant, because of the reduced baroreceptor and chemoreceptor response. If contraction duration is increased to 120 s (column C), the drop in arterial blood pressure is similar to that during
40 Umbilical blood ow reduction
100 [mmHg] um
p A1 B1 C1 D1 0 75
55 [mmHg]
tm,a B2 C2 p A2 D2 35 20 pO 15 2,a pO2,cer [mmHg] 10 2 A3 B3 C3 D3 pO 5
150
100
FHR [bpm]FHR A4 B4 C4 D4 50 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 time [min] time [min] time [min] time [min]
Figure 3.2: Simulation results for uterine contractions with varying contraction amplitude and duration. With respect to the reference contraction with a duration of 60 s and an amplitude of 70 mmHg, indicated in light gray, contraction amplitude was set to 110 mmHg (column A) or 30 mmHg (column B), or contraction duration was set to 120 s (column C), or 30 s (column D). The signals shown in each column are similar to the signals shown in column A of gure 3.1.
the reference contraction. The increased FHR deceleration is mainly caused by the increased chemoreceptor feedback, in response to the lower oxygen levels. Finally, if contraction du- ration is decreased to 30 s, less blood is stored in the villi, and the initial arterial pressure drop is reduced. Arterial oxygen pressure drops less deep, due to the shortened duration of umbilical cord compression. FHR drops less deep because of reduced baroreceptor and chemoreceptor feedback.
Figure 3.3 shows the relative variations in arterial oxygen pressure, blood pressure and FHR during di erent degrees of umbilical cord block as obtained from sheep data [69] and from model simulations. Quantitatively, the simulation results agree well with the experimental data.
41 Chapter 3
60
40
20 ns ns ns 25% 50% 75% 100% 25% 50% 75% 100% 0 25% 50% 75% 100% ns Itskovitz -20 Model
-40
Variation from steady state [%] state steady from Variation -60
-80
pO2,a [mmHg] ptm,a [mmHg] FHR [bpm]
Figure 3.3: Results from simulations of umbilical cord occlusion, in comparison to exper- imental results from sheep studies [69]. From left to right: relative variations in arterial oxygen pressure (pO2,a), transmural arterial blood pressure (ptm,a), and FHR. N.B.: ‘ns’ indi- cates that the relative ow reduction does not result in a signicant variation with respect to the steady-state value.
3.4 Discussion
Parameter estimation. Parameter estimations were described in section 3.2.2. The most important choices will be discussed here.
It has been reported that the baroreceptor sensitivity in the fetus is two to eight times lower than that in the adult [38]. In the model, we used a two-fold decrease with respect to settings for the adult, used by Ursino [154]. With this setting, we observed an initial increase of FHR (clinically referred to as ‘shoulders’) when simulating variable decelerations, which disappeared when further lowering baroreceptor sensitivity.
Clinically, most contractions that a ect uterine blood ow alone, lead to reductions in FHR (‘late decelerations’) that do barely exceed the noise level of the FHR signal in a healthy fetus. In the model, we tuned parameter settings such that simulation of our reference contraction with uterine ow reduction alone yields an FHR deceleration of about 3 bpm. Due to the variable character of the FHR decelerations caused by combined uterine and umbilical ow reduction, there is no typical response for this ‘variable deceleration’ scenario. We chose a target value of 50 bpm during a reference contraction. Deeper decelerations can be reached
42 Umbilical blood ow reduction if contraction duration or amplitude increases (gure 3.2).
Since oxygen pressure dropped by 1.5 mmHg in the former scenario, and by 6 mmHg in the latter scenario, chemoreceptor output had to increase steeply over a small arterial oxygen pressure interval. Finally, to obtain the desired results, the e ector gains k were multiplied by a factor 6 with respect to Wesseling [178]. This adaptation can partly be explained from the fact that in our regulation model the chemoreceptor was added and a larger reduction of FHR was desired. Simulation of other scenarios is needed to test the validity of these parameter settings. However, the clinical or experimental data to validate the model is limited.
Results. Simulation results show that oxygen levels drop more quickly during combined uterine and umbilical ow reduction (gure 3.1) compared to uterine ow reduction alone (gure 2.3). This can be explained by the fact that during cord compression the fetus has no access to the IVS oxygen bu er, since oxygen cannot be transported from the placental villi into the fetus. Until the oxygen threshold is reached below which metabolic rate decreases, oxygen content drops linearly in time. Since the oxygen pressures reached are still in the linear range of the saturation curve, oxygen pressure also drops linearly. We observed that FHR increases before onset of the decelerations. This increase is clinically referred to as ‘shoulder’ [50, 109, 115]. In the clinic these shoulders are often also observed at the end of the deceleration, however this e ect was not obtained in the model, presumably due to the dominant sympathetically-induced blood pressure increase in our model. During a standard contraction, the FHR decreases from baseline to nadir in about 26 s, which is in accordance with the clinical guidelines dening an abrupt decrease in FHR to occur within 30 s [100, 126]. Furthermore, FHR reaches baseline levels again within 2 minutes. This is in accordance with literature [100, 126], although the nal part of FHR return seems somewhat slow.
Simulation results of contraction variations (gure 3.2) show that oxygen pressure reduction depends on the duration and amplitude of the contraction, which will both increase during progression of labor. The time delay between onset and nadir of the FHR deceleration in- creases with increasing contraction amplitude or duration. The wide variation in the shapes of the FHR decelerations corresponds well with the clinical observation that umbilical cord occlusions have a variable character and are therefore called ‘variable decelerations’. Clini- cally, these variations are also caused by variation in the position of the umbilical cord within the uterus. In the model this could be simulated by variation of the weighting factor wum in eq. 3.2. However, since random variation of this factor would complicate comparison of the results in the various scenarios, we kept this factor constant.
If we compare FHR signals obtained with the current model with the results of our previous model [161], we see that FHR decelerations are now preceded by a shoulder, which was not observed in the previous model. This shoulder can partly be attributed to increased lling of the villi, due to the fact that the umbilical arteries remain patent, and partly to the stronger
43 Chapter 3 baroreceptor response in the current model.
The model generates estimates of many physiological signals, while in clinical practice only FHR can be measured continuously. To gain more insight into the complex pathway from uterine contractions to FHR changes, we also show signals that cannot be measured in the clinic. Since these intermediate signals cannot be compared to human data, we used sheep data on oxygen pressure and blood pressure to evaluate the model, noting that quantitative comparison with sheep data is di cult due to the di erences between the ovine and human fetus. For example, in fetal lambs about 40-45% of the cardiac output is directed to the umbilical circulation [73, 115, 133], while in the human fetus this is only 25%. Despite the di erences between human and sheep fetuses, for the simulations of umbilical cord blocking, results were quantitatively in accordance with sheep experiments (gure 3.3).
Limitations. Although we reduced the number of model parameters to be estimated, it is still di cult to arrive at a unique set of model parameter settings from the limited experimental data presented in literature. Consequently, there may be di erent combinations of parameter choices which will lead to similar results. In future, a sensitivity analysis should be performed in order to investigate which parameters dominate model response and should be determined very precisely and for which parameters a more general value can be used.
The model lacks the ability to describe FHR variability, which is an important indicator of fetal distress in clinical practice. Addition of this variability would further improve applicability of the model for training purposes and clinical diagnosis and decision making.
The current model is intended to describe CTG signals during short-term hypoxia and to provide additional information on fetal oxygen status. To be able to describe the e ects caused by stronger and longer contractions, humoral feedback has to be added to the model [109], and the shift of the fetal oxygen dissociation curve due to the changes in pH (Bohr e ect) should be taken into account. Furthermore, cardiac metabolism and the e ect of myocard hypoxia on FHR might be included in the model.
In the hemodynamic model of the fetus, the fetal heart is represented by a combined ven- tricle. To describe improved oxygen supply to the brain due to preferential blood ows, the combined ventricle might be replaced by a separate left and right ventricle.
Conclusion. With the improved model we were able to generate realistic variable deceler- ations for the scenario of combined uterine and umbilical ow reduction. Parameter esti- mation of the simplied model remains di cult due to the limited availability of clinical and experimental data.
44 Chapter 4
Simulation of fetal heart rate variability with a mathematical model
The contents of this chapter are under review for Medical Engineering & Physics Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, and Bovendeerd PHM Chapter 4
Abstract
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 e erent 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 clini- cally observed peak near 0.1 Hz was only obtained by applying white noise to the di erent sources of variability. Similar power spectra were found when peripheral vascular resistance or baroreceptor output was used as source of variability. Sympathetic control predominantly in uenced the low frequency power, while vagal control in uenced both low and high fre- quency 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.
46 Fetal heart rate variability
4.1 Introduction
The cardiotocogram (CTG) is a commonly used technique to monitor fetal well-being during labor and delivery. The CTG represents the combined registration of fetal heart rate (FHR) and uterine contractions. In clinical practice, fetal condition is based on evaluation of di er- ent characteristics of the FHR signal during rest and in response to uterine contractions, such as baseline level, accelerations, decelerations, and baseline variability. The relation between uterine contractions and changes in FHR is very complex. Therefore, previously we developed a mathematical CTG simulation model, describing hemodynamics, oxygenation, and cardio- vascular regulation [81, 82] (chapter 2 and 3). We successfully used the model to investigate the e ect of uterine vein and/or umbilical cord occlusions, initiated by uterine contractions, on fetal hemodynamic and oxygen pressures, which via the baro- and chemore ex lead to changes in FHR. However, the model lacked a description of fetal heart rate variability (FHRV), that is considered to be an important indicator of fetal well-being [181]. FHRV is described as uctuations in the FHR baseline, which are irregular in amplitude and frequency [115, 152]. The presence of FHRV is highly associated with the absence of signicant metabolic acidemia, even if the FHR tracing shows decelerations [116]. Decreased FHRV is related to lower Apgar scores and fetal acidosis [118]. Furthermore, loss of FHRV was found to be the most consis- tent FHR characteristic preceding antepartum fetal death, despite of a usually normal FHR baseline level [128].
In the autonomic control of heart rate (HR), the medulla oblongata of the brain stem, which is part of the central nervous system (CNS), plays an important role [88]. It receives input from baroreceptors, chemoreceptors and respiratory stretch receptors as well as from the hypothalamus and higher brain centers, and a ects HR via the sympathetic and parasym- pathetic nerve system [88]. Sympathetic activation increases HR, while parasympathetic activation decreases HR. In the adult, di erent frequency bands can be dened. Very low frequencies (up to 0.04 Hz) are supposed to originate from thermoregulation and humoral systems, and high frequency variations (0.15 to 0.4 Hz) are related to respiration [146]. Low frequency variations (0.04 to 0.15 Hz) are in uenced by cardiac sympathetic and parasympa- thetic nerve activity [146], however, no consensus is reached about the relative contribution of these two pathways [149]. Many questions about the source and interpretation of heart rate variability (HRV) remain, and the underlying physiological mechanisms are not completely known [106]. Autonomic control of heart rate in the fetus is even less well understood due to changes in baroreceptor sensitivity [38], cardiovascular sensitivity to neurotransmitters [13], and relative strength of the parasympathetic nervous system with respect to the sympathetic nervous system [13, 112] during fetal life.
Since FHRV is an important indicator of fetal distress, aim of this study is to add FHRV to the CTG simulation model to enhance the realism of the model-generated CTG tracings.
47 Chapter 4
In order to shed more light on the possible sources of FHRV, we investigate the e ect of three sources of variability as described by Van Roon et al. [169, 170] and Wesseling et al. [178]: autoregulation of the peripheral blood vessels, in uence of higher brain centers on the processing of the baroreceptor output in the nucleus tractus solitarius of the medulla oblongata, and the in uence of other a erent systems like the heart, lungs and muscles, on the vagal center [169, 170, 178]. The enhanced model would be more suitable as an educational tool, both as stand-alone screen-based training of CTG evaluation, and as an intelligent addition to manikins used in team-training, in order to have them automatically respond to the interventions performed by the trainees.
The three sources of variability were implemented in a similar fashion as described by Wes- seling et al. [178] by applying a noise source on the peripheral resistance, baroreceptor output and e erent vagal signal. We focus on a normal full term fetus and simulate FHR tracings before labor and during uterine contractions resulting in umbilical cord compression. The simulated FHR tracings are assessed by use of spectral analysis and on FHR bandwidth (BW), dened as the di erence between the highest and lowest cardiac frequency in the FHR signal. Spectral analysis gives a quantitative representation of FHRV, and is often used in literature [166]. FHR BW is commonly assessed by visual inspection in the clinic.
4.2 Material and methods 4.2.1 Mathematical model
FHRV is added to our mathematical CTG simulation model, that describes feto-maternal hemodynamics, oxygen distribution and fetal regulation [81, 82] (chapter 2 and 3).
