A model of optimal dosing of antibiotic treatment in biofilm
Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population
2014, 11(3): 523-546. doi: 10.3934/mbe.2014.11.523
Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model
Giovanna Guidoboni 1, , Alon Harris 2, , Lucia Carichino 1, , Yoel Arieli 3, and Brent A. Siesky 4,
Department of Mathematical Sciences, Indiana University - Purdue University at Indianapolis, Indianapolis, IN, United States, United States
Department of Ophthalmology, Department of Cellular & Integrative Physiology, Eugene and Marilyn Glick Eye Institute, Indiana University School of Medicine, Indianapolis, IN, United States
Department of Electro Optics, Jerusalem College of Technology, Jerusalem, Israel
Department of Ophthalmology, Eugene and Marilyn Glick Eye Institute, Indiana University School of Medicine, Indianapolis, IN, United States
Received May 2012 Revised August 2013 Published January 2014
Retinal hemodynamics plays a crucial role in the pathophysiology of several ocular diseases. There are clear evidences that the hemodynamics of the central retinal artery (CRA) is strongly affected by the level of intraocular pressure (IOP), which is the pressure inside the eye globe. However, the mechanisms through which this occurs are still elusive. The main goal of this paper is to develop a mathematical model that combines the mechanical action of IOP and the blood flow in the CRA to elucidate the mechanisms through which IOP elevation affects the CRA hemodynamics. Our model suggests that the development of radial compressive regions in the lamina cribrosa (a collagen structure in the optic nerve pierced by the CRA approximately in its center) might be responsible for the clinically-observed blood velocity reduction in the CRA following IOP elevation. The predictions of the mathematical model are in very good agreement with experimental and clinical data. Our model also identifies radius and thickness of the lamina cribrosa as major factors affecting the IOP-CRA relationship, suggesting that anatomical differences among individuals might lead to different hemodynamic responses to IOP elevation.
Keywords: lamina cribrosa., fluid-structure interaction, central retinal artery, intraocular pressure, Ocular blood flow.
Mathematics Subject Classification: Primary: 76Z05, 74F10, 74L15; Secondary: 76Z0.
Citation: Giovanna Guidoboni, Alon Harris, Lucia Carichino, Yoel Arieli, Brent A. Siesky. Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 523-546. doi: 10.3934/mbe.2014.11.523
Y. Aguomi, G. P. Sharpe, D. H. Hutchison, M. T.Nicolela, P. H.Artes and B. C. Chauhan, Laminar and pre laminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls, Ophthalmology, 118 (2011), 52-59. Google Scholar
R. L. Armentano, J. G. Barra, J. Levenson, A. Simon and R. H. Pichel, Arterial wall mechanics in conscious dogs: Assessment of viscous, inertial, and elastic moduli to characterize aortic wall behavior, Circ. Res., 76 (1995), 468-478. doi: 10.1161/01.RES.76.3.468. Google Scholar
D. Badeanu, M. Ritt, J. Harazny, J. Heckmann, R. E. Schmieder and G. Michelson, Wall-to-lumen ratio of retinal arterioles and arteriole-to-venule ratio of retinal vessels in patients with cerebrovascular damage, Invest. Ophthalmol. Vis. Sci., 50 (2009), 4351-4359. Google Scholar
R. R Buhrmann, H. A. Quigley, Y. Barron, S. K. West, M. S. Oliva and B. B. O. Mmbaga, Prevalence of glaucoma in a rural East African population, Invest. Ophthalmol. Vis. Sci., 41 (2000), 40-48. Google Scholar
