Digital twins in medicine

Medical digital twins, which are potentially vital for personalized medicine, have become a recent focus in medical research. Here we present an overview of the state of the art in medical digital twin development, especially in oncology and cardiology, where it is most advanced. We discuss major challenges, such as data integration and privacy, and provide an outlook on future advancements. Emphasizing the importance of this technology in healthcare, we highlight the potential for substantial improvements in patient-specific treatments and diagnostics.

Modulation of shock-end virtual electrode polarisation as a direct result of 3D fluorescent photon scattering

Due to the large transmural variation in transmembrane potential following the application of strong electric shocks, it is thought that fluorescent photon scattering from depth plays a significant role in optical signal modulation at shock-end. For the first time, a model of photon scattering is used to accurately synthesize fluorescent signals over the irregular geometry of the rabbit ventricles following the application of such strong shocks. A bidomain representation of electrical activity is combined with finite element solutions to the photon diffusion equation, simulating both the excitation and emission processes, over an anatomically-based model of rabbit ventricular geometry and fiber orientation. Photon scattering from within a 3D volume beneath the epicardial optical recording site is shown to transduce differences in transmembrane potential within this volume through the myocardial wall. This leads directly to a significantly modulated optical signal response with respect to that predicted by the bidomain simulations, distorting epicardial virtual electrode polarization produced at shock-end. Furthermore, we show that this degree of distortion is very sensitive to the optical properties of the tissue, an important variable to consider during experimental mapping set-ups. These findings provide an essential first-step in aiding the interpretation of experimental optical mapping recordings following strong defibrillation shocks.

Modelling induction of a rotor in cardiac muscle by perpendicular electric shocks

A strong, properly timed shock applied perpendicularly to a propagating wavefront causes a rotor in the canine myocardium. Experimental data indicate that the induction of this rotor relies on the shock exciting tissue away from the electrodes. The computational study reproduced such direct excitation in a two-dimensional model of a 2.7 x 3 cm sheet of cardiac muscle. The model used experimentally measured extracellular potentials to represent 100 and 150 V shocks delivered through extracellular electrodes. The shock-induced transmembrane potential was computed according to two mechanisms, the activating function and the unit-bundle sawtooth potential. The overall process leading to initiation of a rotor was the same in model and experiment. For the 100 V shock, the directly excited region extended 2.26 cm away from the electrode; the centre of the rotor ('critical point') was 1.28 cm away, where the electric field Ecr was 4.54 Vcm(-1). Increasing the shock strength to 150 V moved the critical point 1.02 cm further and decreased Ecr by 0.39 Vcm(-1). The results are comparable with experimental data. The model suggests that the unit-bundle sawtooth is responsible for the creation of the directly excited region, and the activating function is behind the dependence of Ecr on shock strength.

Reentry in a morphologically realistic atrial model

INTRODUCTION

Atrial fibrillation is the most common cardiac arrhythmia. In ablation procedures, identification of the reentrant pathways is vital. This has proven difficult because of the complex morphology of the atria. The purpose of this study was to ascertain the role of specific anatomic structures on reentry induction and maintenance.

METHOD AND RESULTS

A computationally efficient, morphologically realistic, computer model of the atria was developed that incorporates its major structural features, including discrete electrical connections between the right and left atria, physiologic fiber orientation in three dimensions, muscle structures representing the crista terminalis (CT) and pectinate muscles, and openings for the veins and AV valves. Reentries were induced near the venous openings in the left and right atria, the mouth of the coronary sinus, and the free wall of the right atrium. The roles of certain muscular structures were ascertained by selectively removing the structures and observing how the propagation of activity was affected.

CONCLUSION

(1) The muscular sheath of the coronary sinus acts as a pathway for a reentrant circuit and stabilizes any circuits that utilize the isthmus near the inferior vena cava. (2) Poor trans-CT coupling serves to stabilize flutter circuits. (3) Wall thickness is an important factor in the propagation of electrical activity, especially in the left atrium. (4) The openings of the inferior and superior venae cavae form natural anatomic anchors that make reentry easier to initiate by allowing for smaller ectopic beats to induce reentry.