In gure 4.1 a simplied schematic overview of the CTG simulation model is shown. A more elaborate description can be found in [81] (chapter 2). The maternal circulation contains a heart (left ventricle) from which blood ows into the arteries. From here blood ows into the intervillous space (IVS), which is modeled explicitly, and into the remainder of the tissues, which are lumped together. Blood ows back into the heart via the veins. In the fetus the heart is modeled as a combined ventricle, the umbilical and cerebral circulation are modeled explicitly, and the remainder is lumped into the tissues. Oxygenation in the mother takes place in the veins, since the pulmonary circulation is not explicitly modeled. Oxygen is con- sumed in the maternal tissues and di uses to the fetus in the IVS of the placenta. In the fetus, oxygen consumption takes place in the brain and tissues. During hypoxia, cerebral artery resistance Rcera is reduced via autoregulation in order to increase oxygen transport to the brain. Uterine contractions are modeled through an increase of uterine pressure put, acting on the IVS compartment and on all fetal compartments. Additionally, the external pressure on the umbilical cord pum increases during cord compression. These pressure vari-
48 Fetal heart rate variability
Figure 4.1: Schematic overview of the CTG simulation model. In the mother, blood ows from the heart into the arteries, via the tissues and intervillous space (IVS), into the veins, and back to the heart. In the fetus, the umbilical cord and brain circulation are modeled explicitly. Oxygen ow is indicated with dashed arrows. The IVS compartment and all fe- tal compartments are exposed to the uterine pressure put. Furthermore, during umbilical cord occlusion an additional external pressure pum acts on the umbilical cord, resulting in changes in fetal oxygenation and blood pressure. Via autoregulation, cerebral resistance Rcera is decreased during hypoxia. Changes in mean arterial transmural blood pressure ptm,a and arterial oxygen pressure pO2,a, result in changes of normalized baro- and chemorecep- tor output, rb and rc, respectively. Via weighting factors, in the nervous system (NS), these outputs are combined into normalized e erent vagal and sympathetic signals, ev and es, respectively, nally resulting in variations of the four cardiovascular e ectors (heart period T, cardiac contractility Emax, venous unstressed volume Vven,0, and peripheral resistance Rtisa). These e ector variations will again induce changes in the hemodynamic and oxygena- tion submodel. The three sources of variability are indicated by dashed circles. A detailed description is given in the main text. ations result in changes of the resistances of the IVS vein and umbilical blood vessels, causing variations in fetal mean arterial transmural blood pressure ptm,a and arterial oxygen pressure pO2,a. These changes are input for the fetal central regulation model. Via the baro- and chemoreceptor these variations are translated into a normalized baro- and chemoreceptor output, rb and rc, respectively. Baroreceptor output increases with increasing blood pres-
49 Chapter 4 sure, while chemoreceptor output increases with decreasing oxygen pressure. Via weighting factors these baro- and chemoreceptor outputs are combined into normalized e erent vagal and sympathetic signals, ev and es, respectively. Baro- and chemoreceptor activation both have a stimulating e ect on the vagal nervous system. The sympathetic nervous system is stimulated by the chemoreceptor, but inhibited via the baroreceptor (indicated with the minus sign). Stimulation of the vagal pathway leads to increase of heart period T, while stim- ulation of the sympathetic pathway will decrease T and venous unstressed volume Vven,0, but increase cardiac contractility Emax and peripheral artery resistance Rtisa. The changed e ectors are input for the cardiovascular and oxygen model.
For the purpose of the present study, we modied the model [81, 82] (chapter 2 and 3) by removing the baroreceptor low pass lter. We will illustrate the need and the consequences of this modication in the results section.
4.2.2 Model extension with FHRV
Following Van Roon et al. [170] and Wesseling et al. [178], temporal variations are applied to either the peripheral vascular arterial resistance Rtisa, to the baroreceptor output rb, or to the e erent vagal signal ev, see gure 4.1. We test the model by using either 1/f noise or white noise as temporal variations. We used 1/f noise because it is considered physiologically realistic [178]. White noise is used to better investigate the transfer function of the system. The noise signal N(t) [-] has a mean of 0 and a standard deviation of 1 and is described according to Van Roon et al. [169]:
n ∑ A · sin(2πfkt + φk) ( k=1 A = 1 white noise N(t) = , 1 (4.1) s n A = √ 1/f noise 1 2 fk 2 ∑ A k=1
fmax with fk = k · ∆f and ∆f = n
Here, fmax [Hz] represents the maximum frequency taken into account and n the number of harmonics, which in our model is set to 2 Hz and 2000 harmonics, respectively. The phase shift φk is di erent for each frequency fk, and has a uniformly distributed random value between 0 and 2π.
50 Fetal heart rate variability
The three sources of variability are obtained by superimposing noise on the corresponding e ector or output signal, resulting in new values for the e ector Rtisa,N or signal rb,N and ev,N:
Rtisa,N(t) = Rtisa(t) + mRtisa · N(t) · Rtisa,0
rb,N(t) = rb(t) + mrb · N(t) (4.2)
ev,N(t) = ev(t) + mev · N(t) where m [-] is a multiplication factor dening the standard deviation of the changes applied to each of the sources of variability and Rtisa,0 [mmHg] is the reference peripheral resistance. For each combination of noise type and source, the value of m was chosen such to obtain an FHR BW (dened as 4 times standard deviation) of 15 ± 1 bpm in steady state, which is in the normal range for a healthy full term fetus, while setting m of the other sources to 0.
4.2.3 Spectral analysis
Simulated FHR signals with a length of 30 min are sampled with a frequency of 4 Hz, allowing reliable spectral information for frequencies up to 2 Hz, according to the Nyquist criterion. The FHR tracings are converted into heart period tracings, representing the R-R intervals in ms. Spectral analysis is performed by use of short-time Fourier transformation (STFT), as described by Peters et al. [121, 122]. Similar to Van Laar et al. [165, 167], the STFT is performed using a moving window with a width of 64 s, providing a spectrum every 0.25 s. For comparison with Van Laar et al. [165, 167], the total frequency band is chosen to range from 0.04 to 1.5 Hz, the low frequency band (LF) from 0.04 to 0.15 Hz, and the high frequency band (HF) from 0.4 to 1.5 Hz. The absolute spectral power is calculated in each of these bands, whereafter normalized powers (LFn and HFn) are computed by dividing LF and HF power by total power.
4.2.4 Model simulations
We simulate FHR variability for a full term fetus of 3.5 kg. Parameter settings are identical to the settings described in our previous study [81, 82] (chapter 2 and 3), except for the baroreceptor low pass lter, which was omitted in this study. The e ect of the three di erent sources of variability on FHR variability is investigated by performing simulations without noise, with 1/f noise, and with white noise. For each type of noise (1/f or white) ten random noise signals are created and used to perform simulations of 30 minutes for each source of variability. Hereafter, values for HFn, LFn and BW are computed, and the power spectral density plots are generated. Values and plots shown, are the average of the ten simulations.
The e ect of uterine contractions on FHR and FHRV is investigated by simulating a set of three contractions varying in uterine pressure amplitude (70 ± 20 mmHg) and contraction
51 Chapter 4 duration (60 ± 20 s), resulting in umbilical cord compression, see also our previous study [82] (chapter 3). For the latter simulations, two noise signals (1/f and white) are created and superimposed on each of the three sources of variability.
Finally, the e ect of variation of the vagal and sympathetic gains on FHRV is investigated by repeating the simulations with superimposed white noise, while increasing or decreasing the vagal and sympathetic gains by 50%.
Simulations are performed in MATLAB R2013a (The MathWorks, Inc., USA). Di erential equa- tions are evaluated by explicit time integration with a time step of 0.01 s. Scenarios are initiated from a steady-state situation at which variation of mean arterial transmural blood –4 pressure ptm,a [mmHg] and arterial oxygen pressure pO2,a [mmHg] is less than 1·10 mmHg/s, respectively.
4.3 Results
Results for the simulation without a source of variability are shown in gure 4.2. FHR baseline is about 135 bpm and blood pressure baseline is about 45 mmHg. Three uterine contractions causing umbilical cord occlusion are shown, with varying severity (60 s and 70 mmHg, 80 s and 90 mmHg, 40 s and 50 mmHg). Since the oxygen transport from the placenta to the fetus is blocked, fetal oxygen levels decrease. This decrease activates cerebral autoregulation, which leads to a decrease of cerebral resistance and an increase of cerebral blood ow to compensate for the reduced oxygen supply. The decrease in oxygen pressure also activates the sympathetic nerve system, increasing peripheral vascular resistance to minimize oxygen consumption in non-essential systems, resulting in a rise of blood pressure. The changes in oxygen and blood pressure lead to a net FHR deceleration via the chemo- and baroreceptor. As a result, the FHR tracing shows three decelerations with varying depth. As described in our previous study [82] (chapter 3), the initial FHR increase (i.e. ‘shoulder’) is the result of the baroreceptor-mediated response, evoked by an initial decrease in blood pressure. As shown in gure 4.2, omission of the baroreceptor low pass lter in the current study does not lead to large changes in the FHR signals with respect to simulations performed with the model from our previous study, where the low pass lter was switched on (light gray).
Figure 4.3 shows the results for simulations with noise. Adding noise does not change baseline levels for FHR and blood pressure. For ease of comparison, FHR and blood pressure tracings for simulations with di erent sources of variability are shifted vertically with respect to each other. With 1/f noise, the required BW of about 15 ± 1 bpm was obtained by setting the noise modulation factor m in eq. 4.2 to 17.5%, 8.2% and 2% for variation of peripheral resistance, baroreceptor output and e erent vagal signal, respectively, while maintaining the others at zero. All tracings show similar FHR variability, however blood pressure variability is most
52 Fetal heart rate variability
120 100 80 60
[mmHg] 40
ut 20 p 0
20 15 [mmHg] 10
2,a 5 pO 90
60 [mmHg] tm,a p 30
200
180
160
140
120 FHR [bpm] 100
80
60 0 1 2 3 4 5 6 7 8 9 10 11 12 13 time [min]
Figure 4.2: Overview of simulation results without a source of variability. From top to bot- tom: uterine pressure put; fetal arterial oxygen pressure pO2,a; fetal mean arterial transmural blood pressure ptm,a; and fetal heart rate FHR. The response in each of these signals depends on contraction duration and amplitude. Simulations with low pass lter are shown in light gray.
pronounced if noise is added to the peripheral vascular resistance. With white noise, m was set to 28.5%, 17.5% and 4.8% for variation of peripheral vascular resistance, baroreceptor output and e erent vagal signal, respectively. Compared to the case with 1/f noise, more high frequencies are present. However, when noise is superimposed on the peripheral resistance, large unphysiological variations in blood pressure and blood ow (not shown) are observed. In all simulations FHRV is reduced during decelerations, whether 1/f or white noise is used.
Figure 4.4 shows the average power spectra of the heart period signals, obtained during ten 30-minute simulations without uterine contractions. For simulations with 1/f noise, all spectra show a monotonically decreasing trend. If white noise is applied, the 1/f character in the spectra is observed as well, however now the power spectra show several peaks. If white noise was added to the peripheral resistance, a peak was observed around 0.08 Hz and around 0.5 Hz. These peaks were also seen if white noise was applied to the baroreceptor output. A broader frequency spectrum is obtained if white noise is added to the e erent
53 Chapter 4
Rtisa
r b 20 bpm FHR [bpm] ev
R [mmHg] tisa 30 mmHg rb tm,a p ev 0 1 2 3 4 5 6 7 8 9 10 11 12 13 time [min] A: 1/f noise tm,a p
B: white noise
Figure 4.3: Typical examples of FHR and blood pressure signals if A) 1/f noise or B) white noise is added to peripheral resistance Rtisa (upper signals), baroreceptor output rb (middle signals), or the e erent vagal signal ev (lower signals). To facilitate comparison between the di erent simulations, all signals are shifted on the y-axis (with 50 bpm and 20 mmHg, respectively). Hence for all simulations FHR baseline is around 135 bpm and ptm,a baseline is around 45 mmHg. The bandwidth of FHR variation was aimed at 15 ± 1 bpm.
54 Fetal heart rate variability
R r e tisa b v 8000 8000 8000
7000 7000 7000
6000 6000 6000
5000 5000 5000 /Hz] 2 4000 4000 4000 PSD [ms 3000 3000 3000
2000 2000 2000
1000 1000 1000
0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 f [Hz] f [Hz] f [Hz]
Figure 4.4: Power spectral density (PSD) of simulated heart period signals with baroreceptor low pass lter switched o (black) or on (gray) are shown. Dashed lines represent spectra with 1/f noise as input and solid lines represent spectra with white noise as input. Noise is superimposed on peripheral resistance Rtisa (left); baroreceptor output rb (middle); e erent vagal signal ev (right). Each of the power spectra represents the average of ten simulations of 30 minutes. vagal signal. However, this spectrum only shows one peak near 0.14 Hz. To illustrate the e ect of the baroreceptor low pass lter, the average power spectra of ten 30-minute stimulations with low pass lter are shown in gray. The same noise signals were used as for the simulations without low pass lter, and again m was chosen such to obtain an FHR BW of 15 ± 1 bpm (except for the simulation where white noise was superimposed on the peripheral resistance, since then the model would become unstable). In general, addition of the low pass lter results in narrower power spectra, irrespective of noise type (1/f or white). In the model with baroreceptor low pass lter, the LF peak is shifted to the left. Furthermore, when white noise is superimposed on the peripheral vascular resistance or baroreceptor output, a less pronounced peak around 0.5 Hz is observed in simulations with low pass lter, which means that less high frequencies are present in the FHR tracings.
55 Chapter 4
R tisa b v
4000
3000 3000 3000 /Hz] 2
2000 2000 2000 PSD [ms 1000 1000 1000
0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5
4000 4000 4000
3000 3000 3000 /Hz] 2
2000 2000 2000 PSD [ms 1000 1000 1000
0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 f [Hz] f [Hz] f [Hz]
Figure 4.5: Results of sensitivity analysis on the sympathetic and vagal gains. White noise is superimposed on peripheral resistance Rtisa (left); baroreceptor output rb (middle); e erent vagal signal ev (right). Power spectral densities (PSD) of simulations with the standard model are indicated in gray. The upper row shows results of simulations where all sympathetic gains were increased (dashed black line) or decreased (solid black line) by 50%. The lower row shows results of simulations where the vagal gain was increased (dashed black line) or decreased (solid black line) by 50%. Each of the PSDs represents the average of ten simulations of 30 min.
In gure 4.5 the results of the sensitivity analysis to the sympathetic and vagal gains are shown. For these simulations white noise is used. If all sympathetic gains on heart period, cardiac contractility, venous unstressed volume, and peripheral vascular resistance are in- creased by 50% (dashed black lines), a clear increase of the 0.1 Hz peak and a small increase of the 0.5 Hz peak is observed with respect to powers obtained during standard simulations (gray lines). The power around 0.3 Hz decreases. Opposite e ects are observed if the sym- pathetic gains are decreased by 50% (solid black lines). Variations in sympathetic gains hardly a ect the power spectrum if the noise is applied to the e erent vagal signal. If the vagal gain is increased by 50%, all spectra show an increase of the power in the entire spectrum, without a ecting the shape of the power spectrum. A decrease of the vagal gain by 50% has the opposite e ect.
