Unmet health needs in patients with coronary heart disease: implications and potential for improvement in caring services

BACKGROUND: Improving the quality of health care services requires tailoring facilities to fulfil patients' needs. Satisfying patients' healthcare needs, listening to patients' opinions and building a closer provider-user partnership are central to the NHS. Few published studies have discussed cardiovascular patients' health needs, but they are not comprehensive and fail to explore the contribution of outcome to needs assessment. METHOD: A comprehensive self-administered health needs assessment (HNA) questionnaire was developed for concomitant use with generic (Short Form-12 and EuroQOL) and specific (Seattle Angina Questionnaire) health-related quality of life (HRQL) instruments on 242 patients admitted to the Acute Cardiac Unit, Nottingham. RESULTS: 38% reported difficulty accessing health facilities, 56% due to transport and 32% required a travelling companion. Mean HRQOL scores were lower in those living alone (P < 0.05) or who reported unsatisfactory accommodation. Dissatisfaction with transport affected patients' ease of access to healthcare facilities (P < 0.001). Younger patients (<65 y) were more likely to be socially isolated (P = 0.01). Women and patients with chronic disease were more likely to be concerned about housework (P < 0.05). Over 65 s (p < 0.05) of higher social classes (p < 0.01) and greater physical needs (p < 0.001) had more social needs, correlating moderately (0.32 < r < 0.63) with all HRQL domains except SAQ-AS. Several HRQL components were highly correlated with the HNA physical score (p < 0.001). CONCLUSIONS: Patients wanted more social (suitable accommodation, companionship, social visits) and physical (help aids, access to healthcare services, house work) support. The construct validity and intra-class reliability of the HNA tool were confirmed. Our results indicate a gap between patients' health needs and available services, highlighting potential areas for improvement in the quality of services

The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These non-local models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes.

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

Neural fields with sigmoidal firing rates: approximate solutions

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.