{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T15:48:20Z","timestamp":1792424900114,"version":"4.5.0"},"reference-count":95,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T00:00:00Z","timestamp":1600819200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T00:00:00Z","timestamp":1600819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006575","name":"Institute of Fluid Science, Tohoku University","doi-asserted-by":"publisher","award":["Collaborative Research Grant J19I001"],"award-info":[{"award-number":["Collaborative Research Grant J19I001"]}],"id":[{"id":"10.13039\/501100006575","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["KAKENHI 18K18356"],"award-info":[{"award-number":["KAKENHI 18K18356"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Contemporary paradigm of peripheral and intracranial vascular hemodynamics considers physiologic blood flow to be laminar. Transition to turbulence is considered as a driving factor for numerous diseases such as atherosclerosis, stenosis and aneurysm. Recently, turbulent flow patterns were detected in intracranial aneurysm at Reynolds number below 400 both in vitro and in silico. Blood flow is multiharmonic with considerable frequency spectra and its transition to turbulence cannot be characterized by the current transition theory of monoharmonic pulsatile flow. Thus, we decided to explore the origins of such long-standing assumption of physiologic blood flow laminarity. Here, we hypothesize that the inherited dynamics of blood flow in main arteries dictate the existence of turbulence in physiologic conditions. To illustrate our hypothesis, we have used methods and tools from chaos theory, hydrodynamic stability theory and fluid dynamics to explore the existence of turbulence in physiologic blood flow. Our investigation shows that blood flow, both as described by the Navier\u2013Stokes equation and in vivo, exhibits three major characteristics of turbulence. Womersley\u2019s exact solution of the Navier\u2013Stokes equation has been used with the flow waveforms from HaeMod database, to offer reproducible evidence for our findings, as well as evidence from Doppler ultrasound measurements from healthy volunteers who are some of the authors. We evidently show that physiologic blood flow is: (1) sensitive to initial conditions, (2) in global hydrodynamic instability and (3) undergoes kinetic energy cascade of non-Kolmogorov type. We propose a novel modification of the theory of vascular hemodynamics that calls for rethinking the hemodynamic\u2013biologic links that govern physiologic and pathologic processes.<\/jats:p>","DOI":"10.1038\/s41598-020-72309-8","type":"journal-article","created":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T10:03:36Z","timestamp":1600855416000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":106,"title":["Physiologic blood flow is turbulent"],"prefix":"10.1038","volume":"10","author":[{"given":"Khalid M.","family":"Saqr","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simon","family":"Tupin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sherif","family":"Rashad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Toshiki","family":"Endo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kuniyasu","family":"Niizuma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Teiji","family":"Tominaga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Makoto","family":"Ohta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,9,23]]},"reference":[{"key":"72309_CR1","first-page":"31","volume":"124","author":"JR Womersley","year":"1954","unstructured":"Womersley, J. R. Flow in the larger arteries and its relation to the oscillating pressure. J. Physiol. 124, 31-32P (1954).","journal-title":"J. Physiol."},{"key":"72309_CR2","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1113\/jphysiol.1955.sp005336","volume":"129","author":"JF Hale","year":"1955","unstructured":"Hale, J. F., McDonald, D. A., Taylor, M. G. & Womersley, J. R. The counter chronometer method for recording pulse-wave velocity. J. Physiol. 129, 27-28P (1955).","journal-title":"J. Physiol."},{"key":"72309_CR3","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1113\/jphysiol.1955.sp005330","volume":"128","author":"JF Hale","year":"1955","unstructured":"Hale, J. F., McDonald, D. A. & Womersley, J. R. Velocity profiles of oscillating arterial flow, with some calculations of viscous drag and the Reynolds number. J. Physiol. 128, 629\u2013640. https:\/\/doi.org\/10.1113\/jphysiol.1955.sp005330 (1955).","journal-title":"J. Physiol."},{"key":"72309_CR4","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1113\/jphysiol.1955.sp005276","volume":"127","author":"JR Womersley","year":"1955","unstructured":"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\u2013563. https:\/\/doi.org\/10.1113\/jphysiol.1955.sp005276 (1955).","journal-title":"J. Physiol."