Control of cardiac alternans in an electromechanical model of cardiac tissue

Unsupervised stochastic learning and reduced order modeling for global sensitivity analysis in cardiac electrophysiology models

BACKGROUND AND OBJECTIVE

Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the cardiac cell model, domain geometry, and boundary or initial conditions used in the mathematical modeling. Conventional techniques for uncertainty quantification in modeling electrical activities of the heart encounter significant challenges, primarily due to the high computational costs associated with fine temporal and spatial scales. Additionally, the need for numerous model evaluations to quantify ubiquitous uncertainties increases the computational challenges even further.

METHODS

In the present study, we propose a non-intrusive surrogate model to perform uncertainty quantification and global sensitivity analysis in cardiac electrophysiology models. The proposed method combines an unsupervised machine learning technique with the polynomial chaos expansion to reconstruct a surrogate model for the propagation and quantification of uncertainties in the electrical activity of the heart. The proposed methodology not only accurately quantifies uncertainties at a very low computational cost but more importantly, it captures the targeted quantity of interest as either the whole spatial field or the whole temporal period. In order to perform sensitivity analysis, aggregated Sobol indices are estimated directly from the spectral mode of the polynomial chaos expansion.

RESULTS

We conduct Uncertainty Quantification (UQ) and global Sensitivity Analysis (SA) considering both spatial and temporal variations, rather than limiting the analysis to specific Quantities of Interest (QoIs). To assess the comprehensive performance of our methodology in simulating cardiac electrical activity, we utilize the monodomain model. Additionally, sensitivity analysis is performed on the parameters of the Mitchell-Schaeffer cell model.

CONCLUSIONS

Unlike conventional techniques for uncertainty quantification in modeling electrical activities, the proposed methodology performs at a low computational cost the sensitivity analysis on the cardiac electrical activity parameters. The results are fully reproducible and easily accessible, while the proposed reduced-order model represents a significant contribution to enhancing global sensitivity analysis in cardiac electrophysiology.

Advances in Cardiac Pacing: Arrhythmia Prediction, Prevention and Control Strategies

Cardiac arrhythmias constitute a tremendous burden on healthcare and are the leading cause of mortality worldwide. An alarming number of people have been reported to manifest sudden cardiac death as the first symptom of cardiac arrhythmias, accounting for about 20% of all deaths annually. Furthermore, patients prone to atrial tachyarrhythmias such as atrial flutter and fibrillation often have associated comorbidities including hypertension, ischemic heart disease, valvular cardiomyopathy and increased risk of stroke. Technological advances in electrical stimulation and sensing modalities have led to the proliferation of medical devices including pacemakers and implantable defibrillators, aiming to restore normal cardiac rhythm. However, given the complex spatiotemporal dynamics and non-linearity of the human heart, predicting the onset of arrhythmias and preventing the transition from steady state to unstable rhythms has been an extremely challenging task. Defibrillatory shocks still remain the primary clinical intervention for lethal ventricular arrhythmias, yet patients with implantable cardioverter defibrillators often suffer from inappropriate shocks due to false positives and reduced quality of life. Here, we aim to present a comprehensive review of the current advances in cardiac arrhythmia prediction, prevention and control strategies. We provide an overview of traditional clinical arrhythmia management methods and describe promising potential pacing techniques for predicting the onset of abnormal rhythms and effectively suppressing cardiac arrhythmias. We also offer a clinical perspective on bridging the gap between basic and clinical science that would aid in the assimilation of promising anti-arrhythmic pacing strategies.

