No Access

WAVE PROPAGATION IN A 1D FLUID DYNAMICS MODEL USING PRESSURE-AREA MEASUREMENTS FROM OVINE ARTERIES

CHRISTINA BATTISTA

Department of Mathematics, North Carolina State University, 2311 Stinson Drive Raleigh, North Carolina 27695, USA

Search for more papers by this author

DANIEL BIA

Department of Physiology, Universidad de la Republica, Montevideo, Uruguay

Search for more papers by this author

YANINA ZÓCALO GERMÁN

Department of Physiology, Universidad de la Republica, Montevideo, Uruguay

Search for more papers by this author

RICARDO L. ARMENTANO

Department of Physiology, Universidad de la Republica, Montevideo, Uruguay

Search for more papers by this author

MANSOOR A. HAIDER

Department of Mathematics, North Carolina State University, 2311 Stinson Drive Raleigh, North Carolina 27695, USA

Search for more papers by this author

, and

METTE S. OLUFSEN

Department of Mathematics, North Carolina State University, 2311 Stinson Drive Raleigh, North Carolina 27695, USA

E-mail Address: msolufse@ncsu.edu

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S021951941650007XCited by:7 (Source: Crossref)

Abstract

This study considers a 1D fluid dynamics arterial network model with 14 vessels developed to assimilate ex vivo 0D temporal data for pressure-area dynamics in individual vessel segments from 11 male Merino sheep. A 0D model was used to estimate vessel wall parameters in a two-parameter elastic model and a four-parameter Kelvin viscoelastic model. This was done using nonlinear optimization minimizing the least squares error between model predictions and measured cross-sectional areas. Subsequently, estimated values for elastic stiffness and unstressed area were related to construct a nonlinear relationship. This relation was used in the network model. A 1D single vessel model of the aorta was then developed and used to estimate the inflow profile and parameters for total resistance and compliance for the downstream network and to demonstrate effects of incorporating viscoelasticity in the arterial wall. Lastly, the extent to which vessel wall parameters estimated from ex vivo data can be used to realistically simulate pressure and area in a vessel network was evaluated. Elastic wall parameters in the network simulations were found to yield pressure-area relationships across all vessel locations and sheep that were in ranges comparable to those in the ex vivo data.

Keywords:

