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PRIN 2022 project: Mathematical models for viscoelastic biological matter

The increased availability of experimental data on the mechanics of cells and tissues has stimulated the emergence of the field of mechanobiology, in which mathematics and mechanics are combined to enhance our understanding of biological materials and of the processes involved in physiological activities. The development of mathematical models for such complex systems is challenging, but the possible outcomes in terms of our capability to diagnose and treat pathological conditions provide a strong motivation for pursuing this research direction.

The present project focuses on continuum mechanical models and on a careful analysis of their mathematical properties, with particular emphasis on the description of activation processes. These are important for the control of any physiological activity, as they bring to life what would otherwise be a passive aggregate of heterogeneous substances. Among the many active elements of the human body, we restrict attention to skeletal muscles and neuronal cells, as they feature a rich phenomenology.

The planned research includes both applied and theoretical aspects. On the practical side, its outcomes can open new possibilities in the context of digital twins for personalized medicine. On the mathematical side, a new class of models can stimulate studies of broad interest in continuum mechanics and analysis.

Research Units

Unversità degli Studi di Padova

Giulio G. Giusteri (National Coordinator), Sara Galasso (Postdoc), Silvia Paparini (Postdoc), Francesca Berlinghieri (PhD student)

Università Cattolica del Sacro Cuore

Giulia Giantesio (Local Coordinator), Alessandro Musesti, Alfredo Marzocchi, Francesco Ballarin, Alberto Girelli (Postdoc)

Politecnico di Milano

Pasquale Ciarletta (Local Coordinator), Former Local Coordinator: Davide Riccobelli

Workshops

  • Mechanics of soft, heterogeneous, and biological materials: state of the art and perspectives of the Italian Scientific Community, Bari, February 15-17, 2024
  • Mechanics of soft, heterogeneous, and biological materials: state of the art and perspectives of the Italian Scientific Community 2, Modena, February 20-21, 2025
  • Mathematics and Mechanics of Biological Tissues, Padova, June 16-18, 2025

    Publications

  • M. A. H Alrashdi, G. G. Giusteri. Evolution of local relaxed states and the modeling of viscoelastic fluids, Phys. Fluids 36, 093129 (2024) doi:10.1063/5.0224019.
  • D. Riccobelli, P. Ciarletta, G. Vitale, C. Maurini, L. Truskinovsky. Elastic instability behind brittle fracture, Phys. Rev. Lett., 132(24), 248202 (2024), doi:10.1103/PhysRevLett.132.248202
  • N. A. Barnafi, N. F. Regazzoni, D. Riccobelli. Reconstructing relaxed configurations in elastic bodies: Mathematical formulations and numerical methods for cardiac modeling, Comput. Methods Appl. Mech. Eng., 423, 116845 (2024), doi:10.1016/j.cma.2024.116845
  • M. Magri, D. Riccobelli. Modelling of initially stressed solids: structure of the energy density in the incompressible limit, SIAM J. Appl. Math. 84(6), 2342-2364 (2024), doi:10.1137/24M1670226
  • A. Girelli, G. Giantesio, A. Musesti, R. Penta. Multiscale homogenization for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymph node, Royal Society Open Science, 11(7), 231983 (2024) doi:10.1098/rsos.231983
  • A. Girelli, G. Giantesio, A. Musesti and R. Penta. Multiscale computational analysis of the steady fluid flow through a lymph node, BMMB, Vol. 23, pp 2005–2023 (2024). doi:10.1007/s10237-024-01879-7
  • G. Ciampa, G. G. Giusteri, A. G. Soggiu. Viscoelasticity, logarithmic stresses, and tensorial transport equations, Math. Meth. Appl. Sci. 48(3), 2934-2953 (2025) doi:10.1002/mma.10469.
  • A. Girelli. A quasilinear hyperbolic one-dimensional model of the lymph flow through a lymphangion with valve dynamics and a contractile wall, CMBBE. doi:10.1080/10255842.2024.2399769
  • G. Giantesio, A. Musesti. On the Modeling of Active Deformation in Biological Transversely Isotropic Materials, Journal of Elasticity, 157(1), 10 (2025) doi:10.1007/s10659-024-10101-9
  • S. Paparini, G. G. Giusteri, L. A. Mihai. Shape instabilities driven by topological defects in nematic polymer networks, J. Elast. 157, 69 (2025), doi:10.1007/s10659-025-10160-6
  • S. Galasso, G. G. Giusteri. Adapted and objective Voigt representations in anisotropic nonlinear elasticity, Math. Mech. Complex Syst. 13(3), 253-273 (2025), doi:10.2140/memocs.2025.13.253
  • F. Magni, D. Riccobelli. Elastic Plateau-Rayleigh instability in soft cylinders: Surface elasticity and periodic beading, J. Mech. Phys. Solids 203, 106258 (2025), doi:10.1016/j.jmps.2025.106258
  • D. Cerrone, D. Riccobelli, S. Gazzoni, P. Vitullo, F. Ballarin, J. Falco, F. Acerbi, A. Manzoni, P. Zunino, P. Ciarletta. Patient-specific prediction of glioblastoma growth via reduced order modeling and neural networks, Mathematical Biosciences, 387 (2025), 109468, doi:10.1016/j.mbs.2025.109468
  • S. Rathore, P. C. Africa, F. Ballarin, F. Pichi, M. Girfoglio, G. Rozza. Projection-based reduced order modelling for unsteady parametrized optimal control problems in 3D cardiovascular flows, Computer Methods and Programs in Biomedicine, 269, 108813 (2025) doi:10.1016/j.cmpb.2025.108813
  • V. Pederzoli, M. Corti, D. Riccobelli, P. F. Antonietti. A coupled mathematical and numerical model for protein spreading and tissue atrophy applied to Alzheimer's disease, Comp. Meth. App. Mech. Eng., 444, 118118 (2025), doi:10.1016/j.cma.2025.118118
  • G. Giantesio et al. Thermal Convection in a Higher Velocity Gradient and Higher Temperature Gradient Fluid, J. Math. Fluid Mech. 27, 47 (2025), 10.1007/s00021-025-00950-2
  • G. Giantesio, A. Girelli, C. Lonati, A. Marzocchi, A. Musesti, and B. Straughan. Thermal Convection in a Sixth-Order Generalized Navier-Stokes Fluid, Studies in Applied Mathematics 155, no. 2 (2025), doi:10.1111/sapm.70099
  • D. Riccobelli. Surface tension-driven boundary growth in tumour spheroids, Interface Focus, 15(2), 20240035 (2025), doi:10.1098/rsfs.2024.0035