56 Fetal heart rate variability
experimental experimental model simulations model simulations data: quiet data: active 1 with 1/f noise with white noise sleep sleep
LFn HFn normalized power normalized
0 1 2 1 2 Rtisa (17.5%) rb (8.2%) ev (2%) Rtisa (28.5%) rb (17.5%) ev (4.8%) v. Laar v. Laar v. Laar v. Laar
Figure 4.6: Overview of normalized LF (0.04-0.15 Hz) and HF (0.4-1.5 Hz) powers. LFn and HFn are calculated from ten 30-minute simulations with 1/f noise or white noise superimposed on each of the sources of variability (peripheral resistance Rtisa, baroreceptor output rb or e erent vagal signal ev). The percentages in the horizontal axis indicate the percentage of modulation m as dened in eq. 4.2, chosen such to obtain an FHR bandwidth of 15 ± 1 bpm. On the right side LFn and HFn values represent data obtained during quiet and active sleep as given in literature: Van Laar et al.1 [165] and Van Laar et al.2 [167]. In the latter study standard deviations were not given.
Figure 4.6 shows normalized low frequency (LFn) and high frequency (HFn) values obtained from model simulations and from literature. If 1/f noise is applied to the peripheral resistance, LFn is about 0.82, while HFn is 0.03. If this noise is applied to the baroreceptor output, LFn is similar (0.82), however HFn is slightly increased (0.05). If 1/f noise is added to the e erent vagal signal, LFn decreases to a level of 0.66, while HFn remains similar to the case where noise is added to the baroreceptor output (0.05). The common e ect of replacing 1/f noise by white noise, is the reduction of LFn and the increase of HFn. If white noise is applied to the peripheral resistance, LFn decreases to 0.58 and HFn increases to 0.15. If white noise is applied to the baroreceptor output, these changes are more pronounced, with LFn=0.52 and HFn=0.25. If this noise is applied to the e erent vagal signal, LFn reduces even more to a level of 0.34, and HFn reaches a level of 0.23. As a reference, gure 4.6 also shows values of LFn and HFn obtained in fetuses with a gestational age of 36-37 weeks [165] and 34-41 weeks [167]. During quiet sleep, LFn values of 0.69 and 0.59, and HFn values of 0.14 and 0.26 were found, respectively. During active sleep LFn increased to 0.8 and 0.77, while HFn decreased to 0.07 and 0.1, respectively.
57 Chapter 4
4.4 Discussion
We extended a computer model for simulation of the CTG [81, 82] (chapter 2 and 3), with FHRV, an important clinical indicator of fetal distress. FHRV was added to the model by implementing three possible sources of variability, characterized by 1/f or white noise. The in uence of each of these sources of variability on FHR and blood pressure was investigated by use of visual inspection and spectral analysis.
Methods. In literature, several models for simulation of HRV in adults can be found. In the model of Van de Vooren et al. [157] uctuations were introduced directly to the low- pass ltered baroreceptor output. De Boer et al. [41] introduced uctuations via random disturbances on heart period and pulse pressure. In a study of Ursino et al. [155] a more elaborate circulation model was used that allowed introduction of low frequency variations on the peripheral resistance via an LF noise source (up to 0.12 Hz). High frequency variations (0.2 Hz) were introduced via a respiration model. In this study we followed Ursino in adding a source of variability to the peripheral vascular resistance. In addition we also applied variations on the baroreceptor output and the e erent vagal signal, according to Van Roon et al. [170] and Wesseling et al. [178]. We did not introduce high frequency variations, related to respiration.
It is unclear what type of noise should be used in each of these sources. Ursino used a noise signal with a linear power spectrum decrease between 0 and 0.12 Hz [155], De Boer used Gaussian distributed noise [41]. Following Wesseling [178] and Van Roon [170], in our study 1/f noise was used. As argued by Wesseling, this seems plausible for the peripheral resistance, since this resistance replaces the many parallel resistances representing the microcirculatory capillaries of all organs. In reality the resistance of each individual capillary will be in uenced by autoregulation in order to satisfy local oxygen demands. Due to the large number of cap- illaries contributing to the microcirculation, most of the rapid resistance variations (i.e. high frequencies) are averaged out, leaving the low frequency uctuations [178]. The motivation for the 1/f character describing uctuations originating from higher brain centers or other a erent systems is less clear.
Ideally, for small variations around the homeostatic state, the behavior of the system could be characterized by a transfer function. However, in clinical practice it is not possible to dene a transfer function, since the input variability is unknown. In the model we used white noise as input, for which the spectral output approximates the transfer function. Figure 4.4 shows that even when white noise is used, power spectra of FHR tracings have a 1/f character. This implies that the use of 1/f noise as input for the model is not required to obtain 1/f power density spectra.
58 Fetal heart rate variability
In our previous model [81, 82] (chapter 2 and 3), we included a low pass lter in the barore- ceptor, following Van der Hout-van der Jagt et al. [161]. With this lter, FHR tracings and power spectra show an unphysiological lack of HF components (gure 4.4). Removal of the lter yields power spectra that more closely resemble experimental data. Indeed, including a low pass lter in the baroreceptor seems unrealistic, as it is known that the baroreceptor does not only respond to changes in mean arterial pressure, but also to the rate of pressure change [88]. To include this rate sensitivity, Wesseling introduced a high emphasis lter in the baroreceptor [178]. In the model by Ursino, this e ect was neglected [155]. We did not include this e ect either. Finally, it is known that the set-point of the baroreceptor is not xed and may shift during chronic hypertension or hypotension [88]. Since the time scale of interest in this study is about 30 minutes, we did not take this e ect into account. As shown in gure 4.2, omission of the baroreceptor low pass lter only results in minor changes with respect to the results of our previously described model [81, 82] (chapter 2 and 3).
Results. In general, visual inspection shows that addition of white noise to each of the three sources of variability increases the high frequency FHR variations compared to addition of 1/f noise (gure 4.3). However, no clear di erences are seen between the use of the three di erent sources of variability. In literature it is shown that in a healthy fetus FHRV spectral power increases during contractions, indicating fetal reactivity to external pressure changes [25, 129, 175]. However, visual inspection of the simulated FHR tracings shows that the bandwidth of FHRV is reduced during contractions. For the case where temporal variations are added to the peripheral resistance, this can be explained by the fact that blood pressure increases during cord occlusions. This results in a reduced sensitivity of the baroreceptor, since its working point shifts to a less steep part on the baroreceptor curve. If variations are added to the baroreceptor output or e erent vagal signal, this mechanism is less important. The decreased FHRV during decelerations can then at least partly be explained by the inverse relation between heart period and FHR, as similar absolute variations in heart period will result in smaller absolute variations in FHR, if FHR decreases. The discrepancy between model results and literature ndings may indicate that other mechanisms also play a role.
Since details in the FHR tracings are di cult to interpret by visual inspection (gure 4.3), spectral analysis is used to examine di erences in simulation results. Power spectra obtained after applying 1/f noise to either the peripheral vascular resistance, baroreceptor output, or vagal e erent signal, do show a 1/f character without any peaks (gure 4.4). If white noise is added to each of the sources of variability, a peak around 0.1 Hz is observed in each of the three power spectra. In adults, a peak around 0.1 Hz is observed as well, known as Mayer waves. The mechanism causing the oscillations is still not exactly known [83, 101]. In the human fetus this peak around 0.1 Hz is also observed [54, 89]. Furthermore, our model results show another peak around 0.5 Hz when white noise is applied to the peripheral vascular resistance or baroreceptor output. Ferrazzi et al. [54] observed a HF peak around
59 Chapter 4
0.7-0.9 Hz. However, these peaks occurred during periods of fetal breathing and disappeared during apnea [54]. Since we did not model fetal breathing movements, in future studies it will be interesting to investigate the in uence of these movements on model outcome.
Wesseling et al. [178] also applied noise to each source of variability, one at a time. Although they used 1/f noise, the 1/f character in the power density spectra of the heart rate was only observed if the noise was superimposed on the e erent vagal signal. Their spectra showed a 0.1 Hz peak, which in our model was only observed if white noise was used. Di erences in the model results might be explained by the fact that Wesseling simulated baroreceptor feedback in an adult, while our model describes the fetal regulation. Furthermore, the Wesseling model does not include the sympathetic feedback on the heart, nor the chemore ex. Finally, in contrast to our model, Wesseling does model the dynamic baroreceptor response.
Spectral analysis provides information about the power of di erent frequency components present in the FHR tracings. In order to gain insight into the in uence of the sympathetic and parasympathetic nervous system on FHRV in our model, a sensitivity analysis was performed for the case where white noise was added to each of the sources of variability (gure 4.5). When the sympathetic gains are increased or decreased by 50%, the power spectra show an increase or decrease of the peak around 0.1 Hz, respectively. This is similar to the ndings of Ursino et al. [155]. Variations of the vagal gain in uences both the lower and the higher frequencies, independent of the source of uctuation. In this case the power of the 0.1 Hz peak in our model changed in the opposite direction as shown by Ursino. The power spectra as described by Ursino also show a peak around 0.2 Hz, which is related to an imposed cyclic variation of the intrathoracic and abdominal pressure to model respiration. Our results show a peak around 0.5 Hz, which is not found by Ursino.
Our ndings indicate that sympathetic feedback mainly a ects the lower frequencies and that vagal feedback a ects both low and higher frequencies. This is in accordance with observa- tions from vagal and sympathetic blocking studies in adult dogs, in which high frequencies were found to be mediated by the parasympathetic nervous system and low frequencies by both sympathetic and parasympathetic nervous system [5, 6]. In the dog the parasym- pathetic nervous system seems to play a dominant role in the low frequency range [5]. In addition, in vagal blocking studies in adult mice, absolute LF and HF power were reduced by 93% and 77%, respectively [93]. However, review studies show that in the adult no consen- sus has been reached about the relative contribution of the two branches of the autonomic nervous system to the di erent frequency bands [46, 149].
For the fetus, this discussion is further complicated by the di erent rate of maturation of the sympathetic and parasympathetic nervous system. In studies in fetal sheep it was observed that the sympathetic control of cardiovascular functions becomes active earlier in fetal life than the parasympathetic control [13, 112]. In blocking studies in the fetal sheep, the low
60 Fetal heart rate variability frequency power is found to be largely associated with sympathetic activity, although the parasympathetic nervous system does also play a role [86]. Similar to the e ects found in adult mice [93], vagal blocking studies in the preterm infant showed reduction of the absolute LF and HF powers by 94% and 67%, respectively [10]. Clinical studies showed an increase of LF and HF power with gestational age [37, 165, 167]. In the preterm fetus, this increase was suggested to re ect autonomic development, while in the term fetus, interpretation was more di cult due to the increasing e ect of variations in behavioral state [167]. Our model might be used to further investigate the relation between spectral properties and sympathovagal balance, and behavioral states.
To further compare our model results to experimental data, in gure 4.6 we show normalized powers of the LF and HF frequency bands. The choices for the ranges of the frequency bands is not universal [166]. According to our power spectra, shown in gure 4.4, the low frequency band would be chosen to range from about 0 to 0.3 Hz if white noise is used. However, to be able to compare our results with the clinical results of Van Laar et al. [165, 167], we followed their denition. Van Laar calculated normalized LF and HF powers, which emphasizes the balance between the sympathetic and parasympathetic nervous system by minimizing the e ect of changes in total power on both frequency bands [149]. In our model, addition of 1/f noise yields lower HFn values than found by Van Laar et al. [165, 167], irrespective of the source of variability (see also gure 4.6). When white noise is superimposed on the peripheral vascular resistance or baroreceptor output, LFn and HFn values more closely resemble the clinical data of Van Laar found during quiet sleep. In case white noise is added to the e erent vagal signal, LFn values become much lower than found in literature, while HFn values still correspond to clinical values obtained during quiet sleep.
In the study of van Roon et al. [170] a combination of the three sources of variability was suggested to approximate clinical data. According to our ndings it is hard to give an estima- tion of the contributions of each of the three sources in the fetus. Addition of noise to the peripheral resistance or baroreceptor output, shows similar power spectra (gure 4.4), which makes it di cult to distinguish between the contribution of these two sources of variability to FHRV. Furthermore, it is unknown what type of noise will most closely resemble uctua- tions in each source of variability. In this study we used 1/f and white noise, but physiological variations might show di erent noise patterns. Unfortunately, these input signals cannot be measured in the human fetus. Furthermore, the contribution of the di erent sources and the type of noise probably also depends on the physiological condition of a fetus. For example, variations on the peripheral resistance may be di erent during movements than during rest.
Conclusion. FHRV was included in the model by introducing variations to either peripheral vascular resistance, baroreceptor output or e erent vagal signal. The model is inconclusive about the type of noise to be used as input, since both simulations with 1/f noise and with
61 Chapter 4 white noise, yielded FHR power spectra with a physiological 1/f character. This shows that the ltering characteristics of the model seem physiological. Since the characteristic peak observed clinically at 0.1 Hz was only obtained when white noise was superimposed on each of the di erent sources of variability, it can be hypothesized that white noise is more likely to resemble physiological input. Choosing between peripheral resistance or baroreceptor output as source of variability was found to be di cult, since similar power spectra were found for these sources. In line with clinical observations, sympathetic control was found to determine predominantly LF power, whereas vagal control a ected both LF and HF power. Since the model did not show the clinically observed increase of FHRV during FHR decelerations induced by uterine contractions, it is worthwhile to investigate whether other mechanisms are involved in the origin of FHRV. Still, the capability of the model to generate realistic FHR signals was improved, which increases applicability of the model for research and educational purposes.
