Rhythm Analysis Using Vectorcardiograms

Fourier shape descriptors of vectorcardiograms have been proposed for cardiac rhythm analysis. The technique characterizes the differences in shape and size of the normal and abnormal vectorcardiograms. The specific abnormalities considered are premature ventricular contractions (PVC's) and supraventricular premature contractions (SVPC's).

New Concepts for PVC Detection

A new scheme is proposed for the detection of premature ventricular beats, which is a vital function in rhythm monitoring of cardiac patients. A transformation based on the first difference of the digitized electrocardiogram (ECG) signal is developed for the detection and delineation of QRS complexes. The method for classifying the abnormal complexes from the normal ones is based on the concepts of minimum phase and signal length. The parameters of a linear discriminant function obtained from a training feature vector set are used to classify the complexes. Results of application of the scheme to ECG of two arrhythmia patients are presented.

A Computational Study of the Factors Influencing the PVC-Triggering Ability of a Cluster of Early Afterdepolarization-Capable Myocytes

Premature ventricular complexes (PVCs), which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control chemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

MNDO study of coupled strained hydrocarbons: Additivity of exocyclic C---C bond contraction induced by different ring systems

MNDO geometry optimizations were carried out on a series of symmetrically and unsymmetrically coupled strained ring hydrocarbons, R1-R1 and R1–R2 (R1=methyl, cyclopropyl, 1-bicyclo[1.1.0]butyl, 1-bicyclo[1.1.1]pentyl, prismyl, cubyl, 6-tricyclo [3.1.1.03,6]heptyl, and tetrahedryl groups; R2=methyl and cyclopropyl). The remarkable contraction of the C---C bond connecting the strained rings found experimentally in a few cases was reproduced correctly by the calculations. A linear correlation was found between the bond length shortening and the bond angle widening at the corresponding carbon atoms for all the structures considered. The reduction in C---C bond lengths due to various ring systems is additive. The additivity indicates that inter-ring interactions which effect the central bond length are absent and confirms the common electronic origin of bond contraction in these systems, viz. enhanced s-character in the exocyclic bonds of strained rings.

The reaction of lambda 3-cyclotriphosphazanes with tetrachloro-ortho-benzoquinone: An unusual ring contraction-rearrangement

Oxidative addition of tetrachloro-ortho-benzoquinone to lambda(3)-cyclotriphosphazanes, [EtNP(OR)](3) results in an unprecedented ring contraction-rearrangement to give diazadiphosphetidines (EtN)(2)[P(OR)(O2C6Cl4)] [P(O2C6Cl4)-[N(Et)P(OR)(2)}] (R = C6H4Br-4 or C(6)H(3)Me(2)-2,6), a process indicated to be thermodynamically favourable on the basis of PM3 calculations.

Oxidative addition of tetrachloro-1,2-benzoquinone to lambda(3)-cyclotriphosphazanes. An unusual ring contraction-rearrangement

The lambda(3)-cyclotriphosphazanes, [EtNP(OR)](3) [R = 2,6-Me2C6H3 (1), 4-BrC6H4 (2), or CH2CF3(3)], on treatment with tetrachloro-1,2-benzoquinone (TCB) give the lambda(5)-cyclodiphosphazanes, [EtNP(O2C6Cl4)(OR)][EtNP(O2C6Cl4){N(Et)P(OR)(2)}] (5-7) by an unusual ring contraction-rearrangement. The reaction of the mixed substituent lambda(3)-cyclotriphosphazane, [(EtN)(3)P-3(OR)(2)(OR')] [R = 2,6-Me2C6H3, R' = 4-BrC6H4] (4), with TCB gives the lambda(5)-cyclodiphosphazane, [EtNP(O2C6Cl4)(OR')][EtNP(O2C6Cl4){N(Et)P(OR)(2)}] (8), in which 4-bromophenoxide resides on one of the ring phosphorus atoms. The lambda(3)-bicyclic tetraphosphapentazane, (EtN)(5)P-4(OPh)(2), on treatment with TCB undergoes a double ring contraction-rearrangement to give the lambda(5)-cyclodiphosphazane, (EtN)[(EtN)(2)P-2(O2C6Cl4)(2)(OPh)](2) (9). Variable-temperature and high-field P-31 NMR studies indicate the presence of more than one isomer in solution for the rearranged products 5-9. The solid state structure of 8 reveals a trans arrangement of the substituents with respect to the P2N2 ring in contrast to the gauche arrangement observed for 5.

