Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 2, pp 635–650 | Cite as

Beyond the aorta: partial transmission of reflected waves from aortic coarctation into supra-aortic branches modulates cerebral hemodynamics and left ventricular load

  • Jonathan P. Mynard
  • Remi Kowalski
  • Michael M. H. Cheung
  • Joseph J. Smolich
Original Paper


Wave reflection from the site of aortic coarctation produces a reflected backward compression wave (BCW) that raises left ventricular (LV) afterload. However, not all reflected wave power will propagate back to the LV. This study investigated the hypothesis that the BCW is partially transmitted into supra-aortic vessels as a forward wave and explored the consequences of this phenomenon for cerebral and LV haemodynamic load. In eight sheep, high fidelity pressure and flow were measured in the aortic trunk (AoT) and brachiocephalic trunk (BCT, the single supra-aortic vessel present in sheep) at baseline and during two levels of proximal descending aortic constriction. Wave power analysis showed that aortic constriction produced not only a BCW in the AoT, but also a second forward compression wave (\(\mathrm{FCW}_{2})\) in the BCT that augmented pressure and flow after the initial forward compression wave (\(\mathrm{FCW}_{1})\). Mathematical analysis and a one-dimensional model of the human systemic arteries and aortic coarctation suggested that the relative transmission of waves into supra-aortic vessels versus the aorta was determined by the relative admittances of these vessels. Reducing supra-aortic admittance (1) increased pressure and flow pulsatility in cerebral arteries, (2) produced carotid and middle cerebral arterial flow waveforms with an older adult phenotype, (3) promoted transmission of reflected wave power towards the LV and (4) substantially increased mid- to late-systolic myocardial stress, which may promote LV hypertrophy. These findings suggest that wave transmission into supra-aortic branches has an important impact on both cerebral hemodynamics and LV load in aortic coarctation.


Cerebral artery Myocardial stress Left ventricular afterload Carotid artery Wave reflection Wave intensity Wave power 



We thank Magdy Sourial, Sarah White, Amy Tilley and Aaron Mocciaro for their assistance with experimental studies.

Compliance with ethical standards


JPM was funded by a CJ Martin Early Career Fellowship from the National Health and Medical Research Council of Australia. This work was supported by the Victorian Government’s Operational Infrastructure Support Program.


