New Mechanism of Spiral Wave Initiation in a Reaction-Diffusion-Mechanics System

Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the “classical vulnerable zone.” Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM) model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material) to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the “classical,” and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the “classical vulnerable zone.” We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback

Development and Validation of a Risk Score for Chronic Kidney Disease in HIV Infection Using Prospective Cohort Data from the D:A:D Study

Ristola M. on työryhmien DAD Study Grp ; Royal Free Hosp Clin Cohort ; INSIGHT Study Grp ; SMART Study Grp ; ESPRIT Study Grp jäsen.Background Chronic kidney disease (CKD) is a major health issue for HIV-positive individuals, associated with increased morbidity and mortality. Development and implementation of a risk score model for CKD would allow comparison of the risks and benefits of adding potentially nephrotoxic antiretrovirals to a treatment regimen and would identify those at greatest risk of CKD. The aims of this study were to develop a simple, externally validated, and widely applicable long-term risk score model for CKD in HIV-positive individuals that can guide decision making in clinical practice. Methods and Findings A total of 17,954 HIV-positive individuals from the Data Collection on Adverse Events of Anti-HIV Drugs (D:A:D) study with >= 3 estimated glomerular filtration rate (eGFR) values after 1 January 2004 were included. Baseline was defined as the first eGFR > 60 ml/min/1.73 m2 after 1 January 2004; individuals with exposure to tenofovir, atazanavir, atazanavir/ritonavir, lopinavir/ritonavir, other boosted protease inhibitors before baseline were excluded. CKD was defined as confirmed (>3 mo apart) eGFR In the D:A:D study, 641 individuals developed CKD during 103,185 person-years of follow-up (PYFU; incidence 6.2/1,000 PYFU, 95% CI 5.7-6.7; median follow-up 6.1 y, range 0.3-9.1 y). Older age, intravenous drug use, hepatitis C coinfection, lower baseline eGFR, female gender, lower CD4 count nadir, hypertension, diabetes, and cardiovascular disease (CVD) predicted CKD. The adjusted incidence rate ratios of these nine categorical variables were scaled and summed to create the risk score. The median risk score at baseline was -2 (interquartile range -4 to 2). There was a 1: 393 chance of developing CKD in the next 5 y in the low risk group (risk score = 5, 505 events), respectively. Number needed to harm (NNTH) at 5 y when starting unboosted atazanavir or lopinavir/ritonavir among those with a low risk score was 1,702 (95% CI 1,166-3,367); NNTH was 202 (95% CI 159-278) and 21 (95% CI 19-23), respectively, for those with a medium and high risk score. NNTH was 739 (95% CI 506-1462), 88 (95% CI 69-121), and 9 (95% CI 8-10) for those with a low, medium, and high risk score, respectively, starting tenofovir, atazanavir/ritonavir, or another boosted protease inhibitor. The Royal Free Hospital Clinic Cohort included 2,548 individuals, of whom 94 individuals developed CKD (3.7%) during 18,376 PYFU (median follow-up 7.4 y, range 0.3-12.7 y). Of 2,013 individuals included from the SMART/ESPRIT control arms, 32 individuals developed CKD (1.6%) during 8,452 PYFU (median follow-up 4.1 y, range 0.6-8.1 y). External validation showed that the risk score predicted well in these cohorts. Limitations of this study included limited data on race and no information on proteinuria. Conclusions Both traditional and HIV-related risk factors were predictive of CKD. These factors were used to develop a risk score for CKD in HIV infection, externally validated, that has direct clinical relevance for patients and clinicians to weigh the benefits of certain antiretrovirals against the risk of CKD and to identify those at greatest risk of CKD.Peer reviewe

A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics.

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a masslattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke’s law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects

Electromechanical activity of an isolated fiber.

<p>A pulse is initialized at time by setting voltage to for . Fiber was kept at its resting length during the simulation.</p

Discrete mechanical growth model for plant tissue

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke's law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes

Discrete mechanical growth model for plant tissue

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke's law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes

Dependence of restitution on stretch-activated currents in constantly stretched medium.

<p>(<b>A</b>) APD restitution <i>vs </i>. (<b>B</b>) CV restitution <i>vs </i>. Same parameters were used as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059317#pone-0059317-g004" target="_blank">Figure? 4</a>.</p

Dependence of restitution on stretch-activated currents in contracting medium.

<p>(<b>A</b>) APD restitution <i>vs </i>. (<b>B</b>) CV restitution <i>vs </i>. Same parameters were used as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059317#pone-0059317-g006" target="_blank">Figure? 6</a>.</p

Effect of stretch-activated currents on the action potential in contracting medium.

<p>(<b>A</b>) Action potential <i>vs </i>. (<b>B</b>) APD <i>vs </i>. (<b>C</b>) Upstroke of action potential <i>vs </i>. (<b>D</b>) Maximal upstroke slope <i>vs </i>. Traveling plain waves were periodically () induced for different . Action potentials were measured after . Resting potential was measured in the medium without external stimulations. APD was measured at recovery.</p