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ABSTRACT: During labor and delivery, variable decelerations in the fetal heart rate (FHR) are commonly seen on the cardiotocogram (CTG) that is used to monitor fetal welfare. These decelerations are often induced by umbilical cord compression from uterine contractions. Via changes in oxygenation and blood pressure, umbilical cord compression activates the chemo- and baroreceptor reflex, and thus affects FHR. Since the relation between the CTG and fetal oxygenation is complex, assessment of fetal welfare from the CTG is difficult. We investigated umbilical cord compression-induced variable decelerations with a mathematical model. For this purpose, we extended our model for decelerations originating from caput compression and reduced uterine blood flow with the possibility to induce umbilical venous, arterial and total cord occlusion. Model response during total occlusion is evaluated for varying contractions (duration and amplitude) and sensitivity of the umbilical resistance to the uterine pressure. A clinical scenario is used to simulate a labor CTG with variable decelerations. Simulation results show that fetal mean arterial pressure increases during umbilical cord occlusion, while fetal oxygenation drops. There is a clear relation between these signals and the resulting FHR. The extent of umbilical compression and thus FHR deceleration is positively related to increased contraction duration and amplitude, and increased sensitivity of the umbilical resistance to uterine pressure. No relation is found between contraction interval and FHR response, which can probably be ascribed to the lack of catecholamines in the model. The simulation model provides insight into the complex relation between uterine pressure, umbilical cord compression, fetal oxygenation, blood pressure and heart rate. The model can be used for individual learning, and incorporated in a simulation mannequin, be used to enhance obstetric team training.
Early human development 12/2012; · 2.12 Impact Factor
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ABSTRACT: Fetal welfare during labor and delivery is commonly monitored through the cardiotocogram (CTG), the combined registration of uterus contractions and fetal heart rate (FHR). From the CTG, the fetal oxygen state is estimated as the main indicator of the fetal condition, but this estimate is difficult to make, due to the complex relation between CTG and oxygen state. Mathematical models can be used to assist in the interpretation of the CTG, since they enable quantitative modeling of the flow of events through which uterine contractions affect fetal oxygenation and FHR. We propose a mathematical model to simulate reflex 'late decelerations', i.e. variations in FHR originating from uteroplacental flow reduction during uterine contractions and mediated by the baroreflex and the chemoreflex. Results for the uncompromised fetus show that partial oxygen pressures reduce in relation to the strength and duration of the contraction. Above a certain threshold, hypoxemia will evoke a late deceleration. Results for uteroplacental insufficiency, simulated by reduced uterine blood supply or reduced placental diffusion capacity, demonstrated lower baseline FHR and smaller decelerations during contraction. Reduced uteroplacental blood volume was found to lead to deeper decelerations only. The model response in several nerve blocking simulations was similar to experimental findings by Martin et al. [18], indicating a correct balance between vagal and sympathetic reflex pathways.
Early human development 07/2012; · 2.12 Impact Factor
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ABSTRACT: The left ventricle (LV) of mammals with Situs Solitus (SS, normal organ arrangement) displays hardly any interindividual variation in myofiber pattern and experimentally determined torsion. SS LV myofiber pattern has been suggested to result from adaptive myofiber reorientation, in turn leading to efficient pump and myofiber function. Limited data from the Situs Inversus Totalis (SIT, a complete mirror image of organ anatomy and position) LV demonstrated an essential different myofiber pattern, being normal at the apex but mirrored at the base. Considerable differences in torsion patterns in between human SIT LVs even suggest variation in myofiber pattern among SIT LVs themselves. We addressed whether different myofiber patterns in the SIT LV can be predicted by adaptive myofiber reorientation and whether they yield similar pump and myofiber function as in the SS LV. With a mathematical model of LV mechanics including shear induced myofiber reorientation, we predicted myofiber patterns of one SS and three different SIT LVs. Initial conditions for SIT were based on scarce information on the helix angle. The transverse angle was set to zero. During reorientation, a non-zero transverse angle developed, pump function increased, and myofiber function increased and became more homogeneous. Three continuous SIT structures emerged with a different location of transition between normal and mirrored myofiber orientation pattern. Predicted SIT torsion patterns matched experimentally determined ones. Pump and myofiber function in SIT and SS LVs are similar, despite essential differences in myocardial structure. SS and SIT LV structure and function may originate from same processes of adaptive myofiber reorientation.
