BASIC SCIENCE
Europace (2014) 16, 758–765 doi:10.1093/europace/eut377
Towards computational modelling of the human foetal electrocardiogram: normal sinus rhythm and congenital heart block Eleftheria Pervolaraki 1*, Sam Hodgson 2, Arun V. Holden 1, and Alan P. Benson 1 1
School of Biomedical Sciences, University of Leeds, Leeds LS2 9JT, UK; and 2Division of Medical Sciences, University of Oxford, Oxford OX1 3PL, UK
Received 15 July 2013; accepted after revision 4 November 2013
Aims
----------------------------------------------------------------------------------------------------------------------------------------------------------Keywords
Foetal † Human † Congenital heart block † Tachycardia † Electrocardiogram
Introduction Current computational models of the propagating electrical activity within the adult human heart can provide a quantitative reproduction of the electrocardiogram (ECG) recorded on the body surface,1 and allow the non-invasive reconstruction of spatio-temporal activity on the surface of the heart from the ECG body surface map2 during normal sinus rhythm and arrhythmia. These models are based on segmented, high-resolution (100– 200 mm cubic voxel) datasets of cardiac geometry and anisotropic and orthotropic tissue architecture, derived from diffusion tensor magnetic resonance imaging (DT-MRI)3,4 of ex vivo hearts, and lower resolution clinical MRI datasets of the in vivo beating heart geometry, together with biophysically detailed models of the cellular electrophysiology of the different conducting and contractile tissues of the heart. These models allow a mechanistic rather than empirical interpretation of the ECG and
are being used in virtual screening to predict the effects on the ECG of pharmacological agents whose actions on cardiac ion channel dynamics and cellular electrophysiology have been described quantitatively.5 The in utero human foetal ECG (fECG) can be recorded via electrodes on the mother’s abdominal surface from about 12 weeks gestational age (WGA). The fECG has a small (,50 mV) amplitude but foetal QRS complexes are clearly identifiable, and foetal RR intervals automatically extracted, and foetal bradycardia, tachycardia, and ectopy are readily identified. During gestation the foetus moves, and so the size and shape of the components of the fECG recorded at any one site on the maternal abdomen are not consistent and can change rapidly. However, the timings of the components are consistent and vary with foetal heart rate, and with gestational age. Changes in heart rate variability with time can be obtained directly from RR intervals, and have been related to foetal distress6 in the preterm and sepsis in
* Corresponding author. Tel: +44 113 34 31869, E-mail: [email protected] Published on behalf of the European Society of Cardiology. All rights reserved. & The Author 2013. For permissions please email: [email protected].
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We aim to engineer a computational model of propagation during normal sinus rhythm in the foetal human heart, by modifying models for adult cardiac tissue to match foetal electrocardiogram (fECG) characteristics. The model will be partially validated by fECG data, and applied to explore possible mechanisms of arrhythmogenesis in the foetal heart. ..................................................................................................................................................................................... Methods Foetal electrocardiograms have been recorded during pregnancy, with P- and T-waves, and the QRS complex, identified and results by averaging and signal processing. Intervals of the fECG are extracted and used to modify currently available human adult cardiomyocyte models. RR intervals inform models of the pacemaking cells by constraining their rate, the QT interval and its rate dependence constrain models of ventricular cells, and the width of the P-wave, the QR and PR intervals constrain propagation times, conduction velocities, and intercellular coupling. These cell models are coupled into a one-dimensional (1D) model of propagation during normal sinus rhythm in the human foetal heart. We constructed a modular, heterogeneous 1D model for propagation in the foetal heart, and predicted the effects of reduction in L-type Ca++ current. These include bradycardia and atrioventricular conduction blocks. These may account quantitatively for congenital heart block produced by positive IgG antibodies. ..................................................................................................................................................................................... Conclusion The fECG can be interpreted mechanistically and quantitatively by using a simple computational model for propagation. After further validation, by clinical recordings of the fECG and the electrophysiological experiments on foetal cardiac cells and tissues, the model may be used to predict the effects of maternally administered pharmaceuticals on the fECG.
Towards computational modelling of the human fECG
What’s new? † Models of the action potentials of 20– 40 weeks gestational age human foetal sinoatrial, atrial, atrioventricular Purkinje, and ventricular cells are constructed. † A one-dimensional model for propagation in the foetal heart is constructed that reproduces normal sinus rhythm and predicts conduction block produced by reduction in the L-type Ca conductance of cardiac cells. † These computations are related to bradycardia preceding congenital heart block.
Methods Pacemaker and conducting system cell models Throughout gestation, the foetal heart rate increases, from 95 – 100 b.p.m. at 5 weeks to 160– 180 b.p.m. towards full term, and then
decreases slowly to about 150 b.p.m. at full term.11 – 15 These changes in heart rate reflect changes in pacemaking activity, with the basic cycle length increasing from 350 ms at 8 WGA to 450 ms at 38 WGA. The cellular basis of mammalian cardiac pacemaking involves membrane currents, through ion channels, exchangers, and transporters that form a membrane oscillator,15,16 coupled via Ca++ fluxes to an oscillatory Ca++ release from the sarcoplasmic reticulum through ryanodine receptors.17 Quantitative models, firmly based on voltage clamp analyses of isolated sinoatrial node cell and tissue preparations, and optical recordings of intracellular Ca++ transients, have been constructed for the rabbit and mouse but are not available for either foetal or adult human sinoatrial cells. An initial model of adult sinoatrial cell has been constructed18 by modifying the parameters of a model for human atrial cells19 by the ratio of mRNA expression for membrane channels and sarcoplasmic Ca++ handling between atrial and nodal tissue in a post-mortem heart, and incorporating equations for the T-type calcium current (ICaT) and the hyperpolarization-activated current (the ‘funny’ current; If ) that have been characterized in the rabbit and whose mRNA is expressed in human sinoatrial node tissue. The foetal and adult cells both have the same genes for cardiac ion channels, exchangers, pumps, and intracellular binding and sequestration proteins, but the period of the foetal heart is shorter than that of the adult. These quantitative differences in behaviour between the foetus and the adult may be produced by differences in channel expression (e.g. maximal channel conductances or membrane channel densities, that could be measured by cellular electrophysiological experiments on physiologically viable foetal myocardial cells and tissue, or by mRNA levels that could be estimated by quantitative polymerase chain reaction of ex vivo foetal cardiac tissue) and by different kinetics, due to the expression of different isoforms or insertion into a different membrane microenvironment. In cell models, these can be incorporated by scaling the magnitudes of the currents (via the maximal channel conductance), or altering the kinetics by shifting the voltage-dependence of the activation and inactivation rate coefficients of the gating variables. In the absence of either kinetic data on human foetal cardiac channel isoforms, or specific antibody or mRNA data for foetal channel expression, we simply scale the maximal conductances of the adult model to attempt to reproduce the appropriate periodicity of the pacemaker, to test the hypothesis that the differences in rate can be quantitatively explained by the differences in channel expression alone. To reproduce the period of the fECG, all that is required is for the cycle length driven by the sinoatrial node to be appropriate, and the sinoatrial node model to generate action potentials that can drive the atrial tissue.20,21 Thus, we reproduced the experimentally recorded fECG periodicity (i.e. the R –R interval) in the model by scaling the model ion channel conductances. An increase in the maximal conductances Gf (for the current If ) and GCaL (for ICaL), or a decrease in the maximal conductance (GK1) of the time-independent K+ current (IK1), all individually increase the cycle length of the action potentials, but by not enough. Changes in Gf, GCaL, and GK1 are needed to produce the 400 ms periodicity of the 20 WGA heart (i.e. the approximate R – R interval from the experimentally recorded fECG), and there are ranges of values of Gf, GCaL, and GK1, or a volume in {Gf, GCaL, GK1} parameter space, that can produce the appropriate periodicity. We use two illustrative examples, one in which the foetal cycle length of 400 ms in the sinoatrial node model19 is predominately due to a high GCaL and one in which it is predominantly due to high Gf (‘high GCaL’ and ‘high Gf ’, respectively): see Figures 1A and B. We ignore the electrophysiological complexity of the atrioventricular node, with fast and slow pathways and three cell types,24 and use the human sinoatrial cell model with parameters that give a longer cycle length: see Figure 1D.
