Publications

PhD Thesis, Habilitation Thesis and Book Chapters

• Sur quelques questions de géométrie différentielle liées à la théorie des corps et des fils élastiques. Laboratoire J.-L. Lions, Université Paris 6 (2005), PDF.
• Mathematical modeling, analysis and simulations for fluid mechanics and their relevance to in silico medicine. Université de Strasbourg (2017), PDF.
• Mathematical modeling of the cerebrospinal fluid flow and its interactions. L. Sala, F. Salerni, M. Szopos, Ocular Fluid Dynamics. Anatomy, Physiology, Imaging Techniques, and Mathematical Modeling. Editors: G. Guidoboni, A. Harris, R. Sacco. Springer-Birkhauser, New York (2019), 497--540.

Mathematical modeling of collective cell dynamics. Applications to the simulation of symmetry breaking during morphogenesis.

• [MCD1] S. Lo Vecchio, O. Pertz, M. Szopos, L. Navoret, D. Riveline. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries, Nature Physics (2024), biorxiv (see also Associated content: G.A. Gomez Cells play tug-of-war to start moving collectively, Nature Physics News & Views (2024)).

Reduced and multiscale mathematical and computational models for biofluids. Applications to the study of the coupled eye-cerebral system and of the ballistocardiograms.

• [MS21] L. Sala, K. Lyons, G. Guidoboni, A. Harris, M. Szopos, S. Lapin. Analysis of waveform parameters in the retinal vasculature via mathematical modeling and data analytics methods, La Matematica (2024), in press.


• [MS20] T. Saigre, C. Prud'homme, M. Szopos. Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball, Int. J. Numer. Meth. Biomed. Engng., (2024), in press, HAL.


• [MS19] T. Saigre, C. Prud'homme, M. Szopos, V. Chabannes. A coupled fluid-dynamics-heat transfer model for 3D simulations of the aqueous humor flow in the human eye, 8th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2024) Proceedings, 508--512, HAL.


• [MS18] L. Sala, C. Prud'homme, G. Guidoboni, M. Szopos, A. Harris. The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye, Int. J. Numer. Meth. Biomed. Engng. vol. 40, Issue 2, (2024); e3791.


• [MS17] M. Zaid, R. Invernizzi, L. Sala, L. Despins, M. Popescu, J. Keller, M. Skubic, R. Sacco, M. Szopos, V.H. Huxley, G. Guidoboni. Analysis of the Contribution of Cardiovascular Compartments to the Ballistocardiogram Signal Using Mathematical Modeling, Computing in Cardiology (CinC), Atlanta, GA, USA (2023), Publisher IEEE, HAL.


• [MS16] S. Bertoluzza, G. Guidoboni, R. Hild, D. Prada, C. Prud'homme, R. Sacco, L. Sala, M. Szopos. A HDG method for elliptic problems with integral boundary condition: Theory and Applications, Journal of Scientific Computing, vol. 95, 6 (2023).


• [MS15] A. Vercellin Verticchio, A. Harris, A. Belamkar, R. Zukerman, L. Carichino, M. Szopos, B. Siesky, L. Quaranta, C. Bruttini, F. Oddone, I. Riva, G. Guidoboni. Physiology-enhanced data analytics to evaluate the effect of altitude on intraocular pressure and ocular hemodynamics, Photonics, vol. 9(3), 158 (2022).


• [MS14] L. Sala, C. Prud'homme, M. Szopos. Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator, Mathematical Biosciences and Engineering vol. 18, Issue 3 (2021), 2010--2032.


• [MS13] L. Carichino, G. Guidoboni, M. Szopos. Second-order time accuracy for coupled lumped and distributed fluid flow problems via operator splitting: a numerical investigation, Numerical Mathematics and Advanced Applications ENUMATH 2019, Editors: F.J. Vermolen, C. Vuik, Lecture Notes in Computational Science and Engineering, Springer International Publishing, vol 139 (2021), 959--967.


• [MS12] L. Sala, C. Prud'homme, M. Szopos, G. Guidoboni, A. Harris. Mathematical assessment of the role of three factors entangled in the development of glaucoma by means of the Ocular Mathematical Virtual Simulator, Numerical Mathematics and Advanced Applications ENUMATH 2019, Editors: F.J. Vermolen, C. Vuik, Lecture Notes in Computational Science and Engineering, Springer International Publishing, vol 139 (2021), 851--860.


• [MS11] G. Guidoboni, L. Sala, M. Enayati, R. Sacco, M. Szopos, J. Keller, M. Popescu, L. Despins, V.H. Huxley, M. Skubic. Cardiovascular function and ballistocardiogram: a relationship interpreted via mathematical modeling, IEEE Transactions on Biomedical Engineering, vol. 66, no. 10 (2019), 2906--2917, arxiv.