C. F. Burgoyne, J. C. Downs, A. J. Bellezza, J. K. F. Suh and R. T. Hart, The optic nerve head as a biomechanical structure: A new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage, Prog. Retin. Eye Res., 24 (2005), 39-73. doi: 10.1016/j.preteyeres.2004.06.001. Google Scholar
J. Caprioli and A. L. Coleman, Blood pressure, perfusion pressure, and glaucoma, Am. J. Ophthalmol., 149 (2010), 704-712. doi: 10.1016/j.ajo.2010.01.018. Google Scholar
V. P. Costa, R. Lauande-Pimentel, R. A. Fonseca and L. Magacho, The influence of age, sex, race, refractive error and optic disc parameters on the sensitivity and specificity of scanning laser polarimetry, Acta Ophthalmol. Scand., 82 (2004), 419-425. doi: 10.1111/j.1395-3907.2004.00294.x. Google Scholar
J. E. De León-Ortega, L. M. Sakata, B. E. Monheit, G. Jr McGwin, S. N Arthur and C. A. Girkin, Comparison of diagnostic accuracy of Heidelberg Retina Tomograph II and Heidelberg Retina Tomograph 3 to discriminate glaucomatous and nonglaucomatous eyes, Am. J. Ophthalmol., 144 (2007), 525-532. Google Scholar
H. Dongqi and R. Zeqin, A biomathematical model for pressure-dependent lamina cribrosa behavior, J. Biomech., 32 (1999), 579-584. doi: 10.1016/S0021-9290(99)00025-1. Google Scholar
G. T. Dorner, E. Polska, G. Garhöfer, C. Zawinka, B. Frank and L. Schmetterer, Calculation of the diameter of the central retinal artery from noninvasive measurements in humans, Curr. Eye Res., 25 (2002), 341-345. doi: 10.1076/ceyr.25.6.341.14231. Google Scholar
M. E. Edwards and T. A. Good, Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation, Curr. Eye Res., 23 (2001), 215-225. doi: 10.1076/ceyr.23.3.215.5460. Google Scholar
R. Ehrlich, A. Harris, N. S. Kheradiya, D. M. Winston, T. A. Ciulla and B. Wirostko, Age-related macular degeneration and the aging eye, Clin. Interv. Aging., 3 (2008), 473-482. Google Scholar
O. Findl, K. Strenn, M. Wolzt, R. Menapace, C. Vass, H. G. Eichler and L. Schmetterer, Effects of changes in intraocular pressure on human ocular haemodynamics, Curr. Eye Res., 16 (1997), 1024-1029. doi: 10.1076/ceyr.16.10.1024.9024. Google Scholar
J. Flammer, M. Pache and T. Resink, Vasospasm, its role in the pathogenesis of diseases with particular reference to the eye, Prog. Retin. Eye Res., 20 (2001), 319-349. doi: 10.1016/S1350-9462(00)00028-8. Google Scholar
FreeFem++, version 3.12-0 (2d and 3d), Université Pierre et Marie Curie Laboratoire Jacques-Louis Lions,, , (). Google Scholar
Y. C. Fung, Biomechanics: Circulatio, $2^{nd}$ edition, Springer-Verlag, New York, 1997. Google Scholar
Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, $2^{nd}$ edition, Springer-Verlag, New York, 1993. doi: 10.1115/1.3138285. Google Scholar
P. Ganesan, S. He and H. Xu, Development of an image-based network model of retinal vasculature, Ann. Biomed. Eng., 38 (2010), 1566-1585. doi: 10.1007/s10439-010-9942-4. Google Scholar
P. Ganesan, S. He and H. Xu, Analysis of retinal circulation using an image-based network model of retinal vasculature, Microvasc. Res., 80 (2010), 99-109. doi: 10.1016/j.mvr.2010.02.005. Google Scholar
P. Ganesan, S. He and H. Xu, Development of an image-based model for capillary vasculature of retina, Comput. Methods Programs Biomed., 102 (2011), 35-46. doi: 10.1016/j.cmpb.2010.12.009. Google Scholar
P. Ganesan, S. He and H. Xu, Modelling of pulsatile blood flow in arterial trees of retinal vasculature, Med. Eng. Phys., 33 (2011), 810-823. doi: 10.1016/j.medengphy.2010.10.004. Google Scholar