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the premature neonate.7 Modern instrumentation and signal analysis (averaging, principal component analysis) allow reliable characterization of foetal P- and T-wave characteristics,8 and foetal magnetocardiography provides higher signal-to-noise ratio recordings from 20 WGA, allowing the identification and characterization of foetal arrhythmias from QRS duration and QT intervals.9 The geometry of human ex vivo foetal hearts during the first 12 weeks of gestation has been imaged using MRI and episcopic fluorescent image capture, and an atlas of two-dimensional (2D) data stacks that allow 3D reconstruction of the development of the heart is available.10 The geometry and architecture (myofibre and myolamellar orientation) of hearts from 14 to 20 WGA has been imaged with a resolution of 100 mm cubic voxels using DT-MRI,11 and 3D models of the anisotropic and orthotropic geometry of the developing foetal heart have been reconstructed. These ex vivo hearts were obtained from foetuses following induced abortions. Temporary storage of tissue for imaging was in premises licensed by the 2004 Human Tissues Act. All procedures were approved by both hospital and university ethics committees, and informed maternal consent had been obtained for use of the foetal material in research. Although high-resolution structural data are available, there is little electrophysiological data from physiologically viable foetal cardiac tissue. The components of the fECG, when extracted, can inform models of foetal cardiac electrophysiology: during sinus rhythm the RR intervals reflect the rate of the sinoatrial pacemaker; the RR temporal variability reflects the effects of autonomic inputs to the sinoatrial node; the QT intervals provide an index of ventricular action potential duration and its restitution; the width of the P-wave reflects the timings of the first and last atrial depolarization, or the atrial propagation time determined by atrial size and propagation velocity; the width of the QRS complex reflects the ventricular size/propagation velocity. We construct a preliminary 1D model of propagation during normal sinus rhythm in the foetal heart by modifying the parameters in models of adult human sinoatrial, atrial, atrioventricular, Purkinje, and ventricular cells to reproduce fECG intervals. The 1D model is used to quantitatively explore the possible mechanisms of congenital heart block.
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Figure 1 Comparison of maximal membrane conductances (nS/pF) for the fast Na+ current (NaV1.1, 1.5) GNa, transient outward current
The adult Purkinje fibre model,22 a modified ventricular cell model that includes If and a sustained K+ current, was used, with an intrinsic period of 4.2 s in the tissue.
Atrial and ventricular myocyte models There are a number of current models for human adult atrial25,26 and ventricular cell23,27,28 models: we used the Courtemanche – Ramirez – Nattel18 and ten Tusscher – Panfilov23 models for atrial and ventricular cells, as they form the bases for the pacemaking and conducting cell models. Parameters for the shorter action potential of the atrial ring29 were used to produce a shorter atrial action potential duration, to allow the atrium to be driven by the foetal sinoatrial node. A QT restitution curve for the fECG for 12 – 40 WGA has been constructed11 from data in the literature,13,14,30 together with foetal ventricular action potential duration data in the literature.31 We have previously shown that the action potential duration (at 90% repolarization; APD90) restitution curve computed for the ten Tusscher – Panfilov ventricular cell model provides a good fit to the QT and the APD restitution data when GCaL is set very small (3.98 × 1025 nS/pF) and GKr is increased to 0.153 nS/pF (cf. Figure 8a in Pervolaraki et al.11). We use these parameters for the model presented here. As we are unsure about cell heterogeneity in the foetal ventricles due to a lack of published experimental data, we have for this initial study omitted such heterogeneity and use only endocardial cell formulations in the ventricular tissue region. Inclusion of ventricular heterogeneity in future studies may account for some of the disagreements between the experimental and the model fECGs (see the Results section below). The maximal conductance parameters used here to construct the foetal sinoatrial, atrial, atrioventricular, Purkinje, and ventricular cell models from the published adult cell models18,19,22,23 are presented in Figure 1 and Table 1.
One-dimensional tissue model Propagation of electrical excitation in homogeneous cardiac tissue can be described by the non-linear partial differential equation:32,33 ∂V = ∇(D∇V) − Iion ∂t
(1)
Here, V (mV) is membrane potential, ∇ is a spatial gradient operator, and t is time (ms). D is the diffusion coefficient tensor (mm2 ms21) that characterizes the electrotonic spread of voltage via local circuit currents, through cell-to-cell coupling by gap junctions, and the extracellular and intracellular resistances. Iion is the total membrane ionic current density (mA.mF21). Spatial inhomogeneities can be introduced by segmentation, hence different parts of the model have the excitation properties of different cell types, and different diffusion coefficients. In a 1D model, the type of cell model, its parameters (here, we only change the maximal conductances), and diffusion coefficients change with distance. Such a 1D, heterogenous model for propagation in cardiac tissue was introduced by Gima and Rudy,34 and has been widely applied to model propagation, the rate dependence of APD, the vulnerability to re-entrant arrhythmia effects on the ECG, and cardiac pacemaking.16,21,35,36 The parameters can change smoothly with distance, as in a gradient model,20 or sharply between different types of homogeneous tissue: for simplicity, we use a modular approach, with homogeneous segments of sinoatrial, atrial, atrioventricular, Purkinje, and ventricular tissue, and step changes in the excitation parameters and the diffusion coefficients between them. This 1D partial differential equation model can represent propagation from the sinoatrial node, through the atria, and on to the ventricles. The 1D model is sufficient for simulating normal sinus rhythm and dysrhythmia, but not re-entrant arrhythmia. In addition to the heterogeneity in cell
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(Kv1.4,4.2, and 4.3) Gto, rapid delayed rectifier (ERG) GKr and slow delayed rectifier (KVLQT1) GKs, time-independent K+ current (KV2.1,2.2, and 2.3) GK1, L-type Ca++ current (CaV1.2 and 1.3) GCaL, T-type Ca++ current (CaV3.1) GCaT, and hyperpolarization-activated funny current (HCN1.4) Gf, for (A) high Gf and (B) high GCaL sinoatrial node, (C) atrial, (D) atrioventricular node, (E) Purkinje fibre, and (F ) ventricular foetal cell models, with other parameters and kinetics as in the standard adult models.18,19,22,23
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Table 1 Channel conductance parameters for the 1D human foetal model Cell model maximal conductances (nS/pF)
............................................................................................................................................................ SAN (high Gf )
SAN (high GCa)
Atrium
AVN
Purkinje
Ventricle
............................................................................................................................................................................... GNa Gto
0.468 0.078
0.468 0.078
7.8 0.1
0.468 0.078
130.574 0.082
14.838 0.073
GKr
0.013
0.013
0.2
0.013
0.092
0.153
GKs GK1
0.089 0.003
0.089 0.003
0.129 0.09
0.089 0.007
0.235 0.065
0.392 5.405
GCaL
0.179
0.281
0.4
0.094
3.980 × 1025
3.980 × 1025
GCaT GF
0.242 10.754
0.293 4.963
0.0 0.0
0.22 1.654
0.0 0.015
0.000 0.000
For any given simulation, either the high Gf or high GCa parameter set for the sinoatrial node was used.
