Browsing by Subject "Cardiac electrophysiology"
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Item Open Access Augmentations vs. Restoration: A computational study of the effects of bacterial sodium channels on cardiac conduction.(2022) Needs, Daniel AllenCardiac arrhythmias, including ventricular tachycardia, ventricular fibrillation, and atrial fibrillation, are associated with ectopic triggers such as those resulting from afterdepolarizations and structural changes within the cardiac changes. While ectopic triggers can be dealt with via radio frequency ablation, structural causes of arrhythmia, such as microscale source-load mismatches, do not have available treatments. Augmentation of cardiomyocytes with exogenous sodium channels such as Nav1.4 or prokaryotic voltage-gated sodium channels, or BacNavs, have shown promise for potentially alleviating these arrhythmias. However, due to size constraints, only the BacNavs are available for the highest efficiency viral vectors for stable transduction. Limitations in the ability to test these channels in adult mammalian cardiac tissue, particularly tissue with source-load mismatches, have led to a lack of understanding about BacNav’s therapeutic value. This dissertation aims to build models of engineered BacNavs and compare their impact in simulated diseased and healthy cardiac tissue with increases of the endogenous Nav1.5 current to probe mechanisms for therapy.Patch clamp data was analyzed to derive steady-state values and kinetics for the activation and inactivation gating of the BacNavs using techniques dating back to Hodgkin and Huxley’s squid axon model. Models using a cubic activation function and only a single slow inactivation channel were best able to replicate the data, including action potential traces and restitution curves for both action potential duration and conduction velocity. The single slow inactivation channel matches what has been observed in crystallography studies of other BacNav channels. Including the derived BacNav model into membrane models for guinea pig and human ventricular myocytes revealed general trends of action potential duration reduction, action potential amplitude increase, and increases in conduction velocity and upstroke velocity. The action potential duration and amplitude trends were more significant for BacNav than Nav1.5, but the endogenous channel was superior for conduction velocity increase. These effects existed despite different responses in relative and absolute current densities between the two membrane models. Despite evidence that late sodium current can lead to afterdepolarizations, BacNav did not increase susceptibility to them in vulnerable midmyocardial cells except at extremely high current densities. Finally, reductions in action potential duration removed alternans present in the restitution curves for single cells. To study how BacNav affected arrhythmias, BacNav was incorporated into one-dimensional cables and two-dimensional tissues with source-load mismatches present, premature stimuli that could induce unidirectional block or channelopathies such as mutations leading to Brugada syndrome. BacNavs outperformed the endogenous channel in source-load mismatches due to increased action potential amplitude and slower inactivation kinetics. These conclusions were stable to spatial heterogeneity in the treatment. It was also able to rescue Brugada syndrome in a dose-dependent manner and narrow the vulnerable window to unidirectional block for one-dimensional cables. In two dimensions, Nav1.5 had a smaller window to spiral wave induction but experienced wave breaks and multiple wavelets, whereas rotors with BacNav-treated cells were stable. These findings help generate hypotheses to be tested experimentally and further refine the model. Further studies may uncover engineering principles for designing optimal sodium channels for specific pathologies.
Item Open Access Spatial Variation of Cardiac Restitution and the Onset of Alternans(2008-06-19) Dobrovolny, Hana MariaInstability in the propagation of nonlinear electro-chemical waves in the heart is responsible for life-threatening disease. This thesis describes an investigation of the effects of boundaries on cardiac wave propagation that arises from a site where an electrical stimulus is applied or from boundaries beyond which current does not flow. It is generally believed that the spatial scale for boundary effects is approximately equal to the passive length constant, lambda, of the tissue, the distance over which a a voltage pulse decays when it is below the threshold for wave generation. From the results of in vitro experiments with bullfrog cardiac tissue and through numerical simulations, I find that boundaries affect wave propagation over a much larger spatial scale and that the spatial variation in some cardiac restitution properties is correlated statistically with the onset of alternans, a possible precursor to fibrillation in the human heart.
An optical imaging system using novel illumination based on LEDs is used to determine the spatial dependence of action potential duration (APD) and the slope of the dynamic restitution curve SDRC, which describes the relationship between steady-state APD and diastolic interval. For tissue with nearly identical cells, I find that APD is longest near the stimulus and shortest near the physical boundary with significant changes (~100 ms) over a distance of ~10lambda. SDRC decreases with distance from the stimulus at a constant rate (~0.1-1.5 /mm) over the surface of the tissue. Simulations using a two-variable cardiac model confirm that spatial patterns of APD and SDRC can be induced by boundaries.
