© 2005 The European Society of Cardiology. Published by Elsevier Ltd. All rights reserved.
An integrative model of mouse cardiac electrophysiology from cell to torso
Department of Biomedical Engineering, Duke University 136 Hudson Hall, P.O. Box 90281, Durham, NC 27708-0281, USA
Manuscript submitted 28 January 2005. Revision received 28 July 2005. Accepted after revision 3 May 2005.
*Corresponding author. E-mail address: ch{at}duke.edu (C.S. Henriquez).
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Abstract |
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 Top Abstract IntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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AIMS: Although the transgenic mouse has become an important new tool in the study of human diseases and the design of new therapies, a complete picture of cardiac electrophysiology in the mouse, from genome to body surface, is lacking. A computational model of the mouse heart is presented, which is used to study the impact of ion-channel and structural manipulations on the distributions of extracellular potentials on the heart and body surface.
METHODS: A model of the mouse heart anatomy, fibre organization and torso geometry was constructed from DTMRI images. An anisotropic bidomain model, with a modified Pandit et al. model for the ionic currents, was used to represent the electrical properties of the tissue. Spatial heterogeneity in the ion currents was introduced by modulating the transient outward current. A sinus beat was simulated in hearts with different tissue and membrane properties and the extracellular potentials were computed at both the heart and body surface.
RESULTS: The simulated transmembrane patterns in the heart, and the timing and morphology of the simulated ECG waveforms were consistent with experimental measurements. In addition, the patterns of activation and recovery and the waveforms of the corresponding ECG were found to be relatively insensitive to changes in cell type distribution and tissue anisotropy.
CONCLUSION: Because of the small size of the heart, an integrative model of mouse electrophysiology can be simulated from cell to torso, enabling a new tool to study how extracellular signals might be used to detect molecular changes underlying an arrhythmogenic substrate.
Key Words: mouse electrophysiology, bidomain model, electrogram, ECG
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Introduction |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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In the last decade the transgenic mouse has become a powerful model system for the study of the molecular origin of human cardiovascular disease [1–
13] and the design of new therapies [14–16]. Despite the ability to manipulate the murine genome and the miniaturization of clinical and research measurement techniques [5, 17–20], the relationship between human and mouse electrophysiology is poorly understood, making it challenging to extrapolate results from the mouse to the clinic.
While the human heart and mouse heart have similar anatomy and fibre organization, there are important differences that make the interpretation of the extracellular signals on the body surface to local events in the heart especially challenging. First, the action potential duration of the mouse cardiac action potential ranges from 30–80 ms [18,19,21] compared with 150–400 ms in the human. Agdhr and Stenström in 1929 showed that mice lack a defined T wave [22], due in part to the action potential shape and possible lack of a transmural repolarization gradient. In rodents, Ito contributes substantially to the repolarization of the ventricular myocyte [23,24], whereas in large mammals, and in man, the expression of the fast transient outward current Ito,f accounts for only the notch in the action potential.
While differences exist, extracellular and optical mapping methods have revealed that the electrophysiology in small hearts share many of the features seen in larger hearts. Using monophasic action potential (MAP) recordings, Knollmann et al. found marked regional heterogeneity in action potential durations (APD) from epicardial to endocardial surfaces in the RV, LV and septum [19]. Nygren et al. and Tamaddon et al. used optical mapping to study wavefront propagation in the mouse and found that, like in larger mammals, the Purkinje system plays an important role in determining the conduction patterns of a normal sinus beat [25,26]. Finally, Macchi et al. found that the spatial patterns of extracellular potentials in a rat heart, arising from an epicardial stimulus, were characterized by an elliptical, central negative region flanked by two positive regions that tended to align with the surface fibre direction [27]. This classical pattern has been observed in the dog and has been related to the anisotropic substrate and tissue curvature [28].
The consistency of the patterns of propagation in small and large hearts suggests that the mouse heart can be used to mimic many disease states seen in the human heart. For example, many diseases are believed to augment and alter the natural heterogeneity of tissue and membrane properties found in the heart. This augmented heterogeneity effectively defines the substrate for abnormal conduction. To use the mouse as a model, however, it is critical to understand the length scales over which certain heterogeneities impact function and to determine what features of various electrophysiological measurements relate to underlying heterogeneity. Although the mouse heart is considerably smaller than the human heart, the length scales for diffusion are comparable. Hence, certain spatial gradients that might be established in the human heart may not be achievable in the mouse. A possible consequence of not understanding the length scales is that a therapy or intervention that works in the mouse may produce undesired effects in the human heart due to differences in the interaction of the structure and membrane. A powerful approach to gaining insight into the relationship between the mouse and human electrophysiology is to make use of a biophysically accurate, integrative computer model that enables explorations at multiple spatial scales in the same preparation.