  1. Agnoletti G, Bonnet C, Bonnet D, Sidi D, Aggoun Y (2005) Mid-term effects of implanting stents for relief of aortic recoarctation on systemic hypertension, carotid mechanical properties, intimal medial thickness and reflection of the pulse wave. Cardiol Young 15:245–250. doi: 10.1017/S1047951105000521 CrossRefGoogle Scholar
  2. Arts T, Bovendeerd P, Prinzen FW, Reneman RS (1991) Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall. Biophys J 59:93–102. doi: 10.1016/S0006-3495(91)82201-9 CrossRefGoogle Scholar
  3. Borlotti A, Park C, Parker KH, Khir AW (2015) Reservoir and reservoir-less pressure effects on arterial waves in the canine aorta. J Hypertens 33:564–574. doi: 10.1097/HJH.0000000000000425 CrossRefGoogle Scholar
  4. Brili S, Tousoulis D, Antoniades C, Aggeli C, Roubelakis A, Papathanasiu S, Stefanadis C (2005) Evidence of vascular dysfunction in young patients with successfully repaired coarctation of aorta. Atherosclerosis 182:97–103. doi: 10.1016/j.atherosclerosis.2005.01.030 CrossRefGoogle Scholar
  5. Chirinos JA, Segers P, Gupta AK, Swillens A, Rietzschel ER, De Buyzere ML, Kirkpatrick JN, Gillebert TC, Wang Y, Keane MG (2009) Time-varying myocardial stress and systolic pressure-stress relationship role in myocardial-arterial coupling in hypertension. Circulation 119:2798–2807. doi: 10.1161/CIRCULATIONAHA.108.829366 CrossRefGoogle Scholar
  6. Connolly HM, Huston Iii J, Brown RD Jr, Warnes CA, Ammash NM, Tajik AJ (2003) Intracranial aneurysms in patients with coarctation of the aorta: a prospective magnetic resonance angiographic study of 100 patients. Mayo Clin Proc 78:1491–1499. doi: 10.4065/78.12.1491 CrossRefGoogle Scholar
  7. Coogan JS, Chan FP, Taylor CA, Feinstein JA (2011) Computational fluid dynamic simulations of aortic coarctation comparing the effects of surgical- and stent-based treatments on aortic compliance and ventricular workload. Catheter Cardiovasc Interv 77:680–691. doi: 10.1002/ccd.22878 CrossRefGoogle Scholar
  8. Curtis SL, Bradley M, Wilde P, Aw J, Chakrabarti S, Hamilton M, Martin R, Turner M, Stuart AG (2012) Results of screening for intracranial aneurysms in patients with coarctation of the aorta. Am J Neuroradiol 33:1182–1186. doi: 10.3174/ajnr.A2915 CrossRefGoogle Scholar
  9. de Divitiis M, Pilla C, Kattenhorn M, Donald A, Zadinello M, Wallace S, Redington A, Deanfield J (2003) Ambulatory blood pressure, left ventricular mass, and conduit artery function late after successful repair of coarctation of the aorta. J Am Coll Cardiol 41:2259–2265. doi: 10.1016/s0735-1097(03)00480-7 CrossRefGoogle Scholar
  10. de Divitiis M, Pilla C, Kattenhorn M, Zadinello M, Donald A, Leeson P, Wallace S, Redington A, Deanfield JE (2001) Vascular dysfunction after repair of coarctation of the aorta: impact of early surgery. Circulation 104:I-165–170. doi: 10.1161/hc37t1.094900 CrossRefGoogle Scholar
  11. Dujardin JP, Stone DN (1981) Characteristic impedance of the proximal aorta determined in the time and frequency domain: A comparison. Med Biol Eng Comput 19:565–568. doi: 10.1007/BF02442770 CrossRefGoogle Scholar
  12. Flück D, Beaudin AE, Steinback CD, Kumarpillai G, Shobha N, McCreary CR, Peca S, Smith E, Poulin MJ (2014) Effects of aging on the association between cerebrovascular responses to visual stimulation, hypercapnia and arterial stiffness. Front Physiol 5:49. doi: 10.3389/fphys.2014.00049 CrossRefGoogle Scholar
  13. Gupta TC, Wiggers CJ (1951) Basic hemodynamic changes produced by aortic coarctation of different degrees. Circulation 3:17–31. doi: 10.1161/01.cir.3.1.17 CrossRefGoogle Scholar
  14. Hashimoto J, Ito S (2013) Aortic stiffness determines diastolic blood flow reversal in the descending thoracic aorta: Potential implication for retrograde embolic stroke in hypertension. Hypertension 62:542–549. doi: 10.1161/hypertensionaha.113.01318 CrossRefGoogle Scholar
  15. Hassan W, Awad M, Fawzy ME, Omrani AA, Malik S, Akhras N, Shoukri M (2007) Long-term effects of balloon angioplasty on left ventricular hypertrophy in adolescent and adult patients with native coarctation of the aorta. Up to 18 years follow-up results. Catheter Cardiovasc Interv 70:881–886. doi: 10.1002/ccd.21287 CrossRefGoogle Scholar