Diperoxovanadate can substitute for H(2)O(2) at much lower concentration in inducing features of premature cellular senescence in mouse fibroblasts (NIH3T3)

Stress induced premature senescence (SIPS) in mammalian cells is an accelerated ageing response and experimentally obtained on treatment of cells with high concentrations of H(2)O(2), albeit at sub-lethal doses, because H(2)O(2) gets depleted by abundant cellular catalase. In the present study diperoxovanadate (DPV) was used as it is known to be stable at physiological pH, to be catalase-resistant and to substitute for H(2)O(2) in its activities at concentrations order of magnitudes lower. On treating NIH3T3 cells with DPV, SIPS-like morphology was observed along with an immediate response of rounding of the cells by disruption of actin cytoskeleton and transient G2/M arrest. DPV could bring about growth arrest and senescence associated features at 25 mu M dose, which were not seen with similar doses of either H(2)O(2) or vanadate. A minimal dose of 150 mu M of H(2)O(2) was required to induce similar affects as 25 mu M DPV. Increase in senescent associated markers such as p21, HMGA2 and PAI-1 was more prominent in DPV treated cells compared to similar dose of H(2)O(2). DPV-treated cells showed marked relocalization of Cyclin D1 from nucleus to cytoplasm. These results indicate that DPV, stable inorganic peroxide, is more efficient in inducing SIPS at lower concentrations compared to H(2)O(2). (C) 2011 Elsevier Ireland Ltd. All rights reserved.

The Mathematical modeling of inhomogeneites in ventricular tissue

Cardiac arrhythmias such as ventricular tachycardia (VT) or ventricular fibrillation (VF) are the leading cause of death in the industrialised world. There is a growing consensus that these arrhythmias arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have been carried out to determine the effects of inhomogeneities in cardiac tissue on such arrhythmias. We give a brief overview of such experiments, and then an introduction to partial-differential-equation models for ventricular tissue. We show how different types of inhomogeneities can be included in such models, and then discuss various numerical studies, including our own, of the effects of these inhomogeneities on spiral-wave dynamics. The most remarkable qualitative conclusion of our studies is that the spiral-wave dynamics in such systems depends very sensitively on the positions of these inhomogeneities.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

In praise of H2O2, the versatile ROS, and its vanadium complexes

Hydrogenperoxide (H2O2) is generated in mitochondria in aerobic cells as a minor product of electron transport, is inhibited selectively by phenolic acids (in animals) or salicylhydroxamate (in plants) and is regulated by hormones and environmental conditions. Failure to detect this activity is due to presence of H2O2-consuming reactions or inhibitors present in the reaction mixture. H2O2 has a role in metabolic regulation and signal transduction reactions. A number of enzymes and cellular activities are modified, mostly by oxidizing the protein-thiol groups, on adding H2O2 in mM concentrations. On complexing with vanadate, also occurring in traces, H2O2 forms diperoxovanadate (DPV), stable at physiological pH and resistant to degradation by catalase. DPV was found to substitute for H2O2 at concentrations orders of magnitude lower, and in presence of catalase, as a substrate for user reaction, horseradish peroxidase (HRP), and in inactivating glyceraldehyde-3-phosphate dehydrogenase. superoxide dismutase (SOD)-sensitive oxidation of NADH was found to operate as peroxovanadate cycle using traces of DPV and decameric vanadate (V-10) and reduces O-2 to peroxide (DPV in presence of free vanadate). This offers a model for respiratory burst. Diperoxovanadate reproduces several actions of H2O2 at low concentrations: enhances protein tyrosine phosphorylation, activates phospholipase D, produces smooth muscle contraction, and accelerates stress induced premature senescence (SIPS) and rounding in fibroblasts. Peroxovanadates can be useful tools in the studies on H2O2 in cellular activities and regulation.

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as E-f, the fibroblast resting-membrane potential, the fibroblast conductance G(f), and the MF gap-junctional coupling G(gap). Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as G(gap), G(f), and E-f, and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of G(gap), for zero-sided and one-sided couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of G(gap), and, eventually, we observe that conduction failure occurs for low values of G(gap). In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling G(gap) or E-f. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.