A numerical simulation of neural fields on curved geometries.

Despite the highly convoluted nature of the human brain, neural field models typically treat the cortex as a planar two-dimensional sheet of ne;urons. Here, we present an approach for solving neural field equations on surfaces more akin to the cortical geometries typically obtained from neuroimaging data. Our approach involves solving the integral form of the partial integro-differential equation directly using collocation techniques alongside efficient numerical procedures for determining geodesic distances between neural units. To illustrate our methods, we study localised activity patterns in a two-dimensional neural field equation posed on a periodic square domain, the curved surface of a torus, and the cortical surface of a rat brain, the latter of which is constructed using neuroimaging data. Our results are twofold: Firstly, we find that collocation techniques are able to replicate solutions obtained using more standard Fourier based methods on a flat, periodic domain, independent of the underlying mesh. This result is particularly significant given the highly irregular nature of the type of meshes derived from modern neuroimaging data. And secondly, by deploying efficient numerical schemes to compute geodesics, our approach is not only capable of modelling macroscopic pattern formation on realistic cortical geometries, but can also be extended to include cortical architectures of more physiological relevance. Importantly, such an approach provides a means by which to investigate the influence of cortical geometry upon the nucleation and propagation of spatially localised neural activity and beyond. It thus promises to provide model-based insights into disorders like epilepsy, or spreading depression, as well as healthy cognitive processes like working memory or attention.

Dynamical energy analysis for built-up acoustic systems at high frequencies.

Standard methods for describing the intensity distribution of mechanical and acoustic wave fields in the high frequency asymptotic limit are often based on flow transport equations. Common techniques are statistical energy analysis, employed mostly in the context of vibro-acoustics, and ray tracing, a popular tool in architectural acoustics. Dynamical energy analysis makes it possible to interpolate between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. In this work a version of dynamical energy analysis based on a Chebyshev basis expansion of the Perron-Frobenius operator governing the ray dynamics is introduced. It is shown that the technique can efficiently deal with multi-component systems overcoming typical geometrical limitations present in statistical energy analysis. Results are compared with state-of-the-art hp-adaptive discontinuous Galerkin finite element simulations.

A Burton-Miller inverse boundary element method for near-field acoustic holography.

An inverse boundary element method based on the Burton-Miller integral equation is proposed for reconstructing the Neumann boundary data from pressure values on a conformal surface in the near-field of an arbitrary radiating object. The accuracy of the reconstruction is compared with that of a method based on the more commonly used Helmholtz integral equation. In particular, the behavior at characteristic frequencies, which are known to be problematic in the Helmholtz integral equation for the forward problem, is examined. The effect of regularization is considered, including the L-curve parameter selection method. Numerical computations are given for noisy data generated from an internal point source.

Evaluation of evoked potentials and cerebrospinal fluid analysis in the differential diagnosis of multiple sclerosis.

During the 6 years to December 1988, 191 patients underwent evoked potential (EP) studies and cerebrospinal fluid (CSF) analysis for oligoclonal bands at the Queen Elizabeth Hospital, for the differential diagnosis of multiple sclerosis (MS). Clinical data at the time of study separated patients into 3 groups, as follows: (i) multiple sclerosis (n = 90) - McDonald and Halliday Classification, 1977, (ii) other neurological disease (n = 82) and (iii) no neurological disease (n = 19). In cases of clinically definite MS, visual evoked potentials (VEPs) were abnormal and oligoclonal bands were detected in 64% and 59% of cases, respectively. However, only 15% of patients with suspected MS had abnormal VEPs, and only 23% had oligoclonal bands. Other studies have shown figures differing from these, though not necessarily significantly. We found a substantial number of EP (20%) but few CSF (4%) abnormalities in disorders other than MS, and no abnormalities in cases without neurological disease. The various figures for abnormal results in cases assessed for the differential diagnosis of MS are influenced not only by laboratory methods, but by the degree of clinical suspicion in relation to the cases selected, as well as by differences in populations from which cases are derived. Long-term prospective studies of diagnostically indeterminate cases are still required to determine the diagnostic weighting that can be applied on the basis of abnormal investigational results. Magnetic resonance imaging will not resolve these questions since it has limitations of its own, particularly with regard to specificity.

Atypical LD isoenzymes with five diffuse bands and evidence for two types of binding.

We describe a plasma LD isoenzyme pattern in which all five bands are unusually diffuse and of retarded mobility, an appearance not previously reported. This was shown to be due to binding to immunoglobulin G from which the enzyme could be displaced by an antiserum to gamma chains. Protein A-Sepharose removed most of the LD activity from plasma but did not dissociate the complex, indicating that the Fab end of the Ig molecule was involved in binding. Antiserum to kappa chains displaced LD5 from the complex but had no effect on the anodal bands. By contrast NAD displaced the anodal isoenzymes but not LD5. We suggest that two types of binding are involved. The LD5 complex appears to represent a true antigen-antibody reaction whereas the binding to the faster isoenzymes does not. We also suggest that immunoprecipitation is more reliable than immunoelectrophoresis or immunodiffusion for demonstrating IgG in such complexes and may be of value in defining the nature of binding.

N-[(carbamoylmethyl)amino]ethanesulfonic acid improves phenotyping of alpha 1-antitrypsin by isoelectric focusing on agarose gel.

The hereditary deficiency variants of alpha 1-antitrypsin that are associated with diseases such as emphysema are usually identified by use of isoelectric focusing on polyacrylamide gels. Agarose is a simpler, faster, safer, and more reliable medium for this, but resolution often is not as good. I describe a method in which the ultrathin agarose gel contains N-[(carbamoylmethyl)amino]ethanesulfonic acid as a "separator," to flatten the pH gradient and improve separation of the alpha 1-antitrypsin isoforms. The resolution obtained equals or surpasses that of conventional methods based on use of either polyacrylamide or agarose. Haptoglobin, which interferes with isoelectric focusing on polyacrylamide, does not interfere with this method; other advantages are also discussed.

A second study of tensile fatigue properties of human articular cartilage.

The tensile fatigue properties of the collagen fibre meshwork in normal human articular cartilage were measured by subjecting isolated specimens of post-mortem femoral head cartilage to cyclic tensile stress. The results of the study showed (1) that the collagen fibre meshwork is fatigue prone and (2) that its fatigue strength decreases rapidly with age. Extrapolation of the data to physiologically possible stress levels suggests that tensile fatigue failure of the collagen meshwork could occur in life.