Results Normal sinus rhythm The two illustrative sinoatrial cell models with parameters as in Figures 1A and B generate propagating activity, from the sinoatrial node to the ventricular tissue, with cycle lengths of 413 ms (high GCaL) and 391 ms (high Gf ), both within the normal range for the fECG RR intervals from 14 to 40 WGA.11 The properties, duration, amplitude, maximum rate of rise, and minimum diastolic potential, of the propagating action potentials, and their shape V(t) are presented in Figure 2 for the high Gf model: the action potential characteristics with the high GCaL model are similar. These are for comparison with action potentials in other mammalian hearts, as intracellular, monophasic, or optical recordings of propagating action potentials
are not yet available for foetal human tissue. In principle, as human foetal hearts have been Langendorff-perfused for the extraction of myocytes for electrophysiological experiments,38 optical recordings of propagating action potentials in perfused foetal hearts may become available and allow the construction of the model segments from foetal data, rather than by the modification of adult models. This is a research area which we will pursue in our laboratory. Two propagation cycles are seen in the space –time plot with overlaid action potentials (Figure 2B), beginning at the sinoatrial node, propagating rapidly through the atrial tissue, slower through the atrioventricular node, then rapidly through the Purkinje and ventricular tissues. These are from the last 2 s of a 10 s simulation: since the cell models are not electrochemically neutral, i.e. the pumps and exchangers do not exactly compensate for ion flow during the action potential, there are changes in intracellular concentrations that over a 10 s time scale lead to non-physiological changes in intracellular concentrations and potentials, and so the excitation equations are not valid at long times (10 –100 s). At the start of the simulation, the atrial and ventricular cells are at a resting, not periodically driven, state, and so the first few beats are transients, that settle down by 2–3 s into propagating periodic activity. Figure 2C shows the experimentally recorded human fECG for comparison with the depolarization and repolarization sequence in Figure 2B. One can qualitatively observe from this figure that the components of the fECG match with their underlying electrophysiological determinants in the model. Owing to a lack of spatial detail in this first approximation of the model—particularly the simple geometry, the 1D propagation, and the lack of heterogeneous cell types in the ventricular tissue—we are limited to comparing this fECG with the model membrane potential characteristics (i.e. the depolarization and repolarization sequence through the 1D strand) rather than an unrealistic (compared with the whole-heart fECG) model-generated pseudo-ECG.34 However, as data regarding human foetal electrophysiological heterogeneity become available and are incorporated into the model, and the model is expanded to include realistic geometries11 and propagation sequences, a more direct comparison, between the experimentally measured fECG and the model pseudo-ECG, can be made and will further refine and validate the model.
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properties, it requires the conduction velocity (or diffusion coefficient) and length of the segments. The length can be estimated from the foetal heart size, but is a rough approximation, as the path travelled by the fastest and slowest components of the propagating 3D wavefront are both being mapped onto the same line, e.g. the beginning and the end of the P-wave correspond to the earliest and the last atrial depolarizations. The lengths of the 1D model segments in the examples below are approximate, initial estimates informed in part by high-resolution DT-MRI datasets of human foetal hearts:11 we set sinoatrial node tissue length to 5 mm; the atria to 10 mm; the atrioventricular node to 5 mm; the Purkinje fibres to 5 mm; and the ventricles to 10 mm. Note that a sinoatrial node length (radius of radially symmetric 2D node) of more than 0.9 mm is required to allow driving of the atrial tissue in this model. We then reproduced the intervals from the experimentally recorded fECG (P-Q, Q-T etc.) by modifying the diffusion coefficients D in Eq. (1), that determine the action potential propagation conduction velocities. We set D to 0.06 mm2 ms21 for the sinoatrial node and the atrioventicular nodes, 0.11 mm2 ms21 for the atria, and 0.154 mm2 ms21 for the Purkinje fibre and ventricular tissue. Equation (1), with zero-flux boundary conditions, was solved numerically using a forward-time central-space scheme (with space steps of Dx ¼ 0.1 mm) in conjunction with an operator splitting and adaptive time step method37 (to give time steps between Dt ¼ 0.01 ms and Dt ¼ 0.05 ms).
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Figure 2 Simulation of foetal normal sinus rhythm. (A) Properties of periodic propagating action potentials for sinoatrial node (high Gf model), atrial, atrioventricular, Purkinje, and ventricular tissue models: APD90, peak-to-peak amplitude, dV/dtmax, and minimum diastolic potential/maximum hyperpolarization. These are obtained at the midpoints of the sinoatrial, atrial, atrioventricular, Purkinje, and ventricular tissue segments. (B) Propagating action potentials as V(t), from the sinoatrial node, through the atrial, atrioventricular, Purkinje, and ventricular tissue segments of the strand. Underlying colours show the corresponding space– time plot of the simulated propagation: the standard rainbow colour scale for the voltage is from blue (hyperpolarized/resting) to red (depolarized). (C) The overlaid foetal ECG (fECG) is an averaged cycle of the experimentally measured fECG (from 32 WGA) to indicate the correspondence between the fECG time course and the timings in the 1D strand.
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Towards computational modelling of the human fECG
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Figure 3 Space– time plots, as in Figure 2C, for maintained activity produced by a strand driven by the high GCaL sinaotrial node model with the parameters of Figure 1B, during 7 – 10 s of simulation, with % block of ICaL increasing from 0 (top) to 100% block (bottom). (A) 0% block, 1 : 1 propagation throughout the cardiac axis. (B) 43.7%, 4 : 3 block at the atrioventricular node. (C) 46.9%, 3 : 2 block at the atrioventricular node. (D) 50%, 2 : 1 block at the atrioventricular node. (E) 68%, complete block, with 2 : 1 block at the sinoatrial node – atrial boundary. (F) 75%: sinoatrial node still periodic, but completely failing to drive the atrium. (G) 100% block, spatially uniform resting state. (H ) The ratio of the number of atrial action potentials to the number of ventricular action potentials for high GCaL (black) and high Gf (red) sinoatrial models, as ICaL is blocked from 0 to 100%. (I ) Sinoatrial node cycle length, as ICaL is blocked from 1 to 100%.
