Related papers: Weakly nonlinear analysis of a reaction-diffusion …
Spatially localized 2-D spot patterns occur for a wide variety of two component reaction-diffusion systems in the singular limit of a large diffusivity ratio. Such localized, far-from-equilibrium, patterns are known to exhibit a wide range…
Structural magnetic resonance imaging (MRI) can be used to detect lesions in the brains of multiple sclerosis (MS) patients. The formation of these lesions is a complex process involving inflammation, tissue damage, and tissue repair, all…
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis…
Demyelinating disorders of the central nervous system may have multiple causes, the most common are infections, autoimmune responses, genetic or vascular etiology. Demyelination lesions are characterized by areas were the myelin sheath of…
Multiple sclerosis (MS) is a demyelinating disease of the central nervous system (CNS). A reliable measure of the tissue myelin content is therefore essential for the understanding of the physiopathology of MS, tracking progression and…
This paper aims to investigate a reaction-diffusion model which describes in-host infection for Mycobacterium tuberculosis (Mtb) allowing random motion (i.e. linear diffusion) and chemotaxis (i.e. non-linear diffusion) of macrophages and…
The multiphase Whitham modulation equations with $N$ phases have $2N$ characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for coalescence, where two characteristics change from…
Multiple Sclerosis (MS) is an autoimmune disease that leads to lesions in the central nervous system. Magnetic resonance (MR) images provide sufficient imaging contrast to visualize and detect lesions, particularly those in the white…
Quantitative magnetization transfer (qMT) imaging provides myelin-sensitive biomarkers, such as the pool size ratio (PSR), which is valuable for multiple sclerosis (MS) assessment. However, qMT requires specialized 20-30 minute scans. We…
Multiple sclerosis is an inflammatory disorder of the central nervous system. Quantitative MRI has huge potential to provide intrinsic and normative values of tissue properties useful for diagnosis, prognosis and ultimately clinical…
Degradation of the myelin sheath is a common pathology underlying demyelinating neurological diseases from Multiple Sclerosis to Leukodistrophies. Although large malformations of myelin ultrastructure in the advanced stages of Wallerian…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation…
Multiple sclerosis (MS) is a demyelinating disease that affects more than 2 million people worldwide. The most used imaging technique to help in its diagnosis and follow-up is magnetic resonance imaging (MRI). Fluid Attenuated Inversion…
Multiple sclerosis (MS) is an inflammatory and neurodegenerative disease characterized by diffuse and focal areas of tissue loss. Conventional MRI techniques such as T1-weighted and T2-weighted scans are generally used in the diagnosis and…
Multiple sclerosis is a chronic autoimmune disease that affects the central nervous system. Understanding multiple sclerosis progression and identifying the implicated brain structures is crucial for personalized treatment decisions.…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…