PLoS Computational Biology 07/2012; 8(7):e1002611. · 5.22 Impact Factor
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ABSTRACT: Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and
heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables
the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models
based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are
created that describe heart function at different length and time scales. In this review, we describe basic modules that can
be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling,
excitation–contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss
adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation,
ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While
current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding
mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.
KeywordsAdaptive modeling–Cardiac dyssynchrony–Heart failure–Mechanoelectrical coupling–Multi-scale model–Patient-specific model
Journal of Cardiovascular Translational Research 05/2012; 5(2):159-169. · 2.61 Impact Factor
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ABSTRACT: Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation-contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.
Journal of Cardiovascular Translational Research 04/2012; 5(2):159-69. · 2.61 Impact Factor
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Peter H M Bovendeerd
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ABSTRACT: The heart has the ability to respond to long-term changes in its environment through changes in mass (growth), shape (morphogenesis) and tissue properties (remodeling). For improved quantitative understanding of cardiac growth and remodeling (G&R) experimental studies need to be complemented by mathematical models. This paper reviews models for cardiac growth and remodeling of myofiber orientation, as induced by mechanical stimuli. A distinction is made between optimization models, that focus on the end stage of G&R, and adaptation models, that aim to more closely describe the mechanistic relation between stimulus and effect. While many models demonstrate qualitatively promising results, a lot of questions remain, e.g. with respect to the choice of the stimulus for G&R or the long-term stability of the outcome of the model. A continued effort combining information on mechanotransduction at the cellular level, experimental observations on G&R at organ level, and testing of hypotheses on stimulus-effect relations in mathematical models is needed to answer these questions on cardiac G&R. Ultimately, models of cardiac G&R seem indispensable for patient-specific modeling, both to reconstruct the actual state of the heart and to assess the long-term effect of potential interventions.
Journal of biomechanics 12/2011; 45(5):872-81. · 2.66 Impact Factor
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ABSTRACT: Fetal welfare during labor and delivery is commonly monitored through the cardiotocogram (CTG), the combined registration of uterus contractions and fetal heart rate (FHR). The CTG gives an indication of the main determinant of the acute fetal condition, namely its oxygen state. However, interpretation is complicated by the complex relationship between the two. Mathematical models can be used to assist with the interpretation of the CTG, since they enable quantitative modeling of the cascade of events through which uterine contractions affect fetal oxygenation and FHR. We developed a mathematical model to simulate 'early decelerations', i.e. variations in FHR originating from caput compression during uterine contractions, as mediated by cerebral flow reduction, cerebral hypoxia and a vagal nerve response to hypoxia. Simulation results show a realistic response, both for fetal and maternal hemodynamics at term, as for FHR variation during early decelerations. The model is intended to be used as a training tool for gynaecologists. Therefore 6 clinical experts were asked to rate 5 real and 5 model-generated CTG tracings on overall realism and realism of selected aspects. Results show no significant differences between real and computer-generated CTG tracings.
Medical Engineering & Physics 10/2011; 34(5):579-89. · 1.62 Impact Factor
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Sarah L Waters,
Jordi Alastruey,
Daniel A Beard, Peter H M Bovendeerd,
Peter F Davies,
Girija Jayaraman,
Oliver E Jensen,
Jack Lee,
Kim H Parker,
Aleksander S Popel,
Timothy W Secomb,
Maria Siebes,
Spencer J Sherwin,
Rebecca J Shipley,
Nicolas P Smith,
Frans N van de Vosse
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ABSTRACT: A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.