  16. Hoffman JI (2009) The natural and unnatural history of congenital heart disease. Wiley, OxfordCrossRefGoogle Scholar
  17. Hoffman JI, Kaplan S (2002) The incidence of congenital heart disease. J Am Coll Cardiol 39:1890–1900. doi: 10.1016/S0735-1097(02)01886-7 CrossRefGoogle Scholar
  18. Hoi Y, Wasserman BA, Xie YJ, Najjar SS, Ferruci L, Lakatta EG, Gerstenblith G, Steinman DA (2010) Characterization of volumetric flow rate waveforms at the carotid bifurcations of older adults. Physiol Meas 31:291–302. doi: 10.1088/0967-3334/31/3/002 CrossRefGoogle Scholar
  19. Kenny D, Hijazi ZM (2011) Coarctation of the aorta: from fetal life to adulthood. Cardiol J 18:487–495. doi: 10.5603/CJ.2011.0003 CrossRefGoogle Scholar
  20. Khir AW, O’Brien A, Gibbs JS, Parker KH (2001) Determination of wave speed and wave separation in the arteries. J Biomech 34:1145–1155. doi: 10.1016/S0021-9290(01)00076-8 CrossRefGoogle Scholar
  21. Khir AW, Parker KH (2005) Wave intensity in the ascending aorta: effects of arterial occlusion. J Biomech 38:647–655. doi: 10.1016/j.jbiomech.2004.05.039 CrossRefGoogle Scholar
  22. Kobayashi S, Yano M, Kohno M, Obayashi M, Hisamatsu Y, Ryoke T, Ohkusa T, Yamakawa K, Matsuzaki M (1996) Influence of aortic impedance on the development of pressure-overload left ventricular hypertrophy in rats. Circulation 94:3362–3368. doi: 10.1161/01.cir.94.12.3362 CrossRefGoogle Scholar
  23. Krogmann ON, Rammos S, Jakob M, Corin WJ, Hess OM, Bourgeois M (1993) Left ventricular diastolic dysfunction late after coarctation repair in childhood: influence of left ventricular hypertrophy. J Am Coll Cardiol 21:1454–1460. doi: 10.1016/0735-1097(93)90323-S CrossRefGoogle Scholar
  24. Lam YY, Mullen MJ, Kaya MG, Gatzoulis M, Li W, Henein MY (2009) Left ventricular long axis dysfunction in adults with “corrected” aortic coarctation is related to an older age at intervention and increased aortic stiffness. Heart 95:733–739. doi: 10.1136/hrt.2008.158287 CrossRefGoogle Scholar
  25. Le Gloan L, Chakor H, Mercier L-A, Harasymowycz P, Dore A, Lachapelle P, Pressacco J, Thibault B, Marcotte F, Proietti A, Leduc H, Mondésert B, Mongeon F-P, Tardif J-C, Khairy P (2014) Aortic coarctation and the retinal microvasculature. Int J Cardiol 174:25–30. doi: 10.1016/j.ijcard.2014.03.129 CrossRefGoogle Scholar
  26. Lorenz CH, Walker ES, Morgan VL, Klein SS, Graham TP (1999) Normal human right and left ventricular mass, systolic function, and gender differences by cine magnetic resonance imaging. J Cardiovasc Magn Reson 1:7–21. doi: 10.3109/10976649909080829 CrossRefGoogle Scholar
  27. Manisty CH, Zambanini A, Parker KH, Davies JE, Francis DP, Mayet J, McG Thom SA, Hughes AD (2009) Differences in the magnitude of wave reflection account for differential effects of amlodipine- versus atenolol-based regimens on central blood pressure. An Anglo-Scandinavian Cardiac Outcome Trial substudy. Hypertension 54:724–730. doi: 10.1161/hypertensionaha.108.125740
  28. Meyer AA, Joharchi MS, Kundt G, Schuff-Werner P, Steinhoff G, Kienast W (2005) Predicting the risk of early atherosclerotic disease development in children after repair of aortic coarctation. Eur Heart J 26:617–622. doi: 10.1093/eurheartj/ehi037 CrossRefGoogle Scholar
  29. Mills CJ, Gabe IT, Gault JH, Mason DT, Ross J, Braunwald E, Shillingford JP (1970) Pressure-flow relationships and vascular impedance in man. Cardiovasc Res 4:405–417. doi: 10.1093/cvr/4.4.405 CrossRefGoogle Scholar
  30. Mitchell GF, van Buchem MA, Sigurdsson S, Gotal JD, Jonsdottir MK, Kjartansson Ó, Garcia M, Aspelund T, Harris TB, Gudnason V, Launer LJ (2011) Arterial stiffness, pressure and flow pulsatility and brain structure and function: The age, gene/environment susceptibility - Reykjavik study. Brain 134:3398–3407. doi: 10.1093/brain/awr253 CrossRefGoogle Scholar