Conduction block Congenital heart block can be detected from the fECG from 16 WGA as atrioventricular conduction block, and is an autoimmune disease in which maternal antibodies (positive IgG) cross the placenta and are believed to inhibit the expression of L-type Ca++ channels in the foetal heart, which alters the intrinsic periodicity of the nodal cells: these channels have been identified in the foetal heart, and positive IgG has been demonstrated to inhibit their expression in heterogeneous expression systems.38, 39 Thus, a simple test of the 1D strand
would be to produce a spatially uniform depression in GCaL (to mimic positive IgG antibodies crossing the placenta) and see if it reproduces the defining features of congenital heart block, i.e. failure of the sinoatrial node to initiate propagation through the atria, or conduction block at the atrioventricular node, during normal sinus rhythm. Figure 3 presents space–time plots for normal sinus rhythm and blocked activity, for the last 3 s of a 10 s simulation, analogous to Figure 2C, except for the high GCaL sinoatrial model, with parameters given by Figure 1B. With a spatially uniform increasing block of ICaL, the 1 : 1 propagation of normal sinus rhythm is lost
764 at 40% block for the strands driven by both sinoatrial node models. In the strand driven by the high GCaL node, very narrow parameter intervals of 4 : 3 and 3 : 2 conduction block lead to a 2 : 1 interval that terminates with complete conduction block at 75% ICaL. The high Gf model fails at about 40% ICaL block, with the propagation failure occurring at the sinoatrial node –atrial tissue boundary. In both models, the sinoatrial node period lengthens (i.e. a bradycardia) before conduction block occurs: the high Gf sinoatrial node period prolongs by 25%, while the high GCaL sinoatrial node period prolongs by only 10%. Thus, the two models (with high Gf SAN and with high GCaL SAN) give different predicted behaviours with block of ICaL. These simulation data may therefore be used to further validate either or both of the models by using fECG data showing signs of congenital heart block: such work will form an important next step in further validating the model.
Conclusions
Conflict of interest: none declared.
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3. Aslanidi OV, Colman MA, Stott J, Dobrzynski H, Boyett MR, Holden AV. Zhang HG 3D virtual human atria: a computational platform for studying clinical atrial fibrillation. Prog Biophys Mol Biol 2011;107:156–68. 4. Benson A, Bernus O, Dierckx H, Gilbert S, Greenwood J, Holden AV et al. Construction and validation of anisotropic and orthotropic ventricular geometries for quantitative predictive cardiac electrophysiology. Interface Focus 2011;1:101 –16. 5. Noble D. Computational models of the heart and their use in assessing the actions of drugs. J Pharmacol Sci 2008;107:107–17. 6. Oudijk MA, Kwee A, Visser GH, Blad S, Meijboom EJ, Rose´n KG. The effects of intrapartum hypoxia on the fetal QT interval. BJOG 2004;111:656 –60. 7. Moorman JR, Carlo WA, Kattwinkel J, Schelonka RL, Porcelli PJ, Navarrete CT et al. Mortality reduction by heart rate characteristics monitoring in very low birth weight neonates: a randomized trial. J Pediatr 2011;159:900 –906. 8. Taylor MJ, Smith MJ, Thomas M, Green AR, Cheng F, Oseku-Afful S et al. Noninvasive fetal electrocardiography in singleton and multiple pregnancies. BJOG 2003;110:668 –78. 9. Strasburger JF, Wakai RT. Fetal cardiac arrhythmia detection and in utero therapy. Nat Rev Cardiol 2010;7:177–290. 10. Dhanantwari P, Lee E, Krishnan A, Sarmtani R, Yamada S, Anderson S et al. Human cardiac development in the first trimester: a high-resolution magnetic resonance imaging and episcopic fluorescence image capture atlas. Circulation 2009;120: 343 –51. 11. Pervolaraki E, Anderson RA, Benson AP, Hayes-Gill B, Holden AV, Moore BJR et al. Antenatal architecture and activity of the human heart. Interface Focus 2013;3: 20120065. 12. Yapar EG, Ekici E, Go¨kmen O. First trimester fetal heart rate measurements by transvaginal ultrasound combined with pulsed Doppler: an evaluation of 1331 cases. Eur J Obstet Gynecol Reprod Biol 1995;60:133 – 7. 13. Tezuka N, Sato S, Kanasugi H, Hiroi M. Embryonic heart rates: development in early first trimester and clinical evaluation. Gynecol Obstet Invest 1991;32:210 –2. 14. Hayashi R, Nakai K, Fukushima A, Itoh M, Sugiyama T. Development and significance of a fetal electrocardiogram recorded by signal-averaged high-amplification electrocardiography. Int Heart J 2009;50:161 –71. 15. Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T et al. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am J Physiol Heart Circ Physiol 2000;279:H397 –421. 16. Severi S, Fantini M, Charawi LA, DiFrancesco D. An updated computational model of rabbit sinoatrial action potential to investigate the mechanisms of heart rate modulation. J Physiol 2012;590:4483 – 99. 17. Lakatta EG, Maltsev VA, Vinogradova TM. A coupled SYSTEM of intracellular Ca clocks and surface membrane voltage clocks controls the timekeeping mechanism of the hearts pacemaker. Circ Res 2010;106:659 – 73. 18. Courtemanche M, Ramirez RJ, Nattel S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am J Physiol 1998; 275:H301 –21. 19. Chandler NJ, Greener ID, Tellez JO, Inada S, Musa H, Molenaar P et al. Molecular architecture of the human sinus node insights into the function of the cardiac pacemaker. Circulation 2009;119:1562 –75. 20. Zhang H, Holden AV, Boyett MR. Gradient model versus mosaic model for the sinoatrial node. Circulation 2001;103:584 –8. 21. Zhang H, Zhao Y, Lei M, Dobrzynski H, Liu JH, Holden AV et al. Computational evaluation of the roles of the Na+ current iNa and cell death in cardiac pacemaking and driving. Am J Physiol – Heart 2007;292:H165 –74. 22. Stewart P, Aslaidi OV, Noble D, Noble PJ, Boyett MR, Zhang H. Mathematical models of the electrical action potential of Purkinje fibre cells. Philos Trans R Soc Lond A 2009; 367:2225 –55. 23. ten Tusscher KHWJ, Noble D, Noble PJ, Panfilov AV. A model for human ventricular tissue. Am J Physiol 2004;286:H1573 –89. 24. Dobryzynski H, Anderson RH, Atkinson A, Borbas Z, D’Sousza A, Fraser JF et al. Structure, function and clinical relevance of the cardiac conduction system, including the atrioventricular ring and outflow tract tissues. Pharmacol Ther 2013;139: 260 –88. 25. Cherry EM, Evans SJ. Properties of two human atrial cell models in tissue: resitution, memory, propagation and re-entry. J Theor Biol 2009;254:674–90. 26. Wilhelms M, Hettmann H, Maleckar MM, Koivumaki JT, Dossel O, Seemann G. Benchmarking electrophysiological models of human atrial myocytes. Front Physiol 2013;3:487. 27. Carro J, Rodrı´guez JF, Laguna P, Pueyo E. A human ventricular cell model for investigation of cardiac arrhythmias under hyperkalaemic conditions. Philos Trans A Math Phys Eng Sci 2011;369:4205 – 32. 28. O’Hara T, Vira´g L, Varro´ A, Rudy Y. Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation. PLoS Comput Biol 2011;7:e1002061.
