15 citations · 33 across the 17 of their papers we have counts for
19 papers
Beyond Classical Diffusion: Fractional Derivatives in Transport and Stochastic Systems
Cypres Verbeeck, Nikolaos Sfakianakis
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex…
Mathematical modelling of cancer invasion: Phenotypic transitioning provides insight into multifocal foci formation
Zuzanna Szymańska, Mirosław Lachowicz, Nikolaos Sfakianakis +1
The transition from the epithelial to mesenchymal phenotype and its reverse (from mesenchymal to epithelial) are crucial processes necessary for the progression and spread of cance…
Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs
Anne Dietrich, Niklas Kolbe, Nikolaos Sfakianakis +1
We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasi…
Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner +2
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually…
Modelling cell-cell collision and adhesion with the Filament Based Lamellipodium Model
Nikolaos Sfakianakis, Diane Peurichard, Aaron Brunk +1
We extend the live-cell motility Filament Based Lamellipodium Model to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin indu…
A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix
Nikolaos Sfakianakis, Anotida Madzvamuse, Mark A. J. Chaplain
The ability to locally degrade the extracellular matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a criti…
Stability, convergence, and sensitivity analysis of the Filament Based Lamellipodium Model and the corresponding FEM
Nikolaos Sfakianakis, Aaron Brunk
This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamen…
An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models
Niklas Kolbe, Nikolaos Sfakianakis
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2-…
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model
Jan Giesselmann, Niklas Kolbe, Maria Lukacova-Medvidova +1
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model de…
Chemotaxis and Haptotaxis on Cellular Level
Aaron Brunk, Niklas Kolbe, Nikolaos Sfakianakis
Chemotaxis and haptotaxis have been a main theme in the macroscopic study of bacterial and cellular motility. In this work we investigate the influence these processes have on the…
Energy intake functions of ectotherms and endotherms derived from their body mass growth
Jan Werner, Nikolaos Sfakianakis, Alan Rendall +1
How animals allocate energy to different body functions is still not completely understood and a challenging topic until recently. Here, we investigate in more detail the allocatio…
Numerical simulation of a contractivity based multiscale cancer invasion model
Niklas Kolbe, Maria Lukacova-Medvidova, Nikolaos Sfakianakis +1
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that de…
A multiscale approach to the migration of cancer stem cells: mathematical modelling and simulations
Nikolaos Sfakianakis, Niklas Kolbe, Nadja Hellmann +1
We propose a multiscale model of the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We assume that th…
A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix
Nadja Hellmann, Niklas Kolbe, Nikolaos Sfakianakis
Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are term…
Numerical treatment of the Filament Based Lamellipodium Model (FBLM)
A. Manhart, D. Oelz, C. Schmeiser +1
We describe in this work the numerical treatment of the Filament Based Lamellipodium Model (FBLM). The model itself is a two-phase two-dimensional continuum model, describing the d…
An Extended Filament Based Lamellipodium Model Produces Various Moving Cell Shapes in the Presence of Chemotactic Signals
Angelika Manhart, Christian Schmeiser, Nikolaos Sfakianakis +1
The Filament Based Lamellipodium Model (FBLM) is a two-phase two-dimensional continuum model, describing the dynamcis of two interacting families of locally parallel actin filament…
Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model
Niklas Kolbe, Jana Katuchova, Nikolaos Sfakianakis +2
In the present work we investigate the chemotactically and proteolytically driven tissue invasion by cancer cells. The model employed is a system of advection-reaction-diffusion eq…
Entropy dissipation of moving mesh adaptation
Maria Lukacova-Medvidova, Nikolaos Sfakianakis
Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to…
Adaptive mesh reconstruction: Total Variation Bound
Nikolaos Sfakianakis
We consider 3-point numerical schemes for scalar Conservation Laws, that are oscillatory either to their dispersive or anti-diffusive nature. Oscillations are responsible for the i…