Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations

In this paper we present a macroscopic model of the excitation process in the myocardium. The composite and anisotropic structure of the cardiac tissue is represented by a bidomain, i.e. a set of two coupled anisotropic media. The model is characterized by a non linear system of two partial differential equations of parabolic and elliptic type. A singular perturbation analysis is carried out to investigate the cardiac potential field and the structure of the moving excitation wavefront. As a consequence the cardiac current sources are approximated by an oblique dipole layer structure and the motion of the wavefront is described by eikonal equations. Finally numerical simulations are carried out in order to analyze some complex phenomena related to the spreading of the wavefront, like the front-front or front-wall collision. The results yielded by the excitation model and the eikonal equations are compared.     

Oblique double layer potentials for the direct and inverse problems of electrocardiology

A mathematical analysis of a model of the cardiac bioelectric sources generating the potential field in a bounded conducting volume is carried out. A boundary integral representation of the potential is given, which shows that, if the anisotropy of the cardiac muscle is taken into account, the bioelectric sources are characterized by an “oblique” double layer on the excitation wavefront. Boundedness conditions for the potential and jump relationships across the front are investigated. Uniqueness results for the inverse problem (i.e. the determination of the wavefront surface, given the potential on the volume boundary) are established.     

Dipole characterization of single neurons from their extracellular action potentials

The spatial variation of the extracellular action potentials (EAP) of a single neuron contains information about the size and location of the dominant current source of its action potential generator, which is typically in the vicinity of the soma. Using this dependence in reverse in a three-component realistic probe + brain + source model, we solved the inverse problem of characterizing the equivalent current source of an isolated neuron from the EAP data sampled by an extracellular probe at multiple independent recording locations. We used a dipole for the model source because there is extensive evidence it accurately captures the spatial roll-off of the EAP amplitude, and because, as we show, dipole localization, beyond a minimum cell-probe distance, is a more accurate alternative to approaches based on monopole source models. Dipole characterization is separable into a linear dipole moment optimization where the dipole location is fixed, and a second, nonlinear, global optimization of the source location. We solved the linear optimization on a discrete grid via the lead fields of the probe, which can be calculated for any realistic probe + brain model by the finite element method. The global source location was optimized by means of Tikhonov regularization that jointly minimizes model error and dipole size. The particular strategy chosen reflects the fact that the dipole model is used in the near field, in contrast to the typical prior applications of dipole models to EKG and EEG source analysis. We applied dipole localization to data collected with stepped tetrodes whose detailed geometry was measured via scanning electron microscopy. The optimal dipole could account for 96% of the power in the spatial variation of the EAP amplitude. Among various model error contributions to the residual, we address especially the error in probe geometry, and the extent to which it biases estimates of dipole parameters. This dipole characterization method can be applied to any recording technique that has the capabilities of taking multiple independent measurements of the same single units.     

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.     

Noninvasive assessment of local myocardium repolarization changes using high resolution surface ECG mapping

A method using body surface potential maps for assessment of myocardium lesions with changed repolarization is presented and suitable mapping system is introduced. Differences between normal and altered QRST integral maps together with torso volume conductor model were used to determine the equivalent dipole representing the lesion. Performance of the method was studied on simulated data. Changed repolarization was modeled by shortening of myocyte action potentials in regions typical for stenosis of the main coronary arteries. The equivalent dipole estimated the positions of small lesions with a mean error of 9+/-4 mm (17+/-14 mm for larger transmural lesions). The subepicardial or subendocardial character of the lesions was reflected in the dipole orientation. Tests of the method on patients after myocardial infarction that underwent coronary intervention on a single coronary vessel showed that in 7 of 8 successfully treated patients the dipole position matched well with the treated vessel. A small dipole moment in another patient indicated unsuccessful treatment. The method was implemented in a new 128-channel mapping system. Its active electrodes, battery powered measuring unit and optical computer interface help to minimize noise in ECG and guarantee patient's safety. The results suggest that the method and mapping system offer useful tools for noninvasive identification of local repolarization changes in the myocardium.     