62 Chapter 5
Hypoxia-induced catecholamine feedback on fetal heart rate: A mathematical model study
The contents of this chapter are under review for Medical Engineering & Physics Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, and Bovendeerd PHM Chapter 5
Abstract
During labor and delivery, the cardiotocogram (CTG), the combined continuous registration of fetal heart rate (FHR) and uterine contractions, is used to monitor fetal well-being. To gain insight into FHR responses to mild uterine contractions, leading to short-term hypoxia, previously a mathematical CTG simulation model was developed where FHR response was described by neural feedback through the chemore ex and barore ex. The model was not designed to describe FHR responses to more severe contraction scenarios, leading to pro- longed hypoxic episodes. These secondary FHR responses are thought to involve di erent mechanisms including humoral feedback, vagal inhibition and myocard hypoxia.
In this study, we extended the model to describe secondary FHR responses via a simple catecholamine feedback submodel. Simulation results of repeated severe uterine blood ow reductions showed an initial decrease of inter-occlusion FHR, followed by a gradual increase. This trend was also observed in sheep experiments. Simulations of repeated severe umbilical ow reductions resulted in FHR overshoots, which were less sharp as compared to experi- mental data. Model results might be improved by including feedback through vagal inhibition and myocard hypoxia.
64 Catecholamine feedback
5.1 Introduction
Ideally, during labor and delivery fetal well-being is monitored via fetal oxygen status. Since in current clinical practice reliable continuous intrapartum oxygen measurements are not avail- able, fetal status is mainly estimated from the cardiotocogram (CTG). This is the combined, continuous registration of uterine contractions and fetal heart rate (FHR). Interpretation of the CTG is not straightforward, since FHR is not only a ected by the fetal oxygen level, but also by e.g. blood pressure variations. To obtain insight into the di erent pathways that lead to FHR variations during uterine contractions, in previous studies a mathematical model was developed to simulate the CTG [78, 81, 82] (chapter 2, 3 and 4). It was shown that FHR decelerations during short-term hypoxia, resulting from single uterine contractions inducing uterine blood ow reduction alone, or combined uterine and umbilical blood ow reduction, can be modeled as function of the chemo- and barore ex [81, 82] (chapter 2 and 3). How- ever, secondary FHR e ects, including FHR baseline increase and FHR overshoots, occurring in response to prolonged episodes of hypoxia, could not be mimicked with the existing CTG simulation model.
Clinically, an increase in FHR baseline has been hypothesized to be related to progression of hypoxic insults [115, 152]. Furthermore, FHR overshoots following variable decelerations develop during prolonged umbilical cord compression [138, 177]. In sheep experiments, it was observed that a series of repeated severe uterine blood ow reductions resulted in an initial decrease of inter-occlusion FHR, followed by a gradual increase [71, 130]. Besides, FHR overshoot patterns and inter-occlusion FHR increase were observed in sheep during repeated severe umbilical ow reductions [39, 58, 94, 136, 179, 180]. FHR decelerations are initiated by the baro- and chemoreceptor acting on the vagal and sympathetic nerve system. When the occlusion is continued, the vagal contribution to the deceleration is gradually taken over by myocard depression [136, 179, 180]. The rise of FHR baseline and the appearance of FHR overshoots is presumably caused by beta-adrenergic stimulation that is no longer counteracted by the vagal nerve system at the end of the occlusion [115, 136, 179, 180]. It has been suggested that sympathetic activity is suppressed during the inter-occlusion period and that catecholamines play an important role in the beta-adrenergic stimulation at the end of occlusions [94].
Aim of this study is to gain insight into the development of secondary FHR e ects during repeated severe hypoxic events in the human fetus. Therefore, we extend our previous model with a description of the e ect of catecholamines on FHR. We will focus on the responses to 30 minutes of severe contractions and neglect potential e ects of myocard hypoxia and vagal tone depression for the sake of simplicity. We demonstrate the capability of the model to simulate scenarios of repeated abrupt, complete uterine or umbilical blood ow reduction as performed by Jensen et al. [71], and by the group of Galinsky and Westgate [58, 179]. Finally,
65 Chapter 5 the e ect of catecholamine feedback during scenarios with physiologic uterine contractions, which result in more gradual and less severe blood ow reductions, is investigated. The extended model is expected to be of increased value for educational purposes, such as screen-based training of CTG evaluation and simulation-based (team-)training with manikins.
5.2 Material and methods 5.2.1 Physiological background
Catecholamines a ect the cardiovascular system in a similar fashion as the sympathetic ner- vous system and thus increase heart rate and blood pressure [88, 109, 115]. In fetal sheep and rhesus monkeys, infusion of catecholamines was found to result in an increase of blood pres- sure [4, 28, 75]. FHR was initially decreased, presumably caused by the barore ex, whereafter FHR increased above resting levels [4, 28, 75, 76]. A positive correlation between FHR baseline and umbilical artery catecholamine concentration was found in human fetuses after delivery [119]. However, in other studies, increase in catecholamine level was related to both brady- cardia and tachycardia [16, 91]. Presumably, bradycardia is an initial e ect induced by the vagal re ex, whereas tachycardia occurs as soon as the catecholamine concentration is high enough to overcome this FHR decelerating e ect [16, 91]. Furthermore, signicant increases of catecholamines were observed in human fetuses that showed late or moderate/severe variable FHR decelerations during labor [16, 91].
In this study, we focus on the catecholamines adrenaline and noradrenaline. Catecholamine concentration depends on the balance between catecholamine production and elimination. In adults, catecholamines are removed from the circulation via neuronal and extra-neuronal uptake, where the latter pathway predominates [47]. In the fetus, elimination also takes place in the placenta [23, 47, 119]. Adrenal catecholamine secretion in the sheep fetus is primarily evoked by reduction of arterial oxygen pressure, rather than by changes in arterial pCO2, pH, or lactic acid [31]. The response of the adrenal medulla to asphyxia is established via two pathways: directly, by the drop of oxygen levels, and indirectly, through nerve stimulation [31, 32]. In the fetal sheep, nervous stimulation of the adrenal medulla is already present before birth, and the direct response wanes at the end of pregnancy [31, 32]. However, in other species like the fetal cow [33], pony [34], and rat [141], innervation of the adrenal glands is still immature at birth and the direct hypoxic response on the adrenal medulla still dominates. In the human fetus, the exact mechanism of adrenal catecholamine secretion remains unknown. In sheep, the ratio of adrenaline and noradrenaline release depends on maturation and the relative contribution of adrenaline increases towards the end of pregnancy [32]. The relation between adrenal catecholamine secretion and arterial oxygen pressure has been investigated in fetal lambs [30, 31]. However, to the best of our knowledge, no data is available on the
66 Catecholamine feedback relation between hypoxia and spillover from nerve endings.
5.2.2 Mathematical model
Our CTG simulation model [78, 81, 82] (chapter 2, 3 and 4) describes a full term 3.5 kg human fetus and includes feto-maternal hemodynamics, oxygenation, and fetal regulation, see gure 5.1. In the maternal cardiovascular model the uterine circulation is modeled explicitly, while the remainder of the peripheral circulation is lumped into the tissues. In the fetal model, the cerebral and umbilical circulation are modeled explicitly. The fetal regulation submodel describes the e ect of changes in arterial oxygen pressure and blood pressure on the car- diovascular system. Via the chemo- and baroreceptor and e erent vagal and sympathetic pathways, four cardiovascular e ectors are a ected: heart period T, cardiac contractility Emax, venous unstressed volume Vven,0, and peripheral artery resistance Rtisa. Like in our previous study, the baroreceptor low pass lter was omitted from the model [78] (chapter 4). We use this model as a basis to investigate the e ect of catecholamine feedback on FHR.
5.2.2.1 Catecholamine submodel
In this study, fetal catecholamine feedback (focusing on adrenaline and noradrenaline) is added to the model. For the sake of simplicity, we chose not to di erentiate between the adrenaline and noradrenaline response, thus the catecholamine concentrations represent combined concentrations. The catecholamine submodel consists of the catecholamine dis- tribution model, describing catecholamine appearance, elimination and convection; and a feedback model, describing the e ect of increased catecholamine levels in the blood on the fetal heart (gure 5.1).
Catecholamine distribution The structure of the catecholamine distribution model is similar to that of the oxygen dis- tribution model previously described [81]. Catecholamine appearance, representing adrenal catecholamine secretion and catecholamine spillover from nerve endings, takes place in the fetal tissues. From the tissues, catecholamines are convectively transported to the systemic veins, from which they ow into the heart and to the remainder of the body. Catecholamine elimination takes place in the placental villi as well as in the tissues.
The rate of change of catecholamine content in a compartment (catecholamine concentration cCat [ng/ml] multiplied by the blood volume of the compartment V) is determined by con- vective transport QC, catecholamine plasma appearance QA, and catecholamine extraction QE: d(cCat · V) = Q + Q – Q (5.1) dt C A E
67 Chapter 5
Figure 5.1: Schematic overview of the CTG simulation model. The maternal circulation con- sists of a heart, systemic veins, and arteries. The intervillous space (IVS) is modeled explicitly, while the remainder of the periphery is lumped into the tissues. In the fetus, the umbilical and cerebral circulation are modeled explicitly. Oxygen ows are indicated with thin dashed lines. Oxygen enters the maternal system via the veins and is consumed in the maternal tissues. In the placenta, oxygen di uses from the IVS into the umbilical circulation. In the fetus oxygen metabolism takes place in the tissues and brain. Contractions are simulated via an increase in uterine pressure put, acting on the IVS and on the fetus, a ecting uterine blood ow. Cord compression increases the external pressure on the umbilical cord pum, af- fecting umbilical blood ow. Both scenarios change fetal arterial oxygen pressure pO2,a and transmural blood pressure ptm,a. A decreased oxygen pressure activates the chemoreceptor, which via the output signal rc stimulates the vagal and sympathetic centers. An increased blood pressure activates the baroreceptor, which via the output signal rb increases the vagal, but inhibits the sympathetic center. Via the e erent vagal output signal ev, stimulation of the vagal center increases heart period T. Increased sympathetic output es in uences all four cardiovascular e ectors: T is decreased; cardiac contractility Emax is increased; venous unstressed volume Vven,0 is decreased; peripheral vascular resistance Rtisa is increased. Hu- moral feedback is indicated with thick dashed lines. This model extension consist of two parts: catecholamine distribution and catecholamine feedback. Catecholamine appearance QA takes place in the fetal tissues and elimination tales place in the tissues QEx,tis and pla- centa QEx,plac. An increased arterial catecholamine concentration cCata decreases T. The changed e ectors all in uence the fetal cardiovascular system. Adapted from [78].
68 Catecholamine feedback
Convective transport of catecholamines through the fetal cardiovascular system is described by: i i j QC = ∑qincCatin – ∑qoutcCat (5.2) i j
The rst term represents the sum of catecholamine in ows in the current compartment. i i Here i runs across all segments with an in ow qin in the current compartment, with cCatin the catecholamine concentration of the in ow compartments. The second term represents the sum of catecholamine out ows. Now j runs across all segments with an out ow from the current compartment, with cCat the catecholamine concentration of the current com- partment.
Catecholamine appearance QA is modeled as a delayed response to the arterial oxygen pres- sure pO2,a. The delay represents the limited ability of adrenal catecholamine secretion to instantaneously respond to changes in pO2,a and the time required for the catecholamines derived from nerve endings to reach the blood stream, and is modeled via a low pass lter with time constant τQA : dQA 1 ∗ = QA – QA (5.3) dt τQA ∗ Here QA is related to arterial oxygen pressure pO2,a via a sigmoid relation:
pO2,a–pO2,a,n κpO Amin + Amax · e 2 Q∗ = (5.4) A pO2,a–pO2,a,n κ 1 + e pO2 where Amin and Amax represent the minimum and maximum appearance rate, respectively, pO2,a,n represents the working point of the sigmoid relation, and κpO2 determines the slope in the working point.
Catecholamine extraction takes place in the fetal placenta and tissues and is assumed to be proportional to the catecholamine concentration of the compartment:
QE = E · cCat (5.5)
Here E is a constant.
Catecholamine feedback Catecholamines are assumed to only in uence the fetal heart rate through the model e ector heart period T, see gure 5.1. The actual e ector response is a combination of the vagally and sympathetically induced heart period variations, zTv and zTs , respectively [81] (chapter
2), and the catecholamine induced e ector variation zTCat :
T = Tref · (1 + zTv – zTs – zTCat ) (5.6)
69 Chapter 5
The minus signs indicate the inhibitory e ect of the sympathetic and catecholamine feedback on T. The e ect of catecholamines on heart period is modeled proportionally to the arterial catecholamine concentration cCata:
zTCat = kCat,T · cCata (5.7) where kCat,T is a constant.
5.2.3 Parameter estimation
Where possible, human data was used for parameter estimation, complemented with sheep data if human data was not available. Parameters were scaled to a full term 3.5 kg fetus.
In sheep experiments, steady-state catecholamine plasma appearance rate was found be- tween 85 and 160 ng/min/kg for noradrenaline [23, 113, 142, 143], and between 5 and 26 ng/min/kg for adrenaline [113, 142, 143, 145]. In our model, catecholamine appearance rep- resents the combination of catecholamine spillover from nerve endings and catecholamine secretion by the adrenal medulla. We chose a steady-state catecholamine appearance rate Amin of 500 ng/min for a 3.5 kg fetus, representing the sum of noradrenaline and adrenaline appearance rate, which is equivalent to 143 ng/min/kg. Tuning of catecholamine appearance parameters Amax, pO2,a,n, and κpO2 was based on a study of Jensen et al. [72] where a relation was given between the uterine artery occlusion time (repeated every 3 min) and cat- echolamine concentration after 33 min of occlusions, and on a study of Galinksy et al. [58] in which catecholamine concentrations were measured at several time points during 2 min umbilical cord occlusions, repeated every 5 min. The time constant τQA was set to a value of 5 min such that both a gradual inter-occlusion FHR increase, observed during repeated uterine artery occlusions [71], and FHR overshoots, observed during repeated umbilical cord occlusions [58, 179], could be simulated.
