One Dimensional Modelling

To model a complex arterial or venous network, the use of one-dimensional models (1D) allows to recover a global description of the pressure propagation with a reduced computational effort

The research focused on the numerical discretization of single 1D compartments with different schemes, such as the Taylor-Galerkin method, on the treatment of different mechanical properties, on the study of different vessel laws, on the extension to curve pipes, and on the treatment of bifurcations

The 1D modelling has been applied to different context, e.g. the simulation of the venous system of a human leg and the assisted Fontan procedure,

Arterial network characterized by 55 vessels

Publications:

1. L. Formaggia, D. Lamponi, and A. Quarteroni. One dimensional models for blood flow in
   arteries. Journal of Engineering Mathematics, 47(3/4):251-276, 2003.
2. B.V.R. Kumar, A.Quarteroni, L.Formaggia, and D.Lamponi. On parallel computation of
   blood flow in human arterial network based on 1-D modelling. Computing, 71(4):321-351, 2003.
3. S.J. Sherwin, L. Formaggia, J. Peirò, and V. Franke. Computational modelling of 1D blood
   flow with variable mechanical properties and its application to the simulation of wave propa-
   gation in the human arterial system. Int. Journal Numer. Meth. in Fluids, 43(6-7):673{700,
   2003.
4. D. Amadori, S. Ferrari, and L. Formaggia. Derivation and analysis of a fluid-dynamical model in thin and long elastic vessels. Networks and Heterogeneous Media, 2:99-125, 2007.
5. J. Alastruey, T. Passerini, L. Formaggia, and J Peirò. Physical determinants of the arterial
   pulse waveform: theoretical analysis and estimation using the 1-D formulation. Journal of
   Engineering Mathematics, (on-line):1-19, 2012. doi 10.1007/s10665-012-9555-z.

Thesis

1. Mirabella L., Modelli matematici unidimensionali per il flusso emodinamico in vasi curvi, BSc in Mathematical Engineering – Politecnico di Milano, AA ’03-’04. Advisors: S. Salsa and A. Veneziani
2. Villa U. and Vele S., Modelli 1D per la dinamica del flusso ematico e dei suoi soluti, BSc in Mathematical Engineering – Politecnico di Milano, AA ’04-’05. Advisor: A. Veneziani
3. De Luca M., Modellazione matematico-numerica del Circolo di Willis, – MSc in Biomedical engineering – Politecnico di Milano, AA ’04-’05. Advisor: A. Veneziani
4. Costa A., Modellazione numerica di distretti venosi a partire da modelli matematici monodimensionali – MSc in Biomedical engineering – Politecnico di Milano, AA ’05-’06. Advisor: A. Veneziani
5. Galeazzi A, Modellazione matematica del sistema venoso delle gambe umane, BSc in Mathematical Engineering – Politecnico di Milano, AA ’07-’08. Advisors: L. Formaggia and C. Vergara
6. Bugada A, Modellazione 1D di vasi sanguigni con capillarita’, BSc in Mathematical Engineering – Politecnico di Milano, AA ’08-’09. Advisors: L. Formaggia and C. Vergara
7. Haile M. and Beccaria M., Modellazione matematica numerica dell operazione Fontan assistita, BSc in Mathematical Engineering – Politecnico di Milano, AA ’08-’09. Advisors: L. Formaggia and C. Vergara
8. Giacomini M. and Benincà E., Approssimazione numerica del problema del flusso sanguigno in una rete di arterie monodimensionali, BSc in Mathematical Engineering- Politecnico di Milano, AA ’08-’09. Advisors: L. Formaggia
9. Sandrini G., Modellazione matematica del sistema venoso degli arti inferiori, BSc in Mathematical Engineering – Politecnico di Milano, AA ’08-’09. Advisors: L. Formaggia and C. Vergara
10. Fiorini C. and Gasperoni F., Modellazione matematico-numerica del sistema venoso cerebrale e degli arti inferiori, BSc in Mathematical Engineering, AA ’12-’13. Advisors: L. Formaggia and C. Vergara
11. Melani A., Adjoint-based parameter estimation in human vascular one dimensional models, PhD thesis, school of Mathematical Models and Methods in Engineering, Dipartimento di Matematica, Politecnico di Milano, 2013.
    Advisors: L. Formaggia and F. Nobile