Material properties and residual stress in the stage 12 chick heart during cardiac looping

During the morphogenetic process of cardiac looping, the initially straight cardiac tube bends and twists into a curved tube. The biophysical mechanisms that drive looping remain unknown, but the process clearly involves mechanical forces. Hence, it is important to determine mechanical properties of the early heart, which is a muscle-wrapped tube consisting primarily of a thin outer layer of myocardium surrounding a thick extracellular matrix compartment known as cardiac jelly. In this work, we used microindentation experiments and finite element modeling, combined with an inverse computational method, to determine constitutive relations for the myocardium and cardiac jelly at the outer curvature of stage 12 chick hearts. Material coefficients for exponential strain-energy density functions were found by fitting force-displacement and surface displacement data near the indenter Residual stress in the myocardium also was estimated. These results should be useful for computational models of the looping heart.     

Optically pumped magnetometers disclose magnetic field components of the muscular action potential

AimAiming at analysing the signal conduction in muscular fibres, the spatio-temporal dynamics of the magnetic field generated by the propagating muscle action potential (MAP) is studied.MethodIn this prospective, proof of principle study, the magnetic activity of the intrinsic foot muscle after electric stimulation of the tibial nerve was measured using optically pumped magnetometers (OPMs). A classical biophysical electric dipole model of the propagating MAP was implemented to model the source of the data. In order to account for radial currents of the muscular tubules system, a magnetic dipole oriented along the direction of the muscle was added.ResultsThe signal profile generated by the activity of the intrinsic foot muscles was measured by four OPM devices. Three OPM sensors captured the spatio-temporal magnetic field pattern of the longitudinal intrinsic foot muscles. Changes of the activation pattern reflected the propagating muscular action potential along the muscle. A combined electric and magnetic dipole model could explain the recorded magnetic activity.InterpretationOPM devices allow for a new, non-invasive way to study MAP patterns. Since magnetic fields are less altered by the tissue surrounding the dipole source compared to electric activity, a precise analysis of the spatial characteristics and temporal dynamics of the MAP is possible. The classic electric dipole model explains major but not all aspects of the magnetic field. The field has longitudinal components generated by intrinsic structures of the muscle fibre. By understanding these magnetic components, new methods could be developed to analyse the muscular signal transduction pathway in greater detail. The approach has the potential to become a promising diagnostic tool in peripheral neurological motor impairments.     

Biophysical models of the heart electrical activity

Based on the fundamental knowledge of the space-temporal organization of extracellular electrical fields of the myocardium, a system for 3-D computer modeling of the cardiac electrical activity at different structural levels of the object is being developed at the Institute of Theoretical and Experimental Biophysics. The system is based on the earlier proposed and modified biophysical model of the electrocardiosignal genesis represented by a double electrical layer along the surface of the electrically active myocardium. The system combines the model for activation and repolarization of the heart ventricles; the advanced model for the evaluation of parameters of the cardiac electric field, which makes it possible to derive model electrocardiosignals both in the direct regime of calculation of the potentials and in the regime of calculation of electrocardiosignals from preliminarily determined components of the multipole equivalent electrical heart generator; a database for the model parameters and their combinations in the form of cards of simulated "patients", and a database of modeled electrocardiosignals. In the present paper (first from three within the framework of the problem), simulation methods in electrocardiology are briefly described and a biophysical model of the heart electrical activity is presented, which has made up the basis of the system for computer modeling of forward and inverse problems of the cardiac electric field. The parameters of the model are electrophysiological, anatomical, and biophysical characteristics of the heart.     

Predicting the external formation of callus tissues in oblique bone fractures: idealised and clinical case studies

It is proposed that the external asymmetric formation of callus tissues that forms naturally about an oblique bone fracture can be predicted computationally. We present an analysis of callus formation for two cases of bone fracture healing: idealised and subject-specific oblique bone fractures. Plane strain finite element (FE) models of the oblique fractures were generated to calculate the compressive strain field experienced by the immature callus tissues due to interfragmentary motion. The external formations of the calluses were phenomenologically simulated using an optimisation style algorithm that iteratively removes tissue that experiences low strains from a large domain. The resultant simulated spatial formation of the healing tissues for the two bone fracture cases showed that the calluses tended to form at an angle equivalent to the angle of the oblique fracture line. The computational results qualitatively correlated with the callus formations found in vivo. Consequently, the proposed methods show potential as a means of predicting callus formation in pre-clinical testing.     

