Christina Surulescu

We propose two approaches to a model deduction for Buruli ulcer spread in a tissue, prove global existence of solutions to the obtained macroscopic cross-diffusion PDE-ODE systems, and perform numerical simulations to illustrate the behavior of solutions under various scenarios and compare the outcome of the two approaches.

In this paper, we propose a mathematical model for tumor invasion supported by angiogenesis and interactions with the surrounding tissue. For the model deduction we employ a multiscale approach starting from lower scales and obtaining by an informal parabolic upscaling a system of reaction–diffusion-taxis equations with a so-called ’taxis cascade’, where one species is performing taxis toward a signal whose production/decay is controlled by the other, for which it also serves as a tactic cue. We prove global existence and uniqueness of solutions to the obtained PDE-ODE system and perform numerical simulations to illustrate the behavior of solutions.

We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, according to the strength of spatially nonlocal intra- and interspecific interactions. The two cell phenotypes are interchangeable, the transitions depending on the environmental acidity. We prove global existence of a weak solution to the considered PDE-ODE-PDE system and perform numerical simulations in 1D to informally investigate boundedness and patterning behavior in dependence of the system's parameters and kernels involved in the nonlocal terms.

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 chondrocytes and influences the (de)differentiation of both cell phenotypes. The stem cells perform haptotaxis towards extracellular matrix expressed by the chondrocytes and degraded by themselves. Cartilage production as part of the extracellular matrix is ensured by condrocytes. The growth factor is provided periodically, to maintain the cell dynamics. We provide a proof for the global existence of weak solutions to this model, which is a simplified version of a more complex setting deduced in \cite{surulescu_AMM}.

We study a model for the spread and (de)differentiation of mesenchymal stem cells and chondrocytes in a scaffold whose fibers are coated with hyaluron. The chondrocytes produce new extracellular matrix, which, together with hyaluron, serves as haptotactic cue for the stem cell migration. We prove global existence of weak solutions of the corresponding cross-diffusion system with double haptotaxis.

We propose a mathematical model for tumor invasion supported by angiogenesis and interactions with the surrounding tissue. For the model deduction we employ a multiscale approach starting from lower scales and obtaining by an informal parabolic upscaling a system of reaction-diffusion-taxis equations with a so-called 'taxis cascade', where one species is performing taxis towards a signal whose production/decay is controled by the other, for which it also serves as a tactic cue. We prove global existence and uniqueness of solutions to the obtained PDE-ODE system and perform numerical simulations to illustrate the behavior of solutions.

We develop a model the dynamics of human mesenchymal stem cells (hMSCs) and chondrocytes evolving in a nonwoven polyethylene terephtalate (PET) scaffold impregnated with hyaluron and supplied with a differentiation medium. The scaffold and the cells are assumed to be contained in a bioreactor with fluid perfusion. The differentiation of hMSCs into chondrocytes favors the production of extracellular matrix (ECM) and is influenced by fluid stress. The model takes deformations of ECM and PET scaffold into account. The scaffold structure is explicitly included by statistical assessment of the fibre distribution from CT images. The effective macroscopic equations are obtained by appropriate upscaling from dynamics on lower (microscopic and mesoscopic) scales and feature in the motility terms an explicit cell diffusion tensor encoding the assessed anisotropic scaffold structure. Numerical simulations show its influence on the overall cell and tissue dynamics.

We propose a PDE-ODE model for tissue regeneration, obtained by parabolic upscaling from kinetic transport equations written for the mesoscopic densities of mesenchymal stem cells and chondrocytes which evolve in an artificial scaffold impregnated with hyaluron. Due to the simple chosen turning kernels, the effective equations obtained on the macroscopic level are of the usual reaction-diffusion-taxis type. We prove global existence of solutions to the coupled macroscopic system and perform a stability and bifurcation analysis, which shows that the observed patterns are driven by taxis. Numerical simulations illustrate the model behavior for various tactic sensitivities and initial conditions.

Starting from a mesoscopic description of cell migration and intraspecific interactions, we obtain by upscaling an effective reaction–diffusion–taxis equation for the cell population density involving spatial nonlocalities in the source term and biasing its motility and growth behavior according to environmental acidity. We prove global existence, uniqueness, and boundedness of a nonnegative solution to a simplified version of the coupled system describing cell and acidity dynamics. A 1D study of pattern formation is performed. Numerical simulations illustrate the qualitative behavior of solutions.