Robust Prediction Of Treatment Times In Concurrent Patient Care.

Outpatient centers comprised of many concurrent clinics increasingly see higher patient volumes. In these centers, decisions to improve clinic flow must account for the high degree of interdependence when critical personnel or equipment is shared between clinics. Discrete event simulation models have provided clinical decision support, but rarely address high-volume clinics with shared resources. While highly complex models are now capable of representing clinics in detail, validation techniques often do not evaluate model predictive performance when presented with new data. Cross-validation provides a means to evaluate the robustness of model treatment time predictions when ongoing data collection in clinics is impractical. Ensuring robust predictions assures validity in the use of models to optimize clinic performance. We apply cross-validation in evaluating a model of glaucoma clinic service at Duke Eye Center. In-person observation is used to verify the accuracy of operations data collected through electronic health records (EHR). From the EHR data, we formulate a stochastic reward net model, employing phase-type distributions to represent treatment durations, and solved through discrete event simulation. The model is formulated in two configurations to represent (1) concurrent demand on clinic staff, or (2) independently functioning clinics. Evaluating these two alternatives in cross-validation studies, we find model prediction accuracy improves when interdependence is explicitly modeled in the examined setting.

Design of an Interactive Simulation Environment for Arrays of Cardiac Cells.

The electrical activity of cardiac cells is complex and their collective action difficult to visualize. Understanding what is happening, overall and cell by cell, requires detailed simulation. Here the design of such a simulation is defined by a list of required tasks. An example of the performance of such a simulation is presented, and its time to completion is measured.

Sensor spacing affects the tissue impedance spectra of rabbit ventricular epicardium.

This study was designed to test the hypothesis that a complex composite impedance spectra develops when stimulation and recording of cardiac muscle with sufficiently fine spatial resolution in a four-electrode configuration is used. With traditional (millimeter scale) separations, the ratio between the recorded interstitial central potential difference and total supplied interstitial current is constant at all frequencies. This occurs because the fraction of supplied current that redistributes to the intracellular compartment depends on effective membrane resistance between electrodes, which is low, to a much greater extent than effective membrane capacitance. The spectra should therefore change with finer separations at which effective membrane resistance increases, as supplied current will remain primarily interstitial at lower frequencies and redistribute between compartments at higher frequencies. To test this hypothesis, we built arrays with sensors separated (d) by 804 µm, 452 µm, and 252 µm; positioned those arrays across myocyte axes on rabbit ventricular epicardium; and resolved spectra in terms of resistivity (ρt) and reactivity (χt) over the 10 Hz to 4,000 Hz range. With all separations, we measured comparable spectra with predictions from passive membrane simulations that used a three-dimensional structural framework in which intracellular, interstitial, and membrane properties were prescribed based on the limited data available from the literature. At the finest separation, we found mean ρt at 100 Hz and 4,000 Hz that lowered from 395 Ω-cm to 236 Ω-cm, respectively, with maximal mean χt of 160 Ω-cm. This experimental confirmation of spectra development in whole heart experiments is important because such development is central to achieve measurements of intracellular and interstitial passive electrical properties in cardiac electrophysiological experiments using only interstitial access.

Bioelectricity-AQA, one of the first MOOC courses in engineering.

Bioelectricity-AQA was one of the first massively open online courses in engineering, having been given the first time via Coursera starting in September, 2012. This report provides some detail on its background, presentation, enrollment, and lessons learned.

A structural framework for interpretation of four-electrode microimpedance spectra in cardiac tissue.

Renewed interest in the four-electrode method for identification of passive electrical properties in cardiac tissue has been sparked by a recognition that measurements made with sensors in close proximity are frequency dependent. Therefore, resolution of four-electrode microimpedance spectra (4EMS) may provide an opportunity for routine identification of passive electrical properties for the interstitial and intracellular compartments using only interstitial access. The present study documents a structural framework in which the tissue resistivity (ρt) and reactivity (xt) that comprise spectra are computed using interstitial and intracellular microimpedance distributions that account for differences in compartment size, anisotropic electrical properties in each compartment and electrode separations. We used this framework to consider 4EMS development with relatively wide (d=1 mm) and fine (d=250 µm) electrode separations and sensors oriented along myocyte axes, across myocyte axes and intermediate between those axes.

A new approach for resolution of complex tissue impedance spectra in hearts.

