Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed inhomogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction, conductivity of the cleft and the cleft height, could lead to different shapes of the extracellular signals

Advances in surface EMG signal simulation with analytical and numerical descriptions of the volume conductor

Surface electromyographic (EMG) signal modeling is important for signal interpretation, testing of processing algorithms, detection system design, and didactic purposes. Various surface EMG signal models have been proposed in the literature. In this study we focus on 1) the proposal of a method for modeling surface EMG signals by either analytical or numerical descriptions of the volume conductor for space-invariant systems, and 2) the development of advanced models of the volume conductor by numerical approaches, accurately describing not only the volume conductor geometry, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function is derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fiber orientation. In some cases (e.g., multi-pinnate muscles) accurate description of the conductivity tensor may be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibers is presented and applied to representatively investigate a bi-pinnate muscle with rectilinear and curvilinear fibers. The study thus propose an approach for surface EMG signal simulation in space invariant systems as well as new models of the volume conductor using numerical methods

Neural Dynamics during Anoxia and the “Wave of Death”

Recent experiments in rats have shown the occurrence of a high amplitude slow brain wave in the EEG approximately 1 minute after decapitation, with a duration of 5–15 s (van Rijn et al, PLoS One 6, e16514, 2011) that was presumed to signify the death of brain neurons. We present a computational model of a single neuron and its intra- and extracellular ion concentrations, which shows the physiological mechanism for this observation. The wave is caused by membrane potential oscillations, that occur after the cessation of activity of the sodium-potassium pumps has lead to an excess of extracellular potassium. These oscillations can be described by the Hodgkin-Huxley equations for the sodium and potassium channels, and result in a sudden change in mean membrane voltage. In combination with a high-pass filter, this sudden depolarization leads to a wave in the EEG. We discuss that this process is not necessarily irreversible

Cardiac anisotropy in boundary-element models for the electrocardiogram

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

BACKGROUND: Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level. METHODS: We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG. RESULTS: We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given. CONCLUSIONS: Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described

Ring electrode for radio-frequency heating of the cornea: modelling and in vitro experiments