C. A. Girkin, G. Jr McGwin, S. F. McNeal and J. DeLeon-Ortega, Racial differences in the association between optic disc topography and early glaucoma, Invest. Ophthalmol. Vis. Sci., 44 (2003), 3382-3387. doi: 10.1167/iovs.02-0792. Google Scholar
C. A. Girkin, G. Jr McGwin, C. Long, J. DeLeon-Ortega, C. M. Graf and A. W. Everett, Subjective and objective optic nerve assessment in African Americans and whites, Invest. Ophthalmol. Vis. Sci., 45 (2004), 2272-2278. doi: 10.1167/iovs.03-0996. Google Scholar
C. A. Girkin, G. Jr McGwin, A. Xie and J. E. Deleon-Ortega, Differences in optic disc topography between black and white normal subjects, Ophthalmology, 112 (2005), 33-39. doi: 10.1016/j.ophtha.2004.07.029. Google Scholar
C. A. Girkin, P. A. Sample, J. M. Liebmann, S. Jain, C. Bowd, L. M. Becerra, F. A. Medeiros, L. Racette, K. A. Dirkes and R. N. Weinreb, African Descent and Glaucoma Evaluation Study (ADAGES): II. Ancestry differences in optic disc, retinal nerve fiber layer, and macular structure in healthy subjects, Arch. Ophthalmol., 128 (2010), 541-550. doi: 10.1001/archophthalmol.2010.49. Google Scholar
G. Guidoboni, A. Harris, J.C. Arciero, B.A. Siesky, A. Amireskandari, A.L. Gerber, A.H. Huck, N.J. Kim, S. Cassani and L. Carichino, Mathematical modeling approaches in the study of glaucoma disparities among people of African and European Descents, J. Coupled Syst. Multiscale Dyn., 1(1) (2013), 1-21. Google Scholar
A. Harris, K. Joos, M. Kay, D. Evans, R. Shetty, W. E. Sponsel and B. Martin, Acute IOP elevation with scleral suction: Effects on retrobulbar haemodynamics, Br. J. Ophthalmol., 80 (1996), 1055-1059. doi: 10.1136/bjo.80.12.1055. Google Scholar
A. Harris, C. P. Jonescu-Cuypers, L. Kagemann, T. A. Ciulla and G. K. Krieglstein, Atlas of Ocular Blood Flow. Vascular Anatomy, Pathophysiology, and Metabolism, Elsevier, Philadelphia, 2003. Google Scholar
A. Harris, L. Kagemann, R. Ehrlich, C. Rospigliosi, D. Moore and B. Siesky, Measuring and interpreting ocular blood flow and metabolism in glaucoma, Can. J. Ophthalmol., 43 (2008), 328-336. doi: 10.1139/I08-051. Google Scholar
A. Harris, G. Guidoboni, J.C. Arciero, A. Ameriskandari, L.A. Tobe and B.A. Siesky, Ocular hemodynamics and glaucoma: the role of mathematical modeling, Eur. J. Ophthalmol., 23(2) (2013), 139-146. Google Scholar
S. S. Hayreh, Blood flow in the optic nerve head and factors that may influence it, Prog. Retin. Eye Res., 20 (2001), 595-624. doi: 10.1016/S1350-9462(01)00005-2. Google Scholar
E. M. Hoffmann, L. M. Zangwill, J. G. Crowston and R. N. Weinreb, Optic disk size and glaucoma, Surv. Ophthalmol., 52 (2007), 32-49. doi: 10.1016/j.survophthal.2006.10.002. Google Scholar
I. Januleviciene, R. Ehrlich, B. Siesky, I. Nedzelskiene and A. Harris, Visual function, optic nerve structure, and ocular blood flow parameters after 1 year of glaucoma treatment with fixed combinations, Eur. J. Ophthalmol., 19 (2009), 790-797. Google Scholar
J. B. Jonas, C. Y. Mardin, U. Schlötzer-Schrehardt and G. O. Naumann, Morphometry of the human lamina cribrosa surface, Invest. Ophthalmol. Vis. Sci., 32 (1991), 401-405. Google Scholar
J. B. Jonas and L. Holbach, Central corneal thickness and thickness of the lamina cribrosa in human eyes, Invest. Ophthalmol. Vis. Sci., 46 (2005), 1275-1279. doi: 10.1167/iovs.04-0851. Google Scholar
O. Knight, C. A. Girkin, D. L. Budenz, M. K. Durbin and W. J Feuer, Effect of race, age, and axial length on optic nerve head parameters and retinal nerve fiber layer thickness measured by Cirrus HD-OCT, Arc. Ophthalmol., 130 (2012), 312-318. doi: 10.1001/archopthalmol.2011.1576. Google Scholar