This study was designed to test the feasibility of using sinusoidal approximation in combination with a new instrumentation approach to resolve complex impedance (uCI) spectra from heart preparations. To assess that feasibility, we applied stimuli in the 10-4000 Hz range and recorded potential differences (uPDs) in a four-electrode configuration that allowed identification of probe constants (Kp) during calibration that were in turn used to measure total tissue resistivity ρt from rabbit ventricular epicardium. Simultaneous acquisition of a signal proportional to the supplied current (Vstim) with uPD allowed identification of the V- I ratio needed for ρt measurement, as well as the phase shift from Vstim to uPD needed for uCI spectra resolution. Performance with components integrated to reduce noise in cardiac electrophysiologic experiments, in particular, and provide accurate electrometer-based measurements, in general, was first characterized in tests using passive loads. Load tests showed accurate uCI recovery with mean uPD SNRs between 10 (1) and 10 (3) measured with supplied currents as low as 10 nA. Comparable performance characteristics were identified during calibration of nine arrays built with 250 µm Ag/AgCl electrodes, with uCIs that matched analytic predictions and no apparent effect of frequency ( F = 0.12, P = 0.99). The potential ability of parasitic capacitance in the presence of the electrode-electrolyte interface associated with the small sensors to influence the uCI spectra was therefore limited by the instrumentation. Resolution of uCI spectra in rabbit ventricle allowed measurement of ρt = 134 ± 53 Ω· cm. The rapid identification available with this strategy provides an opportunity for new interpretations of the uCI spectra to improve quantification of disease-, region-, tissue-, and species-dependent intercellular uncoupling in hearts.

A biophysical model for cardiac microimpedance measurements.

Alterations to cell-to-cell electrical conductance and to the structural arrangement of the collagen network in cardiac tissue are recognized contributors to arrhythmia development, yet no present method allows direct in vivo measurements of these conductances at their true microscopic scale. The present report documents such a plan, which involves interstitial multisite stimulation at a subcellular to cellular size scale, and verifies the performance of the method through biophysical modeling. Although elements of the plan have been analyzed previously, their performance as a whole is considered here in a comprehensive way. Our analyses take advantage of a three-dimensional structural framework in which interstitial, intracellular, and membrane components are coupled to one another on the fine size scale, and electrodes are separated from one another as in arrays we fabricate routinely. With this arrangement, determination of passive tissue resistances can be made from measurements taken on top of the currents flowing in active tissue. In particular, our results show that measurements taken at multiple frequencies and electrode separations provide powerful predictions of the underlying tissue resistances in all geometric dimensions. Because of the small electrode size, separation of interstitial from intracellular compartment contributions is readily achieved.

Bayesian quantitative electrophysiology and its multiple applications in bioengineering.

Bayesian interpretation of observations began in the early 1700s, and scientific electrophysiology began in the late 1700s. For two centuries these two fields developed mostly separately. In part that was because quantitative Bayesian interpretation, in principle a powerful method of relating measurements to their underlying sources, often required too many steps to be feasible with hand calculation in real applications. As computer power became widespread in the later 1900s, Bayesian models and interpretation moved rapidly but unevenly from the domain of mathematical statistics into applications. Use of Bayesian models now is growing rapidly in electrophysiology. Bayesian models are well suited to the electrophysiological environment, allowing a direct and natural way to express what is known (and unknown) and to evaluate which one of many alternatives is most likely the source of the observations, and the closely related receiver operating characteristic (ROC) curve is a powerful tool in making decisions. Yet, in general, many people would ask what such models are for, in electrophysiology, and what particular advantages such models provide. So to examine this question in particular, this review identifies a number of electrophysiological papers in bioengineering arising from questions in several organ systems to see where Bayesian electrophysiological models or ROC curves were important to the results that were achieved.

Bayesian analysis of fiber impedance measurements.

The resistivities of microscale components of excitable tissue include the longitudinal intracellular and interstitial resistivities and the membrane resistivity. Measurements of these tissue micro impedances have rarely been obtained, mainly because of the lack of a satisfactory measurement system. Here we evaluate a possible strategy for obtaining such measurements, and begin with a simulation. In the model, a one-dimensional fiber was stimulated with closely space interstitial electrodes at four frequencies, and the voltage differences that occurred in response were recorded. We then considered the inverse question, asking if tissue micro impedances could be found from the voltage measurements plus additive noise. In so doing, we used a Bayesian interpretation of the measured data to find the probability that each of the longitudinal and transmembrane resistivity sets was their origin. The Bayesian procedure proved better suited for interpreting the measurements than was conventional least-squares analysis. It was better because all known data, including realistic noise specifications and a priori probabilities, were included in the defined procedure. The results show that the micro impedances were found satisfactorily using realistic parameters and noise levels. The overall quantitative evaluation is promising for future experimental measurements.

Electric fields around and within single cells during electroporation-a model study.