[EN] Radio-frequency thermokeratoplasty (RF-TKP) is a technique used to reshape the cornea curvature by means of thermal lesions using radio-frequency currents. This curvature change allows refractive disorders such as hyperopia to be corrected. A new electrode with ring geometry is proposed for RF-TKP. It was designed to create a single thermal lesion with a full-circle shape. Finite element models were developed, and the temperature distributions in the cornea were analysed for different ring electrode characteristics. The computer results indicated that the maximum temperature in the cornea was located in the vicinity of the ring electrode outer perimeter, and that the lesions had a semi-torus shape. The results also indicated that the electrode thickness, electrode radius and electrode thermal conductivity had a significant influence on the temperature distributions. In addition, in vitro experiments were performed on rabbit eyes. At 5 IN power the lesions were fully circular. Some lesions showed non-uniform characteristics along their circular path. Lesion depth depended on heating duration (60% of corneal thickness for 20s, and 30% for 10s). The results suggest that the critical shrinkage temperature (55-63degreesC) was reached at the central stroma and along the entire circular path in all the cases.Berjano, E.; Saiz Rodríguez, FJ.; Alió, J.; Ferrero, JM. (2003). Ring electrode for radio-frequency heating of the cornea: modelling and in vitro experiments. Medical & Biological Engineering & Computing. 41(6):630-639. https://doi.org/10.1007/BF02349970S630639416Alió, J. L., Ismail, M. M., Artola, A., andPérez-Santonja, J. J. (1997a): ‘Correction of hyperopia induced by photorefractive keratectomy using non-contact Ho: YAG laser thermal keratoplasty’,J. Refract. Surg.,13, pp. 13–16Alió, J. L., Ismail, M. M., andSanchez, J. L. (1997b): ‘Correction of hyperopia with non-contact Ho: YAG laser thermal keratoplasty’,J. Refract. Surg.,13, pp. 17–22Alió, J. L., andPérez-Santonja, J. J. (1999): ‘Correction of hyperopia by laser thermokeratoplasty (LTK)’ inPallikaris, I., andAgarwal, S. (Eds): ‘Refractive Surgery’ (Jaypee Brothers Medical Publishers Ltd, New Delhi, 1999), pp. 583–591Alió, J. L., andPérez-Santonja, J. J. (2002): ‘Correction of hyperopia by laser thermokeratoplasty (LTK)’ inAgarwal, S., Agarwal, A., Apple, D. J., Buratto, L., Alió, J. L., Pandey, S. K., andAgarwal, A. (Eds): ‘Textbook of ophthalmology’ (Lippincott Williams & Wilkins, Philadelphia, 2002), pp. 1331–1337Ayala, M. J., Alió, J. L., Ismail, M. M., andSánchez-Castro, J. M. (2000): ‘Experimental corneal histological study after thermokeratoplasty with holmium laser’,Arch. Soc. Esp. Oftalmol.,75, pp. 619–626Asbell, P. A., Maloney, R. K., Davidorf, J., Hersh, P., McDonald, M., Manche, E., andConductive Keratoplasty Study Group (2001): ‘Conductive keratoplasty for the correction of hyperopia’,Tr. Am. Ophtalmol. Soc.,99, pp. 79–87Avitall, B., Mughal, K., Hare, J., Helms, R., andKrum, D. (1997): ‘The effects of electrode-tissue contact on radiofrequency lesion generation’PACE,20, pp. 2899–2910Avitall, B., Helms, R. W., Koblish, J. B., Sieben, W., Kotov, A. V., andGupta, G. N. (1999): ‘The creation of linear contiguous lesions in the atria with an expandable loop catheter’,J. Am. Coll. Cardiol.,33, pp. 972–984Berjano, E. J., Saiz, J., andFerrero, J. M. (2002): ‘Radio-frequency heating of the cornea: Theoretical model andin vitro experiments’,IEEE Trans. Biomed. Eng.,49, pp. 196–205Brickmann, R., Kampmeier, J., Grotehusmann, U., Vogel, A., Koop, N., Asiyo-Vogel, M., Kamm, K., andBirngruber, R. (1996): ‘Corneal collagen denaturation in laserthermokeratoplasty’,SPIE Proc.,2681, pp. 56–63Choi, B., Kim, J., Welch, A. J., andPearce, J. A. (2002): ‘Dynamic impedance measurements during radio-frequency heating of cornea’,IEEE Trans. Biomed. Eng.,49, pp. 1610–1616Curley, M. G., andHamilton, P. S. (1997): ‘Creation of large thermal lesions in liver using saline-enhanced RF ablation’. Proc. 19th Ann. Int. Conf. IEEE Eng. Med. Biol. Soc., Chicago, pp. 2516–2519Doss, J. D., andAlbillar, J. I. (1980): ‘A technique for the selective heating of corneal stroma’,Contact Intraocular Lens Med.,6, pp. 13–17Doss, J. D. (1982): ‘Calculation of electric fields in conductive media’,Med. Phys.,9(4), pp. 566–573Gruenberg, P., Manning, W., Miller, D. andOlson, W. (1981): ‘Increase in rabbit corneal curvature by heated ring application’,Ann. Ophthalmol.,13, pp. 67–70Hata, C., andRaymond Chia, W.