Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

International audienceRealistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity

Impact of the Endocardium in a Parameter Optimization to Solve the Inverse Problem of Electrocardiography

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role

Space rescaling in the MFS method improves the ECGI reconstruction

International audienceThe method of fundamental solutions (MFS) has been extensively used for the electrocardiographic imaging (ECGI) inverse problem. One of its advantages is that it is a meshless method. We remarked that the using cm instead of mm as a space unit has a high impact on the reconstructed inverse solution. Our purpose is to refine this observation, by introducing a rescaling coefficient in space and study its effect on the MFS inverse solution. Results are provided using simulated test data prepared using a reaction-diffusion model. We then computed the ECGI inverse solution for rescaling coefficient values varying from 1 to 100, and computed the relative error (RE) and correlation coefficient (CC). This approach improved the RE and CC by at least 10% but can go up to 40% independently of the pacing site. We concluded that the optimal coefficient depends on the heterogeneity and anisotropy of the torso and does not depend on the stimulation site. This suggests that it is related to an optimal equivalent conductivity estimation in the torso domain

A practical algorithm to build geometric models of cardiac muscle structure

International audienceCardiac muscle tissue has a unique, network-like structure. Three-dimensional models of this structure are needed for simulations of cardiac electrophysiology and mechanics. We developed an algorithm to produce such models artificially, using an implicit surface expressed on a tailored unstructured multi-domain mesh to define the cell membranes. The algorithm first creates a random network of cell centers, observing angle and distance criteria inferred from real tissue. The space around the network edges is assigned to the cellular domains based on the nearest half-edge. The network is then immersed in a regular tetrahedral mesh which is refined to fit the domain boundaries and to offer sufficient density around the cell membrane. The refinements are alternated with basic mesh improvement operations to maintain an acceptable mesh quality. On the refined mesh a level-set function is expressed that defines the cell membrane. The remeshing code Mmg3d is then used to discretize the level set while retaining the domains, and to improve the quality of the final mesh. A serial implementation of the algorithm was able to produce meshes of a few hundreds of cardiac cells in 15 minutes, but we are still facing difficulties in the remesher, likely resulting from the unusual complexity of these meshes. It was still possible, however, to correctly mesh a small network of cells that was designed to be replicated by successive mirroring. This allowed us to build models of upto 1 cm 3 of tissue (11 million cells and 370 billion tetrahedra) that now serve in performance tests of a large-scale simulation code

Spatially Coherent Activation Maps for Electrocardiographic Imaging

International audienceObjective: Cardiac mapping is an important diagnostic step in cardiac electrophysiology. One of its purposes is to generate a map of the depolarization sequence. This map is constructed in clinical routine either by directly analyzing cardiac electrograms (EGM) recorded invasively or an estimate of these EGMs obtained by a non-invasive technique. Activation maps based on noninvasively estimated EGMs often show artefactual jumps in activation times. To overcome this problem we present a new method to construct the activation maps from reconstructed unipolar EGMs. Methods: On top of the standard estimation of local activation time from unipolar intrinsic deflections, we propose to mutually compare the EGMs in order to estimate the delays in activation for neighboring recording locations. We then describe a workflow to construct a spatially coherent activation map from local activation times and delay estimates in order to create more accurate maps. The method is optimized using simulated data and evaluated on clinical data from 12 different activation sequences. Results: We found that the standard methodology created lines of artificially strong activation time gradient. The proposed workflow enhanced these maps significantly. Conclusion: Estimating delays between neighbors is an interesting option for activation map computation in ECGi

A practical algorithm to build geometric models of cardiac muscle tissue

Cardiac muscle tissue has a unique, network-like structure. Three-dimensional models of this structure are needed for simulations of cardiac electrophysiology and mechanics. We developed an algorithm to produce such models artificially, using an implicit surface expressed on a tailored unstructured multi-domain mesh to define the cell membranes. The algorithm first creates a random network of cell centers, observing angle and distance criteria inferred from real tissue. The space around the network edges is assigned to the cellular domains based on the nearest half-edge. The network is then immersed in a regular tetrahedral mesh which is refined to fit the domain boundaries and to offer sufficient density around the cell membrane. The refinements are alternated with mesh improvement operations to maintain an acceptable mesh quality. On the refined mesh a level-set function is expressed that defines the cell membrane. The remeshing code Mmg3d is then used to discretize the level set while retaining the domains, and to improve the quality of the final mesh. A serial implementation of the algorithm was able to produce meshes of a few hundreds of cardiac cells in 15 minutes, but we are still facing difficulties in the remesher, likely resulting from the unusual complexity of these meshes. It was still possible, however, to correctly mesh a small network of cells that was designed to be replicated by successive mirroring. This allowed us to build models of upto 1 cm3of tissue (10 million cells and 370 billion tetrahedra) that now serve in performance tests of a large-scale simulation code

Simulation of Fractionated Electrograms at Low Spatial Resolution in Large-Scale Heart Models