Controllability and state feedback control of a cardiac ionic cell model

A phenomenon called alternans, which is a beat-to-beat alternation in action potential (AP) duration, sometimes precedes fatal cardiac arrhythmias. Alternans-suppressing electrical stimulus protocols are often represented as perturbations to the dynamics of membrane potential or AP duration variables in nonlinear models of cardiac tissue. Controllability analysis has occasionally been applied to cardiac AP models to determine whether different control or perturbation strategies are capable of suppressing alternans or other unwanted behavior. Since almost all previous cardiac controllability studies have focused on low-dimensional models, we conducted the present study to assess controllability of a higher-dimensional model, specifically the Luo Rudy dynamic (LRd) model of a cardiac ventricular myocyte. Higher-dimensional models are of interest because they provide information on the influence of a wider range of measurable quantities, including ionic concentrations, on controllability. After computing modal controllability measures, we found that larger eigenvalues of a linearized LRd model were on average more strongly controllable through perturbations to calcium-ion concentrations compared with perturbations to other variables. When only membrane potential was adjusted, the best time to apply perturbations (in the sense of maximizing controllability of the largest alternans eigenvalue) was near the AP peak time for shorter cycle lengths. Controllability results were found to be similar for both the default model parameters and for an alternans-promoting parameter set. Additionally, we developed several alternans-suppressing state feedback controllers that were tested in simulations. For the scenarios examined, our controllability measures correctly predicted which strategies and perturbation timings would lead to better feedback controller performance.

Thermal modulation of epicardial Ca2+ dynamics uncovers molecular mechanisms of Ca2+ alternans

Ca²⁺ alternans (Ca-Alts) are alternating beat-to-beat changes in the amplitude of Ca²⁺ transients that frequently occur during tachycardia, ischemia, or hypothermia that can lead to sudden cardiac death. Ca-Alts appear to result from a variation in the amount of Ca²⁺ released from the sarcoplasmic reticulum (SR) between two consecutive heartbeats. This variable Ca²⁺ release has been attributed to the alternation of the action potential duration, delay in the recovery from inactivation of RYR Ca²⁺ release channel (RYR2), or an incomplete Ca²⁺ refilling of the SR. In all three cases, the RYR2 mobilizes less Ca²⁺ from the SR in an alternating manner, thereby generating an alternating profile of the Ca²⁺ transients. We used a new experimental approach, fluorescence local field optical mapping (FLOM), to record at the epicardial layer of an intact heart with subcellular resolution. In conjunction with a local cold finger, a series of images were recorded within an area where the local cooling induced a temperature gradient. Ca-Alts were larger in colder regions and occurred without changes in action potential duration. Analysis of the change in the enthalpy and Q₁₀ of several kinetic processes defining intracellular Ca²⁺ dynamics indicated that the effects of temperature change on the relaxation of intracellular Ca²⁺ transients involved both passive and active mechanisms. The steep temperature dependency of Ca-Alts during tachycardia suggests Ca-Alts are generated by insufficient SERCA-mediated Ca²⁺ uptake into the SR. We found that Ca-Alts are heavily dependent on intra-SR Ca²⁺ and can be promoted through partial pharmacologic inhibition of SERCA2a. Finally, the FLOM experimental approach has the potential to help us understand how arrhythmogenesis correlates with the spatial distribution of metabolically impaired myocytes along the myocardium.

Efficiency of semi-implicit alternating direction implicit methods for solving cardiac monodomain model

It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operator-splitting alternating direction implicit (ADI) schemes to efficiently solve the nonlinear cardiac monodomain model. The main objective of the proposed methods is to reduce the computational time and memory consumed for solving electrocardiology models, compared to standard numerical methods. The proposed methods have second-order accuracy in both space and time while evaluating the ionic model only once per time-step. Several examples using regular wave, spiral wave reentry, and nonsymmetrical scroll wave are conducted, and the efficiency of the proposed ADI methods is compared to the standard semi-implicit Crank-Nicolson/Adams-Bashforth method. Large-scale two- and three-dimensional simulations are performed.

A Simulation Study of the Role of Mechanical Stretch in Arrhythmogenesis during Cardiac Alternans

The deformation of the heart tissue due to the contraction can modulate the excitation, a phenomenon referred to as mechanoelectrical feedback (MEF), via stretch-activated channels. The effects of MEF on the electrophysiology at high pacing rates are shown to be proarrhythmic in general. However, more studies need to be done to elucidate the underlying mechanism. In this work, we investigate the effects of MEF on cardiac alternans, which is an alternation in the width of the action potential that typically occurs when the heart is paced at high rates, using a biophysically detailed electromechanical model of cardiac tissue. We observe that the transition from spatially concordant alternans to spatially discordant alternans, which is more arrhythmogenic than concordant alternans, may occur in the presence of MEF and when its strength is sufficiently large. We show that this transition is due to the increase of the dispersion of conduction velocity. In addition, our results also show that the MEF effects, depending on the stretch-activated channels’ conductances and reversal potentials, can result in blocking action potential propagation.