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We have constructed a 1D model for normal sinus rhythm, and used it to quantitatively illustrate a possible mechanism for congenital heart block. Minor modifications of the parameters of the pacemaker, to change the cycle rate from 350 to 450 ms to reproduce gestational changes in foetal RR interval, can extend the model throughout the full 12– 40 weeks of gestation when fECGs can be non-invasively recorded, and provide a quantitative reproduction of the fECG throughout gestation. The model can be used predictively, to compute fECG changes to maternally administered pharmaceuticals, and used to explore the mechanisms of foetal arrhythmias. This allows foetal electrocardiology to follow adult electrocardiology, in providing a quantitative explanation for the ECG, and how it is changed by pharmaceuticals or pathologies. The strand model and its components are modular: the 1D strand is composed of different cell types, and each cell type model has different sets of parameters. Any cell type model can be replaced by alternative models, and the parameters of the individual models can be modified to include new experimental information. Owing to the paucity of human foetal electrophysiological data, the current model utilizes adult human cell models with modified parameter sets to reproduce propagation in the foetal heart, informed by intervals taken from the experimentally measured fECG: as data describing human foetal cell electrophysiology in more detail become available (including spatial heterogeneities, especially in the ventricles), the cell models can be adapted to reproduce foetal action potential, conduction, and ECG characteristics (wave morphologies and amplitudes, and intervals) more accurately. Thus, the current 1D strand model is a first approximation that will continually evolve.
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29. Seeman G, Hoper C, Sachse FB, Dossel O, Holden AV, Zhang H. Heterogenous three-dimensional anatomical and electrophysiological model of the human atria. Phil Trans R Soc A 2006;364:1465 –81. 30. Sato N, Hoshiai T, Ito T, Owada K, Chisaka H, Aoyagi A et al. Successful detection of the fetal ECG waveform during various states of singletons. Tohoku J Exp Med 2011; 225:89–94. 31. Jekez K, Pucelik J, Sauer J, Bartak F. Basic electrophysiological parameters and frequency sensitivity of the ventricular myocardium of human embryos. Physiologia Bohemoslvaca 1982;31:11– 9. 32. Panfilov AV, Holden AV (eds). The Computational Biology of the Heart. Chichester: John Wiley; 1997:416. 33. Kogan B. Introduction to Computational Cardiology. New York: Springer; 2010:231. 34. Gima K, Rudy Y. Ionic current basis of electrocardiographic waveforms—a model study. Circ Res 2002;90:889 – 96.
765 35. Holden AV, Aslanidi OV, Benson AP, Clayton RH, Halley G, Li P et al. The virtual ventricular wall: a tool for exploring cardiac propagation and arrhythmogenesis. J Biol Phys 2006;32:355 –68. 36. Aslanidi OV, Clayton RH, Lambert JL, Holden AV. Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia. J Theor Biol 2005;237: 369 –81. 37. Qu Z, Garfinkel A. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans Biomed Eng 1999;46:1166 –8. 38. Boutjdir M, Chen L, Zhang Z, Tseng C, DiDonato F, Rashbaum W et al. Arrhythmogenicity of IgG and Anti –52-kD SSA/Ro affinity-purified antibodies from mothers of children with congenital heart block. Circ Res 1997;80:354–62. 39. Qu Y, Baroudi G, Yue Y, Boutjdir M. Novel molecular mechanism involving a1D (Cav1.3) L-type calcium channel in autoimmune-associated sinus bradycardia. Circulation 2005;111:3034 –41.
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Europace (2014) 16, 758–765 doi:10.1093/europace/eut377
Towards computational modelling of the human foetal electrocardiogram: normal sinus rhythm and congenital heart block Eleftheria Pervolaraki 1*, Sam Hodgson 2, Arun V. Holden 1, and Alan P. Benson 1 1
School of Biomedical Sciences, University of Leeds, Leeds LS2 9JT, UK; and 2Division of Medical Sciences, University of Oxford, Oxford OX1 3PL, UK
Received 15 July 2013; accepted after revision 4 November 2013
Aims
----------------------------------------------------------------------------------------------------------------------------------------------------------Keywords
Foetal † Human † Congenital heart block † Tachycardia † Electrocardiogram
Introduction Current computational models of the propagating electrical activity within the adult human heart can provide a quantitative reproduction of the electrocardiogram (ECG) recorded on the body surface,1 and allow the non-invasive reconstruction of spatio-temporal activity on the surface of the heart from the ECG body surface map2 during normal sinus rhythm and arrhythmia. These models are based on segmented, high-resolution (100– 200 mm cubic voxel) datasets of cardiac geometry and anisotropic and orthotropic tissue architecture, derived from diffusion tensor magnetic resonance imaging (DT-MRI)3,4 of ex vivo hearts, and lower resolution clinical MRI datasets of the in vivo beating heart geometry, together with biophysically detailed models of the cellular electrophysiology of the different conducting and contractile tissues of the heart. These models allow a mechanistic rather than empirical interpretation of the ECG and
are being used in virtual screening to predict the effects on the ECG of pharmacological agents whose actions on cardiac ion channel dynamics and cellular electrophysiology have been described quantitatively.5 The in utero human foetal ECG (fECG) can be recorded via electrodes on the mother’s abdominal surface from about 12 weeks gestational age (WGA). The fECG has a small (,50 mV) amplitude but foetal QRS complexes are clearly identifiable, and foetal RR intervals automatically extracted, and foetal bradycardia, tachycardia, and ectopy are readily identified. During gestation the foetus moves, and so the size and shape of the components of the fECG recorded at any one site on the maternal abdomen are not consistent and can change rapidly. However, the timings of the components are consistent and vary with foetal heart rate, and with gestational age. Changes in heart rate variability with time can be obtained directly from RR intervals, and have been related to foetal distress6 in the preterm and sepsis in
* Corresponding author. Tel: +44 113 34 31869, E-mail: [email protected] Published on behalf of the European Society of Cardiology. All rights reserved. & The Author 2013. For permissions please email: [email protected].
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We aim to engineer a computational model of propagation during normal sinus rhythm in the foetal human heart, by modifying models for adult cardiac tissue to match foetal electrocardiogram (fECG) characteristics. The model will be partially validated by fECG data, and applied to explore possible mechanisms of arrhythmogenesis in the foetal heart. ..................................................................................................................................................................................... Methods Foetal electrocardiograms have been recorded during pregnancy, with P- and T-waves, and the QRS complex, identified and results by averaging and signal processing. Intervals of the fECG are extracted and used to modify currently available human adult cardiomyocyte models. RR intervals inform models of the pacemaking cells by constraining their rate, the QT interval and its rate dependence constrain models of ventricular cells, and the width of the P-wave, the QR and PR intervals constrain propagation times, conduction velocities, and intercellular coupling. These cell models are coupled into a one-dimensional (1D) model of propagation during normal sinus rhythm in the human foetal heart. We constructed a modular, heterogeneous 1D model for propagation in the foetal heart, and predicted the effects of reduction in L-type Ca++ current. These include bradycardia and atrioventricular conduction blocks. These may account quantitatively for congenital heart block produced by positive IgG antibodies. ..................................................................................................................................................................................... Conclusion The fECG can be interpreted mechanistically and quantitatively by using a simple computational model for propagation. After further validation, by clinical recordings of the fECG and the electrophysiological experiments on foetal cardiac cells and tissues, the model may be used to predict the effects of maternally administered pharmaceuticals on the fECG.