Electric dipole theory and thermodynamics of actomyosin molecular motor in muscle contraction

Movements in muscles are generated by the myosins which interact with the actin filaments. In this paper we present an electric theory to describe how the chemical energy is first stored in electrostatic form in the myosin system and how it is then released and transformed into work. Due to the longitudinal polarized molecular structure with the negative phosphate group tail, the ATP molecule possesses a large electric dipole moment (p(0)), which makes it an ideal energy source for the electric dipole motor of the actomyosin system. The myosin head contains a large number of strongly restrained water molecules, which makes the ATP-driven electric dipole motor possible. The strongly restrained water molecules can store the chemical energy released by ATP binding and hydrolysis processes in the electric form due to their myosin structure fixed electric dipole moments (p(i)). The decrease in the electric energy is transformed into mechanical work by the rotational movement of the myosin head, which follows from the interaction of the dipoles p(i) with the potential field V(0) of ATP and with the potential field Psi of the actin. The electrical meaning of the hydrolysis reaction is to reduce the dipole moment p(0)-the remaining dipole moment of the adenosine diphosphate (ADP) is appropriately smaller to return the low negative value of the electric energy nearly back to its initial value, enabling the removal of ADP from the myosin head so that the cycling process can be repeated. We derive for the electric energy of the myosin system a general equation, which contains the potential field V(0) with the dipole moment p(0), the dipole moments p(i) and the potential field psi. Using the previously published experimental data for the electric dipole of ATP (p(0) congruent with 230 debye) and for the amount of strongly restrained water molecules (N congruent with 720) in the myosin subfragment (S1), we show that the Gibbs free energy changes of the ATP binding and hydrolysis reaction steps can be converted into the form of electric energy. The mechanical action between myosin and actin is investigated by the principle of virtual work. An electric torque always appears, i.e. a moment of electric forces between dipoles p(0) and p(i)(/M/ > or = 16 pN nm) that causes the myosin head to function like a scissors-shaped electric dipole motor. The theory as a whole is illustrated by several numerical examples and the results are compared with experimental results.     

Contactless magnetocardiographic mapping in anesthetized Wistar rats: evidence of age-related changes of cardiac electrical activity

Magnetocardiography (MCG) is the recording of the magnetic field (MF) generated by cardiac electrophysiological activity. Because it is a contactless method, MCG is ideal for noninvasive cardiac mapping of small experimental animals. The aim of this study was to assess age-related changes of cardiac intervals and ventricular repolarization (VR) maps in intact rats by means of MCG mapping. Twenty-four adult Wistar rats (12 male and 12 female) were studied, under anesthesia, with the same unshielded 36-channel MCG instrumentation used for clinical recordings. Two sets of measurements were obtained from each animal: 1) at 5 mo of age (297.5 +/- 21 g body wt) and 2) at 14 mo of age (516.8 +/- 180 g body wt). RR and PR intervals, QRS segment, and QTpeak, QTend, JTpeak, JTend, and Tpeak-end were measured from MCG waveforms. MCG imaging was automatically obtained as MF maps and as inverse localization of cardiac sources with equivalent current dipole and effective magnetic dipole models. After 300 s of continuous recording were averaged, the signal-to-noise ratio was adequate for study of atrial and ventricular MF maps and for three-dimensional localization of the underlying cardiac sources. Clear-cut age-related differences in VR duration were demonstrated by significantly longer QTend, JTend, and Tpeak-end in older Wistar rats. Reproducible multisite noninvasive cardiac mapping of anesthetized rats is simpler with MCG methodology than with ECG recording. In addition, MCG mapping provides new information based on quantitative analysis of MF and equivalent sources. In this study, statistically significant age-dependent variations in VR intervals were found.     

Internal electrostatic potentials in bilayers: measuring and controlling dipole potentials in lipid vesicles.