In this paper, we present the first integrative computer model of the mouse heart from ion channel to torso to gain insight into the relationship between the mouse ECG and events in the heart. The model is shown to reproduce the timing and morphology of signals experimentally reported. Next, the model is used to study how changes in the distribution of intrinsic cell types (ionic currents) or structure (tissue anisotropy) affect the ECG. The impact of the distribution of the ionic currents and anisotropy on the ECG are shown to be relatively small, and it is argued that this is due to strong electrotonic effects in the small mouse heart.
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Methods |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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The model of the simulated mouse ventricle was described previously [29]
. In this paper an overview of the whole heart model is presented, as well as the techniques used for varying ionic and structural inhomogeneities and the calculation of the body surface ECG. |
Anatomy and fibre/tissue properties |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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An intact mouse heart (C57BL/6J strain, Jackson Laboratory, Bar Harbor, ME) was fixed in formalin and underwent diffusion tensor magnetic resonance imaging (DTMRI) in a 7.1 T MRI scanner at the Duke University Center for In Vivo Microscopy (Fig. 1A) [30]
to obtain both the geometry and fibre orientation. At each pixel of the DTMRI an average fibre orientation is obtained. These data were segmented into a hexahedral mesh (75 µm resolution), consisting of cardiac tissue and cavities, using the Bioelectric Problem Solving Environment (BioPSE) software system (Scientific Computing and Imaging Institute, University of Utah) [31]. Ventricular cavities were filled with an isotropic extracellular blood bath (
=6 mS/cm). Cardiac tissue was assumed to be either isotropic or anisotropic. For anisotropic cases, intracellular (i) and extracellular (e) bidomain conductivities along (l) fibres (gil=5.0 mS/cm, gel=4.0 mS/cm) and across (t) fibres (git=0.5 mS/cm, get=1.33 mS/cm) were chosen to reproduce normal mouse conduction velocities [25]. Specifically, the anisotropic propagation velocities were approximately 68 cm/s along fibres and 29 cm/s across fibres. For isotropic cases, all directions were assigned averaged intracellular and extracellular conductivities yielding a propagation velocity of 55 cm/s. The cellular surface to volume ratio for all cases was 1666 cm–1. At 75 µm resolution, the volume of the mouse ventricular tissue comprised 194 524 nodes while the blood-filled ventricular cavities comprised 31 505 nodes. These parameters, along with the hexahedral mesh and fibre directions, were passed to a vertex-centred finite volume method [32] to create intracellular and extracellular diffusion matrices. To improve the parallelism of the problem, the bandwidths of these matrices were reduced using the Cuthill-McKee algorithm [33].
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The mouse torso model was derived from the visible mouse data set [34]
. A watershed segmentation algorithm (vTk, Kitware Inc.) was used to identify the heart and torso boundaries. A stair-step mesh was created with regular hexahedral elements with dimensions of 1 mm on a side. The high-resolution heart model was oriented in the torso and the epicardial potentials were averaged and projected onto the coarser torso mesh. The torso was assigned an isotropic conductivity (=1 mS/cm). With the epicardial potential assigned, BioPSE was used to obtain the Finite Element Method (FEM) stiffness matrix. |
Ionic properties |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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Three regions of the heart were segmented by hand (Fig. 1A) to correspond to the right ventricle (RV), left ventricular epicardium (EPI) and left ventricular endocardium (ENDO). The ion channel dynamics in these regions were described by modifying the Pandit et al. rat myocyte model [35,
36] to simulate mouse RV, EPI and ENDO action potentials. The intrinsic RV, EPI and ENDO action potential durations (computed at the –60 mV crossing) were 14 ms, 28 ms and 56.5 ms, respectively (Fig. 2). The primary factor used to modulate the action potential shape in the mouse was the dynamics of the transient outward current (Ito) (Fig. 2) [23,24]. Specifically, the maximum conductance 
and time constant of inactivation were altered as described in Pandit et al. In the nominal model, the three regions (EPI, ENDO, RV) were assigned their respective cell types. In the ionically homogeneous models, all regions were assigned the same Ito dynamics (i.e. the same cell type). Note that in the Pandit et al. model, the maximum sodium channel conductance 
of the EPI tissue is 75% that of the ENDO and RV tissue and therefore, the conduction velocities in EPI tissue are slower.