Progress in Biophysics and Molecular Biology 10/2010; 104(1-3):49-76. · 3.20 Impact Factor
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ABSTRACT: Atrial fibrillation, a common cardiac arrhythmia, is promoted by atrial dilatation. Acute atrial dilatation may play a role in atrial arrhythmogenesis through mechanoelectric feedback. In experimental studies, conduction slowing and block have been observed in acutely dilated atria. In the present study, the influence of the stretch-activated current (I(sac)) on impulse propagation is investigated by means of computer simulations. Homogeneous and inhomogeneous atrial tissues are modeled by cardiac fibers composed of segments that are electrically and mechanically coupled. Active force is related to free Ca(2+) concentration and sarcomere length. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and I(sac) under stretch. In our model, conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Conduction block can be unidirectional in an inhomogeneous fiber and is promoted by a shorter stimulation interval. Slowing of conduction is explained by inactivation of Na(+) channels and a lower maximum upstroke velocity due to a depolarized resting membrane potential. Conduction block at shorter stimulation intervals is explained by a longer effective refractory period under stretch. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria.
AJP Heart and Circulatory Physiology 07/2007; 292(6):H2832-53. · 3.71 Impact Factor
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ABSTRACT: The phasic coronary arterial inflow during the normal cardiac cycle has been explained with simple (waterfall, intramyocardial pump) models, emphasizing the role of ventricular pressure. To explain changes in isovolumic and low afterload beats, these models were extended with the effect of three-dimensional wall stress, nonlinear characteristics of the coronary bed, and extravascular fluid exchange. With the associated increase in the number of model parameters, a detailed parameter sensitivity analysis has become difficult. Therefore we investigated the primary relations between ventricular pressure and volume, wall stress, intramyocardial pressure and coronary blood flow, with a mathematical model with a limited number of parameters. The model replicates several experimental observations: the phasic character of coronary inflow is virtually independent of maximum ventricular pressure, the amplitude of the coronary flow signal varies about proportionally with cardiac contractility, and intramyocardial pressure in the ventricular wall may exceed ventricular pressure. A parameter sensitivity analysis shows that the normalized amplitude of coronary inflow is mainly determined by contractility, reflected in ventricular pressure and, at low ventricular volumes, radial wall stress. Normalized flow amplitude is less sensitive to myocardial coronary compliance and resistance, and to the relation between active fiber stress, time, and sarcomere shortening velocity.
Annals of Biomedical Engineering 01/2007; 34(12):1833-45. · 2.37 Impact Factor
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ABSTRACT: For efficient pump function, contraction of the heart should be as synchronous as possible. Ventricular pacing induces asynchrony of depolarization and contraction. The degree of asynchrony depends on the position of the pacing electrode. The aim of this study was to extend an existing numerical model of electromechanics in the left ventricle (LV) to the application of ventricular pacing. With the model, the relation between pacing site and patterns of depolarization and contraction was investigated.
The LV was approximated by a thick-walled ellipsoid with a realistic myofiber orientation. Propagation of the depolarization wave was described by the eikonal-diffusion equation, in which five parameters play a role: myocardial and subendocardial velocity of wave propagation along the myofiber cm and ce; myocardial and subendocardial anisotropy am and ae; and parameter k, describing the influence of wave curvature on wave velocity. Parameters cm, ae, and k were taken from literature. Parameters am and ce were estimated by fitting the model to experimental data, obtained by pacing the canine left ventricular free wall (LVFW). The best fit was found with cm = 0.75 m/s, ce = 1.3 m/s, am = 2.5, ae = 1.5, and k = 2.1 x 10(-4) m2/s. With these parameter settings, for right ventricular apex (RVA) pacing, the depolarization times were realistically simulated as also shown by the wavefronts and the time needed to activate the LVFW. The moment of depolarization was used to initiate myofiber contraction in a model of LV mechanics. For both pacing situations, mid-wall circumferential strains and onset of myofiber shortening were obtained.