M. C. Leske, A. M. S. Connell, A. P. Schachat and L. Hyman, The Barbados Eye Study: Prevalence of open angle glaucoma, Arc. Ophthalmol., 112 (1994), 821-829. doi: 10.1001/archopht.1994.01090180121046. Google Scholar
M. C. Leske, Open-angle glaucoma - an epidemiologic overview, Ophthalmic Epidemiol., 14 (2007), 166-172. doi: 10.1080/09286580701501931. Google Scholar
M. C. Leske, A. Heijl, L. Hyman, B. Bengtsson, L. Dong and Z. Yang, Predictors of long-term progression in the early manifest glaucoma trial, Ophthalmology, 114 (2007), 1965-1972. doi: 10.1016/j.ophtha.2007.03.016. Google Scholar
A. Mikelic, G. Guidoboni and S. Canic, Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem, Netw. Heterog. Media, 2 (2007), 397-423. doi: 10.3934/nhm.2007.2.397. Google Scholar
D. Moore, A. Harris, D. Wudunn, N. Kheradiya and B. Siesky, Dysfunctional regulation of ocular blood flow: a risk factor for glaucoma? Clin. Ophthalmol., 2 (2008), 849-861. Google Scholar
W. H Morgan, D. Y. Yu, V. A. Alder, S. J. Cringle, R. L. Cooper, P. H. House and I. J. Constable, The correlation between cerebrospinal fluid pressure and retrolaminar tissue pressure, Invest. Ophthalmol. Vis. Sci., 39 (1998), 3236-3242. Google Scholar
W. H Morgan, B. C. Chauhan, D. Y. Yu, S. J. Cringle, V. A. Alder and P. H. House, Optic disc movement with variations in intraocular and cerebrospinal fluid pressure, Invest. Ophthalmol. Vis. Sci., 43 (2002), 1419-1428. Google Scholar
J. Morgan-Davies, N. Taylor, A. R. Hill, P. Aspinall, C. J. O'Brien and A. Azuara-Blanco, Three dimensional analysis of the lamina cribrosa in glaucoma, Br. J. Ophthalmol., 88 (2004), 1299-1304. doi: 10.1136/bjo.2003.036020. Google Scholar
T. Newson and A. El-Sheikh, Mathematical modeling of the biomechanics of the lamina cribrosa under elevated intraocular pressures, J. Biomech. Eng., 128 (2006), 496-504. doi: 10.1115/1.2205372. Google Scholar
R. E. Norman, J. G. Flanagan, S. M. K. Rausch, I. A. Sigal, I. Tertinegg, A. Eilaghi, S. Portnoy, J. G. Sled and C. R. Ethier, Dimensions of the human sclera: Thickness measurement and regional changes with axial length, Exp. Eye Res., 90 (2010), 277-284. doi: 10.1016/j.exer.2009.11.001. Google Scholar
B. Pemp and L. Schmetterer, Ocular blood flow in diabetes and age-related macular degeneration, Can. J. Ophthalmol., 43 (2008), 295-301. doi: 10.1139/I08-049. Google Scholar
D. Poinoosawmy, L. Fontana, J. X. Wu, F. W. Fitzke and R. A. Hitchings, Variation of nerve fibre layer thickness measurements with age and ethnicity by scanning laser polarimetry, Br. J. Ophthalmol., 81 (1997), 350-354. doi: 10.1136/bjo.81.5.350. Google Scholar
C. J. Pournaras, E. Rungger-Brändle, C. E. Riva, S. H. Hardarson and E. Stefansson, Regulation of retinal blood flow in health and disease, Prog. Retin. Eye Res., 27 (2008), 284-330. doi: 10.1016/j.preteyeres.2008.02.002. Google Scholar
A. Quarteroni, M. Tuveri and A. Veneziani, Computational vascular fluid dynamics: Problems, models and methods, Comput. Visual Sci., 2 (2000), 163-197. doi: 10.1007/s007910050039. Google Scholar
L. Racette, M. R. Wilson, L. M. Zangwill, R. N. Weinreb and P. A. Sample, Primary open-angle glaucoma in blacks: A review, Surv. Ophthalmol., 48 (2003), 295-313. doi: 10.1016/S0039-6257(03)00028-6. Google Scholar
L. Racette, C. Boden, S. L. Kleinhandler, C. A. Girkin, J. M. Liebmann, L. M. Zangwill, F. A. Medeiros, C. Bowd, R. N. Weinreb and M. R. Wilson, Differences in visual function and optic nerve structure between healthy eyes of blacks and whites, Arch. Ophthalmol., 123 (2005), 1547-1553. doi: 10.1001/archopht.123.11.1547. Google Scholar