  31. Murakami T, Takeda A (2005) Enhanced aortic pressure wave reflection in patients after repair of aortic coarctation. Ann Thorac Surg 80:995–999. doi: 10.1016/j.athoracsur.2005.03.055 CrossRefGoogle Scholar
  32. Murakami T, Takeda A, Yamazawa H, Tateno S, Kawasoe Y, Niwa K (2013) Aortic pressure wave reflection in patients after successful aortic arch repair in early infancy. Hypertens Res 36:603–607. doi: 10.1038/hr.2013.1 CrossRefGoogle Scholar
  33. Mynard JP (2011) Computer modelling and wave intensity analysis of perinatal cardiovascular function and dysfunction. PhD Thesis, Department of Paediatrics, University of MelbourneGoogle Scholar
  34. Mynard JP (2013) Assessment of conceptual inconsistencies in the hybrid reservoir-wave model. In: Proceedings of the annual international conference of the IEEE engineering in medicine and biology society, Osaka, Japan, 3–7 July 2013. pp 213–216. doi: 10.1109/embc.2013.6609475
  35. Mynard JP, Davidson MR, Penny DJ, Smolich JJ (2012a) A simple, versatile valve model for use in lumped parameter and one-dimensional cardiovascular models. Int J Numer Methods Biomed Eng 28:626–641. doi: 10.1002/cnm.1466 MathSciNetCrossRefGoogle Scholar
  36. Mynard JP, Nithiarasu P (2008) A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Comm Numer Methods Eng 24:367–417. doi: 10.1002/cnm.1117 MathSciNetCrossRefzbMATHGoogle Scholar
  37. Mynard JP, Penny DJ, Davidson MR, Smolich JJ (2012b) The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study. J Hypertens 30:734–743. doi: 10.1097/HJH.0b013e32834f9793 CrossRefGoogle Scholar
  38. Mynard JP, Penny DJ, Smolich JJ (2008) Accurate automatic detection of end-diastole from left ventricular pressure using peak curvature. IEEE Trans Biomed Eng 55:2651–2657. doi: 10.1109/TBME.2008.2001295 CrossRefGoogle Scholar
  39. Mynard JP, Smolich JJ (2014a) The case against the reservoir-wave approach. Int J Cardiol 176:1009–1012. doi: 10.1016/j.ijcard.2014.07.070
  40. Mynard JP, Smolich JJ (2014b) Wave potential and the one-dimensional windkessel as a wave-based paradigm of diastolic arterial hemodynamics. Am J Physiol Heart Circ Physiol 307:H307–H318. doi: 10.1152/ajpheart.00293.2014
  41. Mynard JP, Smolich JJ (2015) One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann Biomed Eng 43:1443–1460. doi: 10.1007/s10439-015-1313-8 CrossRefGoogle Scholar
  42. Mynard JP, Smolich JJ (2016) Novel wave power analysis linking pressure-flow waves, wave potential and the forward and backward components of hydraulic power. Am J Physiol Heart Circ Physiol 310:H1026–H1038. doi: 10.1152/ajpheart.00954.2015 Google Scholar
  43. Mynard JP, Smolich JJ, Avolio A (2015) The ebbing tide of the reservoir-wave model. J Hypertens 33:461–464. doi: 10.1097/hjh.0000000000000528 CrossRefGoogle Scholar
  44. Nichols WW, O’Rourke MF (2011) McDonald’s blood flow in arteries: theoretical, experimental, and clinical principles. CRC Press, Boca RatonGoogle Scholar
  45. O’Rourke MF (1967) Pressure and flow waves in systemic arteries and the anatomical design of the arterial system. J Appl Physiol 23:139–149Google Scholar
  46. O’Rourke MF, Avolio AP (1980) Pulsatile flow and pressure in human systemic arteries. Studies in man and in a multibranched model of the human systemic arterial tree. Circ Res 46:363–372. doi: 10.1161/01.RES.46.3.363 CrossRefGoogle Scholar
  47. O’Rourke MF, Cartmill TB (1971) Influence of aortic coarctation on pulsatile hemodynamics in the proximal aorta. Circulation 44:281–292. doi: 10.1161/01.cir.44.2.281 CrossRefGoogle Scholar
  48. Ou P, Celermajer DS, Jolivet O, Buyens F, Herment A, Sidi D, Bonnet D, Mousseaux E (2008a) Increased central aortic stiffness and left ventricular mass in normotensive young subjects after successful coarctation repair. Am Heart J 155:187–193. doi: 10.1016/j.ahj.2007.09.008
  49. Ou P, Celermajer DS, Raisky O, Jolivet O, Buyens F, Herment A, Sidi D, Bonnet D, Mousseaux E (2008b) Angular (gothic) aortic arch leads to enhanced systolic wave reflection, central aortic stiffness, and increased left ventricular mass late after aortic coarctation repair: Evaluation with magnetic resonance flow mapping. J Thorac Cardiovasc Surg 135:62–68. doi: 10.1016/j.jtcvs.2007.03.059 CrossRefGoogle Scholar