According to Paulick et al. [119], who found a constant placental extraction ratio for a large range of umbilical catecholamine concentrations, we set the placental as well as the tissue extraction ratios to a constant value. For the placental extraction, we assumed that the measured concentrations are described by the steady-state solution of eq. 5.1:
qum · (cCata – cCatvilli) = Eplac · cCatvilli, with cCatvilli = (1 – α) · cCata (5.8)
Here qum represents the umbilical blood ow, cCata and cCatvilli the arterial and villous catecholamine concentration, respectively, Eplac the placental extraction constant as dened in eq. 5.5, and α the placental fractional catecholamine extraction. Substitution results in the following relation: α E = · qum (5.9) plac 1 – α
70 Catecholamine feedback
From human studies in which venous and arterial catecholamine measurements were per- formed in the umbilical cord after birth [48, 91, 119], an extraction ratio of 0.5 to 0.75 could be calculated. With α equal to 0.65 in our study and qum being about 400 ml/min, this results in a value of about 750 ml/min for Eplac.
The steady-state noradrenaline and adrenaline concentrations in the systemic arteries range from 0.53 to 1.0 ng/ml [23, 113, 142, 143] and from 0.04 to 0.19 ng/ml [113, 142, 143, 145], respectively. We chose a combined catecholamine concentration of 1 ng/ml. The tissue extraction constant Etis was set to a value of 180 ml/min in order to obtain the desired arterial catecholamine concentration of 1 ng/ml and a total extraction rate of 500 ng/min in steady state.
–2 The value for kCat,T was set to 1.7 · 10 (ml blood/ng Cat) to obtain a maximum FHR of 255 bpm during repeated 2:5 min umbilical cord occlusions [58, 179]. In these sheep experiments a maximum FHR of about 300 bpm was observed [58, 179]. A value of 255 bpm was chosen for the human fetus, according to the scaling factor between the steady-state FHR level, which is about 160 bpm in the fetal sheep [133] and 135 bpm in our human model. Parameter values can be found in table 5.1.
Table 5.1: Catecholamine distribution and feedback parameters.
Parameter Value Unit Parameter Value Unit Amin 500 ng/min τz 5 min 4 Amax 6.5·10 ng/min Eplac 750 ml blood/min pO2,a,n 10 mmHg Etis 180 ml blood/min –2 κpO2 -1 mmHg kCat,T 1.7·10 (ml blood/ng Cat)
5.2.4 Model simulations
The model was implemented in MATLAB R2013a (The MathWorks, Inc., USA). Di erential equations were evaluated by forward Euler time integration with a time step of 0.02 s. Sce- narios described below, were initiated from a steady-state situation at which variation of –4 ptm,a and pO2,a was less than 1 · 10 mmHg/s, respectively.
5.2.4.1 Sheep experiments
Sheep experiments in which uterine blood ow was repeatedly decreased by use of a balloon catheter in the maternal descending aorta [71, 72], were simulated by linearly increasing uterine artery resistance by a factor 100 in 5 s, keeping it at its maximum level for a certain time period, and linearly decreasing the resistance to steady-state levels at the end of the occlusion (see also [81], chapter 2). Uterine artery occlusions were performed with a duration of 60 s or 90 s, and repeated every 180 s, to simulate the 1:3 and 1.5:3 min repeated occlusions
71 Chapter 5 as performed in the sheep experiments.
Experiments of repeated umbilical cord occlusion in fetal sheep, induced by in ating an occluder cu placed around the umbilical cord [58, 179], were simulated by linearly increasing the external pressure on the umbilical cord pum to a maximum level of 90 mmHg in 5 s, keeping it constant for a predened time period, and linearly decreasing it at the end of the occlusion (see also [82], chapter 3). Umbilical cord occlusions were performed with a duration of 1 min and 2 min, and repeated every 5 min, to simulate the 1:5 and a 2:5 min repeated occlusions in the experiments.
For comparison with experimental data, catecholamine concentration samples from the model were calculated as the mean over the repetition interval (3 min during uterine artery occlusions and 5 min during umbilical cord occlusions) preceding the measurement time.
We observed that the trend in FHR increase strongly depends on the time constant τQA .
Therefore, the e ect of τQA on FHR was investigated by varying its value by 50%.
5.2.4.2 Contraction scenarios
The sheep experiments were repeated while replacing the occluder scenarios by more phys- iological uterine contractions, leading to a more gradual uterine vein and/or umbilical cord resistance increase (see our previous papers for a brief description [81, 82], chapter 2 and 3). The uterine pressure changes are modeled as a sine-squared function [81, 82]. These contractions have an amplitude of 70 mmHg and a contraction duration and interval similar to the occlusion times in the sheep experiments.
5.3 Results
Simulation results for the scenario of 1.5:3 min uterine artery occlusions are shown in gure 5.2. As targeted, in steady state FHR is about 135 bpm, blood pressure 45 mmHg and oxygen pressure 18.5 mmHg. We rst consider the case without catecholamine feedback (light gray). During uterine artery occlusions, the oxygen transport from mother to child is decreased, resulting in reduced fetal oxygen pressures. As a result, fetal cerebral autoregulation is activated, thus increasing cerebral blood ow in order to compensate for the reduced oxygen supply. The drop in oxygen pressure also stimulates the chemoreceptor, which, via activation of the sympathetic nervous system, increases peripheral vascular resistance to raise arterial blood pressure. As a result, blood and oxygen supply are increased to the vital organs and decreased to non-essential organs, known as brain-sparing or blood ow redistribution. Via the sympathetic and vagal pathways, reduced oxygen pressure and increased blood pressure both a ect fetal heart rate, resulting in a net FHR deceleration.
72 Catecholamine feedback
20 15
[mmHg] 10 5 2,a 0 pO 0 5 10 15 20 25 30
80
[mmHg] 60 tm,a
p 40 0 5 10 15 20 25 30
60 40 [ng/ml]
a 20
cCat 0 0 5 10 15 20 25 30
150
100
FHR [bpm] 50 0 5 10 15 20 25 30 time [min]
Figure 5.2: Simulation results of repeated uterine artery occlusion. Uterine artery blood ow was completely blocked for 1:3 min (dark gray) and 1.5:3 min (black). For the more severe scenario of 1.5:3 occlusions, simulation results without catecholamine feedback are shown as well (light gray). Occlusion periods are indicated by the squares. From top to bottom signals represent arterial oxygen pressure pO2,a, mean arterial transmural blood pressure ptm,a, arterial catecholamine concentration cCata, and FHR.
Simulation results of 1.5:3 min uterine artery occlusions with catecholamine feedback are shown in black. Oxygen levels show almost the same pattern as during the simulation without catecholamine feedback. However, blood pressure levels are slightly increased. This can be explained by the increase of FHR (bottom panel) in response to the increase of catecholamine levels. Within 30 min, arterial catecholamine concentration rises from a steady-state level of 1.0 ng/ml to a level of 20.9 ng/ml (averaged over 3 min). The increased arterial catecholamine concentration leads to higher FHR values with subsequent contractions. The minimum FHR values increase as well, but at a slower rate than the FHR maxima. As a consequence, the depth of the FHR decelerations is increased.
During 1:3 min uterine artery occlusions (dark gray), as expected, variations in oxygen and blood pressure are reduced, since the uterine artery occlusions are less severe. Furthermore, oxygen and blood pressure levels have more time to restore during the longer inter-occlusion periods. The 3-minute-averaged arterial catecholamine concentration increases only slightly,
73 Chapter 5 up to a level of 3.4 ng/ml after 30 min. Since catecholamine appearance is reduced, the e ect on FHR during the resting period is diminished, and FHR maxima do no longer increase with subsequent occlusions.
Simulation results of umbilical cord occlusions are shown in gure 5.3. Simulation results of 2:5 min occlusions without catecholamine feedback are indicated in light gray. Similar to the scenario of uterine artery occlusion, oxygen transport to the fetus is reduced, resulting in low oxygen pressures and raised blood pressure. Since the oxygen bu er in the IVS is no longer available, oxygen pressures drop deeper compared to the scenario of uterine artery occlusion, even if occlusion periods are of the same duration. (Also see our previous studies [81, 82], chapter 2 and 3.) Via the baro- and chemoreceptor, increased blood pressure and decreased oxygen pressure result in FHR decelerations.
20 15
[mmHg] 10 5 2,a 0 pO 0 5 10 15 20 25 30
80
[mmHg] 60 tm,a
p 40 0 5 10 15 20 25 30
60 40 [ng/ml]
a 20
cCat 0 0 5 10 15 20 25 30
250 200 150 100
FHR [bpm] 50 0 5 10 15 20 25 30 time [min]
Figure 5.3: Simulation results of repeated umbilical cord occlusion. Umbilical blood ow was blocked for 1:5 min (dark gray) and 2:5 min (black). For the the more severe scenario of 2:5 occlusions, simulation results without catecholamine feedback are shown as well (light gray). Occlusion periods are indicated by the squares. From top to bottom signals represent arterial oxygen pressure pO2,a, mean arterial transmural blood pressure ptm,a, arterial catecholamine concentration cCata, and FHR. (Note the di erence in the axis of the FHR plot compared to gure 5.2.)
74 Catecholamine feedback
If catecholamine feedback is included in the model (black), the oxygen pressure gradually reaches a higher level during the inter-occlusion periods than during simulations without catecholamines, which is caused by the increased FHR, enhancing umbilical blood ow be- tween occlusions (not shown). Furthermore, blood pressure is increased. Again this can be explained by the increased FHR levels, caused by the increased catecholamine concentra- tion, which now reaches a level of 40.9 ng/ml after 30 min (averaged over 5 min). During the inter-occlusion periods, FHR shows an increasing trend, reaching maximum levels of about 255 bpm, whereafter FHR decreases again towards steady-state levels. However, the inter- occlusion intervals are too short for the FHR to actually reach the FHR level preceding the experiment.
During 1:5 min occlusions (dark gray), the reductions in oxygen pressure and increases in blood pressure are less severe compared to 2:5 min occlusions. The 5-minuted-averaged catecholamine concentration increases to a level of 9.4 ng/ml after 30 min. FHR decreases during occlusions and only exceeds the initial steady-state FHR level by maximum 16 bpm during the inter-occlusion periods.
In gure 5.4 the e ect of variations in the low pass lter time constant τQA is shown. If τQA is decreased (dashed black lines), the FHR tracing of 1.5:3 min uterine artery occlusions shows a
150
100 FHR [bpm]
50 0 5 10 15 20 25 30
300
175 FHR [bpm]
50 0 5 10 15 20 25 30 time [min]
Figure 5.4: The e ect of τQA on FHR. The upper panel shows FHR variations during simu- lations of 1.5:3 min uterine artery occlusions, the lower panel shows FHR tracings obtained
during 2:5 min umbilical cord occlusions. The value of τQA is varied with respect to its stan- dard value of 5 s (gray line) and set to a value of 2.5 s (dashed black line) and 7.5 s (solid black line). (Note the di erence in the axis of both plots.)
75 Chapter 5
20 [ng/ml] a
cCat 0 0 5 10 15 20 25 30
200 150 100
FHR [bpm] 50 0 5 10 15 20 25 30
120 100 80 60
[mmHg] 40
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cCat 0 0 5 10 15 20 25 30
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Figure 5.5: Contraction scenarios. The upper three panels represent arterial catecholamine concentration cCata, FHR and uterine pressure put tracings during repeated uterine contrac- tions causing uterine vein occlusion alone. Contractions with an amplitude of 70 mmHg and a duration of 1.5 min are repeated every 3 min. The lower three panels show the results during repeated uterine contractions causing both uterine vein and umbilical cord occlusion. Contractions with an amplitude of 70 mmHg and a duration of 2 min are repeated every 5 min. (Note the di erence in the axis of the cCata plot with respect to gure 5.2 and 5.3.)
76 Catecholamine feedback more abrupt increase of the maximum FHR levels, with respect to the standard settings (gray lines). The maximum inter-occlusion level is reached within four repeated occlusions. If τQA is increased (solid black line), inter-occlusion FHR values show a more gradual increase. For the 2:5 min umbilical cord occlusions, a reduction of τQA leads to more spiky FHR overshoots and a faster FHR reduction at the end of the inter-occlusion period (dashed black lines), while an increase of τQA results in a less spiky pattern and a gradual increase of inter-occlusion FHR levels (solid black lines).
Figure 5.5 shows the results of the contraction scenarios. During repeated uterine contrac- tions with a duration of 1.5 min and a contraction interval of 3 min, which result in uterine ow reduction alone (upper panels), no clear increase in catecholamine concentration is ob- served. As a consequence, no secondary FHR e ects are present. During the inter-occlusion period, FHR reaches baseline levels again. The lower panels show the results of contractions a ecting both uterine and umbilical blood ow. Contractions have a duration of 2 min and are repeated every 5 min. The arterial catecholamine concentration increases up to a level of 10.5 ng/ml. As a result, the inter-occlusion FHR increases with a maximum of 19 bpm. The small initial increases of FHR preceding the decelerations are caused by blood pressure reductions, as explained previously.
5.4 Discussion
Aim of this study was to gain insight into the role of catecholamines in the development of secondary FHR e ects, such as increase of FHR baseline and appearance of FHR overshoots, during repeated severe hypoxic events. To this end we extended our CTG simulation model [78, 81, 82] (chapter 2, 3 and 4) with a catecholamine feedback submodel. Because of the lack of clinical data on hypoxia and catecholamine concentrations in the human fetus, we had to use data from animal experiments for parameter estimation. Therefore, while to the best of our knowledge this is the rst mathematical model describing the e ect of catecholamines on FHR, we must be reticent in interpreting these data for the human fetus. Nevertheless, the simulations in this paper can be regarded as proof of principle and can be used to investigate trends in catecholamine concentrations and cardiovascular responses.
Model setup. In view of the limited experimental data available, catecholamine appearance was modeled as function of oxygen pressure, to describe the combined e ect of nervous spillover and adrenal secretion.
