Mechanisms and Points of Control in the Spread of Inflammation: A Mathematical Investigation.

Understanding the mechanisms that control the body's response to inflammation is of key importance, due to its involvement in myriad medical conditions, including cancer, arthritis, Alzheimer's disease and asthma. While resolving inflammation has historically been considered a passive process, since the turn of the century the hunt for novel therapeutic interventions has begun to focus upon active manipulation of constituent mechanisms, particularly involving the roles of apoptosing neutrophils, phagocytosing macrophages and anti-inflammatory mediators. Moreover, there is growing interest in how inflammatory damage can spread spatially due to the motility of inflammatory mediators and immune cells. For example, impaired neutrophil chemotaxis is implicated in causing chronic inflammation under trauma and in ageing, while neutrophil migration is an attractive therapeutic target in ailments such as chronic obstructive pulmonary disease. We extend an existing homogeneous model that captures interactions between inflammatory mediators, neutrophils and macrophages to incorporate spatial behaviour. Through bifurcation analysis and numerical simulation, we show that spatially inhomogeneous outcomes can present close to the switch from bistability to guaranteed resolution in the corresponding homogeneous model. Finally, we show how aberrant spatial mechanisms can play a role in the failure of inflammation to resolve and discuss our results within the broader context of seeking novel inflammatory treatments.

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.

Network analysis detects changes in the contralesional hemisphere following stroke.

Changes in brain structure occur in remote regions following focal damage such as stroke. Such changes could disrupt processing of information across widely distributed brain networks. We used diffusion MRI tractography to assess connectivity between brain regions in 9 chronic stroke patients and 18 age-matched controls. We applied complex network analysis to calculate 'communicability', a measure of the ease with which information can travel across a network. Clustering individuals based on communicability separated patient and control groups, not only in the lesioned hemisphere but also in the contralesional hemisphere, despite the absence of gross structural pathology in the latter. In our highly selected patient group, lesions were localised to the left basal ganglia/internal capsule. We found reduced communicability in patients in regions surrounding the lesions in the affected hemisphere. In addition, communicability was reduced in homologous locations in the contralesional hemisphere for a subset of these regions. We interpret this as evidence for secondary degeneration of fibre pathways which occurs in remote regions interconnected, directly or indirectly, with the area of primary damage. We also identified regions with increased communicability in patients that could represent adaptive, plastic changes post-stroke. Network analysis provides new and powerful tools for understanding subtle changes in interactions across widely distributed brain networks following stroke.