  50. Parker KH (2009) An introduction to wave intensity analysis. Med Biol Eng Comput 47:175–188CrossRefGoogle Scholar
  51. Parker KH, Jones CJ (1990) Forward and backward running waves in the arteries: analysis using the method of characteristics. J Biomech Eng 112:322–326. doi: 10.1115/1.2891191 CrossRefGoogle Scholar
  52. Pedersen TAL, Pedersen EB, Munk K, Hjortdal VE, Emmertsen K, Andersen NH (2014) High pulse pressure is not associated with abnormal activation of the renin-angiotensin-aldosterone system in repaired aortic coarctation. J Hum Hypertens 29:268–273. doi: 10.1038/jhh.2014.75 CrossRefGoogle Scholar
  53. Ramsey MW, Sugawara M (1997) Arterial wave intensity and ventriculoarterial interaction. Heart Vessels Suppl 12:128–134CrossRefGoogle Scholar
  54. Smolich JJ, Mynard JP, Penny DJ (2009) Ductus arteriosus wave intensity analysis in fetal lambs: midsystolic ductal flow augmentation is due to antegrade pulmonary arterial wave transmission. Am J Physiol Regul Integr Comp Physiol 297:R1171–1179. doi: 10.1152/ajpregu.00384.2009 CrossRefGoogle Scholar
  55. Stergiopulos N, Spiridon M, Pythoud F, Meister JJ (1996) On the wave transmission and reflection properties of stenoses. J Biomech 29:31–38. doi: 10.1016/0021-9290(95)00023-2 CrossRefGoogle Scholar
  56. Swan L, Kraidly M, Muhll IV, Collins P, Gatzoulis MA (2010) Surveillance of cardiovascular risk in the normotensive patient with repaired aortic coarctation. Int J Cardiol 139:283–288. doi: 10.1016/j.ijcard.2008.10.043 CrossRefGoogle Scholar
  57. Szczepaniak-Chicheł L, Trojnarska O, Mizia-Stec K, Gabriel M, Grajek S, Gasior Z, Kramer L, Tykarski A (2011) Augmentation of central arterial pressure in adult patients after coarctation repair. Blood Press Monit 16:22–28. doi: 10.1097/MBP.0b013e328343321e CrossRefGoogle Scholar
  58. Taelman L, Bols J, Degroote J, Muthurangu V, Panzer J, Vierendeels J, Segers P (2015) Differential impact of local stiffening and narrowing on hemodynamics in repaired aortic coarctation: An FSI study. Med Biol Eng Comput 54:497–510. doi: 10.1007/s11517-015-1336-1 CrossRefGoogle Scholar
  59. Van den Bos GC, Westerhof N, Elzinga G, Sipkema P (1976) Reflection in the systemic arterial system: effects of aortic and carotid occlusion. Cardiovasc Res 10:565–573. doi: 10.1093/cvr/10.5.565 CrossRefGoogle Scholar
  60. Vogt M, Kuhn A, Baumgartner D, Baumgartner C, Busch R, Kostolny M, Hess J (2005) Impaired elastic properties of the ascending aorta in newborns before and early after successful coarctation repair: Proof of a systemic vascular disease of the prestenotic arteries? Circulation 111:3269–3273. doi: 10.1161/circulationaha.104.529792 CrossRefGoogle Scholar
  61. Wang JJ, O’Brien AB, Shrive NG, Parker KH, Tyberg JV (2003) Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. Am J Physiol Heart Circ Physiol 284:H1358–H1368. doi: 10.1152/ajpheart.00175.2002 CrossRefGoogle Scholar
  62. Wu M-H, Chen H-C, Kao F-Y, Huang S-K (2015) Risk of systemic hypertension and cerebrovascular accident in patients with aortic coarctation aged<60 years (from a national database study). Am J Cardiol 116:779–784. doi: 10.1016/j.amjcard.2015.05.052 CrossRefGoogle Scholar
  63. Xu J, Shiota T, Omoto R, Zhou X, Kyo S, Ishii M, Rice MJ, Sahn DJ (1997) Intravascular ultrasound assessment of regional aortic wall stiffness, distensibility, and compliance in patients with coarctation of the aorta. Am Heart J 134:93–98. doi: 10.1016/s0002-8703(97)70111-x CrossRefGoogle Scholar
  64. Young DF, Tsai FY (1973) Flow characteristics in models of arterial stenoses - ii Unsteady flow. J Biomech 6:547–559. doi: 10.1016/0021-9290(73)90012-2 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Heart Research, Clinical SciencesMurdoch Childrens Research InstituteParkvilleAustralia
  2. 2.Department of PaediatricsUniversity of MelbourneParkvilleAustralia
  3. 3.Department of CardiologyRoyal Children’s HospitalParkvilleAustralia

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