Termination of spiral waves with biphasic shocks: role of virtual electrode polarization

INTRODUCTION

This simulation study seeks to extend the virtual electrode polarization (VEP) theory for defibrillation to explain the success and failure of biphasic shocks. The goals of the study are to (1) provide insight into why optimal biphasic shocks have a lower voltage defibrillation threshold than monophasic shocks, (2) examine the mechanisms of biphasic shock failure and to determine whether they differ from those of monophasic shocks, and (3) study how the timing of biphasic shock delivery to a spiral wave affects voltage defibrillation threshold.

METHODS AND RESULTS

A spiral wave is initiated in a bidomain representation of a 2-cm x 2-cm sheet of ventricular myocardium. The model incorporates nonuniform fiber curvature, membrane kinetics suitable for high-strength shocks, and electroporation. A spatially uniform extracellular field is delivered by line electrodes. The shock establishes VEP that dictates the postshock activity in the tissue. Our results demonstrate that the second phase of biphasic shocks leaves the tissue with substantially smaller postshock excitable gap, thus eliminating the majority of the substrate for reinitiation of reentrant activity. Further, the occurrence of break excitations for weaker biphasic shocks indicates that the mechanisms for biphasic shock failure are more complex than for monophasic shocks. Biphasic voltage defibrillation thresholds range from 8 to 16 V/cm, depending on the position of the spiral wave. An increase in the amount of preshock excitable gap leads to an increase in voltage defibrillation threshold.

CONCLUSION

This study demonstrates the importance of VEP and its interaction with preshock activity in the success and failure of biphasic defibrillation shocks.

Virtual electrode polarization in the far field: implications for external defibrillation

We recently suggested that failure of implantable defibrillation therapy may be explained by the virtual electrode-induced phase singularity mechanism. The goal of this study was to identify possible mechanisms of vulnerability and defibrillation by externally applied shocks in vitro. We used bidomain simulations of realistic rabbit heart fibrous geometry to predict the passive polarization throughout the heart induced by external shocks. We also used optical mapping to assess anterior epicardium electrical activity during shocks in Langendorff-perfused rabbit hearts (n = 7). Monophasic shocks of either polarity (10-260 V, 8 ms, 150 microF) were applied during the T wave from a pair of mesh electrodes. Postshock epicardial virtual electrode polarization was observed after all 162 applied shocks, with positive polarization facing the cathode and negative polarization facing the anode, as predicted by the bidomain simulations. During arrhythmogenesis, a new wave front was induced at the boundary between the two regions near the apex but not at the base. It spread across the negatively polarized area toward the base of the heart and reentered on the other side while simultaneously spreading into the depth of the wall. Thus a scroll wave with a ribbon-shaped filament was formed during external shock-induced arrhythmia. Fluorescent imaging and passive bidomain simulations demonstrated that virtual electrode polarization-induced scroll waves underlie mechanisms of shock-induced vulnerability and failure of external defibrillation.

Success and failure of the defibrillation shock: insights from a simulation study

INTRODUCTION

This simulation study presents a further inquiry into the mechanisms by which a strong electric shock fails to halt life-threatening cardiac arrhythmias.

METHODS AND RESULTS

The research uses a model of the defibrillation process that represents a sheet of myocardium as a bidomain. The tissue consists of nonuniformly curved fibers in which spiral wave reentry is initiated. Monophasic defibrillation shocks are delivered via two line electrodes that occupy opposite tissue boundaries. In some simulation experiments, the polarity of the shock is reversed. Electrical activity in the sheet is compared for failed and successful shocks under controlled conditions. The maps of transmembrane potential and activation times calculated during and after the shock demonstrate that weak shocks fail to terminate the reentrant activity via two major mechanisms. As compared with strong shocks, weak shocks result in (1) smaller extension of refractoriness in the areas depolarized by the shock, and (2) slower or incomplete activation of the excitable gap created by deexcitation of the negatively polarized areas. In its turn, mechanism 2 is associated with one or more of the following events: (a) lack of some break excitations, (b) latency in the occurrence of the break excitations, and (c) slower propagation through deexcited areas. Reversal of shock polarity results in a change of the extent of the regions of deexcitation, and thus, in a change in defibrillation threshold.

