`a`
Mathematical Biosciences and Engineering (MBE)
 

Flow optimization in vascular networks
Pages: 607 - 624, Issue 3, June 2017

doi:10.3934/mbe.2017035      Abstract        References        Full text (1446.2K)           Related Articles

Radu C. Cascaval - Department of Mathematics, University of Colorado Colorado Springs, Colorado Springs, CO 80919, United States (email)
Ciro D'Apice - Dipartimento di Ingegneria dell'Informazione ed Elettrica e Matematica Applicata, Universita degli Studi di Salerno, Fisciano (SA), 84084, Italy (email)
Maria Pia D'Arienzo - Dipartimento di Ingegneria dell'Informazione ed Elettrica e Matematica Applicata, Universita degli Studi di Salerno, Fisciano (SA), 84084, Italy (email)
Rosanna Manzo - Dipartimento di Ingegneria dell'Informazione ed Elettrica e Matematica Applicata, Universita degli Studi di Salerno, Fisciano (SA), 84084, Italy (email)

1 J. Alastruey, A. W. Khir, K. S. Matthys, P. Segers, S. J. Sherwin, P. R. Verdonck, K. H. Parker and J. Peir, Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vivo measurements, J. Biomech., 44 (2011), 2250-2258.
2 J. Alastruey, K. H. Parker, J. Peiro and S. J. Sherwin, Analysing the pattern of pulse waves in arterial networks: a time-domain study, J. Eng. Math., 64 (2009), 331-351.       
3 J. Alastruey, Numerical Modelling of Pulse Wave Propagation in the Cardiovascular System: Development, Validation and Clinical Applications, PhD Thesis, Imperial College London, 2007.
4 J. J. Batzel, F. Kappel, D. Schneditz and H. T. Tran, Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control, SIAM, Philadelphia, PA, 2007.       
5 S. Canic, C. J. Hartley, D. Rosenstrauch, J. Tambaca, G. Guidoboni and A. Mikelic, Blood flow in compliant arteries: An effective viscoelastic reduced model, numerics and experimental validation, Annals of Biomed. Eng., 34 (2006), 575-592.
6 R. C. Cascaval, A Boussinesq model for pressure and flow velocity waves in arterial segments, Math. Comp. Simulation, 82 (2012), 1047-1055.       
7 R. C. Cascaval, C. D'Apice, M. P. D'Arienzo and R. Manzo, Boundary control for an arterial system, J. Fluid Flow, Heat and Mass Transfer, 3 (2016), 25-33.
8 Q. Chen, L. Jiang, C. Li, D. Hu, J.-W. Bu, D. Cai and J.-L. Du, Haemodynamics-driven developmental pruning of brain vasculature in zebrafish, PLoS Biol., 10 (2012), e1001374.
9 Y. Cheng and C. W. Shu, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher oder derivatives, Mathematics of Computation, 77 (2008), 699-730.       
10 C. D'Apice, R. Manzo and B. Piccoli, A fluid dynamic model for telecommunication networks with sources and destinations, SIAM Journal on Applied Mathematics, 68 (2008), 981-1003.       
11 C. D'Apice, R. Manzo and B. Piccoli, Modelling supply networks with partial differential equations, Quarterly of Applied Mathematics, 67 (2009), 419-440.       
12 C. D'Apice, R. Manzo and B. Piccoli, Optimal input flows for a PDE-ODE model of supply chains, Communications in Mathematical Sciences, 10 (2012), 1225-1240.       
13 C. D'Apice, R. Manzo and B. Piccoli, Numerical schemeas for the optimal input flow of a supply-chain, SIAM Journal of Numerical Analysis (SINUM), 51 (2013), 2634-2650.       
14 L. Formaggia, D. Lamponi and A. Quarteroni, One-dimensional models for blood flow in arteries, J. Eng. Math., 47 (2003), 251-276.       
15 L. Formaggia, D. Lamponi, M. Tuveri and A. Veneziani, Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart, Comp. Meth. Biomech. Biomed. Eng., 9 (2006), 273-288.
16 L. Formaggia, A. Quarteroni and A. Veneziani, The circulatory system: From case studies to mathematical modeling, in Complex Systems in Biomedicine, (eds. A. Quarteroni, L. Formaggia, A. Veneziani), Springer Verlag, (2006), 243-287.       
17 R. M. Kleigman et al, Nelson Textbook of Pediatrics, 19th ed., Saunders (2011).
18 M. Kumada, T. Azuma and K. Matsuda, The cardiac output-heart rate relationship under different conditions, Jpn. J. Physiol., 17 (1967), 538-555.
19 R. Manzo, B. Piccoli and R. Rarità, Optimal distribution of traffic flows at junctions in emergency cases, European Journal of Applied Mathematics, 23 (2012), 515-535.       
20 A. Manzoni, Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics, PhD Thesis, Ecole Polytechnique Federale de Lausanne, 2011.
21 L. O. Muller and E. F. Toro, A global multi-scale model for the human circulation with emphasis on the venous system, Int. J. Numerical Methods in Biomed Eng, 30 (2014), 681-725.       
22 J. P. Mynard and J. J. Smolich, One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation, Ann Biomed Eng, 44 (2016), 1324-1324.
23 J. T. Ottesen, Modelling of the baroreflex-feedback mechanism with time-delay, J Math Biol, 36 (1997), 41-63.       
24 J. T. Ottesen, M. S. Olufsen and J. K. Larsen, Applied Mathematical Models in Human Physiology, SIAM, Philadelphia, PA, 2004.       
25 C. Pozrikidis, Numerical simulation of blood flow through microvascular capillary networks, Bulletin of Mathematical Biology, 71 (2009), 1520-1541.       
26 A. Quarteroni, A. Manzoni and F. Negri, Reduced Basis Methods for Partial Differential Equations, An Introduction, Springer, 2016.       
27 M. U. Qureshi, G. D. A. Vaughan, C. Sainsbury, M. Johnson, C. S. Peskin, M. S. Olufsen and N. A. Hill, Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation, Biomech Model Mechanobiol, 13 (2014), 1137-1154.
28 P. Reymond, F. Merenda, F. Perren, D. Rüfenacht and N. Stergiopulos, Validation of a one-dimensional model of the systemic arterial tree, Am. J. Physiol. Heart. Circ. Physiol., 297 (2009), H208-H222.
29 S. J. Sherwin, L. Formaggia, J. Peiro and V. Franke, Computational modeling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system, Internat. J. for Numerical Methods in Fluids, 43 (2003), 673-700.       
30 Y. Shi, P. Lawford and R. Hose, Review of zero-D and 1-D models of blood flow in the cardiovascular system, BioMedical Enginnering OnLine, (2011), 10-33.
31 B. N. Steele, D. Valdez-Jasso, M. A. Haider and M. S. Olufsen, Predicting arterial flow and pressure dynamics using a 1D fluid dynamics model with a viscoelastic wall, SIAM Journal on Applied Mathematics, 71 (2011), 1123-1143.       
32 T. Takahashi, Microcirculation in Fractal Branching Networks, Springer Japan, 2014.       
33 F. N. van de Vosse and N. Stergiopulos, Pulse wave propagation in the arterial tree, Annual Review of Fluid Mechanics, 43 (2011), 467-499.       
34 M. Zamir, Hemo-Dynamics, Biological and Medical Physics, Biomedical Engineering. Springer, Cham, 2016.       

Go to top