The binding and translocation rates of hydrophobic cation and anion spin labels were measured in unilamellar vesicle systems formed from phosphatidylcholine. As a result of the membrane dipole potential, the binding and translocation rates for oppositely charged hydrophobic ions are dramatically different. These differences were analyzed using a simple electrostatic model and are consistent with the presence of a dipole potential of approximately 280 mV in phosphatidylcholine. Phloretin, a molecule that reduces the magnitude of the dipole potential, increases the translocation rate of hydrophobic cations, while decreasing the rate for anions. In addition, phloretin decreases the free energy of binding of the cation, while increasing the free energy of binding for the anion. The incorporation of 6-ketocholestanol also produces differential changes in the binding and translocation rates of hydrophobic ions, but in an opposite direction to those produced by phloretin. This is consistent with the view that 6-ketocholestanol increases the magnitude of the membrane dipole potential. A quantitative analysis of the binding and translocation rate changes produced by ketocholestanol and phloretin is well accounted for by a point dipole model that includes a dipole layer due to phloretin or 6-ketocholestanol in the membrane-solution interface. This approach allows dipole potentials to be estimated in membrane vesicle systems and permits predictable, quantitative changes in the magnitude of the internal electrostatic field in membranes. Using phloretin and 6-ketocholestanol, the dipole potential can be altered by over 200 mV in phosphatidylcholine vesicles.     

Human iPSC-derived cardiomyocytes and tissue engineering strategies for disease modeling and drug screening

Improved methodologies for modeling cardiac disease phenotypes and accurately screening the efficacy and toxicity of potential therapeutic compounds are actively being sought to advance drug development and improve disease modeling capabilities. To that end, much recent effort has been devoted to the development of novel engineered biomimetic cardiac tissue platforms that accurately recapitulate the structure and function of the human myocardium. Within the field of cardiac engineering, induced pluripotent stem cells (iPSCs) are an exciting tool that offer the potential to advance the current state of the art, as they are derived from somatic cells, enabling the development of personalized medical strategies and patient specific disease models. Here we review different aspects of iPSC-based cardiac engineering technologies. We highlight methods for producing iPSC-derived cardiomyocytes (iPSC-CMs) and discuss their application to compound efficacy/toxicity screening and in vitro modeling of prevalent cardiac diseases. Special attention is paid to the application of micro- and nano-engineering techniques for the development of novel iPSC-CM based platforms and their potential to advance current preclinical screening modalities.     

Noninvasive measurements of transmural myocardial metabolites using 3-D (31)P NMR spectroscopy

A completely noninvasive three-dimensional (3-D) static magnetic field magnitude spatially localized (31)P spectroscopy technique has been developed and applied to study the in vivo canine myocardium at 9.4 T. The technique incorporates both Fourier series windows and selective Fourier transform methods utilizing all three orthogonal gradients for 3-D phase encoding. The number of data acquisitions for each phase-encoding step was weighted according to the Fourier coefficients to define cylindrical voxels. Spatially localized (31)P spectra can be generated for voxels of desired location within the field of view as a postprocessing step. The quality of localization was first demonstrated by using a three-compartment phantom. The technique was then applied to in vivo canine models and yielded (31)P cardiac spectra with an excellent signal-to-noise ratio. The in vivo validation experiments, using an implanted 2-phosphoenolpyruvate-containing marker, demonstrated that the technique is capable of measuring at least two transmural layers of left ventricular myocardium representing the subepicardium and subendocardium.     

The effect of hydrogel injection on cardiac function and myocardial mechanics in a computational post-infarction model

An emerging therapy to limit adverse heart remodelling following myocardial infarction (MI) is the injection of polymers into the infarcted left ventricle (LV). In the few numerical studies carried out in this field, the definition and distribution of the hydrogel in the infarcted myocardium were simplified. In this computational study, a more realistic biomaterial distribution was simulated after which the effect on cardiac function and mechanics was studied. A validated finite element heart model was used in which an antero-apical infarct was defined. Four infarct models were created representing different temporal phases in the progression of a MI. Hydrogel layers were simulated in the infarcted myocardium in each model. Biomechanical and functional improvement of the LV was found after hydrogel inclusion in the ischaemic models representing the early phases of MI. In contrast, only functional but no mechanical restitution was shown in the scar model due to hydrogel presence.     