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Numerical and computational methods |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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The bidomain equations [37]
were solved numerically using a semi-Implicit Crank–Nicholson scheme. Equations describing the state variables were updated using the forward Euler method with a fixed timestep of 2.0 µs. To arrive at a unique solution, an extracellular ground was placed in the RV blood cavity. The resulting system of equations were solved using an iterative Jacobi preconditioned GMRES algorithm as defined by Saad and Schultz [11] with a tolerance of 10–4 mV. To simulate a sinus beat, a template RV action potential (Fig. 2) was applied to eight nodes in the middle of the RV tissue facing the RV cavity and a template ENDO action potential was applied to eight nodes at the bottom of the left ventricular cavity (Fig. 1B). These sites produced two epicardial breakthrough sites that are consistent with optical mapping experiments in a mouse [26]. Note that 3 ms of simulation time elapsed before the template action potentials were applied. All simulations were performed using CARDIOWAVE [38] (http://www.cardiowave.duke.edu) and executed on the Duke CSEM High Performance Computing Cluster of networked Linux machines. The extracellular potentials computed on the high resolution heart model were averaged and projected to the nearest point on the epicardial surface of the coarser torso mesh. These averaged potentials were used to compute the body surface potentials (Fig. 1C) using a FEM solver within BioPSE. A preconditioned conjugate-gradient solver was used with an error tolerance of 10–7. The standard three lead ECG was computed from three body surface potentials as shown in Fig. 1C.
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Analysis |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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Activation was identified as the time the AP upstroke reached –60 mV. Recovery was identified as the time AP falling phase crossed –60 mV. The –60 mV crossing occurs at 80% of repolarization in the RV, EPI and ENDO cell types. The APD at a particular location in the heart was computed as the difference between repolarization and activation times at that location.
Analysis of the ECG was carried out on the three standard body surface leads (Fig. 1C). Since the relationship between electrical activity within the heart and the morphology of the ECG has not been derived for the mouse, we adopted the a–c notation of Danik et al. to refer to the various deflections [18]. The duration of the QRS interval was measured as the time between the initial take-off from baseline (Q) and the peak of the a-deflection (Qa). The Qb interval and Qc interval were computed as the time from Q to the peak of b and c, respectively. The subtraction of the Qc and Qb intervals yield the b–c interval.
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Results |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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Simulations were carried out using three different mouse heart models to investigate how changes in tissue and ionic properties impact the ECG. In the first model (nominal case), both the fibre orientation and ionic heterogeneity were assigned. In the second model, (isotropic case) the heart was assumed to be isotropic but with ionic heterogeneity. In the third model, (ionically homogeneous case) fibre orientation was assigned but the ionic properties were assumed to be homogeneous.
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Nominal case |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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The in silico mouse heart and torso models enabled the simultaneous calculation of transmembrane and extracellular potentials throughout the heart as well as body surface potentials. The nominal heart model with anisotropic properties and ionic heterogeneity represented the most complete description of the mouse electrophysiology and served as a baseline case to compare with subsequent modification in the properties. Consequently, this case is presented in detail below.
Because the model lacks a Purkinje fibre network, a sinus beat was simulated by applying stimuli (a template action potential) on the RV and LV endocardial surfaces to produce epicardial breakthroughs sites consistent with those identified in optical mapping experiments in a mouse [26]. As a result, the first activation occurred at the stimulus site at 4.1 ms (Table 1). The latency was due to the 3 ms delay in the takeoff of the stimulus (template action potential) and the time to reach the activation threshold (–60 mV).
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Fig. 3 shows the transmembrane and extracellular potential distributions at four time instants during activation. Transmembrane voltage maps are on a colour scale from –80 mV (blue) to 40 mV (red). Extracellular voltage maps are on a colour scale from –20 mV (blue) to 10 mV (red).
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After endocardial stimulation, the wavefronts broke through the RV epicardium at approximately 6 ms and the lower LV epicardium at approximately 10 ms. Upon breakthrough, the extracellular potential pattern was characterized by a ring of positive potentials around a central negative region. As shown in Fig. 3 (7 ms to 13 ms), the RV wavefront on the epicardium propagated downward toward the apex.