Towards computational modelling of the human fECG
What’s new? † Models of the action potentials of 20– 40 weeks gestational age human foetal sinoatrial, atrial, atrioventricular Purkinje, and ventricular cells are constructed. † A one-dimensional model for propagation in the foetal heart is constructed that reproduces normal sinus rhythm and predicts conduction block produced by reduction in the L-type Ca conductance of cardiac cells. † These computations are related to bradycardia preceding congenital heart block.
Methods Pacemaker and conducting system cell models Throughout gestation, the foetal heart rate increases, from 95 – 100 b.p.m. at 5 weeks to 160– 180 b.p.m. towards full term, and then
decreases slowly to about 150 b.p.m. at full term.11 – 15 These changes in heart rate reflect changes in pacemaking activity, with the basic cycle length increasing from 350 ms at 8 WGA to 450 ms at 38 WGA. The cellular basis of mammalian cardiac pacemaking involves membrane currents, through ion channels, exchangers, and transporters that form a membrane oscillator,15,16 coupled via Ca++ fluxes to an oscillatory Ca++ release from the sarcoplasmic reticulum through ryanodine receptors.17 Quantitative models, firmly based on voltage clamp analyses of isolated sinoatrial node cell and tissue preparations, and optical recordings of intracellular Ca++ transients, have been constructed for the rabbit and mouse but are not available for either foetal or adult human sinoatrial cells. An initial model of adult sinoatrial cell has been constructed18 by modifying the parameters of a model for human atrial cells19 by the ratio of mRNA expression for membrane channels and sarcoplasmic Ca++ handling between atrial and nodal tissue in a post-mortem heart, and incorporating equations for the T-type calcium current (ICaT) and the hyperpolarization-activated current (the ‘funny’ current; If ) that have been characterized in the rabbit and whose mRNA is expressed in human sinoatrial node tissue. The foetal and adult cells both have the same genes for cardiac ion channels, exchangers, pumps, and intracellular binding and sequestration proteins, but the period of the foetal heart is shorter than that of the adult. These quantitative differences in behaviour between the foetus and the adult may be produced by differences in channel expression (e.g. maximal channel conductances or membrane channel densities, that could be measured by cellular electrophysiological experiments on physiologically viable foetal myocardial cells and tissue, or by mRNA levels that could be estimated by quantitative polymerase chain reaction of ex vivo foetal cardiac tissue) and by different kinetics, due to the expression of different isoforms or insertion into a different membrane microenvironment. In cell models, these can be incorporated by scaling the magnitudes of the currents (via the maximal channel conductance), or altering the kinetics by shifting the voltage-dependence of the activation and inactivation rate coefficients of the gating variables. In the absence of either kinetic data on human foetal cardiac channel isoforms, or specific antibody or mRNA data for foetal channel expression, we simply scale the maximal conductances of the adult model to attempt to reproduce the appropriate periodicity of the pacemaker, to test the hypothesis that the differences in rate can be quantitatively explained by the differences in channel expression alone. To reproduce the period of the fECG, all that is required is for the cycle length driven by the sinoatrial node to be appropriate, and the sinoatrial node model to generate action potentials that can drive the atrial tissue.20,21 Thus, we reproduced the experimentally recorded fECG periodicity (i.e. the R –R interval) in the model by scaling the model ion channel conductances. An increase in the maximal conductances Gf (for the current If ) and GCaL (for ICaL), or a decrease in the maximal conductance (GK1) of the time-independent K+ current (IK1), all individually increase the cycle length of the action potentials, but by not enough. Changes in Gf, GCaL, and GK1 are needed to produce the 400 ms periodicity of the 20 WGA heart (i.e. the approximate R – R interval from the experimentally recorded fECG), and there are ranges of values of Gf, GCaL, and GK1, or a volume in {Gf, GCaL, GK1} parameter space, that can produce the appropriate periodicity. We use two illustrative examples, one in which the foetal cycle length of 400 ms in the sinoatrial node model19 is predominately due to a high GCaL and one in which it is predominantly due to high Gf (‘high GCaL’ and ‘high Gf ’, respectively): see Figures 1A and B. We ignore the electrophysiological complexity of the atrioventricular node, with fast and slow pathways and three cell types,24 and use the human sinoatrial cell model with parameters that give a longer cycle length: see Figure 1D.
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the premature neonate.7 Modern instrumentation and signal analysis (averaging, principal component analysis) allow reliable characterization of foetal P- and T-wave characteristics,8 and foetal magnetocardiography provides higher signal-to-noise ratio recordings from 20 WGA, allowing the identification and characterization of foetal arrhythmias from QRS duration and QT intervals.9 The geometry of human ex vivo foetal hearts during the first 12 weeks of gestation has been imaged using MRI and episcopic fluorescent image capture, and an atlas of two-dimensional (2D) data stacks that allow 3D reconstruction of the development of the heart is available.10 The geometry and architecture (myofibre and myolamellar orientation) of hearts from 14 to 20 WGA has been imaged with a resolution of 100 mm cubic voxels using DT-MRI,11 and 3D models of the anisotropic and orthotropic geometry of the developing foetal heart have been reconstructed. These ex vivo hearts were obtained from foetuses following induced abortions. Temporary storage of tissue for imaging was in premises licensed by the 2004 Human Tissues Act. All procedures were approved by both hospital and university ethics committees, and informed maternal consent had been obtained for use of the foetal material in research. Although high-resolution structural data are available, there is little electrophysiological data from physiologically viable foetal cardiac tissue. The components of the fECG, when extracted, can inform models of foetal cardiac electrophysiology: during sinus rhythm the RR intervals reflect the rate of the sinoatrial pacemaker; the RR temporal variability reflects the effects of autonomic inputs to the sinoatrial node; the QT intervals provide an index of ventricular action potential duration and its restitution; the width of the P-wave reflects the timings of the first and last atrial depolarization, or the atrial propagation time determined by atrial size and propagation velocity; the width of the QRS complex reflects the ventricular size/propagation velocity. We construct a preliminary 1D model of propagation during normal sinus rhythm in the foetal heart by modifying the parameters in models of adult human sinoatrial, atrial, atrioventricular, Purkinje, and ventricular cells to reproduce fECG intervals. The 1D model is used to quantitatively explore the possible mechanisms of congenital heart block.
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Figure 1 Comparison of maximal membrane conductances (nS/pF) for the fast Na+ current (NaV1.1, 1.5) GNa, transient outward current
The adult Purkinje fibre model,22 a modified ventricular cell model that includes If and a sustained K+ current, was used, with an intrinsic period of 4.2 s in the tissue.