},{"key":"72309_CR5","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1113\/jphysiol.1955.sp005276","volume":"127","author":"JR Womersley","year":"1955","unstructured":"Womersley, J. R. Mathematical theory of oscillating flow in an elastic tube. J. Physiol. 127, 37-38P (1955).","journal-title":"J. Physiol."},{"key":"72309_CR6","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1088\/0031-9155\/2\/2\/305","volume":"2","author":"JR Womersley","year":"1957","unstructured":"Womersley, J. R. Oscillatory flow in arteries: The constrained elastic tube as a model of arterial flow and pulse transmission. Phys. Med. Biol. 2, 178\u2013187. https:\/\/doi.org\/10.1088\/0031-9155\/2\/2\/305 (1957).","journal-title":"Phys. Med. Biol."},{"key":"72309_CR7","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1088\/0031-9155\/2\/4\/307","volume":"2","author":"JR Womersley","year":"1958","unstructured":"Womersley, J. R. Oscillatory flow in arteries. III: Flow and pulse-velocity formulae for a liquid whose viscosity varies with frequency. Phys. Med. Biol. 2, 374\u2013382. https:\/\/doi.org\/10.1088\/0031-9155\/2\/4\/307 (1958).","journal-title":"Phys. Med. Biol."},{"key":"72309_CR8","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1152\/physrev.00047.2009","volume":"91","author":"JJ Chiu","year":"2011","unstructured":"Chiu, J. J. & Chien, S. Effects of disturbed flow on vascular endothelium: Pathophysiological basis and clinical perspectives. Physiol. Rev. 91, 327\u2013387. https:\/\/doi.org\/10.1152\/physrev.00047.2009 (2011).","journal-title":"Physiol. Rev."},{"key":"72309_CR9","doi-asserted-by":"publisher","DOI":"10.1177\/0271678X19854640","author":"KM Saqr","year":"2019","unstructured":"Saqr, K. M. et al. What does computational fluid dynamics tell us about intracranial aneurysms? A meta-analysis and critical review. J. Cereb. Blood Flow Metab. https:\/\/doi.org\/10.1177\/0271678X19854640 (2019) ((In-press)).","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"72309_CR10","doi-asserted-by":"publisher","DOI":"10.1002\/jcp.29436","author":"S Rashad","year":"2020","unstructured":"Rashad, S. et al. Epigenetic response of endothelial cells to different wall shear stress magnitudes: A report of new mechano-miRNAs. J. Cell. Physiol. https:\/\/doi.org\/10.1002\/jcp.29436 (2020).","journal-title":"J. Cell. Physiol."},{"key":"72309_CR11","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.compbiomed.2019.01.012","volume":"106","author":"KM Saqr","year":"2019","unstructured":"Saqr, K. M. Wall shear stress in the Navier\u2013Stokes equation: A commentary. Comput. Biol. Med. 106, 82\u201383. https:\/\/doi.org\/10.1016\/j.compbiomed.2019.01.012 (2019).","journal-title":"Comput. Biol. Med."},{"key":"72309_CR12","unstructured":"Tupin, S. et al. Non-Kolmogorov Turbulence and Inverse Energy Cascade in Intracranial Aneurysm: Near-Wall Scales Suggest Mechanobiological Relevance****. arXiv:2001.08234 (2020) (arXiv preprint)."},{"key":"72309_CR13","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1098\/rsif.2012.1031","volume":"10","author":"T Yagi","year":"2013","unstructured":"Yagi, T. et al. Experimental insights into flow impingement in cerebral aneurysm by stereoscopic particle image velocimetry: Transition from a laminar regime. J. R. Soc. Interface 10, 20. https:\/\/doi.org\/10.1098\/rsif.2012.1031 (2013).","journal-title":"J. R. Soc. Interface"},{"key":"72309_CR14","unstructured":"Berg, P., Abdelsamie, A., Janiga, G. & Th\u00e9venin, D. in International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2013"},{"key":"72309_CR15","doi-asserted-by":"publisher","first-page":"2826","DOI":"10.1016\/j.jbiomech.2011.08.015","volume":"44","author":"K Valen-Sendstad","year":"2011","unstructured":"Valen-Sendstad, K., Mardal, K. A., Mortensen, M., Reif, B. A. P. & Langtangen, H. P. Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm. J. Biomech. 44, 2826\u20132832. https:\/\/doi.org\/10.1016\/j.jbiomech.2011.08.015 (2011).","journal-title":"J. Biomech."},{"key":"72309_CR16","unstructured":"Jain, K. Transition to Turbulence in Physiological Flows: Direct Numerical Simulation of Hemodynamics in Intracranial Aneurysms and Cerebrospinal Fluid Hydrodynamics in the Spinal Canal. PhD Thesis (universi-Universit\u00e4tsverlag Siegen, 2016)."},{"key":"72309_CR17","doi-asserted-by":"publisher","first-page":"6186","DOI":"10.1118\/1.4964793","volume":"43","author":"K Jain","year":"2016","unstructured":"Jain, K., Jiang, J., Strother, C. & Mardal, K. A. Transitional hemodynamics in intracranial aneurysms\u2014comparative velocity investigations with high resolution lattice Boltzmann simulations, normal resolution ANSYS simulations, and MR imaging. Med. Phys. 43, 6186\u20136198. https:\/\/doi.org\/10.1118\/1.4964793 (2016).","journal-title":"Med. Phys."