In the LV, the stimulus gave rise to a wavefront that initially propagated on the endocardial surface, due to the fibre orientation, and then broke through the epicardium at three locations within 1 or 2 ms. Fig. 3 (13 ms) shows one of the sites. The other two breakthrough sites are on the back of the heart and quickly merge into a single front. At 13 ms, the epicardial extracellular distribution was characterized by a large positive area covering the bulk of the heart. The LV and RV wavefronts collided at approximately 15 ms in a line that extends from the RV–LV border, through the apex to the LV freewall. The LV wavefront finally propagates toward the LV base, the last region to activate at 19.45 ms.
Recovery of a normal sinus beat is shown in Fig. 4. Note that the colour scale of the extracellular maps (–8 blue; 2 red) have been changed to highlight gradients during recovery. The first time of recovery was 30.9 ms and corresponded to repolarization of the right ventricle (Fig. 4, Table 1). The time for the heart to recover fully was 50.6 ms. Due to electrotonic coupling, the total duration of recovery (19.7 ms) was significantly less than the intrinsic difference in APD (42.5 ms) between the RV and ENDO cell types. Two striking features of repolarization were observed at 25 and 34 ms. First, at both times there was a large extracellular potential gradient between the endocardium (blue, negative) and epicardium (red, positive). This was largely due to the loading of the bath in the LV cavity. Second, there was a relatively large extracellular potential gradient at 34 ms between the LV apex (red, positive) and base (green, zero potential).
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Fig. 5 shows representative transmembrane and extracellular potential time courses on the midwall of the RV epicardium, LV epicardium and LV endocardium. Because of electrotonic coupling, the RV, EPI and ENDO action potentials had different time courses compared with those assigned, with APD80 values of 26 ms, 34 ms and 36 ms, respectively. Note that relative to the template action potential shapes (Fig. 2) the tail of the RV trace was lengthened while the tail of the ENDO trace was shortened. Unlike a paced beat, electrograms initiated at the sinus node did not always display the classic biphasic upstroke followed by repolarization (e.g.
e of ENDO). These differences were due primarily to complex wavefront collision and loading of the bath in the ventricular cavities. Close to the breakthrough sites, however, the morphology of the electrograms was similar to those obtained for a paced beat [29]. In general, surface transmembrane potential signals and the corresponding electrograms at the sites along and across fibres were consistent with recordings from larger animals. Specifically, the amplitudes of the electrograms across fibres were smaller and their shapes less symmetrical than the electrograms along fibres (not shown).
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Body surface potential maps were computed for activation (Fig. 6) and recovery (Fig. 7) from the heart surface extracellular potentials,
e. From the body surface potentials, the three-lead ECG was derived (Fig. 8). To aid the analysis, the signal from lead II was amplified three times. As observed in experimental studies [18,21], some leads (e.g. II) showed a multiphasic deflection (b and c deflections) following the QRS complex.
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The Q time was defined as the initial take-off time from baseline of the ECG leads. This occurred at 7 ms (Fig. 8) and was coincident with the initial heart surface breakthrough of the RV stimulus (Figs. 3 and 6). The peak of the first ECG deflection occurred at 13 ms, and coincided with the first negative potentials breaking through the base of the RV. This led to a decrease in the body surface potential in the upper left lead relative to the body surface. From 15 to 17 ms, the leading positive deflection of
e broke through the LV base of the heart while e at the apex was negative. The result was that the upper left side of the body surface remained positive while the upper right side and lower body surface became negative. The ECG deflections therefore, reversed polarity and reached a peak at 17 ms. As the wavefront propagated upward from the apex to the base, the extracellular potentials near the base became negative and, thus, the left side of the body surface. The ECG once again switched polarity culminating in the final deflection (a wave) of the QRS at 20 ms. Near 20 ms, the RV began to repolarize (Figs. 3,4 and 6,7) and the upper two body surface electrodes were negative relative to the lower electrode. At 25 ms, the entire torso was nearly isopotential and all leads of the ECG were at 0 mV. This time was denoted as the middle of the b wave. The extracellular potentials on the heart, however, were not isopotential. The RV was repolarizing and was therefore positive, while the LV was largely at 0 mV. The result was that the heart surface potentials were averaged on the body surface to an isopotential. As the left ventricle began to repolarize, the LV became more positive, resulting in positive body surface potentials at the lower and upper right electrodes and the beginning of the c wave. At the peak of LV repolarization (34 ms) the c wave reached a peak. As the heart continued to repolarize, the body surface potential distribution slowly returned to isopotential, and the ECG correspondingly to zero. |