Observability analysis and state observer design for a cardiac ionic cell model

To gain insights into cardiac arrhythmias, researchers have developed and employed various measurement techniques, such as electrocardiography, optical mapping, and patch clamping. However, there are no measurement methods that allow simultaneous recording of all cellular quantities, including intracellular ionic concentrations and gating states, that may play an important role in arrhythmia formation. To help address this shortcoming, we applied observability analysis, a method from control theory, to the Luo-Rudy dynamic (LRd) model of a cardiac ventricular myocyte. After linearizing the time-integrated LRd model about selected periodic orbits, we computed the observability properties of the model to determine whether past system states could be reconstructed from different hypothetical sets of measurements. Under the simplifying assumption that only one dynamical variable could be measured periodically, we found that intracellular potassium concentration generally yielded the largest observability values and thus contained the most information about the dominant modes of the system. The impacts on observability of measurement timings, inter-stimulus interval length, and an alternans-promoting parameter shift were also studied. Pole-placement state observer algorithms were designed and tested in simulations for several scenarios, and we found that it is possible to infer unmeasured variables from potassium-concentration measurements, and to an extent from membrane-potential measurements, both for longer periods that represent normal rhythms and shorter periods associated with tachyarrhythmias. Our results could lead to improved data assimilation algorithms that combine model predictions with measurements to estimate quantities that are difficult or impossible to measure during in vitro experiments.

Effects of mechano-electrical feedback on the onset of alternans: A computational study

Cardiac alternans is a heart rhythm instability that is associated with cardiac arrhythmias and may lead to sudden cardiac death. The onset of this instability, which is linked to period-doubling bifurcation and may be a route to chaos, is of particular interest. Mechano-electric feedback depicts the effects of tissue deformation on cardiac excitation. The main effect of mechano-electric feedback is delivered via the so-called stretch-activated ion channels and is caused by stretch-activated currents. Mechano-electric feedback, which is believed to have proarrhythmic and antiarrhythmic effects on cardiac electrophysiology, affects the action potential duration in a manner dependent on cycle length, but the mechanisms by which this occurs remain to be elucidated. In this study, a biophysically detailed electromechanical model of cardiac tissue is employed to show how a stretch-activated current can affect the action potential duration at cellular and tissue levels, illustrating its effects on the onset of alternans. Also, using a two-dimensional iterated map that incorporates stretch-activated current effects, we apply linear stability analysis to study the stability of the bifurcation. We show that alternans bifurcation can be prevented depending on the strength of the stretch-activated current.

Mechanical perturbation control of cardiac alternans

Cardiac alternans is a disturbance in heart rhythm that is linked to the onset of lethal cardiac arrhythmias. Mechanical perturbation control has been recently used to suppress alternans in cardiac tissue of relevant size. In this control strategy, cardiac tissue mechanics are perturbed via active tension generated by the heart's electrical activity, which alters the tissue's electric wave profile through mechanoelectric coupling. We analyze the effects of mechanical perturbation on the dynamics of a map model that couples the membrane voltage and active tension systems at the cellular level. Therefore, a two-dimensional iterative map of the heart beat-to-beat dynamics is introduced, and a stability analysis of the system of coupled maps is performed in the presence of a mechanical perturbation algorithm. To this end, a bidirectional coupling between the membrane voltage and active tension systems in a single cardiac cell is provided, and a discrete form of the proposed control algorithm, that can be incorporated in the coupled maps, is derived. In addition, a realistic electromechanical model of cardiac tissue is employed to explore the feasibility of suppressing alternans at cellular and tissue levels. Electrical activity is represented in two detailed ionic models, the Luo-Rudy 1 and the Fox models, while two active contractile tension models, namely a smooth variant of the Nash-Panfilov model and the Niederer-Hunter-Smith model, are used to represent mechanical activity in the heart. The Mooney-Rivlin passive elasticity model is employed to describe passive mechanical behavior of the myocardium.

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics

Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance.