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Blood–wall fluttering instability as a physiomarker of the progression of thoracic aortic aneurysms

Nature Biomedical Engineering volume 7, pages 1614–1626 (2023)Cite this article

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Abstract

The diagnosis of aneurysms is informed by empirically tracking their size and growth rate. Here, by analysing the growth of aortic aneurysms from first principles via linear stability analysis of flow through an elastic blood vessel, we show that abnormal aortic dilatation is associated with a transition from stable flow to unstable aortic fluttering. This transition to instability can be described by the critical threshold for a dimensionless number that depends on blood pressure, the size of the aorta, and the shear stress and stiffness of the aortic wall. By analysing data from four-dimensional flow magnetic resonance imaging for 117 patients who had undergone cardiothoracic imaging and for 100 healthy volunteers, we show that the dimensionless number is a physiomarker for the growth of thoracic ascending aortic aneurysms and that it can be used to accurately discriminate abnormal versus natural growth. Further characterization of the transition to blood–wall fluttering instability may aid the understanding of the mechanisms underlying aneurysm progression in patients.

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Fig. 1: Model of a distensible blood vessel.
Fig. 2: The marginal stability curve \(\tilde{\mu }=0\) as a function of the dimensionless wavenumber k″ of the perturbation mode and the dimensionless number Nω.
Fig. 3: Flutter instability parameter spatially resolves and temporally predicts abnormal aortic growth.
Fig. 4: The distribution of the aneurysm physiomarker Nω,sp in the patient (n = 117) and normal participant (n = 100) cohorts.

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Data availability

The main data supporting the findings of this study are available within the paper and its Supplementary Information. The raw clinical data in the study are too large to be publicly shared, yet they are available for research purposes from co-author M.M. on reasonable request.

Code availability

Codes for the collection and analysis of data are available on request.

References

  1. Jersey, A. M. & Foster, D. M. Cerebral Aneurysm (Northwell Health, 2020).

  2. Laukka, D. et al. Prevalence of thoracic aortic aneurysms and dilatations in patients with intracranial aneurysms. J. Vasc. Surg. 70, 1801–1808 (2019).

    Article  PubMed  Google Scholar 

  3. Li, X., Zhao, G., Zhang, J., Duan, Z. & Xin, S. Prevalence and trends of the abdominal aortic aneurysms epidemic in general population—a meta-analysis. PLoS ONE 8, e81260 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  4. Johansson, G., Markström, U. & Swedenborg, J. Ruptured thoracic aortic aneurysms: a study of incidence and mortality rates. J. Vasc. Surg. 21, 985–988 (1995).

    Article  PubMed  CAS  Google Scholar 

  5. Gawenda, M. & Brunkwall, J. Ruptured abdominal aortic aneurysm: the state of play. Dtsch. Arztebl. Int. 109, 727–732 (2012).

    PubMed  PubMed Central  Google Scholar 

  6. Kuzmik, G. A., Sang, A. X. & Elefteriades, J. A. Natural history of thoracic aortic aneurysms. J. Vasc. Surg. 56, 565–571 (2012).

    Article  PubMed  Google Scholar 

  7. Coady, M. A., Rizzo, J. A., Hammond, G. L., Kopf, G. S. & Elefteriades, J. A. Surgical intervention criteria for thoracic aortic aneurysms: a study of growth rates and complications. Ann. Thorac. Surg. 67, 1922–1926 (1999).

    Article  PubMed  CAS  Google Scholar 

  8. MA3RS Study Investigators. Aortic wall inflammation predicts abdominal aortic aneurysm expansion, rupture, and need for surgical repair. Circulation 136, 787–797 (2017).

    Article  Google Scholar 

  9. Wilson, K. et al. Relationship between abdominal aortic aneurysm wall compliance and clinical outcome: a preliminary analysis. Eur. J. Vasc. Endovasc. Surg. 15, 472–477 (1998).

    Article  PubMed  CAS  Google Scholar 

  10. Wilson, K. A. et al. The relationship between abdominal aortic aneurysm distensibility and serum markers of elastin and collagen metabolism. Eur. J. Vasc. Endovasc. Surg. 21, 175–178 (2001).

    Article  PubMed  CAS  Google Scholar 

  11. Wilson, K. A. et al. The relationship between aortic wall distensibility and rupture of infrarenal abdominal aortic aneurysm. J. Vasc. Surg. 37, 112–117 (2003).

    Article  PubMed  Google Scholar 

  12. Niestrawska, J. A. et al. The role of tissue remodeling in mechanics and pathogenesis of abdominal aortic aneurysms. Acta Biomater. 88, 149–161 (2019).

    Article  PubMed  CAS  Google Scholar 

  13. Mulè, G. et al. in The Relationship Between Aortic Root Size and Hypertension: An Unsolved Conundrum (ed. Islam, M. S.) 427–445 (Springer, 2017).