CONCLUSION

The results of this study indicate the paramount importance of shock-induced deexcitation in both defibrillation and postshock arrhythmogenesis.

A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium

Presented here is an efficient algorithm for solving the bidomain equations describing myocardial tissue with active membrane kinetics. An analysis of the accuracy shows advantages of this numerical technique over other simple and therefore popular approaches. The modular structure of the algorithm provides the critical flexibility needed in simulation studies: fiber orientation and membrane kinetics can be easily modified. The computational tool described here is designed specifically to simulate cardiac defibrillation, i. e., to allow modeling of strong electric shocks applied to the myocardium extracellularly. Accordingly, the algorithm presented also incorporates modifications of the membrane model to handle the high transmembrane voltages created in the immediate vicinity of the defibrillation electrodes.

Roles of electric field and fiber structure in cardiac electric stimulation

This study investigated roles of the variation of extracellular voltage gradient (VG) over space and cardiac fibers in production of transmembrane voltage changes (DeltaV(m)) during shocks. Eleven isolated rabbit hearts were arterially perfused with solution containing V(m)-sensitive fluorescent dye (di-4-ANEPPS). The epicardium received shocks from symmetrical or asymmetrical electrodes to produce nominally uniform or nonuniform VGs. Extracellular electric field and DeltaV(m) produced by shocks in the absolute refractory period were measured with electrodes and a laser scanner and were simulated with a bidomain computer model that incorporated the anterior left ventricular epicardial fiber field. Measurements and simulations showed that fibers distorted extracellular voltages and influenced the DeltaV(m). For both uniform and nonuniform shocks, DeltaV(m) depended primarily on second spatial derivatives of extracellular voltages, whereas the VGs played a smaller role. Thus, 1) fiber structure influences the extracellular electric field and the distribution of DeltaV(m); 2) the DeltaV(m) depend on second spatial derivatives of extracellular voltage.

Modeling defibrillation: effects of fiber curvature

The goal of this modeling study is to demonstrate extinguishing of a spiral wave reentry in a sheet of myocardium that incorporates curved fibers. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. The spiral wave is initiated via cross-field stimulation of the bidomain sheet. The defibrillation shock is delivered via two line electrodes that occupy opposite tissue boundaries. Simulation results demonstrate that large-scale regions of depolarization are induced under the cathode as well as at locations in the vicinity of the anode. For high shock strengths, the new wavefronts generated from the regions of induced depolarization restrict the spiral wave pathway and render the tissue too refractory to further maintain the reentry. Weak shocks leave large portions of the sheet unaffected allowing the spiral wave to find recovered tissue and thus survive.

Virtual electrode effects in defibrillation

This modeling study demonstrates that a re-entrant activity in a sheet of myocardium can be extinguished by a defibrillation shock delivered via extracellular point-source electrodes which establish spatially non-uniform applied field. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios in the cardiac conductivities. Spiral wave re-entry is initiated in the bidomain sheet following an S1-S2 stimulation protocol. The results indicate that the point-source defibrillation shock establishes large-scale changes in transmembrane potential in the tissue (virtual electrodes) that are 'superimposed' over regions of various degrees of membrane refractoriness in the myocardium. The close proximity of large-scale shock-induced regions of alternating membrane polarity is central to the ability of the shock to terminate the spiral wave. The new wavefronts generated following anode/cathode break phenomena restrict the spiral wave and render the tissue too refractory to further maintain the re-entry. In contrast, shocks delivered via line electrodes establish, in close proximity to the electrode, changes in transmembrane potential that are of same-sign polarity. These shocks are incapable of terminating the re-entrant activation.

