Related papers: Weakly nonlinear analysis of a reaction-diffusion …
Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Multiple Sclerosis (MS) is a chronic neurological condition characterized by the development of lesions in the white matter of the brain. T2-fluid attenuated inversion recovery (FLAIR) brain magnetic resonance imaging (MRI) provides…
We study the discrete nonlinear Schr\"oinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved, but on the other,…
The Mullins effect represents a softening phenomenon observed in rubber-like materials and soft biological tissues. It is usually accompanied by many other inelastic effects like for example residual strain and induced anisotropy. In spite…
Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by…
Multiple sclerosis lesion activity segmentation is the task of detecting new and enlarging lesions that appeared between a baseline and a follow-up brain MRI scan. While deep learning methods for single-scan lesion segmentation are common,…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
Multiple Sclerosis (MS) is a severe neurological disease characterized by inflammatory lesions in the central nervous system. Hence, predicting inflammatory disease activity is crucial for disease assessment and treatment. However, MS…
A new mathematical model of memristive neural networks described by the partly diffusive reaction-diffusion equations with weak synaptic coupling is proposed and investigated. Under rather general conditions it is proved that there exists…
Objective: Multiple Sclerosis (MS) is an autoimmune, and demyelinating disease that leads to lesions in the central nervous system. This disease can be tracked and diagnosed using Magnetic Resonance Imaging (MRI). Up to now a multitude of…
We study a cross-diffusion model for tissue regeneration which involves the dynamics of human mesenchymal stem cells interacting with chondrocytes in a medium containing a differentiation factor. The latter acts as a chemoattractant for the…
We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said…
Multiple sclerosis is one of the most common chronic neurological diseases affecting the central nervous system. Lesions produced by the MS can be observed through two modalities of magnetic resonance (MR), known as T2W and FLAIR sequences,…
Multiple sclerosis is a neurological disorder in which the myelin sheaths of axons are damaged by the immune response. We report here a three-dimensional structural analysis of brain and spinal cord tissues of a mouse model of multiple…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
Brain lesions are abnormalities or injuries in brain tissue that are often detectable using magnetic resonance imaging (MRI), which reveals structural changes in the affected areas. This broad definition of brain lesions includes areas of…
Diffusion kurtosis imaging (DKI), is an imaging modality that yields novel disease biomarkers and in combination with nervous tissue modeling, provides access to microstructural parameters. Recently, DKI and subsequent estimation of…
The elasticity of soft tissues has been widely considered as a characteristic property to differentiate between healthy and vicious tissues and, therefore, motivated several elasticity imaging modalities, such as Ultrasound Elastography,…