# Browsing by Author "Henriquez, Craig S"

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Item Open Access Analysis of a High-resolution technique for Estimation of Conduction Velocity Vectors for Closely Spaced Electrodes Using a 2D Cardiac Tissue Model.(2021) Akino, LydiaBecause of the 1KHz sampling rates, standard clinical systems face a challenge of resolving local activation time (LAT) differences (less than 1ms) for closely spaced electrodes. Recently, Gaeta et al designed a novel technique that calculates LAT differences by transformation of bipolar electrogram (EGM) amplitude known as the DELTA (Determination of EGM Latencies by Transformation of Amplitude) method with a resolution less than 1 millisecond. This thesis evaluates the conduction velocity (CV) vectors measured using the DELTA method against CV vectors obtained using the activation times identified from the underlying transmembrane voltage (VMAT) at high temporal resolution and from the unipolar electrograms (UAT) at clinical temporal resolution. A 2D model of both normal and fibrotic cardiac tissue was developed to compute simulated extracellular EGMs and transmembrane potentials. LAT differences were estimated using the DELTA, UAT and VMAT methods for different stimulation sites. The triangulation technique was used to convert these LAT differences to vector maps and the magnitude and angle generated by both methods were compared. From the analysis, it was determined that the DELTA method gave estimates of the conduction velocity vectors with closely spaced electrodes (1mm,1.4mm and 2mm) that were nearly as accurate as the high resolution VMAT method (error less than 5%) in both normal and low-level fibrotic tissue (below level 3). For more complex wavefronts, defined here as wavefronts generated by using more than one source of simulation, the recorded errors with DELTA were slightly higher (5-10%) and followed no specific trend. In all cases, the DELTA method was more accurate in estimating CV magnitude and angle than the standard UAT method using electrodes separated by 2mm or less.

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 Bridging Scales: How Microstructural Features Impact Macroscopic Cardiac Propagation(2018) Gokhale, Tanmay AnilCardiac arrhythmias such as atrial fibrillation and ventricular tachycardia are closely associated with microscopic fibrotic changes in cardiac structure that result in a heterogeneous myocardium. While the incidence of fibrosis is correlated with arrhythmia burden and recurrence, the mechanisms linking the two remain poorly understood. Previous experimental and simulation studies have identified changes in local conduction due to micron-scale structural heterogeneities. However, because of the limited ability to simultaneously study conduction over a range of spatial scales, it remains unclear how numerous microheterogeneities act in aggregate to alter conduction on the macroscopic scale. The overall objective of this dissertation is to elucidate and characterize the effect of microfibrosis on cardiac conduction, through the use of computational models and directly paired experimental studies.

The impact of fibrotic collagen deposition on reentrant conduction was first examined in a model of cardiac tissue. The presence of collagenous septa was shown to prolong the cycle length of reentry; the magnitude of reentry prolongation is correlated with the overall degree of fibrosis and the length of individual collagenous septa. Mechanistically, cycle length prolongation is caused by lengthening of the reentrant tip trajectory and alteration of restitution properties. An equivalent homogenized model of fibrosis is unable to recapitulate the observed cycle length prolongation, suggesting that the details of the microstructure greatly impact the observed macroscale behavior. A hybrid model generated by adding discrete heterogeneities to the coarse, homogenized model is able to partially reproduce cycle length prolongation by replicating the lengthened tip trajectory.

In order to examine the mechanisms by which cardiac microstructure influences global conduction, a new framework for paired computational and experimental studies using the engineered-excitable Ex293 cell line was developed. The Ex293 mathematical model incorporates several measures of variation in cellular and tissue electrophysiological properties, and is novel in its use of stochastic variation in a multidimensional model of tissue. Replicating the range of experimentally observed single-cell and macro-scale behavior requires introducing ionic conductance variation between individual cells and between tissues, as well as conductivity variation between tissues.