Influence of anisotropy on local and global measures of potential gradient in computer models of defibrillation

A heart-torso model including fiber orientation is used to calculate electric field strength in an active-can transvenous defibrillation system and estimate errors due to inadequate description of the anisotropy of the myocardium. Using a minimum potential gradient (5 V/cm) in a critical mass (95%) of the tissue, the estimated defibrillation voltage threshold for a right ventricular transvenous lead placement differs by only 4.5% when using isotropic myocardial conductivity compared to a model with realistic fiber architecture. In addition, pointwise comparisons of the two solutions reveal differences of 10.8% rms in potential gradient strength and 31.6% rms in current density magnitude in the myocardium, resulting in a change in the location of the low gradient regions. These results suggest that if a minimum potential gradient throughout the heart is necessary to avoid reinitiation of fibrillatory wave fronts, then isotropic models are adequate for modeling the electric field in the heart. Alternatively, the model demonstrates the use of physiologically based descriptions of anisotropy and fiber orientation, which will soon allow simulations of shock induced membrane polarization during defibrillation.

Membrane refractoriness and excitation induced in cardiac fibers by monophasic and biphasic shocks

INTRODUCTION

This modeling study examines the effect of low-intensity monophasic and biphasic waveforms on the response of a refractory cardiac fiber to the defibrillation shock.

METHODS AND RESULTS

Two cardiac fiber representations are considered in this study: a continuous fiber and a discrete fiber that incorporates gap junctions. Each fiber is undergoing a propagating action potential. Shocks of various strengths and coupling intervals are delivered extracellularly at fiber ends during the relative refractory period. In a continuous fiber, monophasic shock strengths of three times the diastolic threshold either elicit no response or, for coupling intervals above 380 msec, reinitiate propagation. In contrast, biphasic shocks of same strength are capable of terminating the existing wavefronts by either invoking a nonpropagating response (coupling intervals 370 to 382 msec) that prolongs the refractory period or inducing wavefront collision (coupling intervals above 400 msec). The fiber response is similar for other shock strengths and when cellular discontinuity is accounted for. Thus, for a refractory fiber, biphasic shocks have only a small "vulnerable" window of coupling intervals over which propagation is reinitiated.

CONCLUSION

At short coupling intervals, a significant extension of refractoriness is generated at regions where the biphasic shock induced hyperpolarization followed by depolarization. At large coupling intervals, the enhanced efficacy of biphasic shocks is associated with their ability to induce wavefront collision, thus decreasing the probability of reinitiating fibrillation. Overall, the defibrillation shock affects the tissue through the induced large-scale hyperpolarization and depolarization, and not through the small-scale transmembrane potential oscillations at cell ends.

Discrete versus syncytial tissue behavior in a model of cardiac stimulation--I: Mathematical formulation

This paper presents a model describing the steady-state response of a two-dimensional (2-D) slice of myocardium to extracellular current injection. The model incorporates a continuous representation of the multicellular, syncytial cardiac tissue based on the bidomain model. The classical bidomain model is modified by introducing periodic conductivities to better represent the electrical properties of the intracellular space. Thus, junctional discontinuity between abutting myocytes is reflected in the macroscopic representation of cardiac tissue behavior. Since a solution to the resulting coupled differential equations governing the intracellular and extracellular potentials in the tissue preparation is not computationally tractable when traditional numerical approaches, such as finite element or finite difference methods are used, spectral techniques are employed to reduce the problem to the solution of a set of algebraic equations for the transform of the bidomain potentials. Further, the solution to the "periodic" bidomain problem in the Fourier space is decomposed into two separate solutions: One for the classical-bidomain potentials where it is assumed that the intracellular conductivity values along and across cells incorporate the average contribution from cytoplasm and junction, and another for the junctional potential component. The decomposition of the total solution allows to approximately solve for the junctional component thus achieving high overall computational efficiency. The results of simulation are presented in an accompanying paper.

Discrete versus syncytial tissue behavior in a model of cardiac stimulation--II: Results of simulation

The research presented here combines mathematical modeling and computer simulation in developing a new model of the membrane polarization induced in the myocardium by the applied electric field. Employing this new model termed the "period" bidomain model, the steady-state distribution of the transmembrane potential is calculated on a slice of cardiac tissue composed of abutting myocytes and subjected to two point-source extracellular current stimuli. The goal of this study is to examine the relative contribution of cellular discreteness and macroscopic syncytial tissue behavior in the mechanism by which the applied electric field alters the transmembrane potential in cardiac muscle. The results showed the existence of oscillatory changes in the transmembrane potential at cell ends owing to the local resistive inhomogeneities (gap-junctions). This low-magnitude sawtooth component in the transmembrane potential is superimposed over large-scale transmembrane potential excursions associated with the syncytial (collective) fiber behavior. The character of the cardiac response to stimulation is determined primarily by the large-scale syncytial tissue behavior. The sawtooth contributes to the overall tissue response only in regions where the large-scale transmembrane potential component is small.

