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.

Conceptual design of three-dimensional scaffolds of powder-based materials for bone tissue engineering applications

Purpose - The purpose of this paper is to investigate the possibility to construct tissue-engineered bone repair scaffolds with pore size distributions using rapid prototyping techniques. Design/methodology/approach - The fabrication of porous scaffolds with complex porous architectures represents a major challenge in tissue engineering and the design aspects to mimic complex pore shape as well as spatial distribution of pore sizes of natural hard tissue remain unexplored. In this context, this work aims to evaluate the three-dimensional printing process to study its potential for scaffold fabrication as well as some innovative design of homogeneously porous or gradient porous scaffolds is described and such design has wider implication in the field of bone tissue engineering. Findings - The present work discusses biomedically relevant various design strategies with spatial/radial gradient in pore sizes as well as with different pore sizes and with different pore geometries. Originality/value - One of the important implications of the proposed novel design scheme would be the development of porous bioactive/biodegradable composites with gradient pore size, porosity, composition and with spatially distributed biochemical stimuli so that stem cells loaded into scaffolds would develop into complex tissues such as those at the bone-cartilage interface.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Tissue culture of forest trees: Clonal multiplication of Eucalyptus grandis L

Axillary shoot proliferation was obtained using explants of Eucalyptus grandis L. juvenile and mature stages on a defined medium. Murashige and Skoog medium (MS) supplemented with benzyladenine (BA), naphthalene acetic acid (NAA) and additional thiamine. Excised shoots were induced to root on a sequence of three media: (1) White's medium containing indoleacetic acid (IAA), NAA and indole butyric acid; (IBA), (2) half-strength MS medium with charcoal and (3) half-strength MS liquid medium. The two types of explants differed in rooting response, with juvenile-derived shoots giving 60% rooting and adult-derived ones only 35%. Thus, the factors limiting cloning of selected trees in vitro are determined to be those controlling rooting of shoots in E. grandis.

In vitro propagation of Eucalyptus grandis L. by tissue culture

Multiple shoots were induced from nodal segments of five year old trees of Eucalyptus grandis L. on solid medium containing Murashige and Skoog's (MS) Basal medium supplemented with additional thiamine, BAP and NAA. Rooting could be achieved from shoot culture on half strength MS salts or white's medium supplemented with low auxins like IAA, IBA and NAA.

Study of turbid media with light: Recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light

We discuss the inverse problem associated with the propagation of the field autocorrelation of light through a highly scattering object like tissue. In the first part of the work, we reconstructed the optical absorption coefficient mu(u) and particle diffusion coefficient D-B from simulated measurements which are integrals of a quantity computed from the measured intensity and intensity autocorrelation g(2)(tau) at the boundary. In the second part we recover the mean square displacement (MSD) distribution of particles in an inhomogeneous object from the sampled g(2)(tau) measure on the boundary. From the MSD, we compute the storage and loss moduli distributions in the object. We have devised computationally easy methods to construct the sensitivity matrices which are used in the iterative reconstruction algorithms for recovering these parameters from the measurements. The results of the reconstruction of mu(a), D-B, MSD and the viscoelastic parameters, which are presented, show reasonable good position and quantitative accuracy.

Lipids of nervous tissue: composition and metabolism

As indicated in the Introduction, the many significant developments in the recent past in our knowledge of the lipids of the nervous system have been collated in this article. That there is a sustained interest in this field is evident from the rather long bibliography which is itself selective. Obviously, it is not possible to summarize a review in which the chemistry, distribution and metabolism of a great variety of lipids have been discussed. However, from the progress of research, some general conclusions may be drawn. The period of discovery of new lipids in the nervous system appears to be over. All the major lipid components have been discovered and a great deal is now known about their structure and metabolism. Analytical data on the lipid composition of the CNS are available for a number of species and such data on the major areas of the brain are also at hand but information on the various subregions is meagre. Such investigations may yet provide clues to the role of lipids in brain function. Compared to CNS, information on PNS is less adequate. Further research on PNS would be worthwhile as it is amenable for experimental manipulation and complex mechanisms such as myelination can be investigated in this tissue. There are reports correlating lipid constituents with the increased complexity in the organization of the nervous system during evolution. This line of investigation may prove useful. The basic aim of research on the lipids of the nervous tissue is to unravel their functional significance.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Interactions between Mast Cells, Fibroblasts and Connective Tissue Components

It has long been recognized that mast cells occur throughout connective tissues. Histologic studies have revealed that such cells release their granules into the surrounding environment upon exposure to both immunologic and nonimmunologic stimuli. By microscopy these extracellular granules appeared to be phagocytosed by fibroblasts and by blood-borne phagocytic cells as they entered the site of mast cell degranulation. Such in vivo observations led to the suggestion that mast cells both altered connective tissue components and influenced fibroblast function through these discharged granules. Recent in vitro studies using cultured fibroblasts and isolated mast cells and mast cell granules have confirmed both these hypotheses. In addition, such studies have also documented that fibroblasts degrade ingested mast cell granules. Such studies document that a number of critical interactions may occur between mast cells and connective tissue components.

Mode of action of antitumour antibiotics: Spectrophotometric studies on the interaction of chromomycin A3 with DNA and chromatin of normal and neoplastic tissue

The binding of chromomycin A3, an antitumour antibiotic, to various DNA and chromatin isolated from mouse and rat liver, mouse fibrosarcoma and Yoshida ascites sarcoma cells was studied spectrophotometrically at 29°C in 10−2 M Tris-HCl buffer, pH 8.0, containing small amounts of MgCl2 (4.5 · 10−5−25 · 10−5 M). An isobestic point at 415 nm was observed when chromomycin A3 was gradually titrated with Image and its spectrum shifted towards higher wavelength. The rates and extent of these spectral changes were found to be dependent on the concentration of Mg2+. The change in absorbance at 440 nm was used to calculate apparent binding constant (Ka p M−1) and sites per nucleotide (n) from Scatchard plots for various DNA and chromatins. As expected, values of n for chromatin (0.06–0.10) were found to be lower than that found for corresponding DNA (0.10–0.15). Apparently no such correlation exists between binding constants (Ka p M−1 · 10−4) of DNA (6.4–11.2) and of chromatin (3.1–8.3), but Ka p M−1 of chromatin isolated from mouse fibrosarcoma and Yoshida ascites sarcoma are 1.5–3 times higher than that found for mouse and rat liver chromatin. These differences may be taken to indicate structural difference in nucleoprotein complexes caused by neoplasia. The relevance of this finding to tumour suppressive action of chromomycin A3 is discussed.

Electron energy distributions and transport coefficients in N2 in E times B fields

Using the concept of energy-dependent effective field intensity, electron transport coefficients in nitrogen have been determined in E times B fields (E = electric field intensity, B = magnetic flux density) by the numerical solution of the Boltzmann transport equation for the energy distribution of electrons. It has been observed that as the value of B/p (p = gas pressure) is increased from zero, the perpendicular drift velocity increased linearly at first, reaches a maximum value, and then decreases with increasing B/p. In general, the electron mean energy is found to be a function of Eavet/p( Eavet = averaged effective electric field intensity) only, but the other transport coefficients, such as transverse drift velocity, perpendicular drift velocity, and the Townsend ionization coefficient, are functions of both E/p and B/p.

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.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.