This framework was then utilized for paired studies in a geometry of idealized fibrosis to examine fibrosis-induced changes in micro- and macro-scale behavior. The presence of microscopic heterogeneities slows conduction and alters the curvature of the macroscopic wavefront. On the microscale, branching of tissue around heterogeneities leads to conduction slowing due to imbalances of electrical source and load, while wavefront collisions at sites of tissue convergence lead to acceleration of propagation. The observed macroscopic behavior is directly attributable to the combination of these microscopic effects and the tortuosity of propagation around heterogeneities. Under diseased conditions involving reduced excitability, alteration of these microscale behaviors leads to reversal of changes in wavefront curvature.

These findings advance our knowledge of the role of myocardial micro-heterogeneities in conduction. Further application of these techniques to examine how the effects of microstructure are dynamically modulated may help improve our understanding of the factors giving rise to cardiac arrhythmia.

Item Open Access Indirect Training Algorithms for Spiking Neural Networks based on Spiking Timing Dependent Plasticity and Their Applications(2017) Zhang, XuSpiking neural networks have been used to investigate the mechanisms of processing

in biological neural circuits or to propose hypotheses that can be tested in exper-

iments. Because of their biological plausibility and event-based information trans-

mission, Spiking Neural Networks (SNNs) have suggested as alternatives to Articial

Neural Networks for pattern recognition, classication and function approximation

problems with fewer neurons. In machine learning, SNNs has been shown to be able

to solve pattern and robotic control. For SNNs to be used for such problems, they

must incorporate some mechanism for learning. Current methods to train SNNs use

learning algorithms which adjust the synaptic weights according to an update rule.

In most cases the weights are modied directly. In potential applications such as

driving plasticity in neural culture (in-vitro) and training neuromorphic chips the

directly manipulation of synaptic weights is not possible. Therefore, indirect algo-

rithms, which cause the SNNs to learn based on some biological learning mechanisms

using stimulation of neurons oer signicant advantages over the existing algorithm

for these real world applications.

Indirect algorithms train the neural network by using external stimuli to modulate

the synaptic strengths of a neural network according to synapses intrinsic mechanisms

for plasticity. The training algorithms have been demonstrated in both Integrate and

Fire neurons and more biologically realistic neural networks. In this thesis, four indi-

rect methods to drive the synaptic weights to its desired value in a network through Spike Time Dependent Plasticity (STDP) are developed: Indirect Perturbation, In-

direct Stochastic Gradient, Indirect ReSuMe, and Indirect Training with Supervised

Teaching Signals. These algorithms are used to solve the temporal and spatial input-

output mapping problem using temporal coding. The other type of problem is to

mapping input output ring rates using rate coding.

To test the algorithms, SNNs are used to control both virtual and real world

robots. For the real world robots with SNNs, known and Neurorobots, two types

of robot localization techniques are used: Optitrack, using ceiling mounted cameras

and onboard markers, and embedded cameras. Both small and large SNNs with

biologically realistic neurons are used to drive the neurorobots are modeled with

input coming from Optitrack or the cameras with GPU accelerated SNN simulator.

The results show that the indirect perturbation and indirect stochastic gradient

algorithms can train an SNN to control the robot to nd targets and avoid obstacles

even in the presence of sensor noise. The results also show that indirect training with

supervised training signals algorithm can train a feedforward network with 1000s of

neurons to process and output the correct movement commands to localize a target

using from real time images captured from an embedded camera. Finally. an indirect

version of the Remote Supervised Method (ReSuMe) algorithm was developed using

a more biologically realistic form of Spike-Timing Dependent Plasticity to produce a

specic temporal pattern of spiking from a group of neurons. The indirect algorithms

developed in this thesis may eventually allow the ability to train in vitro and in

vivo biological circuits to perform specic tasks using patterns of electrical or light

stimulation.