  14. Staarmann, B., Smith, M. & Prestigiacomo, C. J. Shear stress and aneurysms: a review. Neurosurg. Focus 47, E2 (2019).

    Article  PubMed  Google Scholar 

  15. Geisbüsch, S. et al. A prospective study of growth and rupture risk of small-to-moderate size ascending aortic aneurysms. J. Thorac. Cardiovasc. Surg. 147, 68–74 (2014).

    Article  PubMed  Google Scholar 

  16. Chandrashekar, A. et al. Prediction of abdominal aortic aneurysm growth using geometric assessment of computerized tomography images acquired during the aneurysm surveillance period. Ann. Surg. https://doi.org/10.1097/sla.0000000000004711 (2020).

  17. Hirata, K. et al. Machine learning to predict the rapid growth of small abdominal aortic aneurysm. J. Comput. Assist. Tomogr. 44, 37–42 (2020).

    Article  PubMed  Google Scholar 

  18. Tsigklifis, K. & Lucey, A. D. Asymptotic stability and transient growth in pulsatile poiseuille flow through a compliant channel. J. Fluid Mech. 820, 370–399 (2017).

    Article  CAS  Google Scholar 

  19. Davies, C. & Carpenter, P. W. Numerical simulation of the evolution of Tollmien–Schlichting waves over finite compliant panels. J. Fluid Mech. 335, 361–392 (1997).

    Article  CAS  Google Scholar 

  20. Davies, C. & Carpenter, P. W. Instabilities in a plane channel flow between compliant walls. J. Fluid Mech. 352, 205–243 (1997).

    Article  CAS  Google Scholar 

  21. Pitman, M. W. & Lucey, A. D. On the direct determination of the eigenmodes of finite flow–structure systems. Proc. R. Soc. A 465, 257–281 (2009).

    Article  Google Scholar 

  22. Azer, K. & Peskin, C. S. A one-dimensional model of blood flow in arteries with friction and convection based on the womersley velocity profile. Cardiovasc. Eng. 7, 51–73 (2007).

    Article  PubMed  Google Scholar 

  23. Wang, X.-F. et al. Fluid friction and wall viscosity of the 1d blood flow model. J. Biomech. 49, 565–571 (2016).

    Article  PubMed  Google Scholar 

  24. Womersley, J. R. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553–563 (1955).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  25. Raines, J. K., Jaffrin, M. Y. & Shapiro, A. H. A computer simulation of arterial dynamics in the human leg. J. Biomech. 7, 77–91 (1974).

    Article  PubMed  CAS  Google Scholar 

  26. Huang, J. et al. Comparison of dynamic changes in aortic diameter during the cardiac cycle measured by computed tomography angiography and transthoracic echocardiography. J. Vasc. Surg. 69, 1538–1544 (2019).

    Article  PubMed  Google Scholar 

  27. He, X., Ku, D. N. & Moore, J. E. Simple calculation of the velocity profiles for pulsatile flow in a blood vessel using mathematica. Ann. Biomed. Eng. 21, 557–558 (1993).

    Article  Google Scholar 

  28. Coddington, A. & Carlson, R. Linear Ordinary Differential Equations (Society for Industrial and Applied Mathematics, 1997).

  29. Kumar, K. & Tuckerman, L. S. Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 49–68 (1994).

    Article  CAS  Google Scholar 

  30. Ma, Y. et al. Relation between blood pressure and pulse wave velocity for human arteries. Proc. Natl Acad. Sci. USA 115, 11144–11149 (2018).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  31. Aslan, S. et al. Non-invasive prediction of peak systolic pressure drop across coarctation of aorta using computational fluid dynamics. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. 2020, 2295–2298 (2020).

    PubMed  PubMed Central  Google Scholar 

  32. Weininger, G. et al. Growth rate of ascending thoracic aortic aneurysms in a non-referral-based population. J. Cardiothorac. Surg. 17, 14 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  33. Wang, T. K. M. & Desai, M. Y. Thoracic aortic aneurysm: optimal surveillance and treatment. Cleve. Clin. J. Med. 87, 557–568 (2020).

    Article  PubMed  Google Scholar 

  34. Mandrekar, J. N. Receiver operating characteristic curve in diagnostic test assessment. J. Thorac. Oncol. 5, 1315–1316 (2010).

    Article  PubMed  Google Scholar 

  35. Boczar, K. E. et al. Sex differences in thoracic aortic aneurysm growth. Hypertension 73, 190–196 (2019).

    Article  PubMed  CAS  Google Scholar 

  36. Collins, J. A., Munoz, J.-V., Patel, T. R., Loukas, M. & Tubbs, R. S. The anatomy of the aging aorta. Clin. Anat. 27, 463–466 (2014).

    Article  PubMed  Google Scholar 

  37. Ohyama, Y., Redheuil, A., Kachenoura, N., Venkatesh, B. A. & Lima, J. A. Imaging insights on the aorta in aging. Circulation 11, e005617 (2018).

