On the accuracy of displacement-based wave intensity analysis: Effect of vessel wall viscoelasticity and nonlinearity

English version

Autoři: Jingyi Kang ^aff001; Arian Aghilinejad ^aff001; Niema M. Pahlevan ^aff001
Působiště autorů: Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, United States of America ^aff001; Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America ^aff002
Vyšlo v časopise: PLoS ONE 14(11)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0224390

Souhrn

Recent studies showed that wave intensity analysis (WIA) provides clinically valuable information about local and global cardiovascular function. Wave intensity (WI) is computed as the product of the pressure change and the velocity change during short time intervals. The major limitation of WIA in clinical practice is the need for invasive pressure measurement. Since vessel wall displacement can be measured non-invasively, the usage of WI will be expanded if the vessel wall dilation is used instead of pressure in derivation of WI waveform. Our goal in this study is to investigate the agreement between wall displacement-based WI and the pressure-based WI for different vessel wall models including linear elastic, nonlinear and viscoelastic cases. The arbitrary Eulerian Lagrangian finite element method is employed to solve the coupled fluid-structure interaction (FSI). Our computational models also include two types of vascular disease-related cases with geometrical irregularities, aneurysm and stenosis. Our results show that for vessels with linear elastic wall, the displacement-based WI is almost identical to the pressure-based WI. The existence of vessel irregularities does not impact the accuracy of displacement-based WI. However, in a viscoelastic wall where there is a phase difference between pressure and vessel wall dilation, displacement-based WI deviated from pressure-based WI. The error associated with this phase difference increased nonlinearly with increasing viscosity. This results in a maximum error of 6.8% and 7.13% for a regular viscoelastic vessel wall and an irregular viscoelastic vessel wall, respectively. A separate analysis has also been performed on the agreement of backward and forward running waves extracted from a decomposition of the displacement-based and pressure-based WI. Our findings suggest that displacement-based WI is a reliable method of WIA for large central arteries that do not show viscoelastic behaviors. This can be clinically significant since the required information can be measured non-invasively.

Klíčová slova:

Aneurysms – Aorta – Arteries – Deformation – Fluid flow – Reflection – Stenosis – Viscosity

Zdroje

1. Pahlevan NM, Tavallali P, Rinderknecht DG, Petrasek D, Matthews RV, Hou TY, et al. Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications. Journal of The Royal Society Interface. 2014;11(98):20140617.

2. Milnor WR. Hemodynamics. Cardiac dynamics. 1989.

3. Zambanini A, Cunningham SL, Parker KH, Khir AW, McG. Thom S, Hughes AD. Wave-energy patterns in carotid, brachial, and radial arteries: a noninvasive approach using wave-intensity analysis. American Journal of Physiology-Heart and Circulatory Physiology. 2005;289(1):H270–H6. doi: 10.1152/ajpheart.00636.2003 15722409

4. Parker KH, Jones C. Forward and backward running waves in the arteries: analysis using the method of characteristics. Journal of biomechanical engineering. 1990;112(3):322–6. doi: 10.1115/1.2891191 2214715

5. Parker KH. An introduction to wave intensity analysis. Medical & biological engineering & computing. 2009;47(2):175.

6. Khir A, O'brien A, Gibbs J, Parker K. Determination of wave speed and wave separation in the arteries. Journal of biomechanics. 2001;34(9):1145–55. doi: 10.1016/s0021-9290(01)00076-8 11506785

7. Khir A, Parker K. Wave intensity in the ascending aorta: effects of arterial occlusion. Journal of biomechanics. 2005;38(4):647–55. doi: 10.1016/j.jbiomech.2004.05.039 15713284

8. Niki K, Sugawara M, Chang D, Harada A, Okada T, Sakai R, et al. A new noninvasive measurement system for wave intensity: evaluation of carotid arterial wave intensity and reproducibility. Heart and vessels. 2002;17(1):12–21. doi: 10.1007/s003800200037 12434197

9. Quail MA, Knight DS, Steeden JA, Taelman L, Moledina S, Taylor AM, et al. Noninvasive pulmonary artery wave intensity analysis in pulmonary hypertension. American Journal of Physiology-Heart and Circulatory Physiology. 2015;308(12):H1603–H11. doi: 10.1152/ajpheart.00480.2014 25659483

10. Sun Y-H, Anderson TJ, Parker KH, Tyberg JV. Wave-intensity analysis: a new approach to coronary hemodynamics. Journal of Applied Physiology. 2000;89(4):1636–44. doi: 10.1152/jappl.2000.89.4.1636 11007606

11. Ivar Seldinger S. Catheter replacement of the needle in percutaneous arteriography: a new technique. Acta radiologica. 2008;49(suppl_434):47–52.