-K. (2001): ‘Catheter for circular tissue ablation and methods thereof’. US Patent 2001/0044625 A1Jain, M. K., andWolf, P. D. (1998): ‘Effect of electrode contact on lesion growth during temperature controlled radiofrequency ablation’, Proc. 20th Ann. Int. Conf. IEEE Eng. Med. Biol. Soc. Hong Kong (IEEE, Piscataway NJ) pp. 245–247Jain, M. K., andWolf, P. D. (1999): ‘Temperature controlled and constant power radiofrequency ablation: what affects lesion growth?’,IEEE Trans. Biomed. Eng.,46, pp. 1405–1412Krasteva, V. Tz., andPapazov, S. P. (2002): ‘Estimation of current density distribution under electrodes for external defibrillation’,Biomed. Eng. OnLine,1, 7Labonté, S. (1992): ‘A theoretical study of radio-frequency ablation of the myocardium’,PhD dissertation, Department of Electrical Engineering, University of Ottawa, CanadaLabonté, S. (1994): ‘Numerical model for radio-frequency ablation of the endocardium and its experimental validation’,IEEE Trans. Biomed. Eng.,41, pp. 108–115Mannis, M. J., Segal, W. A., andDarlington, J. K. (2001): ‘Making sense of refractive surgery in 2001: Why, when, for whom, and by whom?’,Mayo Clin. Proc.,76, pp. 823–829McCally, R. L., Bargeron, R. A., andGreen, W. R. (1983): ‘Stromal damage in rabbit corneas exposed to CO2 laser radiation’,Exp. Eye Res.,37, pp. 543–550McDonald, M. B., Hersh, P. S., Manche, E. E., Maloney, R. K., Davidorf, J., andSabry, M. (2002): ‘Conductive keratoplasty for the correction of low to moderate hyperopia: U.S. clinical trial 1-year results on 355 eyes’,Ophthalmol.,109, pp. 1978–1989McRury, I. D., Mitchell, M. A., Panescu, D. andHaines, D. E. (1997): ‘Non-uniform heating during radiofrequency ablation with long electrodes: monitoring the edge effect’,Circ.,96, pp. 4057–4064Méndez-g, A., andMéndez-Noble, A. (1997): ‘Conductive keratoplasty of the correction of hyperopia’ inSher, N. A. (Ed.) ‘Surgery for hyperopia and presbyopia’ (Williams & Wilkins, Baltimore, 1997), pp. 163–171Miller, D., andManning, W.J. (1978): ‘Alterations in curvature of bovine cornea using heated rings’,Invest. Ophthalmol., p. 297Mirotznik, M. S., andSchwartzman, D. (1996): ‘Nonuniform heating patterns of commercial electrodes for radiofrequency catheter ablation’,J. Cardiovasc. Electrophysiol.,7, pp. 1058–1062Nakagawa, H., Yamanashi, W. S., Pitha, J. V., Arruda, M., Wang, X., Ohtomo, K., Beckman, K. J., McClelland, J. H., Lazzara, R., andJackman, W. M. (1995): ‘Comparison ofin vivo tissue temperature profile and lesion geometry for radiofrequency ablation with a saline-irrigated electrode versus temperature control in a canine thigh muscle preparation’,Circ.,91, pp. 2264–2273Panescu, D., Whayne, J. G., Fleischman, S. D., Mirotznik, M. S., Swanson, D. K., andWebster, J. G. (1995): ‘Three-dimensional finite element analysis of current density and temperature distributions during radio-frequency ablation’,IEEE Trans. Biomed. Eng.,42, pp. 879–890Plonsey, R., andHeppner, D. B. (1967): ‘Considerations of quasistationarity in electrophysiological systems’,Bull. Math. Biophys.,29, pp. 657–664Rowsey, J. J. (1987): ‘Electrosurgical keratoplasty: Update and retraction’,Invest. Ophthalmol. Vis. Sci.,28, p. 224Rutzen, A. R., Roberts, C. W., Driller, J., Gomez, D., Lucas, B. C., Lizzi, F. L., andColeman, D. J. (1990): ‘Production of corneal lesions using high-intensity focused ultrasound’,Cornea,9, pp. 324–330Schwan, H. P., andFoster, K. R. (1980): ‘RF-fields interactions with biological systems: electrical properties and biophysical mechanism’,Proc. IEEE,68, pp. 104–113Seiler, T., Matallana, M., andBende, T. (1990): ‘Laser thermokeratoplasty by means of a pulsed Holmium:YAG Laser for the hyperopic correction’,Refrac. Corneal Surg.,6, pp. 335–339Silvestrini, T. A. (1998): ‘Electrosurgical procedure for the treatment of the cornea’. US Patent 5,766,171Simmons, W. N., Mackey, S., He, D. S. andMarcus, F. L. (1996): ‘Comparison of gold versus platinum electrodes on myocardial lesion size using radiofrequency energy’,PACE,19, pp. 398–402Stringer, H., andParr, J. (1964): ‘Shrinkage temperature of eye collagen’,Nature,204, p. 1307Trembly, B. S., andKeates, R. H. (1991): ‘Combined microwave heating and surface cooling of the cornea’,IEEE Trans. Biomed. Eng.,38, pp. 85–91Trembly, B. S., Hashizume, N., Moodie, K. L., Cohen, K. L., Tripoli, N. K., andHoopes, P. J. (2001): ‘Microwave thermal keratoplasty for myopia: keratoscopic evaluation in porcine eyes’,J. Refract. Surg.,17, pp. 682–688Tungjitkusolmun, S., Woo, E. J., Cao, H., Tsai, J. Z., Vorperian, V. R., andWebster, J. G. (2000): ‘Thermal-electrical finite element modelling for radio frequency cardiac ablation: effects of changes in myocardial properties’,Med. Biol. Eng. Comput.,38, pp. 562–568Wiley, J. D., andWebster, J. G. (1982): ‘Analysis and control of the current distribution under circular dispersive electrodes’,IEEE Trans. Biomed. Eng,29, pp. 381–38