R. Ren, N. Wang, B. Li, L. Li, F. Gao, X. Xu and J. B. Jonas, Lamina cribrosa and peripapillary sclera histomorphometry in normal and advanced glaucomatous Chinese eyes with various axial length, Invest. Ophthalmol. Vis. Sci., 50 (2009), 2175-2184. doi: 10.1167/iovs.07-1429. Google Scholar
M. I. Seider, R. Y. Lee, D. Wang, M. Pekmezci, T. C. Porco and S. C. Lin, Optic disk size variability between African, Asian, white, Hispanic, and Filipino Americans using Heidelberg retinal tomography, J. Glaucoma, 18 (2009), 595-600. doi: 10.1097/IJG.0b013e3181996f05. Google Scholar
I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Finite element modeling of optic nerve head biomechanics, Invest. Ophthalmol. Vis. Sci., 45 (2004), 4378-4387. doi: 10.1167/iovs.04-0133. Google Scholar
I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Predicted extension, compression and shearing of optic nerve head tissues, Exp. Eye Res., 85 (2007), 312-322. doi: 10.1016/j.exer.2007.05.005. Google Scholar
I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry, Biomech. Model. Mechanobiol., 8 (2009), 85-98. doi: 10.1007/s10237-008-0120-7. Google Scholar
I. A. Sigal, H. Yang, M. D. Roberts, J. L. Grimm, C. F. Burgoyne, S. Demirel and J. C. Downs, IOP-induced lamina cribrosa deformation and scleral canal expansion: Independent or related? Invest. Ophthalmol. Vis. Sci., 52 (2011), 9023-9032. doi: 10.1167/iovs.11-8183. Google Scholar
I. A. Sigal, R. A. Bilonick, L. Kagemann, G. Wollstein, H. Ishikawa, J. S. Schuman and J. L. Grimm, The optic nerve head as a robust biomechanical system, Invest. Ophthalmol. Vis. Sci., 53 (2012), 2658-2667. doi: 10.1167/iovs.11-9303. Google Scholar
I. A. Sigal and J. L. Grimm, A few good responses: which mechanical effects of IOP on the ONH to study? Invest. Ophthalmol. Vis. Sci., 53(7) (2012), 4270-4278. doi: 10.1167/iovs.11-8739. Google Scholar
I. A. Sigal, J. G. Flanagan, K. L. Lathrop, I. Tertinegg and R. Bilonick, Human lamina cribrosa insertion and age, Invest. Ophthalmol. Vis. Sci., 53 (2012), 6870-6879. doi: 10.1167/iovs.12-9890. Google Scholar
A. Sommer, J. M. Tielsch, J. Katz, H. A. Quigley, J. D. Gottsch, J. C. Javitt, J. F. Martone, R. M. Royall, K. A. Witt and S. Ezrine, Racial differences in the cause-specific prevalence of blindness in east Baltimore, N. Engl. J. Med., 325 (1991), 1412-1417. doi: 10.1056/NEJM199111143252004. Google Scholar
A. Sommer, Glaucoma risk factors observed in the Baltimore Eye Survey, Curr. Opin. Ophthalmol., 7 (1996), 93-98. doi: 10.1097/00055735-199604000-00016. Google Scholar
T. Takahashi, T. Nagaoka, H. Yanagida, T. Saitoh, A. Kamiya, T. Hein, L. Kuo and A. Yoshida, A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network, J. Biorheol., 23 (2009), 77-86. doi: 10.1007/s12573-009-0012-1. Google Scholar
J. M. Tielsch, A. Sommer, J. Katz, R. M. Royall, H. A. Quigley and J. Javitt, Racial variations in the prevalence of primary open-angle glaucoma: The Baltimore Eye Survey, JAMA, 266 (1991), 369-374. doi: 10.1001/jama.1991.03470030069026. Google Scholar
R. Varma, J. M. Tielsch, H. A. Quigley, S. C. Hilton, J. Katz, G. L. Spaeth and A. Sommer, Race-, age-, gender-, and refractive error-related differences in the normal optic disc, Arch. Ophthalmol., 112 (1994), 1068-1076. doi: 10.1001/archopht.1994.01090200074026. Google Scholar
S. Woo, A. S. Kobayashi, W. A. Schlegel and C. Lawrence, Nonlinear material properties of intact cornea and sclera, Exp. Eye Res., 14 (1972), 29-39. doi: 10.1016/0014-4835(72)90139-X. Google Scholar