An approximate solution to the periodic bidomain equations in one dimension

An approximate, computationally tractable solution is proposed for the potentials in the bidomain model with periodic intracellular junctions (the periodic bidomain model). This new approach is based on the one-dimensional rigorous spectral method described previously by Trayanova and Pilkington (IEEE Trans. Biomed. Eng., May 1993). The total solution to the one-dimensional periodic bidomain problem is decomposed in the spectral domain into solutions to (1) the single-fiber classical bidomain problem in which the intracellular conductivity value incorporates the average contribution from cytoplasm and junction and (2) the "junctional" potential problem due to the presence of junctions at discrete locations alone. Solving for the junctional term rigorously requires most of the numerical effort in the solution for the periodic bidomain potentials. Here the junctional potential is found approximately with little numerical effort. A comparison between the rigorous and the approximate solutions serves as a justification for the proposed approximate solution procedure. The procedure outlined in this paper is applicable to higher spatial dimensions where both tissue anisotropy and junctional inhomogeneities play a role in establishing the transmembrane potential distribution.

A bidomain model for ring stimulation of a cardiac strand

A bidomain model is developed to represent a cardiac muscle strand undergoing stimulation from a ring electrode. Expressions are derived for the distribution of the potentials in the strand as well as in the bath perfusing the tissue, under the condition of equal anisotropy ratios in the intracellular and interstitial spaces. The present derivation provides an example of an analytical solution technique that might also prove useful for other problems in theoretical electrophysiology.

A bidomain model with periodic intracellular junctions: a one-dimensional analysis

The classical bidomain model of cardiac tissue views the intracellular and extracellular (interstitial) spaces as two coupled but separate continua. In the present study, the classical bidomain model has been extended by introducing a periodic conductivity in the intracellular space to represent the junctional discontinuity between abutting myocytes. In this model the junctional region of a myocyte is represented in a way that permits variation of junction size and conductivity profile. Employing spectral techniques, a new method was developed for solving the coupled differential equations governing the intracellular and extracellular potentials in a tissue preparation of finite dimensions. Different spectral representations are used for the aperiodic intra- and extracellular potentials (finite Fourier integral transform) and for the periodic intracellular conductivity (Fourier series). As a first application of the method, the response of a 50-cell, single interior fiber to a defibrillating current is examined under steady-state conditions. Transmembrane as well as intra- and extracellular potential distributions along the fiber were calculated.

Fatigue-related changes in motor unit action potentials of adult cats

The purpose of this study was to quantify the changes in motor-unit action potentials (MUAP) and force during a standard motor-unit fatigue test. MUAP waveforms were characterized by the measurement of amplitude, duration, area, and shape (as reflected in a coefficient of proportionality). Fatigue-resistant motor units exhibited small, but statistically significant, changes in MUAP amplitude and area during the fatigue test, whereas fatigable motor units displayed variable changes in MUAP amplitude, duration, and area. For all motor-unit types, the coefficient of proportionality did not change, and hence the change in MUAP area was proportional to the combined changes in amplitude and duration. The between- and within-train changes in MUAP were also distinct for the fatigue-resistant and fatigable motor units. Although several mechanisms could be responsible for the changes in the MUAP as the fatigue test proceeded, the dissociation of the time courses for MUAP and force indicated that these MUAP changes were not the principal reason for the decline in force under these conditions.

