A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix

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 termed Cancer Stem Cells (CSCs}, and as opposed to the more usual Differentiated Cancer Cells (DCCs), they exhibit higher motility, they are more resilient to therapy, and are able to metastasize to secondary locations within the organism and produce new tumours. The origin of the CSCs is not completely clear; they seem to stem from the DCCs via a transition process related to the Epithelial-Mesenchymal Transition (EMT) that can also be found in normal tissue. In the current work we model and numerically study the transition between these two types of cancer cells, and the resulting "ensemble" invasion of the extracellular matrix. This leads to the derivation and numerical simulation of two systems: an algebraic-elliptic system for the transition and an advection-reaction-diffusion system of Keller-Segel taxis type for the invasion

Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws

A recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling conditions of the network and does not require a solution of the Riemann problem at the nodes. We numerically compare the dynamics of the solution obtained by the scheme to solutions obtained using a classical coupling condition. In particular, we investigate the case of two outgoing edges in the Lighthill-Whitham-Richards model of traffic flow and in the Buckley-Leverett model of two phase flow. Moreover, we numerically study the asymptotic preserving property of the scheme by comparing it to its preliminary form before the relaxation limit in a 1-to-1 network.Comment: 7 pages, 4 figure

A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model

We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent $\gamma \in [1,3]$ and periodic boundary conditions. We derive conditional a posteriori bounds for the error measured in the $L^\infty(0,T;H^1(\Omega))$ norm for the chemoattractant and by a quasi-norm-like quantity for the density. These results are based on stability estimates and suitable conforming reconstructions of the numerical solution. We perform numerical experiments showing that our error bounds are linear in mesh width and elucidating the behaviour of the error estimator under changes of $\gamma$.Comment: 26 pages, 2 figures, 3 table

Data-Driven Models for Traffic Flow at Junctions

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based on real-world car trajectory data we propose a new class of data-driven models with the requirements of being consistent to networked hyperbolic traffic flow models. To this end the new models combine artificial neural networks with a parametrization of the solution space to the half-Riemann problem at the junction. A method for deriving density and flux corresponding to the traffic close to the junction for data-driven models is presented. The models parameter are fitted to obtain suitable boundary conditions for macroscopic first and second-order traffic flow models. The prediction of various models are compared considering also existing coupling rules at the junction. Numerical results imposing the data-fitted coupling models on a traffic network are presented exhibiting accurate predictions of the new models.Comment: 27 pages, 9 figures, 6 table

Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model

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 equations that features the role of the serine protease urokinase-type plasminogen activator. The analytical and numerical study of this system constitutes a challenge due to the merging, emerging, and travelling concentrations that the solutions exhibit. Classical numerical methods applied to this system necessitate very fine discretization grids to resolve these dynamics in an accurate way. To reduce the computational cost without sacrificing the accuracy of the solution, we apply adaptive mesh refinement techniques, in particular h-refinement. Extended numerical experiments exhibit that this approach provides with a higher order, stable, and robust numerical method for this system. We elaborate on several mesh refinement criteria and compare the results with the ones in the literature. We prove, for a simpler version of this model, $L^\infty$ bounds for the solutions, we study the stability of its conditional steady states, and conclude that it can serve as a test case for further development of mesh refinement techniques for cancer invasion simulations

Multiscale modeling of glioma invasion : from receptor binding to flux-limited macroscopic PDEs

Funding: The work of the first and fourth authors was supported by the German Federal Ministry of Education and Research (BMBF) through project GlioMaTh 05M2016. The work of the third author was supported by the Postdoctoral Fellowship for Research in Japan (Standard) of the Japan Society for the Promotion of Science.We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasion in brain tissue under the influence of hypoxia-triggered angiogenesis. The multiscale procedure links single-cell and mesoscopic dynamics with population level behavior, leading on the macroscopic scale to flux-limited glioma diffusion and multiple taxis. We verify the nonnegativity of regular solutions (provided they exist) to the obtained macroscopic PDE-ODE system and perform numerical simulations to illustrate the solution behavior under several scenarios.Publisher PDFPeer reviewe

A data-driven microscopic on-ramp model based on macroscopic network flows

While macroscopic traffic flow models consider traffic as a fluid, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena remains a challenge for microscopic models, especially in complex road sections such as on-ramps. In this paper, we propose a microscopic model for on-ramps derived from a macroscopic network flow model calibrated to real traffic data. The microscopic flow-based model requires additional assumptions regarding the acceleration and the merging behavior on the on-ramp to maintain consistency with the mean speeds, traffic flow and density predicted by the macroscopic model. To evaluate the model's performance, we conduct traffic simulations assessing speeds, accelerations, lane change positions, and risky behavior. Our results show that, although the proposed model may not fully capture all traffic phenomena of on-ramps accurately, it performs better than the Intelligent Driver Model (IDM) in most evaluated aspects. While the IDM is almost completely free of conflicts, the proposed model evokes a realistic amount and severity of conflicts and can therefore be used for safety analysis.Comment: 15 pages, 5 figure

Linked Vocabulary Recommendation Tools for Internet of Things: A Survey

The Semantic Web emerged with the vision of eased integration of heterogeneous, distributed data on the Web. The approach fundamentally relies on the linkage between and reuse of previously published vocabularies to facilitate semantic interoperability. In recent years, the Semantic Web has been perceived as a potential enabling technology to overcome interoperability issues in the Internet of Things (IoT), especially for service discovery and composition. Despite the importance of making vocabulary terms discoverable and selecting most suitable ones in forthcoming IoT applications, no state-of-the-art survey of tools achieving such recommendation tasks exists to date. This survey covers this gap, by specifying an extensive evaluation framework and assessing linked vocabulary recommendation tools. Furthermore, we discuss challenges and opportunities of vocabulary recommendation and related tools in the context of emerging IoT ecosystems. Overall, 40 recommendation tools for linked vocabularies were evaluated, both, empirically and experimentally. Some of the key ndings include that (i) many tools neglect to thoroughly address both, the curation of a vocabulary collection and e ective selection mechanisms; (ii) modern information retrieval techniques are underrepresented; and (iii) the reviewed tools that emerged from Semantic Web use cases are not yet su ciently extended to t today’s IoT projects

Towards Semantic Interoperability in an Open IoT Ecosystem for Connected Vehicle Services

A present challenge in today’s Internet of Things (IoT) ecosystem is to enable interoperability across hetero- geneous systems and service providers. Restricted access to data sources and services limits the capabilities of a smart city to improve social, environmental and economic aspects. Interoperability in the IoT is concerned with both, messaging interfaces and semantic understanding of heterogeneous data. In this paper, the first building blocks of an emerging open IoT ecosystem developed at the EU level are presented. Se- mantic web technologies are applied to the existing messaging components to support and improve semantic interoperability. The approach is demonstrated with a proof-of-concept for connected vehicle services in a smart city setting