Atrial and ventricular myocyte models There are a number of current models for human adult atrial25,26 and ventricular cell23,27,28 models: we used the Courtemanche – Ramirez – Nattel18 and ten Tusscher – Panfilov23 models for atrial and ventricular cells, as they form the bases for the pacemaking and conducting cell models. Parameters for the shorter action potential of the atrial ring29 were used to produce a shorter atrial action potential duration, to allow the atrium to be driven by the foetal sinoatrial node. A QT restitution curve for the fECG for 12 – 40 WGA has been constructed11 from data in the literature,13,14,30 together with foetal ventricular action potential duration data in the literature.31 We have previously shown that the action potential duration (at 90% repolarization; APD90) restitution curve computed for the ten Tusscher – Panfilov ventricular cell model provides a good fit to the QT and the APD restitution data when GCaL is set very small (3.98 × 1025 nS/pF) and GKr is increased to 0.153 nS/pF (cf. Figure 8a in Pervolaraki et al.11). We use these parameters for the model presented here. As we are unsure about cell heterogeneity in the foetal ventricles due to a lack of published experimental data, we have for this initial study omitted such heterogeneity and use only endocardial cell formulations in the ventricular tissue region. Inclusion of ventricular heterogeneity in future studies may account for some of the disagreements between the experimental and the model fECGs (see the Results section below). The maximal conductance parameters used here to construct the foetal sinoatrial, atrial, atrioventricular, Purkinje, and ventricular cell models from the published adult cell models18,19,22,23 are presented in Figure 1 and Table 1.
One-dimensional tissue model Propagation of electrical excitation in homogeneous cardiac tissue can be described by the non-linear partial differential equation:32,33 ∂V = ∇(D∇V) − Iion ∂t
(1)
Here, V (mV) is membrane potential, ∇ is a spatial gradient operator, and t is time (ms). D is the diffusion coefficient tensor (mm2 ms21) that characterizes the electrotonic spread of voltage via local circuit currents, through cell-to-cell coupling by gap junctions, and the extracellular and intracellular resistances. Iion is the total membrane ionic current density (mA.mF21). Spatial inhomogeneities can be introduced by segmentation, hence different parts of the model have the excitation properties of different cell types, and different diffusion coefficients. In a 1D model, the type of cell model, its parameters (here, we only change the maximal conductances), and diffusion coefficients change with distance. Such a 1D, heterogenous model for propagation in cardiac tissue was introduced by Gima and Rudy,34 and has been widely applied to model propagation, the rate dependence of APD, the vulnerability to re-entrant arrhythmia effects on the ECG, and cardiac pacemaking.16,21,35,36 The parameters can change smoothly with distance, as in a gradient model,20 or sharply between different types of homogeneous tissue: for simplicity, we use a modular approach, with homogeneous segments of sinoatrial, atrial, atrioventricular, Purkinje, and ventricular tissue, and step changes in the excitation parameters and the diffusion coefficients between them. This 1D partial differential equation model can represent propagation from the sinoatrial node, through the atria, and on to the ventricles. The 1D model is sufficient for simulating normal sinus rhythm and dysrhythmia, but not re-entrant arrhythmia. In addition to the heterogeneity in cell
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(Kv1.4,4.2, and 4.3) Gto, rapid delayed rectifier (ERG) GKr and slow delayed rectifier (KVLQT1) GKs, time-independent K+ current (KV2.1,2.2, and 2.3) GK1, L-type Ca++ current (CaV1.2 and 1.3) GCaL, T-type Ca++ current (CaV3.1) GCaT, and hyperpolarization-activated funny current (HCN1.4) Gf, for (A) high Gf and (B) high GCaL sinoatrial node, (C) atrial, (D) atrioventricular node, (E) Purkinje fibre, and (F ) ventricular foetal cell models, with other parameters and kinetics as in the standard adult models.18,19,22,23
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Table 1 Channel conductance parameters for the 1D human foetal model Cell model maximal conductances (nS/pF)
............................................................................................................................................................ SAN (high Gf )
SAN (high GCa)
Atrium
AVN
Purkinje
Ventricle
............................................................................................................................................................................... GNa Gto
0.468 0.078
0.468 0.078
7.8 0.1
0.468 0.078
130.574 0.082
14.838 0.073
GKr
0.013
0.013
0.2
0.013
0.092
0.153
GKs GK1
0.089 0.003
0.089 0.003
0.129 0.09
0.089 0.007
0.235 0.065
0.392 5.405
GCaL
0.179
0.281
0.4
0.094
3.980 × 1025
3.980 × 1025
GCaT GF
0.242 10.754
0.293 4.963
0.0 0.0
0.22 1.654
0.0 0.015
0.000 0.000
For any given simulation, either the high Gf or high GCa parameter set for the sinoatrial node was used.
Results Normal sinus rhythm The two illustrative sinoatrial cell models with parameters as in Figures 1A and B generate propagating activity, from the sinoatrial node to the ventricular tissue, with cycle lengths of 413 ms (high GCaL) and 391 ms (high Gf ), both within the normal range for the fECG RR intervals from 14 to 40 WGA.11 The properties, duration, amplitude, maximum rate of rise, and minimum diastolic potential, of the propagating action potentials, and their shape V(t) are presented in Figure 2 for the high Gf model: the action potential characteristics with the high GCaL model are similar. These are for comparison with action potentials in other mammalian hearts, as intracellular, monophasic, or optical recordings of propagating action potentials
are not yet available for foetal human tissue. In principle, as human foetal hearts have been Langendorff-perfused for the extraction of myocytes for electrophysiological experiments,38 optical recordings of propagating action potentials in perfused foetal hearts may become available and allow the construction of the model segments from foetal data, rather than by the modification of adult models. This is a research area which we will pursue in our laboratory. Two propagation cycles are seen in the space –time plot with overlaid action potentials (Figure 2B), beginning at the sinoatrial node, propagating rapidly through the atrial tissue, slower through the atrioventricular node, then rapidly through the Purkinje and ventricular tissues. These are from the last 2 s of a 10 s simulation: since the cell models are not electrochemically neutral, i.e. the pumps and exchangers do not exactly compensate for ion flow during the action potential, there are changes in intracellular concentrations that over a 10 s time scale lead to non-physiological changes in intracellular concentrations and potentials, and so the excitation equations are not valid at long times (10 –100 s). At the start of the simulation, the atrial and ventricular cells are at a resting, not periodically driven, state, and so the first few beats are transients, that settle down by 2–3 s into propagating periodic activity. Figure 2C shows the experimentally recorded human fECG for comparison with the depolarization and repolarization sequence in Figure 2B. One can qualitatively observe from this figure that the components of the fECG match with their underlying electrophysiological determinants in the model. Owing to a lack of spatial detail in this first approximation of the model—particularly the simple geometry, the 1D propagation, and the lack of heterogeneous cell types in the ventricular tissue—we are limited to comparing this fECG with the model membrane potential characteristics (i.e. the depolarization and repolarization sequence through the 1D strand) rather than an unrealistic (compared with the whole-heart fECG) model-generated pseudo-ECG.34 However, as data regarding human foetal electrophysiological heterogeneity become available and are incorporated into the model, and the model is expanded to include realistic geometries11 and propagation sequences, a more direct comparison, between the experimentally measured fECG and the model pseudo-ECG, can be made and will further refine and validate the model.
