Labyrinthine Turing Pattern Formation in the Cerebral Cortex

I propose that the labyrinthine patterns of the cortices of mammalian brains may be formed by a Turing instability of interacting axonal guidance species acting together with the mechanical strain imposed by the interconnecting axons.Comment: See home page http://lec.ugr.es/~julya

Towards a Framework for Predictive Mathematical Modeling of the Biomechanical Forces Causing Brain Tumor Mass-Effect

GBMs present with different growth phenotypes, ranging from invasive lesions without notable mass-effect to strongly displacing lesions that induce mechanical stresses and result in healthy-tissue deformation, midline shift or herniation. Biomechanical forces, such as those resulting from displacive tumor growth, are recognized to shape the tumor environment and to contribute to tumor progression. We therefore expect that biomechanical forces exerted by lesions on the brain parenchyma have implications on the biophysical level, and that they may affect treatment response and outcome. To better understand the role of biomechanics in the formation of different GBM phenotypes we started developing a framework for the predictive mathematical modeling of mechanical tumor-healthy tissue interaction on the macroscopic level. The tumor’s mass-effect is represented by a solid-mechanics model of brain tissue that computes tumor-induced strain based on local tumor cell concentration. The framework allows to seed tumors at multiple locations in a human brain atlas. It simulates tumor evolution over time and across different brain regions using literature-based parameter estimates for tumor cell proliferation, as well as isotropic motility, and mechanical tissue properties. Despite its simplicity, the mathematical model yielded realistic estimates of the mechanical impact of a growing tumor on intra-cranial pressure. However, comparison to publicly available GBM imaging data showed that asymmetric shapes could not be reproduced by isotropic growth assumptions. Here we present and evaluate an extended version of this mechanically-coupled reaction-diffusion model that takes into account tissue anisotropies based on MRI diffusion tensor imaging (MR-DTI). Structural anisotropies in brain tissue have been found to affect the directionality of tumor cell migration and are critical to mechanical behavior. This makes them likely to play a role also in the development of GBM phenotypes

Disconnected aging: cerebral white matter integrity and age-related differences in cognition.

Cognition arises as a result of coordinated processing among distributed brain regions and disruptions to communication within these neural networks can result in cognitive dysfunction. Cortical disconnection may thus contribute to the declines in some aspects of cognitive functioning observed in healthy aging. Diffusion tensor imaging (DTI) is ideally suited for the study of cortical disconnection as it provides indices of structural integrity within interconnected neural networks. The current review summarizes results of previous DTI aging research with the aim of identifying consistent patterns of age-related differences in white matter integrity, and of relationships between measures of white matter integrity and behavioral performance as a function of adult age. We outline a number of future directions that will broaden our current understanding of these brain-behavior relationships in aging. Specifically, future research should aim to (1) investigate multiple models of age-brain-behavior relationships; (2) determine the tract-specificity versus global effect of aging on white matter integrity; (3) assess the relative contribution of normal variation in white matter integrity versus white matter lesions to age-related differences in cognition; (4) improve the definition of specific aspects of cognitive functioning related to age-related differences in white matter integrity using information processing tasks; and (5) combine multiple imaging modalities (e.g., resting-state and task-related functional magnetic resonance imaging; fMRI) with DTI to clarify the role of cerebral white matter integrity in cognitive aging

Reaction-diffusion systems derived from kinetic models for Multiple Sclerosis

We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic model describes, at mesoscopic level, the dynamics of a high number of interacting agents. We consider both interactions among different populations of human cells and motion of immune cells, stimulated by cytokines. Moreover, we reproduce the consumption of myelin sheath due to anomalously activated lymphocytes and its restoration by oligodendrocytes. Successively, we fix a small time parameter and assume that the considered processes occur at different scales. This allows to perform a formal limit, obtaining macroscopic reaction-diffusion equations for the number densities with a chemotaxis term. A natural step is then to study the system, inquiring about the formation of spatial patterns through a Turing instability analysis of the problem and basing the discussion on microscopic parameters of the model. In particular, we get spatial patterns oscillating in time that may reproduce brain lesions characteristic of different phases of the pathology

A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is however critical both for basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brain-wide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brain-wide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open access data repository; compatibility with existing resources, and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.Comment: 41 page

Computer simulation of glioma growth and morphology

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion

Perspective: network-guided pattern formation of neural dynamics

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs, or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings, lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatiotemporal pattern formation and propose a novel perspective for analyzing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics

Modelling biological invasions: individual to population scales at interfaces

Extracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility