A framework for the design of a closed-loop gastric pacemaker for treating conduction block.

BACKGROUND AND OBJECTIVE: Gastrointestinal (GI) motility disorders can be significantly detrimental to the quality of life. Pacing, or long pulse gastric electrical stimulation, is a potential treatment option for treating GI motility disorders by modulating the slow wave activity. Open-loop pacing of the GI tract is the current standard for modulating dysrhythmic patterns, but it is known to be suboptimal and inefficient. Recent work on sensing intracellular potentials and pacing accordingly in a closed-loop has been shown to be effective at modulating dysrhythmic patterns. However, capturing intracellular potentials in an in-vivo setting is not viable. Therefore a closed-loop gastric electrical stimulation that can sense extracellular potentials and pace accordingly to modulate dysrhythmic patterns is required. This paper presents a closed-loop Gastric Electrical Stimulator (GES) design framework, which comprises of extracellular potential generation, sensing, and closed-loop actuation. METHODS: This work leverages a pre-existing high-fidelity two-dimensional Interstitial Cells of Cajal (ICC) network modeling framework to mimic several normal and dysrhythmic patterns observed in experimental recordings of patients suffering from GI tract diseases. The activation patterns of the of the ICC network are captured by an extracellular potential generation model and is integrated with the GES in a closed-loop to validate the efficacy of the developed pacing algorithms. The proposed GES pacing algorithms extend existing offline filtering and activation detection methods to process the sensed extracellular potentials in real time. The GES detects bradygastric rhythms based on the sensed extracellular potentials and actuates the ICC network via pacing to rectify dysrhythmic patterns. RESULTS: The proposed GES model is able to sense and process the generated noisy extracellular potentials, detect the bradygastric patterns, and modulate the slow wave activities to normal propagation effectively. CONCLUSIONS: A closed-loop GES design, which can be applied in an experimental and clinical setting is developed and validated through the ICC network model. The proposed GES model has the ability to modulate a variety of bradygastric patterns, including conduction block effectively in a closed-loop.

Impulse Data Models for the Inverse Problem of Electrocardiography.

OBJECTIVE: To develop, train and test neural networks for predicting heart surface potentials (HSPs) from body surface potentials (BSPs). The method re-frames traditional inverse problems of electrocardiography into regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions. METHODS: Impulse HSPs were generated with single Gaussian basis functions at discrete heart surface locations and projected to corresponding BSPs using a volume conductor torso model. Both BSP (inputs) and HSP (outputs) were mapped to regular 2D surface meshes and used to train a neural network. Predictive capabilities of the network were tested with unseen synthetic and experimental data. RESULTS: A dense full connected single hidden layer neural network was trained to map body surface impulses to heart surface Gaussian basis functions for reconstructing HSP. Synthetic pulses moving across the heart surface were predicted from the neural network with root mean squared error of 9.1±1.4%. Predicted signals were robust to noise up to 20 dB and errors due to displacement and rotation of the heart within the torso were bounded and predictable. A shift of the heart 40 mm toward the spine resulted in a 4% increase in signal feature localization error. The set of training impulse function data could be reduced, and prediction error remained bounded. Recorded HSPs from in-vitro pig hearts were reliably decomposed using space-time Gaussian basis functions. Activation times calculated from predicted HSPs for left-ventricular pacing had a mean absolute error of 10.4±11.4 ms. Other pacing scenarios were analyzed with similar success. CONCLUSION: Impulses from Gaussian basis functions are potentially an effective and robust way to train simple neural network data models for reconstructing HSPs from decomposed BSPs. SIGNIFICANCE: The HSPs predicted by the neural network can be used to generate activation maps that non-invasively identify features of cardiac electrical dysfunction and can guide subsequent treatment options.

A novel approach for model-based design of gastric pacemakers.

Understanding the slow wave propagation patterns of Interstitial Cells of Cajal (ICC) is essential when designing Gastric Electrical Stimulators (GESs) to treat motility disorders. A GES with the ability to both sense and pace, working in closed-loop with the ICC, will enable efficient modulation of Gastrointestinal (GI) dysrhythmias. However, existing GESs targeted at modulating GI dysrhythmias operate in an open-loop and hence their clinical efficacy is uncertain. This paper proposes a novel model-based approach for designing GESs that operate in closed-loop with the GI tract. GES is modelled using Hybrid Input Output Automata (HIOA), a well-known formal model, which is suitable for designing safety-critical systems. A two-dimensional ICC network working in real-time with the GES is developed using the same compositional HIOA framework. The ICC network model is used to simulate normal and diseased action potential propagation patterns akin to those observed during GI dysrhythmias. The efficacy of the proposed GES is then validated by integrating it in closed-loop with the ICC network. Results show that the proposed GES is able to sense the propagation patterns and modulate the dysrhythmic patterns of bradygastria back to its normal state automatically. The proposed design of the GES is flexible enough to treat a variety of diseased dysrhythmic patterns using closed-loop operation.