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properties, it requires the conduction velocity (or diffusion coefficient) and length of the segments. The length can be estimated from the foetal heart size, but is a rough approximation, as the path travelled by the fastest and slowest components of the propagating 3D wavefront are both being mapped onto the same line, e.g. the beginning and the end of the P-wave correspond to the earliest and the last atrial depolarizations. The lengths of the 1D model segments in the examples below are approximate, initial estimates informed in part by high-resolution DT-MRI datasets of human foetal hearts:11 we set sinoatrial node tissue length to 5 mm; the atria to 10 mm; the atrioventricular node to 5 mm; the Purkinje fibres to 5 mm; and the ventricles to 10 mm. Note that a sinoatrial node length (radius of radially symmetric 2D node) of more than 0.9 mm is required to allow driving of the atrial tissue in this model. We then reproduced the intervals from the experimentally recorded fECG (P-Q, Q-T etc.) by modifying the diffusion coefficients D in Eq. (1), that determine the action potential propagation conduction velocities. We set D to 0.06 mm2 ms21 for the sinoatrial node and the atrioventicular nodes, 0.11 mm2 ms21 for the atria, and 0.154 mm2 ms21 for the Purkinje fibre and ventricular tissue. Equation (1), with zero-flux boundary conditions, was solved numerically using a forward-time central-space scheme (with space steps of Dx ¼ 0.1 mm) in conjunction with an operator splitting and adaptive time step method37 (to give time steps between Dt ¼ 0.01 ms and Dt ¼ 0.05 ms).
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Figure 2 Simulation of foetal normal sinus rhythm. (A) Properties of periodic propagating action potentials for sinoatrial node (high Gf model), atrial, atrioventricular, Purkinje, and ventricular tissue models: APD90, peak-to-peak amplitude, dV/dtmax, and minimum diastolic potential/maximum hyperpolarization. These are obtained at the midpoints of the sinoatrial, atrial, atrioventricular, Purkinje, and ventricular tissue segments. (B) Propagating action potentials as V(t), from the sinoatrial node, through the atrial, atrioventricular, Purkinje, and ventricular tissue segments of the strand. Underlying colours show the corresponding space– time plot of the simulated propagation: the standard rainbow colour scale for the voltage is from blue (hyperpolarized/resting) to red (depolarized). (C) The overlaid foetal ECG (fECG) is an averaged cycle of the experimentally measured fECG (from 32 WGA) to indicate the correspondence between the fECG time course and the timings in the 1D strand.
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Figure 3 Space– time plots, as in Figure 2C, for maintained activity produced by a strand driven by the high GCaL sinaotrial node model with the parameters of Figure 1B, during 7 – 10 s of simulation, with % block of ICaL increasing from 0 (top) to 100% block (bottom). (A) 0% block, 1 : 1 propagation throughout the cardiac axis. (B) 43.7%, 4 : 3 block at the atrioventricular node. (C) 46.9%, 3 : 2 block at the atrioventricular node. (D) 50%, 2 : 1 block at the atrioventricular node. (E) 68%, complete block, with 2 : 1 block at the sinoatrial node – atrial boundary. (F) 75%: sinoatrial node still periodic, but completely failing to drive the atrium. (G) 100% block, spatially uniform resting state. (H ) The ratio of the number of atrial action potentials to the number of ventricular action potentials for high GCaL (black) and high Gf (red) sinoatrial models, as ICaL is blocked from 0 to 100%. (I ) Sinoatrial node cycle length, as ICaL is blocked from 1 to 100%.
Conduction block Congenital heart block can be detected from the fECG from 16 WGA as atrioventricular conduction block, and is an autoimmune disease in which maternal antibodies (positive IgG) cross the placenta and are believed to inhibit the expression of L-type Ca++ channels in the foetal heart, which alters the intrinsic periodicity of the nodal cells: these channels have been identified in the foetal heart, and positive IgG has been demonstrated to inhibit their expression in heterogeneous expression systems.38, 39 Thus, a simple test of the 1D strand
would be to produce a spatially uniform depression in GCaL (to mimic positive IgG antibodies crossing the placenta) and see if it reproduces the defining features of congenital heart block, i.e. failure of the sinoatrial node to initiate propagation through the atria, or conduction block at the atrioventricular node, during normal sinus rhythm. Figure 3 presents space–time plots for normal sinus rhythm and blocked activity, for the last 3 s of a 10 s simulation, analogous to Figure 2C, except for the high GCaL sinoatrial model, with parameters given by Figure 1B. With a spatially uniform increasing block of ICaL, the 1 : 1 propagation of normal sinus rhythm is lost
764 at 40% block for the strands driven by both sinoatrial node models. In the strand driven by the high GCaL node, very narrow parameter intervals of 4 : 3 and 3 : 2 conduction block lead to a 2 : 1 interval that terminates with complete conduction block at 75% ICaL. The high Gf model fails at about 40% ICaL block, with the propagation failure occurring at the sinoatrial node –atrial tissue boundary. In both models, the sinoatrial node period lengthens (i.e. a bradycardia) before conduction block occurs: the high Gf sinoatrial node period prolongs by 25%, while the high GCaL sinoatrial node period prolongs by only 10%. Thus, the two models (with high Gf SAN and with high GCaL SAN) give different predicted behaviours with block of ICaL. These simulation data may therefore be used to further validate either or both of the models by using fECG data showing signs of congenital heart block: such work will form an important next step in further validating the model.
Conclusions
Conflict of interest: none declared.
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We have constructed a 1D model for normal sinus rhythm, and used it to quantitatively illustrate a possible mechanism for congenital heart block. Minor modifications of the parameters of the pacemaker, to change the cycle rate from 350 to 450 ms to reproduce gestational changes in foetal RR interval, can extend the model throughout the full 12– 40 weeks of gestation when fECGs can be non-invasively recorded, and provide a quantitative reproduction of the fECG throughout gestation. The model can be used predictively, to compute fECG changes to maternally administered pharmaceuticals, and used to explore the mechanisms of foetal arrhythmias. This allows foetal electrocardiology to follow adult electrocardiology, in providing a quantitative explanation for the ECG, and how it is changed by pharmaceuticals or pathologies. The strand model and its components are modular: the 1D strand is composed of different cell types, and each cell type model has different sets of parameters. Any cell type model can be replaced by alternative models, and the parameters of the individual models can be modified to include new experimental information. Owing to the paucity of human foetal electrophysiological data, the current model utilizes adult human cell models with modified parameter sets to reproduce propagation in the foetal heart, informed by intervals taken from the experimentally measured fECG: as data describing human foetal cell electrophysiology in more detail become available (including spatial heterogeneities, especially in the ventricles), the cell models can be adapted to reproduce foetal action potential, conduction, and ECG characteristics (wave morphologies and amplitudes, and intervals) more accurately. Thus, the current 1D strand model is a first approximation that will continually evolve.
E. Pervolaraki et al.
Towards computational modelling of the human fECG
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