Additional measurements with the simultaneous impalement of two microelectrodes are used to determine the spatial differences of other restitution properties. These studies indicate that APD and SDRC, as well as the slopes of the constant-BCL and S1S2 restitution curves, vary in space and that the spatial differences and onset of alternans at rapid pacing are correlated. If similar correlations are evident in humans, such measurements may identify patients who are susceptible to arrhythmias and allow for early treatment.
Item Open Access The Effect of Structural Microheterogeneity on the Initiation and Propagation of Ectopic Activity in Cardiac Tissue(2010) Hubbard, Marjorie LetitiaCardiac arrhythmias triggered by both reentrant and focal sources are closely correlated with regions of tissue characterized by significant structural heterogeneity. Experimental and modeling studies of electrical activity in the heart have shown that local microscopic heterogeneities which average out at the macroscale in healthy tissue play a much more important role in diseased and aging cardiac tissue which have low levels of coupling and abnormal or reduced membrane excitability. However, it is still largely unknown how various combinations of microheterogeneity in the intracellular and interstitial spaces affect wavefront propagation in these critical regimes.
This thesis uses biophysically realistic 1-D and 2-D computer models to investigate how heterogeneity in the interstitial and intracellular spaces influence both the initiation of ectopic beats and the escape of multiple ectopic beats from a poorly coupled region of tissue into surrounding well-coupled tissue. An approximate discrete monodomain model that incorporates local heterogeneity in both the interstitial and intracellular spaces was developed to represent the tissue domain.
The results showed that increasing the effective interstitial resistivity in poorly coupled fibers alters the distribution of electrical load at the microscale and causes propagation to become more like that observed in continuous fibers. In poorly coupled domains, this nearly continuous state is modulated by cell length and is characterized by decreased gap junction delay, sustained conduction velocity, increased sodium current, reduced maximum upstroke velocity, and increased safety factor. In inhomogeneous fibers with adjacent well-coupled and poorly coupled regions, locally increasing the effective interstitial resistivity in the poorly coupled region reduces the size of the focal source needed to generate an ectopic beat, reduces dispersion of repolarization, and delays the onset of conduction block that is caused by source-load mismatch at the boundary between well-coupled and poorly-coupled regions. In 2-D tissue models, local increases in effective interstitial resistivity as well as microstructural variations in cell arrangement at the boundary between poorly coupled and well-coupled regions of tissue modulate the distribution of maximum sodium current which facilitates the unidirectional escape of focal beats. Variations in the distribution of sodium current as a function of cell length and width lead to directional differences in the response to increased effective interstitial resistivity. Propagation in critical regimes such as the ectopic substrate is very sensitive to source-load interactions and local increases in maximum sodium current caused by microheterogeneity in both intracellular and interstitial structure.
Item Open Access The Roles of Realistic Cardiac Structure in Conduction and Conduction Block: Studies of Novel Micropatterned Cardiac Cell Cultures(2010) Badie, NimaThe role of cardiac tissue structure in both normal and abnormal impulse conduction has been extensively studied by researchers in cardiac electrophysiology. However, much is left unknown on how specific micro- and macroscopic structural features affect conduction and conduction block. Progress in this field is constrained by the inability to simultaneously assess intramural cardiac structure and function, as well as the intrinsic complexity and variability of intact tissue preparations. Cultured monolayers of cardiac cells, on the other hand, present a well-controlled in vitro model system that provides the necessary structural and functional simplifications to enable well-defined studies of electrical phenomena. In this thesis, I developed a novel, reproducible cell culture system that accurately replicates the realistic microstructure of cardiac tissues. This system was then applied to systematically explore the influence of natural structure (e.g. tissue boundaries, expansions, local fiber directions) on normal and arrhythmogenic electrical conduction.
Specifically, soft lithography techniques were used to design cell cultures based on microscopic DTMRI (diffusion tensor magnetic resonance imaging) measurements of fiber directions in murine ventricles. Protein micropatterns comprised of mosaics of square pixels with angled lines that followed in-plane cardiac fiber directions were created to control the adhesion and alignment of cardiac cells on a two-dimensional substrate. The high accuracy of cell alignment in the resulting micropatterned monolayers relative to the original DTMRI-measured fiber directions was validated using immunofluorescence and image processing techniques.
Using this novel model system, I first examined how specific structural features of murine ventricles influence basic electrical conduction. (1) Realistic ventricular tissue boundaries, either alone or with (2) microscopic fiber directions were micropatterned to distinguish their individual functional roles in action potential propagation. By optically mapping membrane potentials and applying low-rate pacing from multiple sites in culture, I found that ventricular tissue boundaries and fiber directions each shaped unique spatial patterns of impulse propagation and additively increased the spatial dispersion of conduction velocity.