Abstract To compute extracellular potentials from transmembrane potentials an elliptic boundary-value problem must be solved. This must be done at a spatial resolution of 0.2 mm or better to avoid artefacts in the form of large spikes before and after major deflections. For macroscopic heart models, this leads to very large linear systems. Artefacts in low-resolution solutions are related to the restriction operator that is used to translate the sources from high to low resolution. Typically, this restriction is done by injecting transmembrane potentials. We propose to use transmembrane current as a source, with weighted summation rather than simple injection. We tested this method in a model of the human ventricles. We found that using the proposed scheme, a good visual match could be obtained between electrograms computed at 1-mm and 0.2-mm resolution, even in regions where strong sub-millimeter heterogeneity in tissue conductivity was present. Introduction Computation of extracellular potentials from transmembrane potentials is a common problem in cardiac electrophysiology Artefacts in low-resolution solutions are related to the restriction operator that is used to translate the source data from the high-resolution to the low-resolution mesh. Typically, this restriction is done by injecting transmembrane potentials. We propose to use transmembrane current as a source, with regional summation rather than simple injection. The summation algorithm must fulfill the following criteria: • No contribution may be lost, otherwise a solution for the linear problem would not exist. • Contributions should remain as local as possible. • The summation should not introduce artefacts. We tested the performance of a summation method with trilinear weighting to fulfill these criteria. Methods An anatomic model of a human heart and torso was created from MRI data as described earlier The resulting model represented the subject's heart with 50 million cubic elements having sides of 0.2 mm. To each element, a local fiber orientation and cell type (subendocardial, subepicardial, or M cell) were assigned. Propagating action potentials (AP) were simulated with a monodomain reaction-diffusion equation, using software that has been described previously Computation of extracellular potentials (electrograms) from the simulated membrane potentials was based on the bidomain model for cardiac tissue where We evaluated I(x, t) at the full 0.2 mm resolution of the reaction-diffusion model. Uniform finite-difference meshes were used for both the simulation of propagation and for the computation of φ e (x, t). To solve equation where N is the ratio of fine to coarse grid resolution (N = 5 in this paper) and ∆x, ∆y, ∆z is the number of finemesh edges between the C node and the F node along the x, y, and z axis, respectively. Thus, both the sum of all weights for a single C node and the sum of the weights for a single F node were unity. To obtain a unique solution to equation Electrograms were computed at 1-mm resolution both for the isolated heart and for the in-situ heart. These simulations were performed with 1 million and with 42 million nodes, respectively. To test the validity of the lowresolution results, electrograms were also computed at the full 0.2-mm resolution in the isolated heart; this took 113 million nodes. Simulations were performed on 32-128 processors of an SGI Altix 4700 supercomputer. To create a situation where inhomogeneous tissue caused fractionated electrograms, fibrofatty replacement and Na-channel block were simulated as in previous work 3. Results Discussion and conclusions We have shown that using regionally summated transmembrane current as a source, electrograms may be computed at a resolution as low as 1 mm in a model of the human ventricles without introducing visible artefacts. Assuming that the transmembrane current itself is computed with a reaction-diffusion model at 0.2-mm to 0.1-mm resolution, this reduces the computational load associated with electrogram simulation by at least a factor 125 to 1000. The proposed method is easy to implement in an existing bidomain solver. It worked well even in the presence of sub-millimeter heterogeneity in tissue conductivity. The method is probably less accurate in small-scale simulations, where most of the electrogram shape originates from nearby tissue. We consider it useful for whole-heart and whole-body models of large mammals, especially man. It may also be valuable as a restriction operator in (geometric) multigrid methods

Estimation of Serum Potassium and Calcium Concentrations from Electrocardiographic Depolarization and Repolarization Waveforms

