Computation of the drift velocity of spiral waves using response functions.

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave's center of rotation and fiducial phase may change over time, i.e., the spiral wave drifts. In linear approximation, the velocity of the drift is proportional to the convolution of the perturbation with the spiral's response functions, which are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues λ=0,±iω . Here, we demonstrate that the response functions give quantitatively accurate prediction of the drift velocities due to a variety of perturbations: a time dependent, periodic perturbation (inducing resonant drift); a rotational symmetry-breaking perturbation (inducing electrophoretic drift); and a translational symmetry-breaking perturbation (inhomogeneity induced drift) including drift due to a gradient, stepwise, and localized inhomogeneity. We predict the drift velocities using the response functions in FitzHugh-Nagumo and Barkley models, and compare them with the velocities obtained in direct numerical simulations. In all cases good quantitative agreement is demonstrated.

Computational study of subcritical response in flow past a circular cylinder.

Flow past a circular cylinder is investigated in the subcritical regime, below the onset of Bénard-von Kármán vortex shedding at Reynolds number Re(c)≃47 . The transient response of infinitesimal perturbations is computed. The domain requirements for obtaining converged results is discussed at length. It is shown that energy amplification occurs as low as Re=2.2 . Throughout much of the subcritical regime the maximum energy amplification increases approximately exponentially in the square of Re reaching 6800 at Re(c). The spatiotemporal structure of the optimal transient dynamics is shown to be transitory Bénard-von Kármán vortex streets. At Re≃42 the long-time structure switches from exponentially increasing downstream to exponentially decaying downstream. Three-dimensional computations show that two-dimensional structures dominate the energy growth except at short times.

Orbital motion of spiral waves in excitable media.

Spiral waves in active media react to small perturbations as particlelike objects. Here we apply asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the spiral rotation center along circular orbits around the inhomogeneity. The stationary orbits have fixed radii and alternating stability, determined by the properties of the bulk medium and the type of inhomogeneity, while the drift speed along an orbit depends on the strength of the inhomogeneity. Direct numerical simulations confirm the validity and robustness of the theoretical predictions and show that these unexpected effects should be observable in experiment.

Alternative stable scroll waves and conversion of autowave turbulence.

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh-Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop. The predictions are confirmed by direct simulations. Further investigations show that the slow-period scrolls display features similar to delayed after-depolarization and tend to develop into turbulence similar to ventricular fibrillation (VF). Scrolls with positive filament tension collapse or stabilize, similar to monomorphic ventricular tachycardia (VT). Perturbations, such as boundary interaction or shock stimulus, can convert the vortex with negative filament tension into the vortex with positive filament tension. This may correspond to transition from VF to VT unrelated to pinning.

Computation of the response functions of spiral waves in active media.

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological natures. A small perturbation causes gradual change in spatial location of spiral's rotation center and frequency, i.e., drift. The response functions (RFs) of a spiral wave are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues lambda=0,+/-iomega. The RFs describe the spiral's sensitivity to small perturbations in the way that a spiral is insensitive to small perturbations where its RFs are close to zero. The velocity of a spiral's drift is proportional to the convolution of RFs with the perturbation. Here we develop a regular and generic method of computing the RFs of stationary rotating spirals in reaction-diffusion equations. We demonstrate the method on the FitzHugh-Nagumo system and also show convergence of the method with respect to the computational parameters, i.e., discretization steps and size of the medium. The obtained RFs are localized at the spiral's core.

Selection of twisted scroll waves in three-dimensional excitable media.

The selection of shape and rotation frequency for scroll waves in reaction-diffusion equations modeling excitable media is investigated. For scrolls with uniform twist about straight filaments, asymptotic methods are used to derive free-boundary equations at leading and first order. Both orders are validated against full solutions of the reaction-diffusion equations. Using these two orders and with no adjustable parameters, the shape and frequency of waves are correctly predicted except possibly near the point of propagation failure where the core becomes large.

Bifurcation theory for three-dimensional flow in the wake of a circular cylinder

A bifurcation scenario is presented for three-dimensional vortex shedding in the wake of a circular cylinder for Reynolds numbers up to 300. Amplitude equations are proposed to describe the nonlinear interaction between two three-dimensional modes of shedding with different spanwise wave numbers and different spatiotemporal symmetries. The amplitude equations explain many features of the transition scenario observed experimentally.

Modeling the dynamics of cardiac action potentials.

The nonlinear dynamics of cardiac action potentials is explained via simple model equations describing the membrane potential and the inward and outward currents through the membrane. The equations approximate ionic models, yet are expressed as polynomial functions, and robustly capture the phase-space dynamics of action potentials.

The role of local school quality in rural employment and population growth.

"This study investigates the influence of school quality (measured at the high school level) on 1980 to 1990 population and employment change for nonmetropolitan fringe and hinterland census tracts in South Carolina. A Boarnet variation of the Carlino-Mills model is used to examine the interdependence of population and employment change.... Results...indicate that fringe tracts' population growth was positively related to student test scores, and hinterland tracts population and employment growth were negatively related to student-teacher ratios. Empirical results suggest that local school quality provided a positive influence on rural growth, primarily in terms of residential growth. The role of school quality for employment growth was less clear."

Evaluation of an inservice training program on dementia and wandering.

This study assessed the impact of an inservice training program in four nursing homes on nursing staff's knowledge of dementia, pacing/wandering behavior and management strategies, staff satisfaction, and their perceptions of work difficulty and quality of care. Additionally, unit-level behavioral observations of agitated behavior and the nature of resident interactions with staff members and other residents were also performed to assess whether changes in nursing staff's knowledge impacted the residents or interactions with the residents. Analyses revealed that quiz scores were significantly improved immediately following the inservice program as compared to pretest but returned to near pretest levels at the 1-month follow-up. Additionally, nursing staff reported that residents were allowed to pace/wander to a greater extent at follow-up compared to pretest. Methods for improving the effectiveness of inservice training are discussed.

Antibodies to the mycobacterial 65-kd heat-shock protein are reactive with synovial tissue of adjuvant arthritic rats and patients with rheumatoid arthritis and osteoarthritis.

The expression of 65-kd mycobacterial heat-shock protein (HSP)-related antigens in synovial membrane from rats and humans with arthritis was studied using three monoclonal antibodies and one polyclonal antiserum directed to antigens of mycobacteria. The antibodies labeled synovial tissue sections from both adjuvant arthritis (AA) rats and from patients with either rheumatoid arthritis (RA) or osteoarthritis (OA); especially the synovial lining cells appeared to be positive. The cytoplasmic staining patterns in rats and humans were essentially the same and were not related to the extent of inflammation ie, the size of lymphoid infiltration. In control tissues no cytoplasmic staining was observed. The results suggest a role for a 65-kd HSP or a cross-reactive molecule in the immunopathologic process of arthritic disease.