Item Open Access Modeling an Excitable Biosynthetic Tissue with Inherent Variability for Paired Computational-Experimental Studies.(PLoS Comput Biol, 2017-01) Gokhale, Tanmay A; Kim, Jong M; Kirkton, Robert D; Bursac, Nenad; Henriquez, Craig STo understand how excitable tissues give rise to arrhythmias, it is crucially necessary to understand the electrical dynamics of cells in the context of their environment. Multicellular monolayer cultures have proven useful for investigating arrhythmias and other conduction anomalies, and because of their relatively simple structure, these constructs lend themselves to paired computational studies that often help elucidate mechanisms of the observed behavior. However, tissue cultures of cardiomyocyte monolayers currently require the use of neonatal cells with ionic properties that change rapidly during development and have thus been poorly characterized and modeled to date. Recently, Kirkton and Bursac demonstrated the ability to create biosynthetic excitable tissues from genetically engineered and immortalized HEK293 cells with well-characterized electrical properties and the ability to propagate action potentials. In this study, we developed and validated a computational model of these excitable HEK293 cells (called "Ex293" cells) using existing electrophysiological data and a genetic search algorithm. In order to reproduce not only the mean but also the variability of experimental observations, we examined what sources of variation were required in the computational model. Random cell-to-cell and inter-monolayer variation in both ionic conductances and tissue conductivity was necessary to explain the experimentally observed variability in action potential shape and macroscopic conduction, and the spatial organization of cell-to-cell conductance variation was found to not impact macroscopic behavior; the resulting model accurately reproduces both normal and drug-modified conduction behavior. The development of a computational Ex293 cell and tissue model provides a novel framework to perform paired computational-experimental studies to study normal and abnormal conduction in multidimensional excitable tissue, and the methodology of modeling variation can be applied to models of any excitable cell.Item Open Access Non-Linear Adaptive Bayesian Filtering for Brain Machine Interfaces(2010) Li, ZhengBrain-machine interfaces (BMI) are systems which connect brains directly to machines or computers for communication. BMI-controlled prosthetic devices use algorithms to decode neuronal recordings into movement commands. These algorithms operate using models of how recorded neuronal signals relate to desired movements, called models of tuning. Models of tuning have typically been linear in prior work, due to the simplicity and speed of the algorithms used with them. Neuronal tuning has been shown to slowly change over time, but most prior work do not adapt tuning models to these changes. Furthermore, extracellular electrical recordings of neurons' action potentials slowly change over time, impairing the preprocessing step of spike-sorting, during which the neurons responsible for recorded action potentials are identified.

This dissertation presents a non-linear adaptive Bayesian filter and an adaptive spike-sorting method for BMI decoding. The adaptive filter consists of the n-th order unscented Kalman filter and Bayesian regression self-training updates. The unscented Kalman filter estimates desired prosthetic movements using a non-linear model of tuning as its observation model. The model is quadratic with terms for position, velocity, distance from center of workspace, and velocity magnitude. The tuning model relates neuronal activity to movements at multiple time offsets simultaneously, and the movement model of the filter is an order n autoregressive model.

To adapt the tuning model parameters to changes in the brain, Bayesian regression self-training updates are performed periodically. Tuning model parameters are stored as probability distributions instead of point estimates. Bayesian regression uses the previous model parameters as priors and calculates the posteriors of the regression between filter outputs, which are assumed to be the desired movements, and neuronal recordings. Before each update, filter outputs are smoothed using a Kalman smoother, and tuning model parameters are passed through a transition model describing how parameters change over time. Two variants of Bayesian regression are presented: one uses a joint distribution for the model parameters which allows analytical inference, and the other uses a more flexible factorized distribution that requires approximate inference using variational Bayes.

To adapt spike-sorting parameters to changes in spike waveforms, variational Bayesian Gaussian mixture clustering updates are used to update the waveform clustering used to calculate these parameters. This Bayesian extension of expectation-maximization clustering uses the previous clustering parameters as priors and computes the new parameters as posteriors. The use of priors allows tracking of clustering parameters over time and facilitates fast convergence.