Chronic kidney disease (CKD), a condition defined by a gradual decline in kidney function over time, has become a global health concern affecting between 11 and 13% of the world population [1]. As renal function declines, CKD patients gradually lose their ability to maintain normal values of potassium concentration ([K+]) in their blood. Elevated serum [K+], known as hyperkalemia, increases the risk for life-threatening arrhythmias and sudden cardiac death [2].An increase in serum [K+] outside the physiological range is commonly silent and is only detected when hyperkalemia is already very severe or when a blood test is performed. Maintenance and monitoring of [K+] in the blood is an important component in the treatment of CKD patients because therapies for hyperkalemia management in CKD patients are designed to prevent arrhythmias and to immediately lower serum [K+] to safe ranges. However, this is currently only possible by taking a blood sample and is associated with a long analysis time. Therefore it is useful to have a simple, noninvasive method to estimate serum [K+], particularly using the electrocardiogram (ECG). Indeed, variations in serum electrolyte levels have been shown to alter the electrical behavior of the heart and to induce changes in the ECG [3¿6]. However, large inter-individual variability existsin the relationship between ion concentrations and ECG features. Previous attempts to estimate serum [K+] from the ECG have therefore shown limitations [7¿9], such as not being applicable to some common types of ECG waveforms or relying on specific ECG characteristics that may present large variations not necessarily associated with hyperkalemia.The aim of this thesis is to develop novel estimates of serum [K+] that are robust enough to detect hypokalemia (reduced [K+]) or hyperkalemia in a timely manner to provide life-saving treatment. Additionally, the effect of changes in other electrolyte levels, like calcium concentration ([Ca2+]), and in heart rate are investigated. These aims are achieved by combining novel ECG signal processing techniques with in silico modeling and simulation of cardiac electrophysiology.The specific objectives are:1. Characterization of hypokalemia or hyperkalemia and hypocalcemia (reduced [Ca2+]) or hypercalcemia (elevated [Ca2+])-induced changes in ventricular repolarization from ECGs (T wave) of CKD patients. This is addressed in chapter 3 and chapter 4. In these chapters, we describe how T waves are extracted from ECGs and how we characterize changes in T waves at varying potassium, calcium and heart rate using analyses based on time warping and Lyapunov exponents. Next, univariable and multivariable regression models including markers of T wave nonlinear dynamics in combination with warping-based markers of T wave morphology are built and their performance for [K+] estimation is assessed.2. Characterization of hypo- or hyperkalemia and hypo- or hypercalcemia-induced changes in ventricular depolarization from the QRS complex of CKD patients. This is reported in chapter 5. In this chapter, we present how QRS complexes from ECGs of CKD patients are processed and how we measure changes at varying [K+], [Ca2+] and heart rate. Univariate and multivariate regression analyses including novel QRS morphological markers in combination with T wave morphological markers are performed to assess the contribution of depolarization and repolarization features for electrolyte monitoring in CKD patients.3. Identification of potential sources underlying inter-individual variability in ECG markers in response to changes in [K+] and [Ca2+]. In silico investigations of cardiac electrophysiology are conducted and ECG features are computed. Simulation results are compared with patient data. This is explained in chapter 3 using one-dimensional (1D) fibers and in chapter 6 using three-dimensional (3D) human heart-torso models. Chapter 6 includes the development of a population of realistic computational models of human ventricular electrophysiology, based on human anatomy and electrophysiology, to better understand how changes in individual characteristics influence the ECG (QRS and T wave) markers that we introduced in previous chapters. ECG waveforms are characterized by their amplitude, duration and morphology. Simulations are performed with the most realistic available techniques to model the electrophysiology of the heart and the resulting ECG. We establish mechanisms that contribute to inter-individual differences in the characterized ECG features.In conclusion, we identify several markers of ECG morphology, including depolarization and repolarization features, that are highly correlated with serum electrolyte (potassium and calcium) concentrations. ECG morphological variability markers vary significantly with [K+] and [Ca2+] in both simulated and measured ECGs, with a wide range of patterns observed for such relationships. The proportions of endocardial, midmyocardial and epicardial cells have a large impact on ECG markers, particularly for serum electrolyte concentrations out of their physiological levels. This suggests that transmural heterogeneities can modulate ECG responses to changes in electrolyte concentrations in CKD patients. Agreement between actual potassium and calcium levels and their estimates derived from the ECG is promising, with lower average errors than previously proposed markers in the literature. These findings can have major relevance for noninvasive monitoring of serum electrolyte levels and prediction of arrhythmic events in these patients.<br /

A Patchwork Method to improve the performance of the current ECGI methods for sinus rythm

International audienceNoninvasive electrocardiographic imaging (ECGI) pro-vides real-time panoramic images of epicardial electri-cal activity from potential measurements on the torso surface. This non-invasive imaging modality can be-come a powerful clinical tool to help understand themechanisms underlying many cardiac diseases, and to define the appropriate treatment. ECGI is mathematically represented by a Cauchy problem for the Laplace equatio

Accelerating stabilization of whole-heart models after changes in cycle length

International audienceParameter changes can cause long-term drift in membrane models. To reduce the cost of whole-heart simulations with such changes the stabilization can be performed in isolated-cell models, but it can then still take many beats to stabilize the full model. We hypothesized that differences in activation time leading to cycle length (CL) variability before the first beat contribute to this. To remove this variability we froze most state variables of the model until the sodium current activated. Simulations were performed with CL 400, 500, 600 and 1000 ms and modified Ten Tusscher-Panfilov 2006 dynamics. Isolated endocardial, mid-myocardial, and epicardial cells were simulated for 1000 beats. Their final states were then copied to a model of the whole human ventricles, which was run for 5 beats, with and without freezing. Stabilization of the full model took three to four beats. Freezing of the membrane state accelerated stabilization in some cell types but caused opposite drifts in others. Drifts were largest in the epicardial and mid-myocardial layers, and not in particular at their interfaces. Freezing of membrane state may help to accelerate stabilization but in our scenarios other types of drift dominate and may be aggravated by freezing, as it inhibits electrotonic interactions