Nanoelectropulse-driven membrane perturbation and small molecule permeabilization

BACKGROUND: Nanosecond, megavolt-per-meter pulsed electric fields scramble membrane phospholipids, release intracellular calcium, and induce apoptosis. Flow cytometric and fluorescence microscopy evidence has associated phospholipid rearrangement directly with nanoelectropulse exposure and supports the hypothesis that the potential that develops across the lipid bilayer during an electric pulse drives phosphatidylserine (PS) externalization. RESULTS: In this work we extend observations of cells exposed to electric pulses with 30 ns and 7 ns durations to still narrower pulse widths, and we find that even 3 ns pulses are sufficient to produce responses similar to those reported previously. We show here that in contrast to unipolar pulses, which perturb membrane phospholipid order, tracked with FM1-43 fluorescence, only at the anode side of the cell, bipolar pulses redistribute phospholipids at both the anode and cathode poles, consistent with migration of the anionic PS head group in the transmembrane field. In addition, we demonstrate that, as predicted by the membrane charging hypothesis, a train of shorter pulses requires higher fields to produce phospholipid scrambling comparable to that produced by a time-equivalent train of longer pulses (for a given applied field, 30, 4 ns pulses produce a weaker response than 4, 30 ns pulses). Finally, we show that influx of YO-PRO-1, a fluorescent dye used to detect early apoptosis and activation of the purinergic P2X(7 )receptor channels, is observed after exposure of Jurkat T lymphoblasts to sufficiently large numbers of pulses, suggesting that membrane poration occurs even with nanosecond pulses when the electric field is high enough. Propidium iodide entry, a traditional indicator of electroporation, occurs with even higher pulse counts. CONCLUSION: Megavolt-per-meter electric pulses as short as 3 ns alter the structure of the plasma membrane and permeabilize the cell to small molecules. The dose responses of cells to unipolar and bipolar pulses ranging from 3 ns to 30 ns duration support the hypothesis that a field-driven charging of the membrane dielectric causes the formation of pores on a nanosecond time scale, and that the anionic phospholipid PS migrates electrophoretically along the wall of these pores to the external face of the membrane

Mathematical Modeling and Simulation of Ventricular Activation Sequences: Implications for Cardiac Resynchronization Therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy

The Role of the Frank–Starling Law in the Transduction of Cellular Work to Whole Organ Pump Function: A Computational Modeling Analysis

We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca2+ sensitivity of tension (Ca50), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca2+ to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca50 and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca50 was caused by an inversion in the regional distribution of strain