We also did not distinguish between adrenaline and noradrenaline, neither in the cate- cholamine distribution submodel, nor in the catecholamine feedback submodel. Experimental data in the sheep fetus show mixed cardiovascular responses [28, 75, 76]. Although all studies show an increase in blood pressure if adrenaline or noradrenaline is infused, in some studies
77 Chapter 5 an initial decrease of FHR is observed by infusing adrenaline [75], while others observe this e ect by infusing noradrenaline [28]. In all studies the initial FHR decrease is followed by an FHR increase. Due to the limited and ambiguous experimental data, it is very di cult to model the individual e ect of both catecholamines on the fetal cardiovascular system.
Finally, we only included the e ect of catecholamines on FHR and neglected the e ect on the other sympathetic e ectors: cardiac contractility, peripheral vascular resistance and venous unstressed volume. This choice was motivated by the availability of information on catecholamine feedback on FHR [71, 179], and the lack thereof on peripheral vascular resistance, venous unstressed volume, or cardiac contractility.
Choice of experimental studies. Since most studies are performed in sheep, we focus on sheep experiments to estimate model parameter values. Ideally, sheep studies should pro- vide a well dened description of occlusion severity, and measurements of oxygen pressure, FHR and catecholamine concentrations at several time points. Unfortunately, such experi- ments are not available. In the studies of Jensen et al. [71, 72], catecholamine concentrations were only measured at the beginning and end of the occlusion experiments. In the studies of Galinsky and Westgate [58, 179], oxygen pressure was measured in between occlusions and not during the occlusions. In the study of Lewis et al. [95], the timing and severity of cord occlusion was based on the drop in oxygen pressure, and thus occlusion parameters were not exactly known. There are several sheep studies available that describe the e ect of repeated uterine artery occlusions on FHR and catecholamine concentration [71, 72, 130]. However, these studies show di erent FHR responses during 1:3 min occlusions. We chose to use the studies of Jensen et al. [71, 72] for model tuning. The e ects of repeated umbilical cord occlusions have also been investigated in several sheep studies [39, 58, 94, 136, 179, 180]. We used the studies of Galinsky [58] and Westgate [179] to estimate parameter values. When we subsequently tested the model by simulating the experiments performed by Saito [136] (15 times 40:120 s followed by 45 times 60:120 s umbilical cord occlusions), we found that the catecholamine concentration was similar to the sheep data, but that oxygen saturation remained higher in the model (data not shown). Inter-occlusion FHR baseline increased, al- though the increase was smaller than observed in sheep data. It is unclear whether the discrepancies between model and experimental results are caused by fundamental short- comings of the model or by large inter-subject variations in sheep [58, 71, 72].
Results. Simulation results of 1:3 min uterine artery occlusions show FHR decelerations during the occlusion periods, which is in accordance with sheep data of Jensen et al. [71] (gure 5.2). In between occlusions, FHR returns towards the steady-state level, preceding the occlusion experiment. This is also observed in the study of Jensen, however, in the sheep, FHR inter-occlusion baseline remains lower as compared to our simulation results [71]. Simulation results of 1.5:3 min uterine artery occlusions show a similar FHR deceleration
78 Catecholamine feedback during the rst occlusion as compared to the sheep experiments [71]. Furthermore, an initial decrease of inter-occlusion FHR is observed, followed by a gradual increase. However, both the initial decrease and the subsequent increase are not as large as observed in the sheep experiments. In addition, the drop of oxygen saturation (data not shown) in the model is smaller compared to the sheep studies. Since catecholamines are not yet expected to play a signicant role after the rst occlusion, the cause of these di erences must be sought in the original model without catecholamine feedback, possibly in the oxygen submodel. Furthermore, one should keep in mind that in this study a human model of hemodynamics, oxygenation and regulation is used to simulate sheep catecholamine responses.
During 1:5 min umbilical cord occlusions, simulated FHR tracings did not show an overshoot pattern (gure 5.3), which is in accordance with sheep experiments [179]. During 2:5 min umbilical cord occlusions, FHR overshoots are obtained in the simulation results, which are also observed in experimental tracings [58, 179]. Target maximum FHR levels are reached (here 255 bpm based on scaling). These values still seem to be quite high for the human fetus. However, such severe experiments have never been performed on human fetuses. The shape of the overshoots is less sharp compared to the sheep experiments. This can be improved by decreasing the low pass lter time constant τQA (gure 5.4). However, decreasing τQA would result in a more abrupt rise of FHR baseline during repeated uterine artery occlusions (gure 5.4), which is not in accordance with experiments of repeated uterine artery occlusion in sheep [71]. As a compromise, we set τQA to a value of 5 min.
The model also predicts the initial increase of blood pressure during the repeated uterine artery [71] or umbilical cord [58, 179] occlusions, but fails to predict the secondary decrease during the occlusion period. Furthermore, inter-occlusion blood pressure does not show a clear increase.
Comparison of catecholamine concentrations between model and experiments is not straight- forward. During simulations of umbilical cord occlusions, catecholamine concentrations showed large uctuations (see gure 5.3), suggesting that knowledge on the exact timing and duration of the experimental sampling procedure is crucial. However, this detailed in- formation is not available in the experimental data. In order to compare simulation results with experimental data, simulated arterial catecholamine concentrations were averaged over a whole occlusion-repetition period (3 min in case of uterine artery occlusions and 5 min for umbilical cord occlusions). With the chosen parameters settings for catecholamine ap- pearance and elimination, after 30 min of simulation, arterial catecholamine concentrations corresponded well with experimental data, for both repeated uterine artery occlusions (1:3 min: 3.4 ng/ml model vs. 2.8 ng/ml after 33 min by Jensen et al. [72], and 1.5:3 min: 20.9 ng/ml model vs. 20.5 ng/ml after 33 min by Jensen [72]) and umbilical cord occlusions (2:5 min: 40.9 ng/ml vs. 43.1 ng/ml after 12 min and 33.1 ng/ml after 42 min by Galinsky et al. [58]).
79 Chapter 5
Catecholamine concentrations were not measured during 1:5 min umbilical cord occlusions [58], therefore we cannot evaluate model predictions for this scenario.
In the sheep experiments, occluders are used to block uterine or umbilical blood ow, leading to a direct and complete ow reduction in contrast to the gradual ow reduction in response to increasing uterine pressure during actual uterine contractions. Therefore, we also sim- ulated the e ect of uterine contraction patterns. To enable comparison with the occluder experiments, we adopted the same timing of the contractions. When the contraction sce- narios (gure 5.5) are compared to the simulated sheep experiments (gure 5.2 and 5.3), a smaller increase in arterial catecholamine concentration is observed, resulting in smaller secondary FHR responses. During the 1.5:3 min uterine contractions, causing uterine ow re- duction alone, FHR does not show inter-occlusion tachycardia. Apparently, the catecholamine threshold to induce additional changes in FHR was not reached. During 2:5 min uterine con- tractions, causing combined uterine and umbilical ow reduction, inter-occlusion tachycardia is observed, however no overshoots are present in the FHR tracing. The FHR values of 255 bpm, that were reached in the simulations of the sheep experiments, were not reached in these scenarios, indicating that the e ect of complete uterine artery or cord occlusions is much stronger than the occluding e ect of physiological uterine contractions with similar duration.
Recommendations. In our model, secondary FHR responses are evoked by catecholamines. Although we can mimic experimental FHR data, inter-oclussion blood pressure increase could not be simulated. It is suggested that other mechanisms such as vagal inhibition and myocard hypoxia, may also play a role [136, 179, 180]. Likely, fetal blood pressure is also in uenced by other vasoconstrictor agents e.g. arginine vasopressin, angiotensin II, and neuropeptide Y [60, 115]. Vagal inhibition was recently included in a model by Wang et al. [173]. They also added feedback of carbon dioxide on the chemoreceptor. With their model, FHR overshoots could be obtained after three hours of 1:2.5 min umbilical cord occlusions. However, it remains unclear if their model can also predict FHR responses during the rst 30 min of severe uterine artery or umbilical cord occlusions. It would be interesting to combine the mechanisms as implemented by Wang, with the catecholamine feedback proposed in this study. During longer simulations of severe hypoxia, other e ects such as catecholamine depletion and myocard hypoxia might also play a role. Although experimental data concerning myocard hypoxia is scarce, it would be very interesting to include these e ects in the model.
The current model was based on a mixture of experimental observations in human and sheep, making comparison between model data and experimental data a di cult task. In view of the many questions on catecholamine feedback, adapting the model for sheep physiology might be an option, since for fetal sheep much more data is available. With this model, the in uence of catecholamines on FHR responses can then be investigated in the sheep fetus.
80 Catecholamine feedback
Still, even when a coherent model for the sheep fetus is obtained, translation to the human fetus is not straightforward.
Conclusion. A catecholamine feedback model was developed and included in the CTG simu- lation model to simulate secondary FHR responses that occur during repeated severe hypoxic episodes. Simulation results of repeated severe uterine blood ow reductions showed an ini- tial decrease of inter-occlusion FHR, followed by a gradual increase, which is in qualitative agreement with sheep data. Simulations of repeated severe umbilical ow reductions resulted in FHR overshoots, which were less sharp as compared to experimental data. We conclude that catecholamines might at least partly play a role in the origin of secondary heart rate responses, but we can not exclude that other mechanisms, such as myocard hypoxia and vagal inhibition, are also involved.
81 Chapter 5
82 Chapter 6
General discussion Chapter 6
6.1 Introduction
Although improvements have been made between 2004 [51] and 2010 [52], currently in Eu- rope still babies die during the perinatal period. Steps have to be taken to reduce perinatal mortality. Therefore, in 2012, the perinatal IMPULS program, a collaboration between Máx- ima Medical Center, Eindhoven University of Technology, and Philips, was initiated. In this program about 20 PhDs with a medical or technical background, work together in order to improve perinatal care and to contribute to medical research and education. The research within the perinatal IMPULS program focuses on development of patient studies, design of new measurement techniques, and development of signal processing tools. Another impor- tant aspect within the IMPULS program is the development of mathematical models, to be used to improve understanding of fetal and neonatal physiology and to contribute to clinical research, education, and decision making.
In the research described in this thesis, a mathematical model is used to improve under- standing of the CTG. Despite its high intra- and inter-observer variability [27, 110, 125], the CTG is commonly used to evaluate fetal well-being during labor and delivery. Interpreta- tion of the CTG signals is very complex, which hampers evaluation of fetal well-being and recognition of fetal distress. Timely intervention during emergency scenarios will reduce fetal morbidity and mortality. In this thesis, the CTG simulation model of Van der Hout-van der Jagt [161–163] was used as a starting point. It was adapted and extended to gain more insight into the mechanisms underlying the FHR variations and to improve applicability of the model for research and education.
6.2 Main achievements
First, the new CTG simulation model was described (chapter 2 and 3). With respect to the previous model, the physical description of the e ect of uterine pressure on uterine and umbilical blood vessels was enhanced. Furthermore, the complexity of the cardiac function and central regulation submodels was drastically reduced.
In chapter 2, the e ects of uterine contractions, inducing uterine vein occlusion, on the fetal cardiovascular system were investigated. During a contraction, the uterine vein is com- pressed, which results in a reduced uterine blood ow. As a consequence, less oxygen will be supplied to the fetus. This results in a chemoreceptor-mediated increase of peripheral resis- tance, reducing peripheral blood ow. Concurrently, cerebral blood ow is increased via cere- bral autoregulation. This mechanism is called redistribution or brain-sparing. The increased blood pressure and decreased oxygen pressure lead to a net baro- and chemoreceptor- mediated FHR reduction. Due to the oxygen bu er function of the IVS, which delays the oxygen drop in the fetus, these simulations result in so-called ‘late decelerations’. The pre-
84 General discussion dicted FHR decelerations are considered more realistic than those obtained with the previous model, since they only show a drop of 3 bpm during a standard contraction. Usually, regular contractions do not cause signicant FHR decelerations in an uncompromised fetus.
The e ect of combined uterine vein and umbilical cord occlusions resulting from contractions was investigated in chapter 3. The direct e ect of cord occlusion is a blood volume shift from the fetus to the fetal placenta, and a reduction of fetal blood pressure. As a consequence, an initial baroreceptor-mediated FHR increase is observed in the FHR tracings, referred to as a ‘shoulder’. This shoulder is followed by an FHR deceleration, initiated by the reduction in oxygen pressure and the subsequent increase in blood pressure. Since cord occlusion immediately reduces oxygen levels in the fetus, FHR decelerations are less delayed compared to the scenario of uterine vein occlusion alone. Simulations of contractions with varying contraction amplitude or duration, reveal the wide variation in deceleration shapes caused by umbilical cord occlusions, which therefore are referred to as ’variable decelerations’.
In chapter 4, fetal heart rate variability (FHRV) was added to the model. Whereas FHRV was previously added in the post-processing step [161–163], now a more fundamental approach was used. In this chapter the e ect of three possible sources of variability was investigated: peripheral autoregulation, in uence of higher brain centers on the processing of the barore- ceptor output in the nucleus tractus solitarius of the medulla oblongata, and in uence of a erent systems on the vagal nerve center. To each of the sources of variability either 1/f or white noise was applied. By use of spectral analysis of the FHR tracings, power density spectra were obtained, showing a physiological 1/f character, independent of the noise type used. This reveals the physiological ltering characteristic of the model. However, the clin- ically observed peak around 0.1 Hz [54, 89] was only obtained when white noise was used. Realistic FHRV could be obtained by using di erent sources of variability, although the exact contribution of each of these sources in the human fetus remains unknown. The main issue in this research is that the output (FHRV), which can be measured in clinic, is in uenced by both the input (source of variability and type of noise) and the system itself (fetal body). With the model it is possible to systematically distinguish between the noise source and type, and the characteristics of the fetal regulation system. Thereby, the model might assist in the assessment of the physiological causes of FHRV. Although the clinically observed FHRV increase during contractions [25, 129, 175] was not observed in model simulations, addition of FHRV improved the realism of the simulated FHR tracings, which enhances application of the model for research and education.