With a relatively simple model setup, simulated depolarization timing patterns agreed with measurements for pacing at the LVFW and RVA in an LV. Myocardial cross-fiber wave velocity is estimated to be 0.40 times the velocity along the myofiber direction (0.75 m/s). Subendocardial wave velocity is about 1.7 times faster than in the rest of the myocardium, but about 3 times slower than as found in Purkinje fibers. Furthermore, model and experiment agreed in the following respects. (1) Ventricular pacing decreased both systolic pressure and ejection fraction relative to natural sinus rhythm. (2) In early depolarized regions, early shortening was observed in the isovolumic contraction phase; in late depolarized regions, myofibers were stretched in this phase. Maps showing timing of onset of shortening were similar to previously measured maps in which wave velocity of contraction appeared similar to that of depolarization.
Journal of Cardiovascular Electrophysiology 11/2003; 14(10 Suppl):S188-95. · 3.06 Impact Factor
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ABSTRACT: Introduction: For efficient pump function, contraction of the heart should be as synchronous as possible. Ventricular pacing induces asynchrony of depolarization and contraction. The degree of asynchrony depends on the position of the pacing electrode. The aim of this study was to extend an existing numerical model of electromechanics in the left ventricle (LV) to the application of ventricular pacing. With the model, the relation between pacing site and patterns of depolarization and contraction was investigated.Methods and Results: The LV was approximated by a thick-walled ellipsoid with a realistic myofiber orientation. Propagation of the depolarization wave was described by the eikonal-diffusion equation, in which five parameters play a role: myocardial and subendocardial velocity of wave propagation along the myofiber cm and ce; myocardial and subendocardial anisotropy am and ae; and parameter k, describing the influence of wave curvature on wave velocity. Parameters cm, ae, and k were taken from literature. Parameters am and ce were estimated by fitting the model to experimental data, obtained by pacing the canine left ventricular free wall (LVFW). The best fit was found with cm= 0.75 m/s, ce= 1.3 m/s, am= 2.5, ae= 1.5, and k= 2.1 × 10−4 m2/s. With these parameter settings, for right ventricular apex (RVA) pacing, the depolarization times were realistically simulated as also shown by the wavefronts and the time needed to activate the LVFW. The moment of depolarization was used to initiate myofiber contraction in a model of LV mechanics. For both pacing situations, mid-wall circumferential strains and onset of myofiber shortening were obtained.Conclusion: With a relatively simple model setup, simulated depolarization timing patterns agreed with measurements for pacing at the LVFW and RVA in an LV. Myocardial cross-fiber wave velocity is estimated to be 0.40 times the velocity along the myofiber direction (0.75 m/s). Subendocardial wave velocity is about 1.7 times faster than in the rest of the myocardium, but about 3 times slower than as found in Purkinje fibers. Furthermore, model and experiment agreed in the following respects. (1) Ventricular pacing decreased both systolic pressure and ejection fraction relative to natural sinus rhythm. (2) In early depolarized regions, early shortening was observed in the isovolumic contraction phase; in late depolarized regions, myofibers were stretched in this phase. Maps showing timing of onset of shortening were similar to previously measured maps in which wave velocity of contraction appeared similar to that of depolarization. (J Cardiovasc Electrophysiol, Vol. 14, pp. S188-S195, October 2003, Suppl.)
Journal of Cardiovascular Electrophysiology 09/2003; 14(s10):S188 - S195. · 3.06 Impact Factor
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ABSTRACT: In current Finite Element (FE) head models, brain tissue is commonly assumed to display linear viscoelastic material behaviour. However, brain tissue behaves like a non-linear viscoelastic solid for shear strains above 1%. The main objective of this study was to study the effect of non-linear material behaviour on the predicted brain response. We used a non-linear viscoelastic constitutive model, developed on the basis of experimental shear data presented elsewere. First we tested the numerical implementation of the constitutive model by simulating the response of a silicone gel (Sylgard 572 A&B) filled cylindrical cup, subjected to a transient rotational acceleration. The experimental results could be reproduced within 9%. Subsequently, the effect of non-linear material modelling on computed brain response was investigated in an existing three-dimensional head model subjected to an eccentric rotation. At the applied external load strains in the brain were approximately ten times larger than was expected on the basis of published data. This is probably caused by the values of the shear moduli applied in the model. These are at least a factor of ten lower than the ones used in head models in literature but comparable to material data in recent literature. Non-linear material behaviour was found to influence the levels of predicted strains (+20%) and stresses (-11%) but not their temporal and spatial distribution. The pressure response was independent of non-linear material behaviour. In fact it could be predicted by the equilibrium of momentum, and thus it is independent of the choice of the brain constitutive model.