Monte-Carlo Simulation of Molten CsCl Using a ‘Deformation Dipole’ Polarisable Ion Potential

Abstract

We have simulated the structure of molten CsCl at 943 K using a form of interionic potential, based on the deformation dipole model of Hardy and Karo, where ions have both point charges and dipoles. The magnitude of the dipole on an ion is determined by two factors, one being the local electric field and the other the repulsive potential due to overlap with neighbouring ions. Parameters are determined directly from the crystal lattice constant, compressibility and dielectric constants. Good agreement with experimental results is obtained. The potential is compared to the shell model of ionic polarisability which does not produce good agreement with experiment.     

Functional and morphological cardiac magnetic resonance imaging of mice using a cryogenic quadrature radiofrequency coil

Cardiac morphology and function assessment by magnetic resonance imaging is of increasing interest for a variety of mouse models in pre-clinical cardiac research, such as myocardial infarction models or myocardial injury/remodeling in genetically or pharmacologically induced hypertension. Signal-to-noise ratio (SNR) constraints, however, limit image quality and blood myocardium delineation, which crucially depend on high spatial resolution. Significant gains in SNR with a cryogenically cooled RF probe have been shown for mouse brain MRI, yet the potential of applying cryogenic RF coils for cardiac MR (CMR) in mice is, as of yet, untapped. This study examines the feasibility and potential benefits of CMR in mice employing a 400 MHz cryogenic RF surface coil, compared with a conventional mouse heart coil array operating at room temperature. The cryogenic RF coil affords SNR gains of 3.0 to 5.0 versus the conventional approach and hence enables an enhanced spatial resolution. This markedly improved image quality - by better deliniation of myocardial borders and enhanced depiction of papillary muscles and trabeculae - and facilitated a more accurate cardiac chamber quantification, due to reduced intraobserver variability. In summary the use of a cryogenically cooled RF probe represents a valuable means of enhancing the capabilities of CMR of mice.     

Meet me on the other side: trans-bilayer modulation of a model voltage-gated ion channel activity by membrane electrostatics asymmetry

While it is accepted that biomembrane asymmetry is generated by proteins and phospholipids distribution, little is known about how electric changes manifested in a monolayer influence functional properties of proteins localized on the opposite leaflet. Herein we used single-molecule electrophysiology and investigated how asymmetric changes in the electrostatics of an artificial lipid membrane monolayer, generated oppositely from where alamethicin--a model voltage-gated ion channel--was added, altered peptide activity. We found that phlorizin, a membrane dipole potential lowering amphiphile, augmented alamethicin activity and transport features, whereas the opposite occurred with RH-421, which enhances the monolayer dipole potential. Further, the monolayer surface potential was decreased via adsorption of sodium dodecyl sulfate, and demonstrated that vectorial modification of it also affected the alamethicin activity in a predictive manner. A new paradigm is suggested according to which asymmetric changes in the monolayer dipole and surface potential extend their effects spatially by altering the intramembrane potential, whose gradient is sensed by distantly located peptides.     

Integral characteristics of the cardiac electrical excitation wave]

A set of characterisitics of the cardiac electrical generator is described which expresses in an integral form some important properties of the electrical excitation wave, in particular its summary intensity, average spatial localization and distinction from a uniform double layer with planar rim. Relation of the proposed model to the multipole equivalent generator is discussed, and procedures for computing its characteristics are given. Calculation results for these characteristics on the basis of experimentally measured electrical field potentials of isolated dog hearts are presented.     

Pitx2 regulates cardiac left-right asymmetry by patterning second cardiac lineage-derived myocardium

Current models of left-right asymmetry hold that an early asymmetric signal is generated at the node and transduced to lateral plate mesoderm in a linear signal transduction cascade through the function of the Nodal signaling molecule. The Pitx2 homeobox gene functions at the final stages of this cascade to direct asymmetric morphogenesis of selected organs including the heart. We previously showed that Pitx2 regulated an asymmetric pathway that was independent of cardiac looping suggesting a second asymmetric cardiac pathway. It has been proposed that in the cardiac outflow tract Pitx2 functions in both cardiac neural crest, as a target of canonical Wnt-signaling, and in the mesoderm-derived cardiac second lineage. We used fate mapping, conditional loss of function, and chimera analysis in mice to investigate the role of Pitx2 in outflow tract morphogenesis. Our findings reveal that Pitx2 is dispensable in the cardiac neural crest but functions in second lineage myocardium revealing that this cardiac progenitor field is patterned asymmetrically.