    PubMed  Google Scholar 

  38. Bild, D. E. et al. Multi-ethnic study of atherosclerosis: objectives and design. Am. J. Epidemiol. 156, 871–881 (2002).

    Article  PubMed  Google Scholar 

  39. Voges, I. et al. Normal values of aortic dimensions, distensibility, and pulse wave velocity in children and young adults: a cross-sectional study. J. Cardiovasc. Magn. Reson. 14, 77 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  40. Rabkin, S. W., Chan, K. K., Chow, B. & Janusz, M. T. Pulse wave velocity involving proximal portions of the aorta correlates with the degree of aortic dilatation at the sinuses of Valsalva in ascending thoracic aortic aneurysms. Ann. Vasc. Dis. 7, 404–409 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  41. Thompson, B. G. et al. Guidelines for the management of patients with unruptured intracranial aneurysms. Stroke 46, 2368–2400 (2015).

    Article  PubMed  Google Scholar 

  42. Liu, Q. et al. Prediction of aneurysm stability using a machine learning model based on pyradiomics-derived morphological features. Stroke 50, 2314–2321 (2019).

    Article  PubMed  Google Scholar 

  43. Soulat, G. et al. Association of regional wall shear stress and progressive ascending aorta dilation in bicuspid aortic valve. JACC Cardiovasc. Imaging 15, 33–42 (2022).

    Article  PubMed  Google Scholar 

  44. Markl, M. et al. Analysis of pulse wave velocity in the thoracic aorta by flow-sensitive four-dimensional MRI: reproducibility and correlation with characteristics in patients with aortic atherosclerosis. J. Magn. Reson. Imaging 35, 1162–1168 (2012).

    Article  PubMed  Google Scholar 

  45. Quint, L. E., Liu, P. S., Booher, A. M., Watcharotone, K. & Myles, J. D. Proximal thoracic aortic diameter measurements at CT: repeatability and reproducibility according to measurement method. Int. J. Cardiovasc. Imaging 29, 479–488 (2013).

    Article  PubMed  Google Scholar 

  46. Nejatian, A., Yu, J., Geva, T., White, M. T. & Prakash, A. Aortic measurements in patients with aortopathy are larger and more reproducible by cardiac magnetic resonance compared with echocardiography. Pediatr. Cardiol. 36, 1761–1773 (2015).

    Article  PubMed  Google Scholar 

  47. Elefteriades, J. A., Mukherjee, S. K. & Mojibian, H. Discrepancies in measurement of the thoracic aorta: JACC review topic of the week. J. Am. Coll. Cardiol. 76, 201–217 (2020).

    Article  PubMed  Google Scholar 

  48. Frazao, C. et al. Multimodality assessment of thoracic aortic dimensions: comparison of computed tomography angiography, magnetic resonance imaging, and echocardiography measurements. J. Thorac. Imaging https://doi.org/10.1097/rti.0000000000000514 (2020).

  49. Flores, J., Alastruey, J. & Poiré, E. C. A novel analytical approach to pulsatile blood flow in the arterial network. Ann. Biomed. Eng. 44, 3047–3068 (2016).

    Article  PubMed  Google Scholar 

  50. Reymond, P., Merenda, F., Perren, F., Rüfenacht, D. & Stergiopulos, N. Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 297, H208–H222 (2009).

    Article  PubMed  CAS  Google Scholar 

  51. Munneke, A. G., Lumens, J., Arts, T. & Delhaas, T. A closed-loop modeling framework for cardiac-to-coronary coupling. Front. Physiol. 13, 830925 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

Research reported in this publication was supported by the National Heart, Lung, and Blood Institute of the National Institutes of Health under award number F32HL162417. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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  1. These authors contributed equally: Tom Y. Zhao, Ethan M. I. Johnson.

Authors and Affiliations

  1. Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA

    Tom Y. Zhao, Guy Elisha, Sourav Halder & Neelesh A. Patankar

  2. Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA

    Ethan M. I. Johnson & Michael Markl

  3. Feinberg School of Medicine, Northwestern University, Chicago, IL, USA

    Ben C. Smith

  4. Department of Radiology, Northwestern University, Chicago, IL, USA

    Bradley D. Allen & Michael Markl

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Contributions

Conceptualization—N.A.P. and T.Y.Z.; planning and supervision—N.A.P., M.M., T.Y.Z. and E.M.I.J.; theoretical analysis—N.A.P. and T.Y.Z.; clinical methodology—M.M., E.M.I.J., B.D.A., T.Y.Z., S.H., B.C.S. and G.E.; writing—N.A.P., M.M., T.Y.Z., G.E., E.M.I.J. and S.H.

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Correspondence to Tom Y. Zhao or Neelesh A. Patankar.

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Zhao, T.Y., Johnson, E.M.I., Elisha, G. et al. Blood–wall fluttering instability as a physiomarker of the progression of thoracic aortic aneurysms. Nat. Biomed. Eng 7, 1614–1626 (2023). https://doi.org/10.1038/s41551-023-01130-1

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