AMSC: 76D05, 76Z05, 35Q30, 92C35, 92B05, 92C10

References

1. H Do, A Owida and Y Morsi, Intimal hyperplasia and wall shear in arterial bypass y-grafting and consequence grafting: A numerical study, J Mech Med Biol 14 (3) (2014) 1450044–1450079. Link, Web of Science, Google Scholar
2. Y Morsi, A Owida, H Do, M Arefin and X Wang, Graft-artery junctions: Design optimization and cad development, Methods Mol Biol 868 (2012) 269–287. Google Scholar
3. H Do, A Owida, W Yang and Y Morsi, Numerical simulation of the haemodynamics in end-to-side anastomoses, Int J Numer Methods Fluids 67 (5) (2011) 638–650. Web of Science, Google Scholar
4. I Freshwater, Y Morsi and T Lai, The effect of angle on wall shear stresses in a lima to lad anastomosis: Numerical modelling of pulsatile flow, Proc Inst Mech Eng [H] 220 (7) (2006) 743–757. Web of Science, Google Scholar
5. U Quinn, L Tomlinson and J Cockcroft, Arterial stiffness, JRSM Cardiovasc Disease 1 (18) (2012) 1–8. Google Scholar
6. W Boron and E Boulpaep, eds., Medical Physiology: A Cellular and Molecular Approach (Saunders/Elsevier, Philadelphia, PA, 2009). Google Scholar
7. W Nichols and M O’Rourke, Properties of the Arterial Wall (Edward Arnold, London, UK, 2005). Google Scholar
8. R Armentano, J Barra, J Levenson, A Simon and R Pichel, Arterial wall mechanics in conscious dogs. assessment of viscous, intertial, and elastic moduli to characterize aortic wall behavior, Circ Res 76 (1995) 468–478. Web of Science, Google Scholar
9. A Quarteroni, M Tuveri and A Veneziani, Computational vascular fluid dynamics: Problems, models, and methods, Comput Vis Sci 2 (2000) 163–197. Google Scholar
10. J Cebral, P Yim, R Lohner, O Soto and P Choyke, Blood flow modeling in carotid arteries with computational fluid dynamics and mr imaging, Acad Radiol 9 (2002) 1286–1299. Web of Science, Google Scholar
11. M Olufsen, C Peskin, W Kim, E Pederson, A Nadim and J Larsen, Numerical simulation and experimental validationg of blood flow in arteries with structured tree outflow conditions, Ann Biomed Eng 28 (11) (2000) 1281–1299. Web of Science, Google Scholar
12. C Taylor and M Draney, Experimental and computational methods in cardiovascular fluid mechanics, Ann Rev Fluid Mech 36 (2006) 197–231. Web of Science, Google Scholar
13. C Smith, On the introduction of viscoelasticity into one-dimensional models of arterial blood flow, Eng Phys Astron 43 (1982) 1286–1299. Google Scholar
14. S Čanić, C Hartley, D Rosenstrauch, J Tambača, G Guidoboni and A Mikelić, Blood flow in compliant arteries: An effective viscoelastic reduced model, numerics, and experimental validation, Ann Biomed Eng 34 (2006) 575–592. Web of Science, Google Scholar
15. B Steele, D Valdez-Jasso, M Haider and M Olufsen, Predicting arterial flow and pressure dynamics using a 1d fluid dynamics model with a viscoelastic wall, SIAM J Appl Math 71 (4) (2011) 1123–1143. Web of Science, Google Scholar
16. R Raghu, I Vignon-Clementel, C Figueroa and C Taylor, Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow, J Biomech Eng 133 (2011) 081003. Web of Science, Google Scholar
17. D Bessems, C Giannopapa, M Rutten and F van de Vosse, Experiment validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels, J Biomech 41 (2008) 284–291. Web of Science, Google Scholar
18. R Reymond, F Merena, 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. Web of Science, Google Scholar
19. A Noordergraaf, Physical Basis of Ballistocardiography (Excelsior, The Netherlands, 1956). Google Scholar
20. N Westerhof, F Bosman, C De Vries and A Noordergraaf, Analog studies of the human systemic arterial tree, J Biomech 2 (1969) 121–143. Web of Science, Google Scholar
21. N Stergiopulos, D Young and T Rogge, Computer simulation of arterial flow with applications to arterial and aortic stenoses, J Biomech 25 (12) (1992) 1477–1488. Web of Science, Google Scholar