• [MS10] F. Salerni, R. Repetto, A. Harris, P. Pinsky, C. Prud'homme, M. Szopos, G. Guidoboni. Biofluid modeling of the coupled eye-brain system and insights into simulated microgravity conditions, PLoS One, 14(8):e0216012 (2019).


• [MS9] L. Sala, C. Prud'homme, G. Guidoboni, M. Szopos. The Ocular Mathematical Virtual Simulator: towards uncertainty quantification, 6th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2019) Proceedings, 429--432.


• [MS8] G. Guidoboni, F. Salerni, R. Repetto, M. Szopos, A. Harris. Relationship between intraocular, blood, and cerebrospinal fluid pressures: a theoretical approach, J. for Modeling in Ophthalmology, 3 (2019), 9--13 (Meeting Highlights Article: ARVO 2018).


• [MS7] L. Sala, C. Prud'homme, G. Guidoboni, M. Szopos. Ocular mathematical virtual simulator: A hemodynamical and biomechanical study towards clinical applications, J. of Coupled Systems and Multiscale Dynamics, 6 (2018), 241--247.


• [MS6] L. Carichino, G. Guidoboni, M. Szopos. Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: the Stokes case, J. of Computational Physics, 364 (2018), 235--256, arxiv.


• [MS5] F. Salerni, R. Repetto, A. Harris, P. Pinsky, C. Prud'homme, M. Szopos, G. Guidoboni. Mathematical modeling of ocular and cerebral hemo-fluid dynamics: application to VIIP, J. for Modeling in Ophthalmology, 2 (2018), 64--68 (ESB-ITA 2017 special issue).


• [MS4] L. Sala, C. Prud'homme, M. Szopos, G. Guidoboni. Towards a full model for ocular biomechanics, fluid dynamics, and hemodynamics, J. for Modeling in Ophthalmology, 2 (2018), 7--13 (ESB-ITA 2017 special issue).


• [MS3] F. Stefanoni, A. Harris, M. Szopos, C. Prud'homme, R. Sacco, D. Messenio, M.L. Costantino, G. Guidoboni. Clinical assessment of intraocular pressure: a whole-eye dynamic model, J. for Modeling in Ophthalmology, 2 (2018), 18--23 (ESB-ITA 2017 special issue).


• [MS2] M. Szopos, S. Cassani, G. Guidoboni, C. Prud'homme, R. Sacco, B. Siesky, A. Harris. Mathematical modeling of aqueous humor flow and intraocular pressure under uncertainty: towards individualized glaucoma management, J. for Modeling in Ophthalmology, 1 (2016), 29--39 (invited paper, special issue following the International Congress on Advanced Technologies and Treatments for Glaucoma, Milan 2015).


• [MS1] R. Sacco, S. Cassani, G. Guidoboni, M. Szopos, C. Prud'homme, A. Harris. Modeling the coupled dynamics of ocular blood flow and production and drainage of aqueous humor, 4th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2015) Proceedings, 608--611.

Three-dimensional models, analysis and efficient simulations for fluid equations. Applications to computational hemodynamics in the cerebral network.

• [C10] G. Guidoboni, R. Sacco, M. Szopos, L. Sala, A.C. Verticchio-Vercellin, B. Siesky, A. Harris. Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling, Frontiers in Neuroscience, 14 (2020) 566428.


• [C9] S. Bertoluzza, V. Chabannes, C. Prud'homme, M. Szopos. Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics, Computer Methods in Applied Mechanics and Engineering, 322 (2017), 58--80, HAL.


• [C8] O. Miraucourt, S. Salmon, M. Szopos, M. Thiriet. Blood flow in the cerebral venous system: modeling and simulation, Computer Methods in Biomechanics and Biomedical Engineering, 20 (2017), 471--482, HAL.


• [C7] V. Chabannes, C. Prud'homme, M. Szopos, R. Tarabay. High order finite element simulations for fluid dynamics validated by experimental data from the FDA benchmark nozzle model, 5th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2017) Proceedings, 1150--1153, HAL.


• [C6] N. Passat, S. Salmon, J.-P. Armspach, B. Naegel, C. Prud'homme, H. Talbot, A. Fortin, S. Garnotel, O. Merveille, O. Miraucourt, R. Tarabay, V. Chabannes, A. Dufour, A. Jezierska, O. Balédent, E. Durand, L. Najman, M. Szopos, A. Ancel, J. Baruthio, M. Delbany, S. Fall, G. Pagé, O. Génevaux, M. Ismail, P. Loureiro de Sousa, M. Thiriet, J. Jomier. From Real MRA to Virtual MRA: Towards an Open-Source Framework. International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2016), Lecture Notes in Computer Science, vol. 9902, 335--343, Springer, Athens, Greece, 2016.