Cardiac Electrical Modeling for Closed-Loop Validation of Implantable Devices.

OBJECTIVE: Evaluating and testing cardiac electrical devices in a closed-physiologic-loop can help design safety, but this is rarely practical or comprehensive. Furthermore, in silico closed-loop testing with biophysical computer models cannot meet the requirements of time-critical cardiac device systems, while simplified models meeting time-critical requirements may not have the necessary dynamic features. We propose a new high-level (abstracted) physiologically-based computational heart model that is time-critical and dynamic. METHODS: The model comprises cardiac regional cellular-electrophysiology types connected by a path model along a conduction network. The regional electrophysiology and paths are modeled with hybrid automata that capture non-linear dynamics, such as action potential and conduction velocity restitution and overdrive suppression. The hierarchy of pacemaker functions is incorporated to generate sinus rhythms, while abnormal automaticity can be introduced to form a variety of arrhythmias such as escape ectopic rhythms. Model parameters are calibrated using experimental data and prior model simulations. CONCLUSION: Regional electrophysiology and paths in the model match human action potentials, dynamic behavior, and cardiac activation sequences. Connected in closed loop with a pacing device in DDD mode, the model generates complex arrhythmia such as atrioventricular nodal reentry tachycardia. Such device-induced outcomes have been observed clinically and we can establish the key physiological features of the heart model that influence the device operation. SIGNIFICANCE: These findings demonstrate how an abstract heart model can be used for device validation and to design personalized treatment.

Closing the Loop: Validation of Implantable Cardiac Devices With Computational Heart Models.

OBJECTIVE: Cardiovascular Implantable Electronic Devices (CIEDs) are used extensively for treating life-threatening conditions such as bradycardia, atrioventricular block and heart failure. The complicated heterogeneous physical dynamics of patients provide distinct challenges to device development and validation. We address this problem by proposing a device testing framework within the in-silico closed-loop context of patient physiology. METHODS: We develop an automated framework to validate CIEDs in closed-loop with a high-level physiologically based computational heart model. The framework includes test generation, execution and evaluation, which automatically guides an integrated stochastic optimization algorithm for exploration of physiological conditions. CONCLUSION: The results show that using a closed loop device-heart model framework can achieve high system test coverage, while the heart model provides clinically relevant responses. The simulated findings of pacemaker mediated tachycardia risk evaluation agree well with the clinical observations. Furthermore, we illustrate how device programming parameter selection affects the treatment efficacy for specific physiological conditions. SIGNIFICANCE: This work demonstrates that incorporating model based closed-loop testing of CIEDs into their design provides important indications of safety and efficacy under constrained physiological conditions.

Resonant model-A new paradigm for modeling an action potential of biological cells.

Organ level simulation of bioelectric behavior in the body benefits from flexible and efficient models of cellular membrane potential. These computational organ and cell models can be used to study the impact of pharmaceutical drugs, test hypotheses, assess risk and for closed-loop validation of medical devices. To move closer to the real-time requirements of this modeling a new flexible Fourier based general membrane potential model, called as a Resonant model, is developed that is computationally inexpensive. The new model accurately reproduces non-linear potential morphologies for a variety of cell types. Specifically, the method is used to model human and rabbit sinoatrial node, human ventricular myocyte and squid giant axon electrophysiology. The Resonant models are validated with experimental data and with other published models. Dynamic changes in biological conditions are modeled with changing model coefficients and this approach enables ionic channel alterations to be captured. The Resonant model is used to simulate entrainment between competing sinoatrial node cells. These models can be easily implemented in low-cost digital hardware and an alternative, resource-efficient implementations of sine and cosine functions are presented and it is shown that a Fourier term is produced with two additions and a binary shift.

A Formal Approach for Scalable Simulation of Gastric ICC Electrophysiology.

OBJECTIVE: Efficient and accurate organ models are crucial for closed-loop validation of implantable medical devices. This paper investigates bio-electric slow wave modeling of the stomach, so that gastric electrical stimulator (GES) can be validated and verified prior to implantation. In particular, we consider high-fidelity, scalable, and efficient modeling of the pacemaker, Interstitial cells of Cajal (ICC), based on the formal hybrid input output automata (HIOA) framework. METHODS: Our work is founded in formal methods, a collection of mathematically sound techniques originating in computer science for the design and validation of safety-critical systems. We modeled each ICC cell using an HIOA. We also introduce an HIOA path model to capture the electrical propagation delay between cells in a network. The resultant network of ICC cells can simulate normal and diseased action potential propagation patterns, making it useful for device validation. RESULTS: The simulated slow wave of a single ICC cell had high correlation ( ≈ 0.9) with the corresponding biophysical models. CONCLUSIONS: The proposed model is able to simulate the slow wave activity of a network of ICC cells with high-fidelity for device validation. SIGNIFICANCE: The proposed HIOA model is significantly more efficient than the corresponding biophysical models, scales to larger networks of ICC cells, and is capable of simulating varying propagation patterns. This has the potential to enable verification and validation of implantable GESs in closed-loop with gastrointestinal models in the future.