22. P Mangell, T Länne, B Sonesson, F Hansen and D Bergqvist, Regional differences in mechanical properties between major arteries–an experimental study in sheep, Eur J Vasc Endovasc Surg 12 (1996) 189–195. Web of Science, Google Scholar
23. T Länne, F Hansen, P Mangell and B Sonesson, Differences in mechanical properties of the common carotid artery and abdominal aorta in healthy males, J Vasc Surg 20 (1994) 218–225. Web of Science, Google Scholar
24. J Zhao, J Day, Y Yuan and H Gregersen, Regional arterial stress-strain distributions referenced to the zero-stress state in the rat, Am J Physiol Heart Circ Physiol 282 (2002) H622–H629. Web of Science, Google Scholar
25. G Kassab, Biomechanics of the cardiovascular system: The aorta as an illustory example, J R Soc Interface 3 (2006) 719–740. Web of Science, Google Scholar
26. D Valdez-Jasso, D Bia, Y Zócalo, R Armentano, M Haider and M Olufsen, Linear and nonlinear viscoelastic modeling of aorta and carotid pressure-area dynamics under in vivo and ex vivo conditions, Ann Biomed Eng 39 (5) (2011) 1438–1456. Web of Science, Google Scholar
27. J Grotberg and O Jensen, Biofluid mechanics in flexible tubes, Ann Rev Fluid Mech 36 (2004) 121–147. Web of Science, Google Scholar
28. J Alastruey, T Passerini, L Formaggia and J Peiró, Physical determining factors of the arterial pulse waveform: Theoretical analysis and calculation using the 1-d formulation, J Eng Math 77 (2012) 19–37. Web of Science, Google Scholar
29. E Kung, A Les, C Figueroa, F Medina, K Arcaute, R Wicker, M McConnell and C Taylor, In vitro validation of finite element analysis of blood flow in deformable models, Ann Biomed Eng 39 (7) (2011) 1947–1960. Web of Science, Google Scholar
30. N Williams, Ø Wind-Willassen, R Program, J Mehlsen, J Ottesen and M Olufsen, Patient-specific modelling of head-up tilt, Math Med Bio (2013). Web of Science, Google Scholar
31. USNR Council, Guide for the Care and Use of Laboratory Animals (The National Academies Press, Washington, DC, 1996). Google Scholar
32. D Valdez-Jasso, M Haider, H Banks, D Bia, Y Zócalo, R Armentano and M Olufsen, Analysis of viscoelastic wall properties in ovine arteries, IEEE Trans on Biomed Eng 56 (2009) 210–219. Web of Science, Google Scholar
33. Y Fung, Biomechanics: Mechanical Properties of Living Tissues, 2nd edn. (Springer, 1993). Google Scholar
34. Y Fung, Biomechanics: Circulation, 2nd edn. (Springer, 1996). Google Scholar
35. M Olufsen, Modeling the arterial system with reference to an anesthesia simulator, PhD thesis, Universitas Roskildensis, 1998. Google Scholar
36. J Smith and J Kampine, Circulatory Physiology: The Essentials, 3rd edn. (Williams & Wilkins, 1990). Google Scholar
37. R Klabunde, Cardiovascular Physiology Concepts, 2nd edn. (Williams & Wilkins, MD, Baltimore, 2012). Google Scholar
38. G Coates, H O’Brodovich, A Jefferies and G Gray, Effects of exercise on lung lymph flow in sheep and goats during normoxia and hypoxia, J Clin Invest 74 (1984) 133–141. Web of Science, Google Scholar
39. M Olufsen, A structured tree outflow condition for blood flow in the larger systemic arteries, Am J Physiol 276 (1999) H257–H268. Web of Science, Google Scholar
40. T Hughes, L Franca and G Hulbert, A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations*, Comp Methods Appl Mech Eng 73 (1989) 173–189. Web of Science, Google Scholar
41. J Wan, B Steele, S Spicer, S Strohband, G Feijóo, T Hughes and C Taylor, A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease, Comput Methods Biomech Biomed Eng 5 (3) (2002) 195–206. Google Scholar
42. K DeVault, P Gremaud, V Novak, M Olufsen, G Vernières and P Zhao, Blood flow in the circle of willis: Modeling and calibration, Multiscale Model Simul 7 (2008) 888–909. Web of Science, Google Scholar
43. J Alastruey, K Parker, J Peiró and S Sherwin, Lumped parameter outflow models for 1-d blood flow simulations: Effect on pulse waves and parameter estimation, Commun Comput Phys 4 (2008) 317–336. Web of Science, Google Scholar