To evaluate the proposed methods, experiments were performed with 3 Rhesus monkeys implanted with micro-wire electrode arrays in arm-related areas of the cortex. Off-line reconstructions and on-line, closed-loop experiments with brain-control show that the n-th order unscented Kalman filter is more accurate than previous linear methods. Closed-loop experiments over 29 days show that Bayesian regression self-training helps maintain control accuracy. Experiments on synthetic data show that Bayesian regression self-training can be applied to other tracking problems with changing observation models. Bayesian clustering updates on synthetic and neuronal data demonstrate tracking of cluster and waveform changes. These results indicate the proposed methods improve the accuracy and robustness of BMIs for prosthetic devices, bringing BMI-controlled prosthetics closer to clinical use.

Item Open Access Non-uniform Interstitial Loading in Cardiac Microstructure During Impulse Propagation(2009) Roberts, Sarah F.Impulse propagation in cardiac muscle is determined not only by the excitable properties of the myocyte membrane, but also by the gross and fine structure of cardiac muscle. Ionic diffusion pathways are defined by the muscle's interconnected myocytes and interweaving interstitial spaces. Resistive variations arising from spatial changes in tissue structure, including geometry, composition and electrical properties have a significant impact on the success or failure of impulse propagation. Although much as been learned about the impact of discrete resistive architecture of the intracellular space, the role of the interstitial space in the spread of electrical activity is less well understood or appreciated at the microscopic scale.

The interstitial space, or interstitium, occupies from 20-25% of the total heart volume.

The structural and material composition of the interstitial space is both complex and

heterogeneous, encompassing non-myocyte cell structures and a conglomeration of

extracellular matrix proteins. The spatial distribution of the interstitium can vary from confined spaces between abutting myocytes and tightly packed cardiac fibers to large gaps between cardiac bundles and sheets

This work presents a discrete multidomain formulation that describes the three-dimensional ionic diffusion pathways between connected myocytes within a variable interstitial physiology and morphology. Unlike classically used continuous and discontinuous models of impulse propagation, the intracellular and extracellular spaces are represented as spatially distinct volumes with dynamic and static boundary conditions that electrically couple neighboring spaces to form the electrically cooperative tissue model. The discrete multidomain model provides a flexible platform to simulate impulse propagation at the microscopic scale within a three-dimensional context. The three-dimensional description of the interstitial space that

encompasses a single cell improves the capability of the model to realistically investigate the impact of the discontinuous and electrotonic inhomogeneities of the myocardium's interstitium.

Under the discrete multidomain representation, a non-uniformly described interstitium

capturing the passive properties of the intravascular space or variable distribution and

composition of the extracellular space that encompasses a cardiac fiber creates an

electrotonic load perpendicular to the direction of the propagating wavefront. During

longitudinal propagation along a cardiac fiber, results demonstrate waveshape

alterations due to variations in loads experienced radially that would have been otherwise masked in traditional model descriptions. Findings present a mechanism for eliminating myocyte membrane participation in impulse propagation, as the result of decreased loading experienced radially from a non-uniformly resistive extracellular space. Ultimately, conduction velocity increases by decreasing the "effective" surface-to-volume ratio, as theoretically hypothesized to occur in the conducting Purkinje tissue.