One of the key issues in electric field-mediated molecular delivery into cells is how the intracellular field is altered by electroporation. Therefore, we simulated the electric field in both the extracellular and intracellular domains of spherical cells during electroporation. The electroporated membrane was modeled macroscopically by assuming that its electric resistivity was smaller than that of the intact membrane. The size of the electroporated region on the membrane varied from zero to the entire surface of the cell. We observed that for a range of values of model constants, the intracellular current could vary several orders of magnitude whereas the maximum variations in the extracellular and total currents were less than 8% and 4%, respectively. A similar difference in the variations was observed when comparing the electric fields near the center of the cell and across the permeabilized membrane, respectively. Electroporation also caused redirection of the extracellular field that was significant only within a small volume in the vicinity of the permeabilized regions, suggesting that the electric field can only facilitate passive cellular uptake of charged molecules near the pores. Within the cell, the field was directed radially from the permeabilized regions, which may be important for improving intracellular distribution of charged molecules.

Mechanism of origin of conduction disturbances in aging human atrial bundles: experimental and model study.

BACKGROUND: Aging is associated with a significant increase in atrial tachyarrhythmias, especially atrial fibrillation. A macroscopic repolarization gradient created artificially by a stimulus at one site before a premature stimulus from a second site is widely considered to be part of the experimental protocol necessary for the initiation of such arrhythmias in the laboratory. How such gradients occur naturally in aging atrial tissue is unknown. OBJECTIVE: The objective of this study was to determine if the pattern of cellular connectivity in aging human atrial bundles produces a mechanism for variable early premature responses. METHODS: Extracellular and intracellular potentials were recorded after control and premature stimuli at a single site in aging human atrial bundles. We also measured cellular geometry, the distribution of connexins, and the distribution of collagenous septa. A model of the atrial bundles was constructed based on the morphological results. Action potential propagation and the sodium current were analyzed after premature stimuli in the model. RESULTS: Similar extracellular potential waveform responses occurred after early premature stimuli in the aging bundles and in the model. Variable premature conduction patterns were accounted for by the single model of aging atrial structure. A major feature of the model results was that the conduction events and the magnitude of the sodium current at multiple sites were very sensitive to small changes in the location and the timing of premature stimuli. CONCLUSION: In aging human atrial bundles stimulated from only a single site, premature stimuli induce variable arrhythmogenic conduction responses. The generation of these responses is greatly enhanced by remodeling of cellular connectivity during aging. The results provide insight into sodium current structural interactions as a general mechanism of arrhythmogenic atrial responses to premature stimuli.

A computer model of electrical stimulation of peripheral nerves in regional anesthesia.

BACKGROUND: Nerve stimulation for regional anesthesia can be modeled mathematically. The authors present a mathematical framework to model the underlying electrophysiology, the development of software to implement that framework, and examples of simulation results. METHODS: The mathematical framework includes descriptions of the needle, the resulting potential field, and the active nerve fiber. The latter requires a model of the individual membrane ionic currents. The model geometry is defined by a three-dimensional coordinate system that allows the needle to be manipulated as it is clinically and tracked in relation to the nerve fiber. The skin plane is included as an electrical boundary to current flow. The mathematical framework was implemented in the Matlab (The MathWorks, Natick, MA) computing environment and organized around a graphical user interface. Simulations were performed using an insulated needle or an uninsulated needle inserted perpendicular to the skin with the nerve fiber at a depth of 2 cm. For each needle design, data were obtained with the needle as cathode or anode. Data are presented as current-distance maps that highlight combinations of current amplitude and tip-to-nerve distance that evoked a propagated response. RESULTS: With the needle tip positioned 2 mm proximal to the depth of the nerve, an insulated needle required a current greater than 0.457 mA for impulse propagation when attached to the cathode; when attached to the anode, the minimal current was 2.354 mA. In the same position, an uninsulated needle attached to the cathode required a current greater than 2.395 mA to generate a response. However, when an uninsulated needle was attached to the anode, currents up to 7 mA were inadequate to produce a propagated response. Of particular interest were combinations of current amplitude and needle position that activated the fiber but blocked impulse propagation for cathodal stimulation. CONCLUSIONS: Mathematical modeling of nerve stimulation for regional anesthesia is possible and could be used to investigate new equipment or needle designs, test nerve localization protocols, enhance clinical and experimental data, and ultimately generate new hypotheses.

Electric fields in tumors exposed to external voltage sources: implication for electric field-mediated drug and gene delivery.