A machine learning approach to reconstruction of heart surface potentials from body surface potentials.

Invasive cardiac catheterisation is a precursor to ablation therapy for ventricular tachycardia. Invasive cardiac diagnostics are fraught with risks. Decades of research has been conducted on the inverse problem of electrocardiography, which can be used to reconstruct Heart Surface Potentials (HSPs) from Body Surface Potentials (BSPs), for non-invasive cardiac diagnostics. State of the art solutions to the inverse problem are unsatisfactory, since the inverse problem is known to be ill-posed. In this paper we propose a novel approach to reconstructing HSPs from BSPs using a Time-Delay Artificial Neural Network (TDANN). We first design the TDANN architecture, and then develop an iterative search space algorithm to find the parameters of the TDANN, which results in the best overall HSP prediction. We use recorded BSPs and HSPs from individuals suffering from serious cardiac conditions to validate our TDANN. The results are encouraging, in that the predicted and recorded HSPs have an average correlation coefficient of 0.7 under diseased conditions.

Parametric Modeling of Electrocardiograms using Particle Swarm optimization.

The electrocardiogram (ECG) is commonly used to monitor or diagnose adverse heart conditions. While general ECG recordings are widely available, parametric ECG models have been proposed to generate ECG-like signals. Such ECG generators can create extended segments of specific beat morphology or cardiac rhythm, especially in disease states, which can be used to validate cardiac devices or evaluate ECG processing algorithms. Furthermore, ifthe parameters can be fit to a variety of ECGs, these models are valuable tools in ECG compression and modeling. In this paper we propose a framework to fit parameter values of an ECG generator such that the generated signal is similar to a reference signal. We first design a parametric ECG generator with relatively minimal assumptions of single beat waveform morphology. We then use Particle Swarm optimization to find ideal values for parameters of our ECG generator which minimize the percent root mean square difference (PRD) between the reference and generated signals. We were able to capture waveform morphologies of normal, idioventricular, and ventricular flutter rhythms with Pearson correlation coefficients above 0.9 between generated and pre-recorded signals from the MIT-BIH database.

A Parametric Computational Model of the Action Potential of Pacemaker Cells.

OBJECTIVE: A flexible, efficient, and verifiable pacemaker cell model is essential to the design of real-time virtual hearts that can be used for closed-loop validation of cardiac devices. A new parametric model of pacemaker action potential is developed to address this need. METHODS: The action potential phases are modeled using hybrid automaton with one piecewise-linear continuous variable. The model can capture rate-dependent dynamics, such as action potential duration restitution, conduction velocity restitution, and overdrive suppression by incorporating nonlinear update functions. Simulated dynamics of the model compared well with previous models and clinical data. CONCLUSION: The results show that the parametric model can reproduce the electrophysiological dynamics of a variety of pacemaker cells, such as sinoatrial node, atrioventricular node, and the His-Purkinje system, under varying cardiac conditions. SIGNIFICANCE: This is an important contribution toward closed-loop validation of cardiac devices using real-time heart models.

An intracardiac electrogram model to bridge virtual hearts and implantable cardiac devices.

Virtual heart models have been proposed to enhance the safety of implantable cardiac devices through closed loop validation. To communicate with a virtual heart, devices have been driven by cardiac signals at specific sites. As a result, only the action potentials of these sites are sensed. However, the real device implanted in the heart will sense a complex combination of near and far-field extracellular potential signals. Therefore many device functions, such as blanking periods and refractory periods, are designed to handle these unexpected signals. To represent these signals, we develop an intracardiac electrogram (IEGM) model as an interface between the virtual heart and the device. The model can capture not only the local excitation but also far-field signals and pacing afterpotentials. Moreover, the sensing controller can specify unipolar or bipolar electrogram (EGM) sensing configurations and introduce various oversensing and undersensing modes. The simulation results show that the model is able to reproduce clinically observed sensing problems, which significantly extends the capabilities of the virtual heart model in the context of device validation.

Hybrid automata models of cardiac ventricular electrophysiology for real-time computational applications.

Virtual heart models have been proposed for closed loop validation of safety-critical embedded medical devices, such as pacemakers. These models must react in real-time to off-the-shelf medical devices. Real-time performance can be obtained by implementing models in computer hardware, and methods of compiling classes of Hybrid Automata (HA) onto FPGA have been developed. Models of ventricular cardiac cell electrophysiology have been described using HA which capture the complex nonlinear behavior of biological systems. However, many models that have been used for closed-loop validation of pacemakers are highly abstract and do not capture important characteristics of the dynamic rate response. We developed a new HA model of cardiac cells which captures dynamic behavior and we implemented the model in hardware. This potentially enables modeling the heart with over 1 million dynamic cells, making the approach ideal for closed loop testing of medical devices.