Isotropic case |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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To eliminate the effect of anisotropy, conductivities along and across fibres were made equal (gi=3.1 mS/cm, ge=2 mS/cm). The most significant effect was a reduction in the total activation time. The earliest and latest activation were 4.09 ms and 18.79 ms, respectively, yielding a total activation time of 14.7 ms (Table 1). As noted above, in the nominal heart (anisotropic), the LV breakthrough point occurred at three sites on the LV epicardium within 1–2 ms. In the isotropic heart, the wavefront broke through on the LV epicardium at only one location. This difference in activation pattern was detected on the body surface most clearly in lead II where the initial negative deflection was absent (Fig. 8). Since Q was the first take-off from baseline, the absence of this deflection resulted in the apparent shortening of the Qa interval. The Qa interval of the isotropic ECG (7 ms) was significantly smaller than obtained in the nominal ECG (13 ms). Furthermore, the difference in timing of Q accounted for the uniformly smaller values for Qb and Qc in the isotropic heart. The earliest and latest recoveries were 33.72 ms and 48.51 ms respectively, yielding a total recovery time of 14.79 ms. The APD range (22.69 ms to 39.01 ms) was smaller than the APD range in the nominal heart. This global APD difference, however, was only detected in the b–c interval of Lead I (Table 1).
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Ionically homogeneous case |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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To simulate the effects of ionic homogeneity, Ito at every node in the tissue was assigned the same cell type (i.e. RV only, EPI only or ENDO only). In all three cases, the resulting activation patterns were qualitatively similar to the nominal case and therefore the Qa interval did not change significantly. The exception was the EPI case, where the Qa interval was greater, again due to the reduced conduction velocity in the EPI cells. The recovery, however, was significantly affected. Table 1 shows that as the magnitude of Ito decreased and the time constant increased, the APD increased (e.g. ENDO only case). This ion channel manipulation was clear in all leads of the ECG (Figs. 9, 10) as a shift in the c wave from early (RV only), to late (ENDO only). The APD ranges (RV=13.22 ms, EPI=12.29 ms, ENDO=8.6 ms) were significantly smaller than the nominal range (21.64 ms). The homogeneous b–c intervals, however, were of the same order as the wild-type b–c interval. Note that in the ENDO only case, the b and c waves were significantly decreased in amplitude. In an experimental setting (e.g. noisy signal), these b and c waves would be difficult to detect.
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Discussion |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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Insight into the origin of the mouse ECG
In this paper, we have presented a model of cardiac electrophysiology that involves both simultaneous computation of the transmembrane and extracellular potentials in the heart during a normal sinus beat at near cellular spatial resolution with a realistic ionic model, and computation of the body surface potential. The approach allows changes at the ion channel or tissue structure to be related to changes in signals that can be obtained non-invasively. While the sequence of activation and recovery predicted by the model awaits complete validation, the patterns of transmembrane potential are qualitatively similar to those recorded optically by Nygren et al. [25]
in the mouse heart and the extracellular potential patterns are consistent with those measured by Macchi et al. [27] in the rat. The relative magnitudes, polarity and timing of the deflections in the QRS complex in each of the three leads are consistent with those reported by Danik et al. [18]. Furthermore, the morphology and timing of the multiphasic repolarization deflections (b and c waves) are consistent with the findings of Danik et al. and Liu et al. [18,21]. It is clear from the model that while activation and recovery necessarily overlap in the mouse, due to the short action potentials, they do so less than expected. There is approximately 10 ms between the last activation (first crossing of –60 mV) and the first recovery (second crossing of –60). Between these times, some populations of cells are undergoing rapid repolarization which leads to the b wave of the ECG. The c wave on the other hand is coincident with late repolarization.
In some experimental studies [18,21,22], only the b wave is present. Although a small c wave was observed when the heart was given uniform membrane properties (see Fig. 10), in an experimental preparation, the late repolarization phase of the ECG would most likely be assumed to be flat. It is possible that in the mouse heart, a small intrinsic difference in the APD range, due to the preparation, strain, or gender, may have a very large impact on the presence or absence of the c wave.