Examination of the choice of models for computing the extracellular potential of a single fibre in a restricted volume conductor

The paper compares the rigorous and the conventional approximate line source solution of Laplace's equation used to evaluate the potential of a single cylindrical fibre. Particular attention is given to the solutions for a radially restricted circular cylindrical volume conductor. The effect of the extent of the volume conductor b on the difference between the potentials evaluated according to the different models is examined. For values of b larger than 10 times the fibre radius, the relative difference is less than 1 per cent and the values of b around 2 times the fibre radii, the error reaches as much as 17 per cent.

Modification of a cylindrical bidomain model for cardiac tissue

Previous models based on a cylindrical bidomain assumed either that the ratio of intracellular and interstitial conductivities in the principal directions were the same or that there was no radial variation in potential (i.e., a planar front, delta Vm/delta rho = 0). This paper presents a formulation and the expressions for the intracellular, interstitial, extracellular, and transmembrane potentials arising from nonplanar propagation along a cylindrical bundle of cardiac tissue represented as a bidomain with arbitrary anisotropy. For unequal anisotropy, the transmembrane current depends not only on the local change of the transmembrane potential but also on the nature of the transmembrane potential throughout the volume.

A planar slab bidomain model for cardiac tissue

A fully three-dimensional model of the ventricular or atrial free wall will involve a planar geometry of finite thickness. The governing equations for the interstitial and extracellular potential of a planar slab of cardiac tissue comprised of parallel fibers undergoing uniform plane-wave activation are presented. A comparison with a bidomain of cylindrical geometry with the same half-thickness shows that the potentials in the planar bidomain (as a function of depth) approach core-conductor behavior more quickly.

Extracellular potentials and currents of a single active fiber in a restricted volume conductor

Based on mathematical expressions governing the electric field, the extracellular potentials generated by a single active fiber in a restricted circular cylindrical volume conductor are evaluated. This paper examines the effect of the extent of the volume conductor, with radius b, on the extracellular potentials at different field points. For values of b less than 1.5 times the fiber radius, the extracellular potentials in the volume conductor are always the core conductor potentials, independent of the shape and amplitude of the transmembrane potential. For b greater than a critical radius (a value that depends on the transmembrane potential waveform), the extracellular potentials at and near the membrane are the same as if the volume conductor were unbounded. Near the boundary with the insulator, the amplitude of the extracellular potentials is equal to the core conductor amplitude, although the potentials are much broader than the core conductor potential.

Electrotonic potentials of myelinated nerve fibers

The extracellular electrotonic potentials of a single myelinated nerve fiber in a volume conductor of infinite extent were studied. The spatial distribution of the transmembrane electrotonic potential was obtained by integrating the system of differential equations constituting the model of the activation of a myelinated nerve fiber. The stimulus was step-like. The present investigation was concerned with the steady-state conditions only. The spatial distribution of the extracellular potentials at various radial distances in the conducting medium was calculated using the line source model. Up to a certain radial distance the discontinuous structure of the myelinated fiber is reflected in the oscillatory nature of the extracellular potentials, while further in the volume conductor the potentials are smooth. The magnitude of the radial decline of the extracellular potentials were compared for myelinated fibers of various internodal distances.

Potential and current distributions in a cylindrical bundle of cardiac tissue

The intracellular and interstitial potentials associated with each cell or fiber in multicellular preparations carrying a uniformly propagating wave are important for characterizing the electrophysiological behavior of the preparation and in particular, for evaluating the source contributed by each fiber. The aforementioned potentials depend on a number of factors including the conductivities characterizing the intracellular, interstitial, and extracellular domains, the thickness of the tissue, and the distance (depth) of the field point from the surface of the tissue. A model study is presented describing the extracellular and interstitial potential distribution and current flow in a cylindrical bundle of cardiac muscle arising from a planar wavefront. For simplicity, the bundle is considered as a bidomain. Using typical values of conductivity, the results show that the intracellular and interstitial potential of fibers near the center of a very large bundle (greater than 10 mm) may be approximated by the potentials of a single fiber surrounded by a limited extracellular space (a fiber in oil), hence justifying a core-conductor model. For smaller bundles, the peak interstitial potential is less than that predicted by the core-conductor model but still large enough to affect the overall source strength. The magnitude of the source strength is greatest for fibers lying near the center of the bundle and diminishes sharply for fibers within 50 microns of the surface.