12. Feng J, Khir A, editors. Determination of wave intensity in flexible tubes using measured diameter and velocity. 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society; 2007: IEEE.

13. Negoita M, Hughes AD, Parker KH, Khir AW. A method for determining local pulse wave velocity in human ascending aorta from sequential ultrasound measurements of diameter and velocity. Physiological measurement. 2018;39(11):114009. doi: 10.1088/1361-6579/aae8a0 30475745

14. Li Y, Hickson SS, McEniery CM, Wilkinson IB, Khir AW. Stiffening and ventricular–arterial interaction in the ascending aorta using MRI: ageing effects in healthy humans. Journal of hypertension. 2019;37(2):347. doi: 10.1097/HJH.0000000000001886 30645209

15. Raghu R, Vignon-Clementel IE, Figueroa CA, Taylor CA. Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow. Journal of biomechanical engineering. 2011;133(8):081003. doi: 10.1115/1.4004532 21950896

16. Gasser TC, Ogden RW, Holzapfel GA. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of the royal society interface. 2005;3(6):15–35.

17. Fung Y-c. Biomechanics: mechanical properties of living tissues: Springer Science & Business Media; 2013.

18. Valdez-Jasso D, Bia D, Zócalo Y, Armentano RL, Haider MA, Olufsen MS. Linear and nonlinear viscoelastic modeling of aorta and carotid pressure–area dynamics under in vivo and ex vivo conditions. Annals of biomedical engineering. 2011;39(5):1438–56. doi: 10.1007/s10439-010-0236-7 21203846

19. Pahlevan NM, Amlani F, Gorji MH, Hussain F, Gharib M. A physiologically relevant, simple outflow boundary model for truncated vasculature. Annals of biomedical engineering. 2011;39(5):1470–81. doi: 10.1007/s10439-011-0246-0 21240638

20. Peattie RA, Riehle TJ, Bluth EI. Pulsatile flow in fusiform models of abdominal aortic aneurysms: flow fields, velocity patterns and flow-induced wall stresses. Journal of Biomechanical Engineering. 2004;126(4):438–46. doi: 10.1115/1.1784478 15543861

21. Chow JC, Apter JT. Wave propagation in a viscous incompressible fluid contained in flexible viscoelastic tubes. The Journal of the Acoustical Society of America. 1968;44(2):437–43. doi: 10.1121/1.1911100 5665522

22. Keramat A, Tijsseling A, Hou Q, Ahmadi A. Fluid–structure interaction with pipe-wall viscoelasticity during water hammer. Journal of Fluids and Structures. 2012;28:434–55.

23. Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of elasticity and the physical science of solids. 2000;61(1–3):1–48.

24. Bathe K-J, Zhang H, Ji S. Finite element analysis of fluid flows fully coupled with structural interactions. Computers & Structures. 1999;72(1–3):1–16.

25. Middleman S. Transport phenomena in the cardiovascular system: John Wiley & Sons; 1972.

26. ADINA R. ADINA theory and modeling guide–volume III: ADINA CFD & FSI. Watertown, Mass. 2005.

27. Bathe M, Kamm R. A fluid-structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery. Journal of Biomechanical Engineering. 1999;121(4):361–9. doi: 10.1115/1.2798332 10464689

28. Bathe K, Zhang H, Wang M. Finite element analysis of incompressible and compressible fluid flows with free surfaces and structural interactions. Computers & Structures. 1995;56(2–3):193–213.

29. Bathe K-J. Finite element procedures: Klaus-Jurgen Bathe; 2006.

30. Holzapfel GA, Gasser TC, Stadler M. A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis. European Journal of Mechanics-A/Solids. 2002;21(3):441–63.

31. Park S, Schapery R. Methods of interconversion between linear viscoelastic material functions. Part I—A numerical method based on Prony series. International Journal of Solids and Structures. 1999;36(11):1653–75.

32. Matthys KS, Alastruey J, Peiró J, Khir AW, Segers P, Verdonck PR, et al. Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements. Journal of biomechanics. 2007;40(15):3476–86. doi: 10.1016/j.jbiomech.2007.05.027 17640653

33. Pahlevan NM, Gharib M. Aortic wave dynamics and its influence on left ventricular workload. PloS one. 2011;6(8):e23106. doi: 10.1371/journal.pone.0023106 21853075

34. Bessems D, Rutten M, Van De Vosse F. A wave propagation model of blood flow in large vessels using an approximate velocity profile function. Journal of Fluid Mechanics. 2007;580:145–68.