The intratumoral field, which determines the efficiency of electric field-mediated drug and gene delivery, can differ significantly from the applied field. Therefore, we investigated the distribution of the electric field in mouse tumors and tissue phantoms exposed to a large range of electric stimuli, and quantified the resistances of tumor, skin, and electrode-tissue interface. The samples used in the study included 4T1 and B16.F10 tumors, mouse skin, and tissue phantoms constructed with 1% agarose gel with or without 4T1 cells. When pulsed electric fields were applied to samples using a pair of parallel-plate electrodes, we determined the electric field and resistances in each sample as well as the resistance at the electrode-tissue interface. The electric fields in the center region of tissue phantoms and tumor slices ex vivo were macroscopically uniform and unidirectional between two parallel-plate electrodes. The field strengths in tumor tissues were significantly lower than the applied field under both ex vivo and in vivo conditions. During in vivo stimulation, the ratio of intratumoral versus applied fields was approximately either 20% or 55%, depending on the applied field. Meanwhile, the total resistance of skin and electrode-tissue interface was decreased by approximately 70% and the electric resistance at the center of both tumor models was minimally changed when the applied field was increased from 50 to 400 V/cm. These results may be useful for improving electric field-mediated drug and gene delivery in solid tumors.

Cardiac microimpedance measurement in two-dimensional models using multisite interstitial stimulation.

We analyzed central interstitial potential differences during multisite stimulation to assess the feasibility of using those recordings to measure cardiac microimpedances in multidimensional preparations. Because interstitial current injected and removed using electrodes with different proximities allows modulation of the portion of current crossing the membrane, we hypothesized that multisite interstitial stimulation would give rise to central interstitial potential differences that depend on intracellular and interstitial microimpedances, allowing measurement of those microimpedances. Simulations of multisite stimulation with fine and wide spacing in two-dimensional models that included dynamic membrane equations for guinea pig ventricular myocytes were performed to generate test data ( partial differentialphio). Isotropic interstitial and intracellular microimpedances were prescribed for one set of simulations, and anisotropic microimpedances with unequal ratios (intracellular to interstitial) along and across fibers were prescribed for another set of simulations. Microimpedance measurements were then obtained by making statistical comparisons between partial differentialphio values and interstitial potential differences from passive bidomain simulations (Deltaphio) in which a wide range of possible microimpedances were considered. Possible microimpedances were selected at 25% increments. After demonstrating the effectiveness of the overall method with microimpedance measurements using one-dimensional test data, we showed microimpedance measurements within 25% of prescribed values in isotropic and anisotropic models. Our findings suggest that development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.

Multisite interstitial stimulation for cardiac micro-impedance measurements.

On theoretical grounds, interstitial current injected and removed using electrodes in close proximity does not cross the membrane, while equilibration of intracellular and interstitial potentials occurs distant from electrodes widely separated. Multisite interstitial stimulation should therefore give rise to interstitial potential differences recorded centrally that depend on intracellular and interstitial micro-impedances, allowing independent measurement. We tested the feasibility of completing such measurements using simulations of multisite stimulation with fine and wide spacing in models that included Luo-Rudy dynamic (LRd) membrane equations. Using two-dimensional models, test data (delta phi o) were generated with isotropic interstitial and intracellular micro-impedances prescribed for one set of simulations, and with anisotropic micro-impedances including unequal ratios (intracellular/interstitial) along and across fibers prescribed for another set of simulations. Micro-impedance measurements were then obtained by making statistical comparisons between delta phi o values and interstitial potential differences from passive bidomain simulations (Delta phi o) in which a wide range of possible micro-impedances were considered. Our findings suggest development of microfabricated devices to implement the multisite stimulation procedure would facilitate routine measurement as a component of cardiac electrophysiologic study.

The perplexing complexity of cardiac arrhythmias: beyond electrical remodeling.

Cardiac arrhythmias continue to pose a major medical challenge and significant public health burden. Atrial fibrillation, the most prevalent arrhythmia, affects more than two million Americans annually and is associated with a twofold increase in mortality. In addition, more than 250,000 Americans each year suffer ventricular arrhythmias, often resulting in sudden cardiac death. Despite the high incidence and societal impact of cardiac arrhythmias, presently there are insufficient insights into the molecular mechanisms involved in arrhythmia generation, propagation, and/or maintenance or into the molecular determinants of disease risk, prognosis, and progression. In addition, present therapeutic strategies for arrhythmia abatement often are ineffective or require palliative device therapy after persistent changes in the electrical and conduction characteristics of the heart have occurred, changes that appear to increase the risk for arrhythmia progression. This article reviews our present understanding of the complexity of mechanisms that regulate cardiac membrane excitability and cardiac function and explores the role of derangements in these mechanisms that interact to induce arrhythmogenic substrates. Approaches are recommended for future investigations focused on providing new mechanistic insights and therapeutic interventions.

