Reducing the number of parameters in 1D arterial blood flow modeling: Less is more for patient-specific simulations

American Journal of Physiology - Heart and Circulatory Physiology

Volumn 309, Issue 1, 2015, Pages H222-H234

  Epstein, Sally ^a   Willemet, Marie ^a   Chowienczyk, Phil J ^a   Alastruey, Jordi ^a  

^a ST THOMAS HOSPITAL   (United Kingdom)

Author keywords

1D modeling; Aortic pulse wave; Digital pulse wave; Hypertension; Windkessel model

Indexed keywords

AORTA PRESSURE; ARTERY BLOOD FLOW; ARTERY COMPLIANCE; ARTICLE; HUMAN; KIDNEY ARTERY; MODEL; PRIORITY JOURNAL; PULSE WAVE; SIMULATION; THORACIC AORTA; WAVEFORM; AORTA; ARTERY; BIOLOGICAL MODEL; BLOOD FLOW VELOCITY; BLOOD PRESSURE; COMPUTER SIMULATION; HEMODYNAMICS; PHYSIOLOGY;

AORTA; ARTERIES; BLOOD FLOW VELOCITY; BLOOD PRESSURE; COMPUTER SIMULATION; HEMODYNAMICS; HUMANS; MODELS, CARDIOVASCULAR; RENAL ARTERY;

EID: 84935494704     PISSN: 03636135     EISSN: 15221539     Source Type: Journal    
DOI: 10.1152/ajpheart.00857.2014     Document Type: Article

References (52)