The relationship between heart and body surface potentials in a mouse has been experimentally explored. Danik et al. found that the ECG deflections did not correspond to APD50 or APD80 on the heart surface [18]. Our modelling studies may help explain this lack of correlation. First, examining potentials from particular locations in the heart gives an incomplete picture of the electrical activity on the heart surface. Second, it was shown in our model and elsewhere [39] that Activation Recovery Intervals (ARIs) only report a single number that is at some unknown percentage of repolarization. For similar reasons, analysing only APD50 or APD80 may not accurately reflect the timing of either the b or c waves.
The mouse as a model of human electrophysiology
As mentioned earlier, despite the differences in size, the length scales for diffusion in the mouse and human hearts are comparable. As a consequence of this the small mouse heart is much more influenced by the electrotonic effects of stimuli, wavefront curvature and wavefront collision [40–42]. This is most apparent in the cases where no intrinsic gradient exists (e.g. all EPI case). The APD ranges in the homogeneous cases were approximately 10 ms, nearly half of the maximum APD range in the nominal case (21 ms).
These results are consistent with those obtained by Sampson and Henriquez for paced beats [43]. Simulations in models of the mouse and rabbit ventricles showed that electrotonic modulation of APD tends to dominate intrinsic differences in cell properties. In larger hearts, however, the intrinsic heterogeneity in membrane properties has many length constants over which to be manifest. In addition, this work showed that the spatial extent of the modulation can be related, in part, to increases in the membrane resistance during repolarization. As a result, the spatial scale over which repolarization currents flow is larger than that expected from consideration of resting length constant and approach a length in the order of the thickness of the mouse LV, diminishing any transmural variation in APD.
The ECG of the mouse and human have important differences owing in part to the differences in the action potential duration and the influence of the electrotonic effects on repolarization. The multi-phasic repolarization (b and c waves) that have been observed experimentally and reproduced in the simulation, are not evident in the normal human ECG. In fact, the J wave, which is assumed to be absent in the normal human ECG because it is lumped in with activation, only appears in pathological states. In the mouse heart, where complete activation takes approximately 12 ms, the fast repolarization phase is unmasked. It is therefore probable that the mouse is less than ideal for studying diseases such as Long-QT or Brugada syndrome that affect the J wave and ST segment.
The use of transgenic animals offers a new experimental approach to manipulate processes at the protein level and study the consequence at the organ level. Unfortunately, not all variables of interest can be measured in a single preparation. If sufficiently realistic, computer models of heart electrophysiology can play a major role in relating information that can be measured experimentally with information that cannot and, perhaps more importantly, provide linkages across disparate scales. The model used in this work was derived directly from image data and thus represents a preparation-specific model that can integrate electrophysiological changes from ion-channel to torso. Preparation-specific models are particularly important for understanding how the same molecular mechanisms can lead to different macroscopic pathologies simply depending on the spatial and temporal distribution of the molecular change. This computational approach should be amenable to larger hearts and thus eventually allow studies relating a clinical ECG to molecular changes in a given patient's heart and helping to identify molecular targets for arrhythmia therapy.
Limitations and future work
While our proposed model is in good qualitative and quantitative agreement with experimental data, it has not been directly validated and we have necessarily simplified some aspects of the link between the ion channel and body surface. Further segmentation of the torso could be performed to vary conductivities on an organ-by-organ basis. The lungs in particular are regions where the conductivity changes abruptly and may establish secondary sources [44] that influence the ECG. Since, the epicardium was not loaded by a bathing fluid as it would be in vivo, the surface RV and EPI electrograms are slightly larger in magnitude than the ENDO electrograms. We expect that loading of the surface potentials would not significantly affect the general features or timing of propagation, but may reduce the amplitude of the heart and body surface potentials. The heart and torso models were also run separately and ideally would be coupled together more tightly. Recently, a detailed model of mouse ion channel dynamics has been published [45] that is more appropriate than the modified Pandit et al. rat model. Due to lack of experimental data, we also assumed that the mouse RV–LV and EPI–ENDO gradients in APD were similar to those in the rat. Despite these shortcomings, we believe we have captured the salient features, from ion channel to body surface, that contribute to the electrophysiology of the mouse.
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Acknowledgements |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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This work was supported by a grants from the NIH (RO1HL076767 and RO1HL72831).
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References |
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TopAbstractIntroductionMethodsAnatomy and fibre/tissue...Ionic propertiesNumerical and computational...AnalysisResultsNominal caseIsotropic caseIonically homogeneous caseDiscussionAcknowledgementsReferences |
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