In chapter 5, the model was used as a basis to investigate the contribution of catecholamine feedback to the generation of secondary FHR responses during repeated episodes of severe hypoxia. A simple model describing the combined e ect of adrenal catecholamine secre- tion and catecholamine nerve spillover as function of oxygen pressure, and catecholamine
85 Chapter 6 elimination in the placenta and tissues, was developed. Catecholamine feedback on FHR was modeled as a linear relation between arterial catecholamine concentration and change in heart period. The e ect of adrenaline and noradrenaline was combined in the model. Tuning of the model was based on sheep experiments in which the uterine artery [71, 72] or umbilical cord [58, 179] was repeatedly occluded. Parameter estimation and scaling was di cult due to the limited available human data and the known large interspecies di er- ences. Therefore, model simulations can be regarded as proof of principle, but one must be reticent in interpreting the results for the human fetus. Simulation results of repeated se- vere uterine blood ow reductions showed an initial decrease of inter-occlusion FHR, followed by a gradual increase. This trend was also observed in sheep experiments. Simulations of repeated severe umbilical blood ow reductions showed FHR overshoots, following the FHR decelerations. However, these overshoots were less sharp compared to experimental nd- ings in sheep. The model shows that catecholamines at least partly play a role in developing inter-occlusion tachycardia and FHR overshoots during severe hypoxic episodes. However, likely other mechanisms, such as vagal inhibition or myocard hypoxia, are also involved.
6.3 Application of the CTG simulation model
The current CTG simulation model can be used to gain understanding of the underlying mechanisms and serve as a tool for hypothesis testing and formation. As an example, the previously developed CTG simulation model of Van der Hout-van der Jagt et al. [161–163] was used to investigate the e ect of maternal hyperoxygenation on fetal oxygenation and FHR decelerations during labor [22]. Results of that study showed a reduction of deceleration depth and duration when 100% oxygen was administered to the mother. These e ects were also observed in small, non-randomized human studies [8, 85]. As a result, this e ect is currently tested in a larger patient population in a randomized clinical trial.
It has been shown that team-training of obstetric emergency scenarios is associated with improved team performance and medical technical skills [42, 56, 104], and with neonatal outcome [44, 45]. During these training sessions, simulation manikins can be used to prac- tice various delivery scenarios [42, 56, 104]. The fetal and maternal state are projected on monitors. During training sessions, the instructor has to observe medical interventions and actions from the trainees and has to adapt the fetal CTG accordingly. This is not only very time consuming, but also requires detailed physiological knowledge by the instructor. This system can be improved by using the CTG simulation model as an intelligent addition to the simulation manikins, in order to have them automatically and consistently respond to the clinical interventions during training sessions.
86 General discussion
Another relatively new eld in medical education is computer-based serious gaming. Serious games can be used to simulate scenarios which are di cult to practice in real life and to train clinical skills at relatively low costs [40]. Our model for CTG simulation can be implemented in such a game in order to gain understanding of the e ect of di erent interventions on fetal well-being and to gain insight into the clinical consequences of such actions. Simula- tion training, either manikin-based or computer-based, is especially useful to practice skills necessary in emergency situations that do not occur on a regular basis in the clinic.
Ultimately, the CTG simulation model could be used as a clinical decision support system. Two successful examples were discussed in chapter 1. However, there are several reasons why it is less straightforward for the current model to be used for clinical decision support. First, the previously discussed model examples focus on a limited part of the human system. In contrast, the CTG-simulation model describes the complete feto-maternal system, includ- ing circulation, oxygenation, and regulation. The mathematical relations describing most of these submodels are less well known. Besides, in our model, feedback mechanisms are included, which complicates the analysis of the input-output relations. Second, the given model examples require input data, which to a large extent consists of geometric data, for which measurement tools, such as CT, ultrasound or MRI, are available. These measurement techniques allow patient-specic parameter estimation. Since from the human fetus most parameters cannot be measured, especially for the regulation and catecholamine feedback submodels, parameters have to be estimated and scaled from human adult or animal data, as discussed in chapter 3 and 5. A sensitivity analysis can help in assessing which parameters can be set to generic values, and which parameters have to be set to patient-specic values. The model can be used to guide the design of experiments in order to obtain measurement values of parameters that dominate model response, and thus have to be determined very accurately. Third, ideally, patient measurements are performed to establish the input for the mathematical model, prior to clinical interventions. Hereafter the model is used to simulate di erent scenarios and treatment options. Simulation results can then be used to assist in the treatment selection. However, the time frame during labor and delivery, when most mea- surements should be performed, is relatively short. Finally, the limited data available from measurements in the human fetus and mother impair validation of the model. Therefore, use of the CTG simulation model as a clinical decision support system is not straightfor- ward. Whereas patient-specic modeling will be di cult, pathology-specic modeling, which gives insight into the di erent processes involved in various pathologies, might be an option. However, still for these pathology-specic models, parameter estimation will be a challenge.
87 Chapter 6
6.4 Future perspectives
As discussed previously, one of the main concerns for development of the CTG simulation model is the availability of experimental data. Further development of the model will require additional parameter estimation and model evaluation. Since a lot of research is performed in fetal sheep, a sheep model might be developed, as a rst step, combining hemodynamics, oxygenation, neuronal regulation, and humoral feedback for one single species. With the mathematical sheep model, the di erent processes in the fetal lamb can be investigated and understanding of the regulation of FHR can be improved. Hereafter, it might be more feasible to translate the model to a human fetus. Nevertheless, one has to keep in mind the di erences between the sheep and human fetus. For example, in the fetal sheep brain size is smaller, while umbilical blood ow is larger [133]. Besides, many interspecies di erences are observed concerning catecholamine feedback, as discussed in chapter 5.
There are di erent possibilities to extend the fetal model in order to make it more useful for eduction and research. For example, the hemodynamic model of the fetus might be enhanced by including shunts and preferential blood ows. In the fetus, several shunts are present in the circulatory system [109, 115]. The ductus venosus partly shunts the oxygen-rich blood that enters the fetal system via the umbilical vein, directly into the inferior vena cava. The oxygenated blood thereby short-cutts the liver circulation, and ows directly towards the heart. Here, the oxygen-rich blood preferentially ows, through the foramen ovale, which is another shunt that allows blood to ow from the right atrium into the left atrium, in order to supply the coronary and cerebral circulation with relatively well-oxygenated blood. Blood from the right ventricle is partly directed to the pulmonary circulation, but mostly enters the ascending aorta via another shunt, the ductus arteriosus. Explicitly modeling these shunts will improve estimation of the di erence between cerebral and peripheral oxygenation and enhance evaluation of the risks of asphyxia.
During severe hypoxic episodes, myocard hypoxia, which plays a role when the oxygen trans- port to the heart is insu cient, will also e ect FHR and might result in late decelerations [63, 103, 115]. Besides, it is suggested that vagal inhibition is involved in the origin of FHR overshoots during severe repeated umbilical cord occlusions [136, 173, 179]. In future studies, it will be interesting to include both of these mechanisms in the fetal model.
In clinical practice, fetal blood sampling is performed, in order to gain more insight into the fetal condition in case of a suboptimal CTG. From this blood sample, amongst others, the pH can be obtained. A decreased pH indicates a distressed fetus, and intervention is performed if the pH drops below 7.20 [159]. Addition of a pH submodel would improve clinical relevance of the model. It will also enable implementation of the Bohr e ect, which leads to a shift of the fetal oxygen dissociation curve, resulting from variations in pH. Several candidate models have been described in literature [24, 36, 173]. After birth, neonatal well-being is assessed via
88 General discussion the one and ve minute Apgar scores. This score is based on the breathing e ort, heart rate, re exes, muscle tone, and skin color of the newborn. Although it will be a challenging task to estimate the Apgar score from the model, an indication of the Apgar score will further increase the clinical relevance of the model.
Also the maternal model can be extended. Except for changes in uterine blood ow follow- ing uterine contractions, the maternal cardiovascular system is currently not subjected to cardiovascular changes during labor. Clinical studies have shown variations in heart rate and cardiac output during the di erent stages of labor as well as during periods of rest and con- tractions [127, 144]. Especially during active pushing, high heart rate levels were reached [144]. However, when accounting for cardiovascular changes during labor, a maternal cardiovascular regulation model should be included as well. The maternal model might further be enhanced by including a breathing model. Since labor and delivery require much e ort of the mother, presumably breathing patterns will change during labor, a ecting maternal oxygenation and subsequently fetal oxygen delivery.
89 Chapter 6
90 Bibliography Bibliography
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104 Samenvatting
105 Samenvatting
Simulatie van het cardiotocogram tijdens de bevalling: meer inzicht in de foetale fysiologie met behulp van een model
Tijdens de bevalling is het van belang om de toestand van het ongeboren kind te bewaken om tijdig in te kunnen grijpen in geval van nood. Bij voorkeur zou meting van de foetale zuurstofhuishouding onderdeel uit moeten maken van de bewaking. Echter, betrouwbare zuurstofmetingen kunnen alleen tijdens de bevalling, na het breken van de vliezen, verricht worden. Bovendien kunnen deze metingen niet continu, maar op slechts een beperkt aan- tal momenten in de tijd uitgevoerd worden. In de kliniek wordt daarom gebruik gemaakt van cardiotocograe om het foetale welzijn in te schatten. Het cardiotocogram (CTG) be- treft de gelijktijdige registratie van het foetale hartritme (FHR) en de baarmoedercontracties (weeën). De relatie tussen baarmoedercontracties en de uiteindelijke veranderingen van het FHR wordt gevormd door een complexe keten van fysiologische gebeurtenissen. Zo zullen veranderingen in bloed- en zuurstofdruk, via de baro- en chemore ex, invloed hebben op het FHR. Waarschijnlijk speelt ook de terugkoppeling via hormonen een rol. Door de com- plexiteit van dit systeem is het afschatten van de foetale toestand aan de hand van het CTG een moeilijke taak.
Om meer inzicht te verkrijgen in de complexe keten waarlangs baarmoedercontracties leiden tot veranderingen de bloed- en zuurstofdruk en uiteindelijk tot veranderingen in het FHR, kan een wiskundig computermodel gebruikt worden. In voorgaande studies is zo‘n com- putermodel ontwikkeld. Het model beschrijft de hemodynamica van moeder en kind, de zuurstofhuishouding, de foetale regulatie en de generatie van baarmoedercontracties. Het model kan gebruikt worden om verschillende scenario‘s te simuleren die kunnen optreden tijdens een baarmoedercontractie, zoals compressie van het hoofdje van het kind, reductie van de bloedstroom naar de baarmoeder, of compressie van de navelstreng. Deze sce- nario‘s leiden tot het ontstaan van respectievelijk vroege, late en variabele deceleraties in het FHR-signaal.
In dit proefschrift is eerst de complexiteit van het bestaande computermodel gereduceerd voor die submodellen waar parameterschatting gecompliceerd was (door een gebrek aan ex- perimentele data) of waar volstaan kon worden met minder gedetailleerde modeluitkomsten. Bovendien is de fysische beschrijving van andere submodellen verbeterd. Omdat de foetale hartritme variabiliteit (FHRV) een belangrijke indicator is voor foetale stress, is in een vol- gende stap de FHRV toegevoegd aan het model. Als laatste is de bijdrage van terugkoppeling via hormonen, die van belang wordt tijdens herhaaldelijke ernstige perioden van hypoxie, onderzocht met het model.
Met het verbeterde model uit de eerste stap is de cascade van gebeurtenissen tussen baar- moedercontracties en FHR veranderingen onderzocht. Baarmoedercontracties kunnen leiden tot een afname van de bloedstroom in de baarmoeder en/of de navelstreng en beïnvloeden
106 zo de foetale bloed- en zuurstofdruk, wat leidt tot stimulatie van de baro- en chemoreceptor. Uiteindelijk zullen via het sympatische en parasympathische zenuwstelsel veranderingen in het FHR teweeg gebracht worden. Baarmoedercontracties die zowel leiden tot bloedstroom- reducties in de baarmoeder als in de navelstreng, leiden tot een snellere en ernstigere afname in het FHR dan contracties die alleen invloed hebben op de bloedstroom naar de baarmoeder. Dit verschil kan verklaard worden door de zuurstofbu erfunctie van de intervilleuze ruimte in de baarmoeder. Indien alleen de bloedstroom naar de baarmoeder verminderd wordt, is deze zuurstofbu er namelijk nog beschikbaar voor de foetus, wat leidt tot een vertraagde en langzamere afname van de foetale zuurstofdruk. Als gevolg hiervan zal de chemoreceptor pas later gestimuleerd worden en de FHR reductie ook vertraagd en minder sterk zijn. In- dien ook de navelstreng afgekneld wordt, is de zuurstofbu er in de intervilleuze ruimte niet beschikbaar voor de foetus. Tijdens beide scenario’s vindt er herverdeling van de foetale bloedstroom plaats van de perifere naar de cerebrale circulatie. Op deze manier wordt het zuurstoftransport naar de hersenen zo veel mogelijk op peil gehouden. De initiële toename van het FHR tijdens navelstrengcompressies wordt veroorzaakt door de verplaatsing van bloed vanuit de foetus naar de foetale placenta. Deze resulteert in een afname van de bloeddruk en leidt via de baroreceptor tot een toename van het FHR. De verplaatsing van het foetale bloed wordt veroorzaakt door een vertraging tussen het sluiten van de navel- strengvene en de navelstrengarterieën. Het model is geëvalueerd aan de hand van data uit schapenexperimenten: er worden vergelijkbare trends in bloeddruk, zuurstofdruk en FHR verkregen. Dit laat zien dat het model in staat is om realistische deceleraties te beschrijven.