44. P Molino, C Cerutti, C Julien, G Cuisinaud, M Gustin and C Paultre, Beat-to-beat estimation of windkessel model parameters in conscious rats, Am J Physiol Heart Circ Physiol 274 (1998) H171–H177. Web of Science, Google Scholar
45. Y Shim, A Pasipoularides, C Straley, T Hampton, P Soto, C Owen, J Davis and D Glower, Arterial windkessel parameter estimation: A new time-domain method, Ann Biomed Eng 22 (1994) 66–77. Web of Science, Google Scholar
46. M Ismail, W Wall and M Gee, Adjoint-based inverse analysis of windkessel parameters for patient-specific vascular models, J Comput Phys 244 (2013) 113–130. Web of Science, Google Scholar
47. C Lucas, R Benson, B Wilcox and G Henry, Comparison of time domain algorithms for estimating aortic characteristic impedance in humans, IEEE Trans Biomed Eng 35 (1988) 62–68. Web of Science, Google Scholar
48. J Raines, M Jaffrin and A Shapiro, A computer simulation of arterial dynamics in the human leg, J Biomechanics 7 (1974) 77–91. Web of Science, Google Scholar
49. D McDonald, Blood Flow in Arteries, 2nd edn. (Edward Arnold, London, UK, 1974). Google Scholar
50. N Xiao, J Alastruey and C Figueroa, A systematic comparison between 1-d and 3-d hemodynamics in compliant arterial models, Int J Numer Methods Biomed Eng 30 (2013) 204–231. Web of Science, Google Scholar
51. J Alastruey, A Hunt and P Weinberg, Novel wave intensity analysis of arterial pulse wave propagation accounting for peripheral reflections, Int J Numer Methods Biomed Eng 30 (2014) 249–279. Web of Science, Google Scholar
52. M Anliker, R Rockwell and E Ogden, Nonlinear analysis of flow pulses and shock waves in arteries, Angew Math Phys 22 (2) (1971) 217–246. Web of Science, Google Scholar
53. P Segers, E Rietzschel, M De Buyzere, N Stergiopulos, N Westerhof, L Van Bortel, T Gillebert and P Verdonck, Three- and four-element windkessel models: Assessment of their fitting performance in a large cohort of healthy middle-aged individuals, Proc Inst Mech Eng [H] 222 (2008) 417–428. Web of Science, Google Scholar
54. F van de Vosse and N Stergiopulos, Pulse wave propagation in the arterial tree, Annu Rev Fluid Mech 43 (2011) 467–499. Web of Science, Google Scholar
55. L Ellwein, Cardiovascular and respiratory regulation, modeling and parameter estimation, PhD thesis, Department of Mathematics, North Carolina State University, 2008. Google Scholar
56. A Guyton, T Coleman and H Granger, Circulation: Overall regulation, Annu Rev Physiol 34 (1972) 13–46. Web of Science, Google Scholar
57. J Li, T Cui and G Drzewiecki, A nonlinear model of the arterial system incorporating a pressure-dependent compliance, IEEE Trans Biomed Eng 37 (1990) 673–678. Web of Science, Google Scholar
58. A Cappello, G Gnudi and C Lamberti, Identification of the three-element windkessel model incorporating a pressure-dependent compliance, Ann Biomed Eng 23 (1995) 164–177. Web of Science, Google Scholar
59. I Vignon-Clementel, C Figueroa, K Jansen and C Taylor, Outflow boundary conditions for 3d simulations of non-periodic blood flow and pressure fields in deformable arteries, Comput Methods Biomech Biomed Eng 13 (2010) 625–640. Web of Science, Google Scholar
60. P Moireau, C Bertoglio, N Xiao, C Figueroa, C Taylor, D Chapelle and J-F Gerbeau, Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data, Biomech Model Mechanobiol 12 (2013) 475–496. Web of Science, Google Scholar
61. L Grinberg, E Cheever, T Anor, J Madsen and G Karniadakis, Modeling blood flow circulation in intracranial arterial networks: A comparative 3d/1d simulation study, Ann Biomed Eng (2010). Web of Science, Google Scholar
62. R Reymond, O Vardoulis and N Stergiopulos, Generic and patient-specific models of the arterial tree, J Clin Monit Comput 26 (2012) 375–382. Web of Science, Google Scholar
63. A Benim, A Nahavandi, A Assmann, D Schubert, P Feindt and S Suh, Simulation of blood flow in human aorta with emphasis on outlet boundary conditions, App Math Model 35 (2011) 3175–3188. Web of Science, Google Scholar