Electric fields within cells as a function of membrane resistivity--a model study.

Externally applied electric fields play an important role in many therapeutic modalities, but the fields they produce inside cells remain largely unknown. This study makes use of a three-dimensional model to determine the electric field that exists in the intracellular domain of a 10-microm spherical cell exposed to an applied field of 100 V/cm. The transmembrane potential resulting from the applied field was also determined and its change was compared to those of the intracellular field. The intracellular field increased as the membrane resistance decreased over a wide range of values. The results showed that the intracellular electric field was about 1.1 mV/cm for Rm of 10,000 omega x cm2, increasing to about 111 mV/cm as Rm decreased to 100 omega x cm2. Over this range of Rm the transmembrane potential was nearly constant. The transmembrane potential declined only as Rm decreased below 1 omega x cm2. The simulation results suggest that intracellular electric field depends on Rm in its physiologic range, and may not be negligible in understanding some mechanisms of electric field-mediated therapies.

Feasibility of cardiac microimpedance measurement using multisite interstitial stimulation.

This study was designed to test the hypothesis that analyses of central interstitial potential differences recorded during multisite stimulation with a set of interstitial electrodes provide sufficient data for accurate measurement of cardiac microimpedances. On theoretical grounds, interstitial current injected and removed using electrodes in close proximity does not cross the membrane, whereas equilibration of intracellular and interstitial potentials occurs distant from electrodes widely separated. Multisite interstitial stimulation should therefore give rise to interstitial potential differences recorded centrally that depend on intracellular and interstitial microimpedances, allowing independent measurement. Simulations of multisite stimulation with fine (25 microm) and wide (400 microm) spacing in one-dimensional models that included Luo-Rudy dynamic membrane equations were performed. Constant interstitial and intracellular microimpedances were prescribed for initial analyses. Discrete myoplasmic and gap-junctional components were prescribed intracellularly in later simulations. With constant microimpedances, multisite stimulation using 29 total electrode combinations allowed interstitial and intracellular microimpedance measurements at errors of 0.30% and 0.34%, respectively, with errors of 0.05% and 0.40% achieved using 6 combinations and 10 total electrodes. With discrete myoplasmic and junctional components, comparable accuracy was maintained following adjustments to the junctions to reflect uncoupling. This allowed uncoupling to be quantified as relative increases in total junctional resistance. Our findings suggest development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.

Field stimulation of 2-D sheets of excitable tissue.

This paper develops equations for the transmembrane potentials (Vm) that occur in two-dimensional (2-D) sheets of tissue in response to field stimulation from an electrode near but not on the surface of the tissue. Comparison of results with those for one dimension shows that an additional term is present in the 2-D equations that influences the evolution of Vm in the interval between the end of the stimulus and the active propagation that may follow. The results provide an analytical framework for understanding Vm in response to field stimulation in two dimensions, both during the tissue's critical linear phase and thereafter.

Cell size and communication: role in structural and electrical development and remodeling of the heart.

With the advent of new information about alterations of cardiac gap junctions in disease conditions associated with arrhythmias, there have been major advances in the genetic and metabolic manipulation of gap junctions. In contrast, in naturally occurring cardiac preparations, little is known about cell-to-cell transmission and the subcellular events of propagation or about structural mechanisms that may affect conduction events at this small size scale. Therefore, the aim of this article is to review results that produce the following unifying picture: changes in cardiac conduction due to remodeling cardiac morphology ultimately are limited to changes in three morphologic parameters: (1) cell geometry (size and shape), (2) gap junctions (distribution and conductivity), and (3) interstitial space (size and distribution). In this article, we consider changes in conduction that result from the remodeling of cell size and gap junction distribution that occurs with developmental ventricular hypertrophy from birth to maturity. We then go on to changes in longitudinal and transverse propagation in aging human atrial bundles that are produced by remodeling interstitial space due to deposition of collagenous septa. At present, experimental limitations in naturally occurring preparations prevent measurement of the conductance of individual gap junctional plaques, as well as the delays in conduction associated with cell-to-cell transmission. Therefore, we consider the development of mathematical electrical models based on documented cardiac microstructure to gain insight into the role of specific morphologic parameters in generating the changes in anisotropic propagation that we measured in the tissue preparations. A major antiarrhythmic implication of the results is that an "indirect" therapeutic target is interstitial collagen, because regulation of its deposition and turnover to prevent or alter microfibrosis can enhance side-to-side electrical coupling between small groups of cells in aging atrial bundles.