To elucidate the roles that natural tissue structure play in arrhythmogenesis, I applied rapid-rate pacing from multiple sites in culture in an attempt to induce unidirectional conduction block remote from the pacing site--a precursor to reentry. The incidence of remote block was found to be highly dependent on the direction of wave propagation relative to the underlying tissue structure, and with a susceptibility that was synergistically increased by both realistic tissue boundaries and fiber directions. Furthermore, all instances of remote block in these micropatterned cultures occurred at the anterior and posterior junctions of the septum and right ventricular free wall. At these sites, rapid excitation yielded more abrupt conduction slowing and promoted wavefront-waveback interactions that ultimately evolved into transmural lines of conduction block. The location and shape of these lines of block was found to strongly correlate with the spatial distribution of the electrotonic source-load mismatches introduced by ventricular structures, such as tissue expansions and sharp turns in fiber direction.
In summary, the overall objective of the work described in this thesis was to reveal the distinct influences of realistic cardiac tissue structure on action potential conduction and conduction block by engineering neonatal rat cardiomyocyte monolayers that reproducibly replicated the anatomical details of murine ventricular cross-sections. In the future, this novel model system is expected to further our understanding of structure-function relationships in normal and structurally diseased hearts, and possibly enable the development of novel gene, cell, and ablation therapies for cardiac arrhythmias.
Item Open Access Uncertainty in the Bifurcation Diagram of a Model of Heart Rhythm Dynamics(2014) Ring, CarolineTo understand the underlying mechanisms of cardiac arrhythmias, computational models are used to study heart rhythm dynamics. The parameters of these models carry inherent uncertainty. Therefore, to interpret the results of these models, uncertainty quantification (UQ) and sensitivity analysis (SA) are important. Polynomial chaos (PC) is a computationally efficient method for UQ and SA in which a model output Y, dependent on some independent uncertain parameters represented by a random vector ξ, is approximated as a spectral expansion in multidimensional orthogonal polynomials in ξ. The expansion can then be used to characterize the uncertainty in Y.
PC methods were applied to UQ and SA of the dynamics of a two-dimensional return-map model of cardiac action potential duration (APD) restitution in a paced single cell. Uncertainty was considered in four parameters of the model: three time constants and the pacing stimulus strength. The basic cycle length (BCL) (the period between stimuli) was treated as the control parameter. Model dynamics was characterized with bifurcation analysis, which determines the APD and stability of fixed points of the model at a range of BCLs, and the BCLs at which bifurcations occur. These quantities can be plotted in a bifurcation diagram, which summarizes the dynamics of the model. PC UQ and SA were performed for these quantities. UQ results were summarized in a novel probabilistic bifurcation diagram that visualizes the APD and stability of fixed points as uncertain quantities.
Classical PC methods assume that model outputs exist and reasonably smooth over the full domain of ξ. Because models of heart rhythm often exhibit bifurcations and discontinuities, their outputs may not obey the existence and smoothness assumptions on the full domain, but only on some subdomains which may be irregularly shaped. On these subdomains, the random variables representing the parameters may no longer be independent. PC methods therefore must be modified for analysis of these discontinuous quantities. The Rosenblatt transformation maps the variables on the subdomain onto a rectangular domain; the transformed variables are independent and uniformly distributed. A new numerical estimation of the Rosenblatt transformation was developed that improves accuracy and computational efficiency compared to existing kernel density estimation methods. PC representations of the outputs in the transformed variables were then constructed. Coefficients of the PC expansions were estimated using Bayesian inference methods. For discontinuous model outputs, SA was performed using a sampling-based variance-reduction method, with the PC estimation used as an efficient proxy for the full model.
To evaluate the accuracy of the PC methods, PC UQ and SA results were compared to large-sample Monte Carlo UQ and SA results. PC UQ and SA of the fixed point APDs, and of the probability that a stable fixed point existed at each BCL, was very close to MC UQ results for those quantities. However, PC UQ and SA of the bifurcation BCLs was less accurate compared to MC results.
The computational time required for PC and Monte Carlo methods was also compared. PC analysis (including Rosenblatt transformation and Bayesian inference) required less than 10 total hours of computational time, of which approximately 30 minutes was devoted to model evaluations, compared to approximately 65 hours required for Monte Carlo sampling of the model outputs at 1 × 106 ξ points.
PC methods provide a useful framework for efficient UQ and SA of the bifurcation diagram of a model of cardiac APD dynamics. Model outputs with bifurcations and discontinuities can be analyzed using modified PC methods. The methods applied and developed in this study may be extended to other models of heart rhythm dynamics. These methods have potential for use for uncertainty and sensitivity analysis in many applications of these models, including simulation studies of heart rate variability, cardiac pathologies, and interventions.