1. Alastruey J, Parker KH, Peiró J, Sherwin SJ. Can the modified Allen’s test always detect sufficient collateral flow in the hand? A computational study. Comput Methods Biomech Biomed Engin 9: 353–361, 2006.
2. Alastruey J, Parker K, Peiró J, Sherwin SJ. Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation. Commun Math Phys 4: 317–336, 2008.
3. Alastruey J, Parker KH, Peiró J, Sherwin SJ. Analysing the pattern of pulse waves in arterial networks: a time-domain study. J Eng Math 64: 331–351, 2009.
4. Alastruey J, Parker K, Sherwin S. Arterial pulse wave haemodynamics. In: 11th International Conference on Pressure Surges, edited by Anderson S. Lisbon, Portugal: Virtual PiE Led t/a BHR Group, 2012, chapt. 7, p. 401–442.
5. Almond NE, Jones DP. Noninvasive measurement of the human peripheral circulation: relationship between laser Doppler flowmeter and photo-plethysmograph signals from the finger. Angiology 39: 819–829, 1988.
6. Armentano R, Graf S, Barra J, Velikovsky G, Baglivo H, Sanchez R, Simon A, Pichel RH, Levenson J. Carotid wall viscosity increase is related to intima-media thickening in hypertensive patients. Hypertension 31: 534–539, 1998.
7. Avolio AP. Multi-branched model of the human arterial system. Med Biol Eng Comput 18: 709–718, 1980.
8. Avolio A. The finger volume pulse and assessment of arterial properties. J Hypertens 20: 2341–2343, 2002.
9. Baruch MC, Warburton DE, Bredin SS, Cote A, Gerdt DW, Adkins CM. Pulse decomposition analysis of the digital arterial pulse during hemorrhage simulation. Nonlinear Biomed Phys 5: 1–15, 2011.
10. Baruch M, Kalantari K, Gerdt D, Adkins CM. Validation of the pulse decomposition analysis algorithm using central arterial blood pressure. Biomed Eng Online 13: 1–19, 2014.
11. Blanco PJ, Watanabe SM, Dari EA, Passos MA, Feijóo RA. Blood flow distribution in an anatomically detailed arterial network model: criteria and algorithms. Biomech Model Mechanobiol 13: 1303–1330, 2014.
12. Chowienczyk PJ, Kelly RP, Maccallum H, Millasseau SC, Andersson TL, Gosling RG, Ritter JM, Anggard EE. Photoplethysmographic assessment of pulse wave reflection. J Am Coll Cardiol 34: 2007–2014, 1999.
13. Davies JE, Alastruey J, Francis DP, Hadjiloizou N, Whinnett ZI, Manisty CH, Aguado-Sierra J, Willson K, Foale AR, Malik IS, Hughes AD, Parker KH, Mayet J. Attenuation of wave reflection by wave entrapment creates a “horizon effect” in the human aorta. Hypertension 60: 778–785, 2012.
14. Dick DE, Kendrick JE, Matson GL, Rideout VC. Measurement of nonlinearity in the arterial system of the dog by a new method. Circ Res 22: 101–111, 1968.
15. Formaggia L, Nobile F. Multiscale modelling of the circulatory system: a preliminary analysis. Comput Visual Sci 2: 75–83, 1999.
16. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A. On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 191: 561–582, 2001.
17. Frank O. Die Grundform des arteriellen Pulses. Z Biol 37: 483–526, 1899.
18. Imholz B, Wieling W, Montfrans G, Wesseling K. Fifteen years experience with finger arterial pressure monitoring: assessment of the technology. Cardiovasc Res 38: 605–616, 1998.
19. Jaeger G, Westerhof N, Noordergraaf A. Oscillatory flow impedance in electrical analog of arterial system. Circ Res 16: 121–34, 1965.
20. Kakar P, Lip GY. Towards understanding the aetiology and pathophys-iology of human hypertension: where are we now? J Hum Hypertens 20: 833–836, 2006.
21. Karamanoglu M, Gallagher D, Avolio A, O’Rourke M. Functional origin of reflected pressure waves in a multibranched model of the human arterial system. Am J Physiol Heart Circ Physiol 267: H1681–H1688, 1994.
22. Kearney P, Whelton M, Reynolds K. Global burden of hypertension: analysis of worldwide data. Lancet 365: 217–223, 2005.
23. Khir A, Parker K. Wave intensity in the ascending aorta: effects of arterial occlusion. J Biomech 38: 647–655, 2005.
24. Kind T, Faes TJ, Lankhaar JW, Vonk-Noordegraaf A, Verhaegen M. Estimation of three- and four-element windkessel parameters using sub-space model identification. IEEE Trans Biomed Eng 57: 1531–1538, 2010.
25. Laurent S, Boutouyrie P, Asmar R, Gautier I, Laloux B, Guize L, Ducimetiere P, Benetos A. Aortic stiffness is an independent predictor of all-cause and cardiovascular mortality in hypertensive patients. Hypertension 37: 1236–1241, 2001.
26. Leguy CA, Bosboom EM, Gelderblom H, Hoeks AP, van de Vosse FN. Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way. Med Eng Phys 32: 957–967, 2010.
27. Mancia G; The Task Force for the Management of Arterial Hypertension of the European Society of Hypertension (ESH) and of the European Society of Cardiology (ESC). 2013 ESH/ESC guidelines for the management of arterial hypertension. Eur Heart J 34: 2159–2219, 2013.
28. Milisic V, Quarteroni A. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM 38: 613–632, 2004.
29. Millasseau S, Kelly R, Ritter J, Chowienczyk P. Determination of age-related increases in large artery stiffness by digital pulse contour analysis. Clin Sci 377: 371–377, 2002.
30. Mynard JP, Nithiarasu P. A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Commun Numer Meth Eng 24: 367–417, 2008.
31. Olufsen M, Nadim A. On deriving lumped models for blood flow and pressure in the systemic arteries. Math Biosci Eng 1: 61–80, 2004.
32. Olufsen M. Structured tree outflow condition for blood flow in larger systemic arteries. Am J Physiol Heart Circ Physiol 276: H257–H268, 1999.
33. Perdikaris P, Grinberg L, Karniadakis GE. An effective fractal-tree closure model for simulating blood flow in large arterial networks. Ann Biomed Eng 2014 Dec 16 [Epub ahead of print].
34. Quarteroni A, Formaggia L. Mathematical Modelling and Numerical Simulation of the Cardiovascular System. Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne, 2002.
35. Quick CM, Young WL, Noordergraaf A. Infinite number of solutions to the hemodynamic inverse problem. Am J Physiol Heart Circ Physiol 280: H1472–H1479, 2001.
36. Quick CM, Berger DS, Stewart RH, Laine, a G, Hartley CJ, Noor-dergraaf A. Resolving the hemodynamic inverse problem. IEEE Trans Biomed Eng 53: 361–368, 2006.
37. Raines JK, Jaffrin MY, Shapiro AH. A computer simulation of arterial dynamics in the human leg. J Biomech 7: 77–91, 1974.
38. Reymond P, Merenda F, Perren F, Rufenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 297: H208–H222, 2009.
39. Segers P, Rietzschel ER, De Buyzere ML, Stergiopulos N, Westerhof N, Van Bortel LM, Gillebert T, Verdonck PR. 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: 417–428, 2008.
40. Sherwin S, Franke V, Peiró, J, Parker K. One-dimensional modelling of a vascular network in space-time variables. J Eng Math 47: 217–250, 2003.
41. Smith NP, Pullan AJ, Hunter PJ. An anatomically based model of transient coronary blood flow in the heart. SIAM J Appl Math 62: 990–1018, 2002.
42. Stergiopulos N, Young DF, Rogge TR. Computer simulation of arterial flow with applications to arterial and aortic stenoses. J Biomech 25: 1477–1488, 1992.
43. Stergiopulos N, Westerhof BE, Westerhof N. Total arterial inertance as the fourth element of the windkessel model. Am J Physiol Heart Circ Physiol 276: H81–H88, 1999.
44. Valdez-Jasso D, Bia D, Zócalo Y, Armentano RL, Haider AM, Olufsen MS. Linear and nonlinear viscoelastic modeling of aorta and carotid pressure-area dynamics under in vivo and ex vivo conditions. Ann Biomed Eng 39: 1438–1456, 2011.
45. van den Bos G, Westerhof N, Elzinga G, Sipkema P. Reflection in the systemic arterial system: effects of aortic and carotid occlusion. Cardio-vasc Res 10: 565–573, 1976.
46. Wang JJ, O’Brien AB, Shrive NG, Parker KH, Tyberg JV. Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. Am J Physiol Heart Circ Physiol 284: H1358–H1368, 2003.
47. Wang TJ, Gona P, Larson MG, Levy D, Benjamin EJ, Tofler GH, Jacques PF, Meigs JB, Rifai N, Selhub J, Robins SJ, Newton-Cheh C, Vasan RS. Multiple biomarkers and the risk of incident hypertension. Hypertension 49: 432–438, 2007.
48. Westerhof N, Lankhaar JW, Westerhof BE. The arterial windkessel. Med Biol Eng Comput 47: 131–141, 2009.
49. Willemet M, Lacroix V, Marchandise E. Inlet boundary conditions for blood flow simulations in truncated arterial networks. J Biomech 44: 897–903, 2011.
50. Willemet M, Lacroix V, Marchandise E. Validation of a 1D patient-specific model of the arterial hemodynamics in bypassed lower-limbs: simulations against in vivo measurements. Med Eng Phys 35: 1573–1583, 2013.
51. Willemet M, Alastruey J. Arterial pressure and flow wave analysis using time-domain 1-D hemodynamics. Ann Biomed Eng 43: 190–206, 2015.
52. Xiao N, Alastruey J, Alberto Figueroa C. A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. Int J Numer Method Biomed Eng 30: 204–231, 2013.