Stapp car crash journal 12/2002; 46:103-21.
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ABSTRACT: The aim of this study was to investigate the influence of fiber orientation in the left ventricular (LV) wall on the ejection fraction, efficiency, and heterogeneity of the distributions of developed fiber stress, strain and ATP consumption. A finite element model of LV mechanics was used with active properties of the cardiac muscle described by the Huxley-type cross-bridge model. The computed variances of sarcomere length (SL(var)), developed stress (DS(var)), and ATP consumption (ATP(var)) have several minima at different transmural courses of helix fiber angle. We identified only one region in the used design space with high ejection fraction, high efficiency of the LV and relatively small SL(var), DS(var), and ATP(var). This region corresponds to the physiological distribution of the helix fiber angle in the LV wall. Transmural fiber angle can be predicted by minimizing SL(var) and DS(var), but not ATP(var). If ATP(var) was minimized, then the transverse fiber angle was considerably underestimated. The results suggest that ATP consumption distribution is not regulating the fiber orientation in the heart.
AJP Heart and Circulatory Physiology 10/2002; 283(3):H1072-81. · 3.71 Impact Factor
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ABSTRACT: The aim of this thesis is to investigate the link between biochemical intracellular processes and mechanical contraction of the cardiac muscle. First, the regulation of intracellular energy fluxes between mitochondria and myofibrils is studied. It is shown, that the experimentally observed metabolic stability of the cardiac muscle is reproducible by a simple feedback regulation mechanism, i.e., ATP consumption in myofibrils and ATP production in mitochondria are balanced by the changes of the high energy phosphate concentrations. Second, an important property of energy transformation from biochemical form to mechanical work in the cardiac muscle, the linear relationship between the oxygen consumption and the stress-strain area, is replicated by a cross-bridge model. Third, by using the developed cross-bridge model, the correlation between ejection fraction of the left ventricle and heterogeneity of sarcomere strain, developed stress and ATP consumption in the left ventricular wall is established. Fourth, an experimentally observed linear relationship between oxygen consumption and the pressure-volume area can be predicted theoretically from a linear relationship between the oxygen consumption and the stress-strain area. Summing up, it is shown how the macrovariables of a cardiac muscle are interwoven with intracellular physiological processes into a whole.
Neuro endocrinology letters 03/2002; 23(1):13-20. · 1.30 Impact Factor
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ABSTRACT: The aim of this work is to reproduce the experimentally measured linear dependence of cardiac muscle oxygen consumption on stress–strain area using a model, composed of a three-state Huxley-type model for cross-bridge interaction and a phenomenological model of Ca2+-induced activation. By selecting particular cross-bridge cycling rate constants and modifying the cross-bridge activation model, we replicated the linear dependence between oxygen consumption and stress–strain area together with other important mechanical properties of cardiac muscle such as developed stress dependence on the sarcomere length and force-velocity relationship. The model predicts that (1) the amount of the passenger cross bridges, i.e., cross bridges that detach without hydrolyzing ATP molecule, is relatively small and (2) ATP consumption rate profile within a beat and the amount of the passenger cross bridges depend on the contraction protocol. 2000 Biomedical Engineering Society.
PAC00: 8719Rr, 8719Ff, 8710+e, 8719Hh
Annals of Biomedical Engineering 01/2000; 28(6):629-640. · 2.37 Impact Factor