Item Open Access On the Significance of Stimulus Waveform in the Modulation of Oscillatory Activity in Excitable Tissues(2021) Eidum, Derek MitchellElectrical stimulation can influence the natural rhythms of activity in heart and brain tissue and has numerous applications in the treatment of cardiac and neurological conditions. The design and optimization of electrical stimulus treatments relies on the ability of researchers to predict the physiological responses of the target tissue to external stimulation. These responses vary greatly depending on the stimulus waveform and parameters as well as the state of ongoing activity in the target region, in ways that are not yet fully understood. The objective of this dissertation is to examine the theoretical basis for differential responses to rhythmic external stimulation based on the properties of the stimulus and target tissue and provide insights for future stimulus technique design.Synaptic plasticity plays a key role in neurostimulation as it allows for the effects of stimulus treatments to persist long after the stimulus ends. Rhythmic stimulation can entrain natural neural oscillations and produce persistent changes in the frequency content of neural activity. However, the mechanisms behind these changes are largely unknown. To this end, simple neural oscillator models were constructed in order to examine the role of synaptic plasticity and sinusoidal stimulation on the synchronization between oscillating regions. Sinusoidal stimulation of different frequencies and strengths can disrupt the intrinsic patterns of network activity, causing information to propagate through the network via different synaptic paths. These new pathways are reinforced through spike timing dependent plasticity, fundamentally altering the network behavior post-stimulation. The resulting network activity depends on the stimulus strength and frequency as well as the intrinsic frequencies of the neural oscillators and the strength of inter-oscillator coupling. Additionally, the effects of rhythmic stimulation depend on the spatial properties of the applied stimulus. By applying out-of-phase sinusoidal current to transverse pairs of electrodes, electric fields may be generated which maintain an approximately fixed strength but rotate in space. Rotational fields may provide utility in the modulation of spiral wave dynamics in excitable tissues, which are associated with reentrant cycles in cardiac arrythmias as well as a number of processes within the brain. To explore this, spiral waves were generated in computational models of engineered excitable tissue and were subjected to rotating and sinusoidal electric fields of varying strength and frequency. Rotational fields which match the direction of spiral propagation provide significant efficiency gains in entraining spiral frequency when compared to sinusoidal stimulus, while retrograde rotational fields can reverse the direction of spiral propagation. Even in the absence of spiral wave dynamics, rotational field stimulation may provide utility in the modulation of neural oscillations. The response of a neuron external stimulation depends on its orientation relative to the electric field gradient, which gives rise to orientation-dependent responses to stimulus treatments. Rotational fields may therefore improve neurostimulus efficacy by influencing the excitability of neurons regardless of their orientation. To explore how rotating fields influence neural oscillations, two neural network model architectures were utilized: large-scale bursting networks, and networks of linked idealized oscillators with plastic inter-oscillator connections. Networks were subjected to rotational and sinusoidal fields, and their behaviors were measured as a function of stimulus strength, frequency, and orientation, as well as the degree of axonal alignment within the network. In spatially aligned networks, rotational fields entrain oscillations and promote network synchrony regardless of orientation, whereas the effects of sinusoidal fields exhibit strong orientation-dependence. In spatially disordered networks, however, rotational fields promote activity in different neurons at different stimulus phases, resulting in reduced network synchrony. These findings expand our knowledge on the significance of stimulus waveform in the modulation of electrically excitable tissues. The ability to understand and predict physiological responses to stimulation will open new doors in the design and optimization of stimulus techniques to achieve desired outcomes.

Item Open Access Study of Lorentz Effect Imaging and Neuronal Current MRI Using Electromagnetohydrodynamic Models(2013) Pourtaheri, NavidNeuronal current MRI (ncMRI) is a field of study to directly map electrical activity in the brain using MRI, which has many benefits over functional MRI. One potential ncMRI method, Lorentz effect imaging (LEI), has shown promise but needs a better theoretical understanding to improve its use.

We develop three computational models to simulate the LEI experiments of an electrolyte filled phantom subject to a current dipole based on: ion flow, particle drift, and electromagnetohydrodynamics (EMHD). With comparative experimental results, we use the EMHD model to better understand the Lorentz effect over a range of current strengths. We also quantify the LEI experimental images and assess ways to measure the underlying current strength, which would greatly benefit comparative brain mapping.

EMHD is a good predictor of LEI signal loss. We can measure the underlying current strength and polarity in the phantom using LEI images. We can also use trends from the EMHD model results to predict the required current density for signal detection in future LEI experiments. We can also infer the electric field strength, flow velocity, displacement, and pressure from the predicted current magnitude in an LEI experiment.

The EMHD model provides information that greatly improves the utility and understanding of LEI. Future study with our EMHD model should be performed using shorter dipole lengths, higher density and lower strength of current sources, and varying current source frequencies to understand LEI in the setting of mapping brain activity.

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.