List of publications

Cancer Growth and Metastasis

• • A genuinely hybrid, multiscale 3D cancer invasion and metastasis modelling framework, (D. Katsaounis, N. Harbour, T. Williams, M.A.J. Chaplain, and N. Sfakianakis), Bull.Math.Biol. (2024).

  • Mathematical modelling of cancer invasion: phenotypic transitioning provides insight into multifocal foci formation, (Z. Szymanska, M. Lachowitz, N. Sfakianakis, and M.A.J. Chaplain),  J. Comput. Sciences , 85 (2024).

  • Stochastic differential equation modelling of cell migration and invasion, (D. Katsaounis, M.A.J. Chaplain, and N. Sfakianakis), J. Math. Biol. 87(1), (2023).

  • Multiscale Modeling of Glioma Invasion: From Receptor Binding to Flux-Limited Macroscopic PDEs, (A. Dietrich, N. Kolbe, N. Sfakianakis, and Chr. Surulescu),  J. Theor. Biol. 522, (2021).

  • A novel 3D atomistic-continuum cancer invasion model: In silico simulations of an in vitro organotypic invasion assay, (L. C. Franssen, N. Sfakianakis, and M.A.J. Chaplain), Multiscale Model. Simul. , 20(2), 675-713 (2022).

  • The First Step Towards the Mathematical Understanding of the Role of Matrix Metalloproteinase-8 in Cancer Invasion, (A. Wilson, Th. Williams, and N. Sfakianakis ),   In: Suzuki, T., Poignard, C., Chaplain, M., Quaranta, V. (eds) MMDS 2020: Methods of Mathematical Oncology, Springer Proceedings in Mathematics & Statistics, vol 370. Springer, Singapore (2021). 

  • Mathematical Modelling of Cancer Invasion: A Review,   (N. Sfakianakis, and M.A.J. Chaplain), In: Suzuki, T., Poignard, C., Chaplain, M., Quaranta, V. (eds) MMDS 2020: Methods of Mathematical Oncology, Springer Proceedings in Mathematics & Statistics, vol 370. Springer, Singapore (2021). 

  • Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence,  (N. Kolbe, N. Sfakianakis, Chr. Stinner, Chr. Surulescu, and J. Lenz), Discr. Cont. Dyn. Systems B, 26(1),  (2021)  824-50.

  • A hybrid, multiscale, two species modelling approach in the cancer invasion of the extracellular matrix, (N. Sfakianakis, A. Madzvamuse, and M.A.J. Chaplain),  Mult. Model. Simul. 18(2) (2020)  824-50.

  • Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model, (J. Giesselmann, N. Kolbe, M. Lukacova, and N. Sfakianakis), Discrete Cont. Dyn.-B, 22, (2018)

  • Numerical Simulation of a Contractivity Based Multiscale Cancer Invasion Model, (N. Kolbe, M. Lukacova, N. Sfakianakis, and B. Wiebe), In: A. Gerisch, R. Penta, and J. Lang,  Multiscale Models in Mechano- and Tumor Biology. Lecture Notes in Computational Science and Engineering, 122, Springer Cham. (2017).

  • A multiscale approach to the migration of cancer stem cells : mathematical modelling and simulations, (N. Sfakianakis, N. Kolbe, N. Hellmann, and M. Lukacova), Bull. Math. Biol., 79, (2016), 209-235

  • A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: the urokinase model, (N. Kolbe, J. Katuchova, N. Sfakianakis, N. Hellmann, and M. Lukacova), Appl. Math. Comput.,  273, (2016), 353-376

  • A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix, (N. Hellmann, N. Kolbe, and N. Sfakianakis), Bull. Braz. Math. Soc., 47(1), (2016),  1-16

Live Cell Motility

• • Stability, convergence, and sensitivity analysis of the Filament Based Lamellipodium Model and the corresponding FEM, (N. Sfakianakis and A. Brunk) Bull. Math. Biol. , 80 (2018) 2789-2827.

  • The effect of cadherins in the motility of living cells. Modelling under the FBLM prism, (N. Sfakianakis, D. Peurichard, A. Brunk, and Chr. Schmeiser)  Biomath, 7 (2018).

  • Chemotaxis and haptotaxis on a cellular level,  (A. Brunk, N. Kolbe, and N. Sfakianakis) in Theory Num. and Applications of Hyperbolic Problems edited by Chr. Klingenberg, M. Westdickenberg (2018). 

  • Numerical treatment of the Filament Based Lamellipodium Model (FBLM), (A. Manhart, D. Oelz, Ch. Schmeiser, and N. Sfakianakis),  in Mod. Cell. Syst. edited by F. Matthaeus, F. Graw, J. Pahle, (2016)

  • An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals, (A. Manhart, D. Oelz, Ch. Schmeiser, and N. Sfakianakis),  J. Theor. Biol., 382, (2015) 244-258

  • Stable length distributions in co-localized polymerizing and depolymerizing protein filaments, (H. Freistuehler, Chr. Schmeiser, and N. Sfakianakis), SIAM J. Appl. Math., 72, (2012), 1428-1448

Adaptive Mesh Refinement methods

• • An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models, (N. Kolbe and N. Sfakianakis) J. Comput. Applied Mathematics, 416 (2022).

  • Entropy dissipation of moving mesh adaptation, (M. Lukacova and N. Sfakianakis), J. Hyperbol. Differ. Eq., 11 (2014), 633-653

  • Theoretical study of entropy dissipation of moving meshes, (M. Lukacova, and N. Sfakianakis), AIMS on Appl. Math., 8, (2014), 931-94

  • Adaptive mesh reconstruction for hyperbolic conservation laws with total variation bound, (N. Sfakianakis) Math. Comput., 82, (2013), 129-151

  • Entropy conservative schemes and adaptive mesh selection for hyperbolic conservation laws, (Chr. Arvanitis, Ch. Makridakis, and N. Sfakianakis), J. Hyperbol. Differ. Eq., 7, (2010), 383-404

Other Problems

• • Energy intake functions of ectotherms and endothemrs derived from their body mass growth, (J. Werner, N. Sfakianakis, E.M. Griebeler, and A. Rendall), J. Theor. Biol. (2018)

  • Symetries and Asymetries of the Immune System: a categorification approach, (J.F. Mascari, D. Giacchero, and N. Sfakianakis), IEEE International Conference on Bioinformatics and Biomedicine (2017) 

  • Inverse modeling of the Drosophila gap gene system: Sparsity Promoting Bayesian parameter estimation and uncertainty quantification, (N. Sfakianakis, M. Simon), Proc. 10th Int. Comput. Systems Biology (2013), 86-91