• [C5] V. Chabannes, M. Ismail, C. Prud'homme, M. Szopos. Hemodynamic simulations in the cerebral venous network: a study on the influence of different modeling assumptions , J. of Coupled Systems and Multiscale Dynamics, 3 (2015), 23--37, HAL.


• [C4] O. Miraucourt, O. Génevaux, M. Szopos, M. Thiriet, H. Talbot, S. Salmon, N. Passat. 3D CFD in Complex Vascular Systems: A Case Study , International Symposium on Biomedical Simulation (ISBMS 2014), Lecture Notes in Computer Science, vol. 8789, 86--94, Springer, Strasbourg, France, 2014.


• [C3] C. Caldini-Queiros, V. Chabannes, M. Ismail, G. Pena, C. Prud'homme, M. Szopos, R. Tarabay. Towards large-scale three-dimensional blood flow simulations in realistic geometries, ESAIM, Proc. 43 (2013), 195--212.


• [C2] O. Miraucourt, S. Salmon, M. Szopos, M. Thiriet. Blood flow simulations in the cerebral venous network, 3rd International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2013) Proceedings, 187--190.


• [C1] S. Salmon, S. Sy, M. Szopos. Cerebral blood flow simulations in realistic geometries, ESAIM, Proc. 35 (2012), 281--286.

Numerical strategies for coupled fluid-structure problems. Applications to multiphysics computational models in biology and medicine.

• [FSI2] M. Szopos, N. Poussineau, Y. Maday, C. Canniffe, D.S. Celermajer, D. Bonnet, P. Ou. Computational modelling of blood flow in the aorta - insights into eccentric dilatation of the ascending aorta following surgery for coarctation, J. of Thoracic and Cardiovascular Surgery, 148 (2014), 1572--1582.


• [FSI1] M. Hillairet, A. Lozinski, M. Szopos. On discretization in time in simulations of particulate flows, Discrete and Continuous Dynamical Systems - B, 15 (2011), 935--956.

Methods of mathematical analysis and differential geometry in the theory of elasticity

• [T6] M. Szopos. An existence and uniqueness result for isometric immersions with little regularity, Rev. Roum. Math. Pures Appl., 53 (2008), 555--565 (invited paper, special volume dedicated to P.G. Ciarlet's 70th birthday).


• [T5] M. Szopos. On the recovery and continuity of a submanifold with boundary, Analysis and Applications, 3 (2005), 119--143.


• [T4] S. Mardare, M. Szopos. Linear and nonlinear Korn inequalities on curves in $\mathbb{R}^3$, Analysis and Applications, 3 (2005), 251--270.


• [T3] M. Szopos. On the recovery of a curve isometrically immersed in ${\mathbb E}^n$, Chinese Annals of Mathematics Ser. B, 25 (2004), 507--522.


• [T2] M. Szopos. On the recovery and continuity of a submanifold with boundary in higher dimensions, C.R. Acad. Sci. Paris Sér. I, 339 (2004), 265--270.


• [T1] M. Szopos. On the recovery of a curve isometrically immersed in a Euclidean space, C.R. Acad. Sci. Paris Sér. I, 338 (2004), 447--452.

Other Publications

• G. Guidoboni, V. Huxley, S. Lapin, M. Szopos , L. Sala, M. Zaid. A SQuaRE With a Lot of Heart. Exploring an Intersection of Math and Cardiology. American Institute of Mathematics Newsletter, pp. 17-18 (2024).


• C. Prud'homme, P. Helluy, M. Maumy-Bertrand, C. Caldini-Queiros, M. Szopos, V. Chabannes. Cemosis: Centre de Modélisation et de Simulation de Strasbourg. Matapli, 115 (2018).


• A. Rousseau, M. Szopos. Calendrier mathématique 2017 - Un défi quotidien : Les modèles de fluides.


• E. Frénod, E. Maitre, A. Rousseau, S. Salmon, M. Szopos. guest-editors of a special issue of ESAIM ProcS entitled CEMRACS 2015: Coupling multi-physics models involving fluids Editorial: Foreword to the proceedings of Cemracs 2015. ESAIM: ProcS 55 (2016), I-II.


• V. Chabannes, M. Ismail, V. Huber, C. Prud'homme, M. Szopos. Calcul haute performance pour la simulation d'écoulements sanguins dans des géométries complexes. HPC Today, No. 1, Vol. 7 (2013), 62--63.