35. Bathe K, Zhang H, Zhang X. Some advances in the analysis of fluid flows. Computers & Structures. 1997;64(5–6):909–30.

36. Segers P, Swillens A, Taelman L, Vierendeels J. Wave reflection leads to over-and underestimation of local wave speed by the PU-and QA-loop methods: theoretical basis and solution to the problem. Physiological measurement. 2014;35(5):847. doi: 10.1088/0967-3334/35/5/847 24710904

37. MacRae JM, Sun Y-H, Isaac DL, Dobson GM, Cheng C-P, Little WC, et al. Wave-intensity analysis: a new approach to left ventricular filling dynamics. Heart and vessels. 1997;12(2):53–9. 9403308

38. Ohte N, Narita H, Sugawara M, Niki K, Okada T, Harada A, et al. Clinical usefulness of carotid arterial wave intensity in assessing left ventricular systolic and early diastolic performance. Heart and vessels. 2003;18(3):107–11. doi: 10.1007/s00380-003-0700-5 12955424

39. Pahlevan NM, Gharib M. Low pulse pressure with high pulsatile external left ventricular power: influence of aortic waves. Journal of biomechanics. 2011;44(11):2083–9. doi: 10.1016/j.jbiomech.2011.05.016 21679951

40. Ernst CB. Abdominal aortic aneurysm. New England Journal of Medicine. 1993;328(16):1167–72. doi: 10.1056/NEJM199304223281607 8455684

41. Ahamed T, Peattie R, Dorfmann L, Cherry Kemmerling E. Pulsatile flow measurements and wall stress distribution in a patient specific abdominal aortic aneurysm phantom. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. 2018;98(12):2258–74.

42. Asgharzadeh H, Borazjani I. A non-dimensional parameter for classification of the flow in intracranial aneurysms. I. Simplified geometries. Physics of Fluids. 2019;31(3):031904. doi: 10.1063/1.5033942 30967744

43. Asgharzadeh H, Asadi H, Meng H, Borazjani I. A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries. Physics of Fluids. 2019;31(3):031905. doi: 10.1063/1.5081451 30967745

44. Young DF, Tsai FY. Flow characteristics in models of arterial stenoses—I. Steady flow. Journal of biomechanics. 1973;6(4):395–410. doi: 10.1016/0021-9290(73)90099-7 4732939

45. Sugawara M, Niki K, Ohte N, Okada T, Harada A. Clinical usefulness of wave intensity analysis. Medical & biological engineering & computing. 2009;47(2):197–206.

46. Bleasdale RA, Mumford CE, Campbell RI, Fraser AG, Jones CJ, Frenneaux MP. Wave intensity analysis from the common carotid artery: a new noninvasive index of cerebral vasomotor tone. Heart and vessels. 2003;18(4):202–6. doi: 10.1007/s00380-003-0711-2 14520489

47. Su J, Manisty C, Parker KH, Simonsen U, Nielsen‐Kudsk JE, Mellemkjaer S, et al. Wave intensity analysis provides novel insights into pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension. Journal of the American Heart Association. 2017;6(11):e006679. doi: 10.1161/JAHA.117.006679 29089339

48. Davies JE, Sen S, Broyd C, Hadjiloizou N, Baksi J, Francis DP, et al. Arterial pulse wave dynamics after percutaneous aortic valve replacement: fall in coronary diastolic suction with increasing heart rate as a basis for angina symptoms in aortic stenosis. Circulation. 2011;124(14):1565–72. doi: 10.1161/CIRCULATIONAHA.110.011916 21911781

49. De Silva K, Guilcher A, Lockie T, Marber M, Redwood S, Plein S, et al. Coronary wave intensity: a novel invasive tool for predicting myocardial viability following acute coronary syndromes. Journal of the American College of Cardiology. 2012;59(13 Supplement):E421.

50. Lockie TP, Rolandi MC, Guilcher A, Perera D, De Silva K, Williams R, et al. Synergistic adaptations to exercise in the systemic and coronary circulations that underlie the warm-up angina phenomenon. Circulation. 2012;126(22):2565–74. doi: 10.1161/CIRCULATIONAHA.112.094292 23124033

51. Broyd C, Davies J, Escaned J, Hughes A, Parker K. Wave intensity analysis and its application to the coronary circulation. Global Cardiology Science and Practice. 2016;2015(5):64.

On the accuracy of displacement-based wave intensity analysis: Effect of vessel wall viscoelasticity and nonlinearity

Souhrn

Klíčová slova:

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