J. R. Zelefsky, N. Harizman, R. Mora, E. Ilitchev, C. Tello, R. Ritch and J. M. Liebmann, Assessment of a race-specific normative HRT-III database to differentiate glaucomatous from normal eyes, J. Glaucoma, 15 (2006), 548-551. doi: 10.1097/01.ijg.0000212289.00917.a8. Google Scholar
Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012
Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633
Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluid-structure interaction problem. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 199-220. doi: 10.3934/dcdsb.2008.9.199
Serge Nicaise, Cristina Pignotti. Asymptotic analysis of a simple model of fluid-structure interaction. Networks & Heterogeneous Media, 2008, 3 (4) : 787-813. doi: 10.3934/nhm.2008.3.787
Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete & Continuous Dynamical Systems, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355
George Avalos, Roberto Triggiani. Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability. Evolution Equations & Control Theory, 2013, 2 (4) : 563-598. doi: 10.3934/eect.2013.2.563
B. Wiwatanapataphee, D. Poltem, Yong Hong Wu, Y. Lenbury. Simulation of Pulsatile Flow of Blood in Stenosed Coronary Artery Bypass with Graft. Mathematical Biosciences & Engineering, 2006, 3 (2) : 371-383. doi: 10.3934/mbe.2006.3.371
Daniele Boffi, Lucia Gastaldi, Sebastian Wolf. Higher-order time-stepping schemes for fluid-structure interaction problems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3807-3830. doi: 10.3934/dcdsb.2020229
Andro Mikelić, Giovanna Guidoboni, Sunčica Čanić. Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Networks & Heterogeneous Media, 2007, 2 (3) : 397-423. doi: 10.3934/nhm.2007.2.397
George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817
Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349
Salim Meddahi, David Mora. Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 269-287. doi: 10.3934/dcdss.2016.9.269
Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295-318. doi: 10.3934/mbe.2013.10.295
George Avalos, Thomas J. Clark. A mixed variational formulation for the wellposedness and numerical approximation of a PDE model arising in a 3-D fluid-structure interaction. Evolution Equations & Control Theory, 2014, 3 (4) : 557-578. doi: 10.3934/eect.2014.3.557
Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete & Continuous Dynamical Systems, 2017, 37 (5) : 2315-2373. doi: 10.3934/dcds.2017102
Henry Jacobs, Joris Vankerschaver. Fluid-structure interaction in the Lagrange-Poincaré formalism: The Navier-Stokes and inviscid regimes. Journal of Geometric Mechanics, 2014, 6 (1) : 39-66. doi: 10.3934/jgm.2014.6.39
George Avalos, Roberto Triggiani. Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 417-447. doi: 10.3934/dcdss.2009.2.417
Olivier Delestre, Arthur R. Ghigo, José-Maria Fullana, Pierre-Yves Lagrée. A shallow water with variable pressure model for blood flow simulation. Networks & Heterogeneous Media, 2016, 11 (1) : 69-87. doi: 10.3934/nhm.2016.11.69
Mette S. Olufsen, Ali Nadim. On deriving lumped models for blood flow and pressure in the systemic arteries. Mathematical Biosciences & Engineering, 2004, 1 (1) : 61-80. doi: 10.3934/mbe.2004.1.61
Derek H. Justice, H. Joel Trussell, Mette S. Olufsen. Analysis of Blood Flow Velocity and Pressure Signals using the Multipulse Method. Mathematical Biosciences & Engineering, 2006, 3 (2) : 419-440. doi: 10.3934/mbe.2006.3.419
Giovanna Guidoboni Alon Harris Lucia Carichino Yoel Arieli Brent A. Siesky