Aangezien de exacte bron voor FHRV niet bekend is, hebben we drie mogelijke bronnen voor FHRV onderzocht met het model: autoregulatie van de perifere bloedvaten, de invloed van hogere breincentra op de verwerking van de baroreceptor-output in de nucleus tractus solitarius van de medulla oblongata, en de invloed van a erente systemen, zoals het hart, de longen en spieren, op het vagale centrum. Tijdens de simulaties is er 1/f-ruis of witte ruis geplaatst op respectievelijk de perifere vaatweerstand, de baroreceptor-output, en de vagale e erente output van het zenuwstelsel. We hebben de FHR-signalen geëvalueerd op basis van visuele inspectie en met behulp van spectraalanalyse. Alle vermogensspectra lieten een fysiologisch 1/f-karakter zien, ongeacht de ruisbron en het ruistype dat gebruikt werd. De klinisch waargenomen piek rondom 0.1 Hz was alleen zichtbaar in het spectrum indien witte ruis gebruikt werd. Daarom kan verondersteld worden dat de fysiologische input waarschijn- lijk door witte ruis beschreven kan worden. De sympathische tak van het zenuwstelsel heeft overwegend invloed op het vermogen van lage frequenties, terwijl de vagale tak het vermogen van zowel lage als de hoge frequenties beïnvloedt. Dit is in overeenstemming met klinische data. Door de toevoeging van FHRV aan het model is het model beter in staat om realistische FHR signalen te simuleren. Dit is belangrijk indien het model gebruikt wordt voor educatieve doeleinden.
107 Samenvatting
Tijdens ernstige episodes van hypoxie, veroorzaakt door ernstige contracties, worden vaak secundaire FHR responsen gezien, zoals toename van het FHR basisniveau en korte FHR verhogingen (‘overshoots’). Waarschijnlijk worden deze FHR responsen veroorzaakt door ver- schillende mechanismen, waaronder terugkoppeling via stresshormonen en afname van de vagale tonus. Om deze secundaire FHR responsen te simuleren, hebben we het model uitge- breid met een eenvoudig submodel dat de feedback via catecholamines beschrijft. Resultaten van simulaties waarin de bloedstroom naar de baarmoeder verminderd wordt laten een trend zien die vergelijkbaar is met de trend die waargenomen is tijdens experimenten in schapen: een initiële afname van het FHR tussen de occlusies in, gevolgd door een geleidelijke toe- name. Simulaties van herhaalde ernstige navelstrengcompressies laten FHR overshoots zien, volgend op FHR deceleraties. Echter, deze overshoots hebben een minder scherp verloop dan overshoots waargenomen in schapenexperimenten. Het model laat zien dat catecholamines een rol spelen in het ontstaan van secundaire FHR responsen, maar dat andere mechanismen, zoals vagale inhibitie en myocard hypoxie, niet uitgesloten kunnen worden.
Het verbeterde en uitgebreide CTG-simulatiemodel is geschikter dan het oude model voor het vormen en toetsen van hypothesen en voor gebruik voor educatieve doeleinden. Het nieuwe model draagt bij aan het begrip van de cascade van gebeurtenissen tussen de baar- moedercontracties en veranderingen in het FHR.
108 Dankwoord
109 Dankwoord
Promoveren doe je niet alleen. Buiten de samenwerking op wetenschappelijk gebied, is de steun van familie, vrienden en collega’s ook belangrijk om je een weg te banen door alle ups en downs die een promotietraject kent. Graag wil ik dan ook een aantal mensen bedanken voor hun bijdrage aan de totstandkoming van dit proefschrift.
Allereerst mijn dagelijks begeleider en copromotor Peter Bovendeerd. Peter, bedankt voor al je steun, hulp en feedback de afgelopen vier jaar. Ik had me geen betere copromotor kunnen wensen. Je maakte altijd tijd als ik vastliep en advies nodig had. Ik waardeer je geduld en het meedenken, vooral als ik, vanwege mijn kritische en precieze instelling, nogmaals terugkwam op bepaalde keuzes die we gemaakt hadden. Naast de inhoudelijke besprekingen was er ook altijd ruimte voor informele gesprekken. We hebben vaak goed kunnen lachen. Ik kijk hier met heel veel plezier op terug.
Dan mijn tweede begeleider en adviseur van de promotiecommissie Beatrijs van der Hout. Beatrijs, aan het begin van mijn promotie, toen jij ook nog met je promotieonderzoek bezig was, hebben we veel samengewerkt. Het was erg jn om iemand te hebben die ik vanalles en nog wat kon vragen over het model. Ook later, toen je als postdoc in MMC ging werken, bleven we veel contact houden. Door jouw achtergrond in zowel de biomedische technologie als in de verloskunde wist je het technische en medische aspect van het onderzoek goed in het oog te houden. Bedankt voor de leuke gesprekken, die overigens lang niet allemaal over het onderzoek gingen. Net als jij, zal ook ík de BG’s, de oneindige catecholamineconcentraties en de chocolademelkmomentjes in MMC nooit vergeten!
Frans van de Vosse, mijn eerste promotor. Frans, bedankt voor je tijd en waardevolle feedback tijdens onze twee-maandelijkse overlegmomenten. Ondanks dat de verloskunde op sommige punten toch wel heel iets anders is dan cardiovasculaire biomechanica, zijn er wat het model betreft toch zeker ook een hoop raakvlakken. Bedankt voor al jouw meedenken en voor de waardevolle adviezen.
Mijn tweede promotor, Guid Oei. Guid, bedankt voor al je klinische input. Het is mooi om te zien hoe jij voor ieder probleem weer een oplossing probeert te zoeken en bovendien bij iedere vraag weer een leuk onderzoeksproject weet te verzinnen. Bedankt ook voor je gastvrijheid tijdens de FUN-meetings, die eens per maand bij jou thuis worden gehouden. Het zeer gevarieerde programma met de vele workshops, en natuurlijk het lekkere eten, zal ik niet vergeten!
Verder wil ik prof. dr. ir. Bergmans, prof. dr. Vandenbussche en prof. dr. Hilbers bedanken voor het beoordelen van mijn proefschrift en voor hun deelname in de promotiecommissie. Prof. dr. Ursino, thank you very much for being part of the committee and for reviewing my dissertation. Prof. dr. ir. Brunsveld, bedankt voor het overnemen van de voorzittersrol tijdens de ceremonie.
110 Zoals bij elke promovendus bekend is, kent ieder promotieonderzoek zijn dalen, maar zeker ook zijn pieken, zoals de acceptatie van een artikel of een succesvolle presentatie op een congres. Ik heb het erg jn gevonden om al deze momenten te kunnen delen met mijn col- lega’s. Ik wil dan ook mijn kamergenootjes van 4.09 bedanken! Andrès, Arianna, Franscesco, Gitta, Inge, Johanna, Joke, Jeroen, Lorenza, Lúcia, Marc, Marieke, Marleen, Renee, Saskia, Tilaï en Tomasso, bedankt voor alle gezelligheid, zowel op kantoor maar ook tijdens onze vele etentjes met ‘hok’ 4.09!
Dan wil ik de CVBM-groep bedanken, niet alleen voor de inspirerende meetings, maar ook voor de gezelligheid tijdens de verschillende etentjes en natuurlijk het jaarlijkse dagje uit. Mijn dank gaat ook uit naar de verschillende Bachelor en Master studenten aan de TU/e die ik begeleid heb en die elk hun steentje hebben bijgedragen aan dit onderzoek. Ik wil alle IMPULS-collega’s bedanken voor de vele inhoudelijke meetings. En dan uiteraard nog de FUN-groep, bedankt dat ik deel mocht uitmaken van deze multidisciplinaire groep. Door jullie verschillende achtergronden konden er altijd levendige discussies gevoerd worden over allerlei uiteenlopende onderwerpen. Ondanks dat ik maar een keer per week in MMC was, heb ik me er altijd welkom gevoeld. En niet te vergeten, bedankt voor de gezelligheid tijdens de onvergetelijke buitenlandse congressen in Orlando, Parijs, Saint-Vincent en Lyon.
Beste BMT-vrienden, we zijn in 2006 samen begonnen aan de opleiding BMT. Inmiddels heeft iedereen zijn eigen draai gevonden en zijn we allemaal op onze pootjes terecht gekomen. Een groot aantal van jullie is ook gaan promoveren. Het is heel jn dat we elkaar zo nu en dan een steuntje in de rug kunnen geven. Anneloes, Bart, Ellen Klein, Ellen Nijssen, Jeire, Joke, Raf, Stefan en Stijn, bedankt! In het speciaal wil ik Anne en Esther bedanken. Super tof dat jullie mijn paranimfen willen zijn! Bedankt voor al jullie steun, bij jullie kon ik echt altijd terecht. Ik hoop dat we nog heel lang zulke goede vriendinnen mogen blijven.
Lieve (schoon)familie, ondanks dat promoveren voor jullie ook allemaal nieuw is en jullie je waarschijnlijk wel vaker hebben afgevraagd wat ik nu precies aan het doen ben en waarvoor dan eigenlijk, voelde ik me altijd door jullie gesteund. Hortense, lief zusje, het is echt heel jn om iemand zo dichtbij te hebben die precies weet wat promoveren is en waar je altijd bij terecht kunt. Ondanks dat de onderwerpen van onze studies compleet verschillend zijn, begrijpen wij elkaar wat promoveren betreft volkomen. Bedankt voor je luisterend oor, en je peptalks. Heel veel succes bij het afronden van jouw promotieonderzoek, dat gaat je zeker lukken! Papa en mama, bedankt voor jullie onvoorwaardelijke steun, jullie geduld en advies. Promoveren was voor jullie ook nog onbekend terrein, totdat beide dochters besloten om na hun studie een promotietraject in te gaan. Zo langzaamaan kregen jullie steeds meer mee van wat promoveren inhoudt en ondertussen weten jullie er alles van. Bedankt dat ik altijd bij jullie terecht kan, altijd kan bellen en mag langskomen!
111 Dankwoord
En als laatste en belangrijkste natuurlijk, lieve Rob, bedankt voor al je steun de afgelopen vier jaar. Met name ook in de afrondende fase waarin de laatste hoofdstukken van mijn proefschrift geschreven moesten worden, maar we ondertussen ook al aan het verhuizen waren naar onze nieuwe woning om vanuit daar allebei met een nieuwe, uitdagende baan te starten. Ik kijk er naar uit om samen nog vele gezellige, leuke en mooie momenten te gaan meemaken, maar vooral ook om te gaan genieten van alles wat we tot nu toe samen hebben opgebouwd!
112 About the author About the author
Curriculum Vitae
Germaine Jongen was born on the 5th of September 1988 in Maastricht, the Netherlands. She attended secondary education at the Sint-Maartenscollege in Maastricht, where she obtained her atheneum (pre- university) diploma in 2006. Hereafter, she started studying Biomedical Engineering at Eindhoven Uni- versity of Technology. She obtained her Bachelor’s degree (cum laude) in 2009. In the same year, she started her Master’s program Medical Engineering, also at Eindhoven University of Technology. Dur- ing her Master’s she did a four-month internship at SINTEF, department of Medical Technology in Trond- heim, Norway, where she worked on the displacement and strain estimation in abdominal aortic aneurysms, using 2D ultrasound. For her Master’s project she performed research at the Biomedical Engineering department at Maastricht University and investigated the mechanical characterization and imaging of healthy aortas and abdominal aortic aneurysms with 2D ultrasound. She obtained her Master’s degree in Medical Engineering (cum laude) in 2011. In 2012 she started her PhD- project, which focused on the improvement and extension of a mathematical CTG simulation model, to be used for research and education. This research project was performed within the IMPULS perinatology framework, a collaboration between Máxima Medical Center, Eind- hoven University of Technology and Philips. As of May 2016, she works as a medical physicist in training at Radboudumc in Nijmegen.
114 Publications
Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, Bovendeerd PHM. Hypoxia-induced catecholamine feedback on fetal heart rate: A mathematical model study, under review for Med Eng Phys.
Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, Bovendeerd PHM. Simulation of fetal heart rate variability with a mathematical model, under review for Med Eng Phys.
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG, Bovendeerd PHM. A mathematical model to simulate the cardiotocogram during labor. Part B: Parameter es- timation and simulation of variable decelerations, J Biomech, 2016, http://dx.doi.org/10.1016/j. jbiomech.2016.01.046.
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG, Bovendeerd PHM. A mathematical model to simulate the cardiotocogram during labor. Part A: Model setup and simulation of late decelerations, J Biomech, 2016, http://dx.doi.org/10.1016/j.jbiomech.2016.01. 036. van der Hout-van der Jagt MB, Jongen GJLM, Bovendeerd PHM, Oei SG. Insight into variable fetal heart rate decelerations from a mathematical model, Early Hum Dev, 89:361-369, 2013.
Non peer-reviewed publications
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. De rol van mathematische modellen in de kliniek: Een CTG-simulatiemodel als voorbeeld, MT Integraal, 2016, www.mtintegraal.nl.
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. Wat doet een medisch ingenieur in het ziekenhuis?, Medisch Journaal, 44:108-112, 2015.
115 About the author
Conference abstracts
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG, Bovendeerd PHM. A new model for simulation of fetal heart rate variations during labor, oral presentation, 2nd Jan Beneken Conference, Nijmegen (NL), April 23-24, 2015.
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. Computer simulation of the cardiotocogram: the e ect of catecholamines, oral presentation, FNPS, Saint Vincent (IT), August 31 - September 3, 2014.
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. Modeling the contribution of humoral feedback to fetal heart rate responses during labor, oral presentation, SESAM 2013, Paris (FR), June 13-15, 2013.
Jongen GJLM, van der Hout-van der Jagt MB, Bullens L, Fransen AF, Oei SG. Simulation of the circulation: Hands-on simulation & model development, workshop, SESAM 2013, Paris (FR), June 13-15, 2013.
Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. Modeling the contribution of humoral feedback to fetal heart rate responses during labor, oral presentation, 1st Jan Beneken Conference, Eindhoven (NL), April 25-26, 2013. van der Hout-van der Jagt MB, Jongen GJLM, Bullens L, Fransen AF, Oei SG. Physiologic models in simulation: An OB case study, workshop, IMSH 2013, Orlando (FL, USA), January 27-30, 2013.
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