},{"key":"72309_CR18","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.compfluid.2015.12.011","volume":"127","author":"K Jain","year":"2016","unstructured":"Jain, K., Roller, S. & Mardal, K. A. Transitional flow in intracranial aneurysms\u2014a space and time refinement study below the Kolmogorov scales using Lattice Boltzmann Method. Comput. Fluids 127, 36\u201346. https:\/\/doi.org\/10.1016\/j.compfluid.2015.12.011 (2016).","journal-title":"Comput. Fluids"},{"key":"72309_CR19","doi-asserted-by":"publisher","first-page":"2341","DOI":"10.1161\/STROKEAHA.107.510644","volume":"39","author":"SW Lee","year":"2008","unstructured":"Lee, S. W., Antiga, L., Spence, J. D. & Steinman, D. A. Geometry of the carotid bifurcation predicts its exposure to disturbed flow. Stroke 39, 2341\u20132347. https:\/\/doi.org\/10.1161\/STROKEAHA.107.510644 (2008).","journal-title":"Stroke"},{"key":"72309_CR20","doi-asserted-by":"publisher","first-page":"698","DOI":"10.5555\/uri:pii:0039606079902204","volume":"86","author":"WM Blackshear Jr","year":"1979","unstructured":"Blackshear, W. M. Jr. et al. Detection of carotid occlusive disease by ultrasonic imaging and pulsed Doppler spectrum analysis. Surgery 86, 698\u2013706. https:\/\/doi.org\/10.5555\/uri:pii:0039606079902204 (1979).","journal-title":"Surgery"},{"key":"72309_CR21","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1111\/jon199444222","volume":"4","author":"JF Toole","year":"1994","unstructured":"Toole, J. F. & Castaldo, J. E. Accurate measurement of carotid stenosis. J. Neuroimaging 4, 222\u2013230 (1994).","journal-title":"J. Neuroimaging"},{"key":"72309_CR22","doi-asserted-by":"publisher","first-page":"H1535","DOI":"10.1152\/ajpheart.00510.2009","volume":"297","author":"D Nam","year":"2009","unstructured":"Nam, D. et al. Partial carotid ligation is a model of acutely induced disturbed flow, leading to rapid endothelial dysfunction and atherosclerosis. Am. J. Physiol-Heart C 297, H1535\u2013H1543. https:\/\/doi.org\/10.1152\/ajpheart.00510.2009 (2009).","journal-title":"Am. J. Physiol-Heart C"},{"key":"72309_CR23","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1115\/1.2354211","volume":"128","author":"HA Himburg","year":"2006","unstructured":"Himburg, H. A. & Friedman, M. H. Correspondence of low mean shear and high harmonic content in the porcine iliac arteries. J. Biomech. Eng. 128, 852\u2013856. https:\/\/doi.org\/10.1115\/1.2354211 (2006).","journal-title":"J. Biomech. Eng."},{"key":"72309_CR24","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/j.jbiomech.2013.09.007","volume":"47","author":"S Kefayati","year":"2014","unstructured":"Kefayati, S., Holdsworth, D. W. & Poepping, T. L. Turbulence intensity measurements using particle image velocimetry in diseased carotid artery models: Effect of stenosis severity, plaque eccentricity, and ulceration. J. Biomech. 47, 253\u2013263. https:\/\/doi.org\/10.1016\/j.jbiomech.2013.09.007 (2014).","journal-title":"J. Biomech."},{"key":"72309_CR25","doi-asserted-by":"publisher","first-page":"2200","DOI":"10.1007\/s10439-009-9769-z","volume":"37","author":"L Grinberg","year":"2009","unstructured":"Grinberg, L., Yakhot, A. & Karniadakis, G. E. Analyzing transient turbulence in a stenosed carotid artery by proper orthogonal decomposition. Ann. Biomed. Eng. 37, 2200\u20132217. https:\/\/doi.org\/10.1007\/s10439-009-9769-z (2009).","journal-title":"Ann. Biomed. Eng."},{"key":"72309_CR26","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.medengphy.2017.06.030","volume":"47","author":"C Vergara","year":"2017","unstructured":"Vergara, C., Le Van, D., Quadrio, M., Formaggia, L. & Domanin, M. Large eddy simulations of blood dynamics in abdominal aortic aneurysms. Med. Eng. Phys. 47, 38\u201346. https:\/\/doi.org\/10.1016\/j.medengphy.2017.06.030 (2017).","journal-title":"Med. Eng. Phys."},{"key":"72309_CR27","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0167-2789(85)90011-9","volume":"16","author":"A Wolf","year":"1985","unstructured":"Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. Determining Lyapunov exponents from a time series. Phys. D. 16, 285\u2013317. https:\/\/doi.org\/10.1016\/0167-2789(85)90011-9 (1985).","journal-title":"Phys. D."},{"key":"72309_CR28","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1017\/S0022112004008134","volume":"504","author":"H Faisst","year":"2004","unstructured":"Faisst, H. & Eckhardt, B. Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343\u2013352. https:\/\/doi.org\/10.1017\/S0022112004008134 (2004).","journal-title":"J. Fluid Mech."},{"key":"72309_CR29","first-page":"84","volume":"41","author":"T Yambe","year":"1995","unstructured":"Yambe, T. et al. Deterministic chaos in the hemodynamics of an artificial heart. ASAIO J. (Am. Soc. Artif. Internal Organs: 1992) 41, 84\u201388 (1995).","journal-title":"ASAIO J. (Am. Soc. Artif. Internal Organs: 1992)"},{"key":"72309_CR30","doi-asserted-by":"publisher","first-page":"R17","DOI":"10.1088\/0951-7715\/18\/6\/r01","volume":"18","author":"RR Kerswell","year":"2005","unstructured":"Kerswell, R. R. Recent progress in understanding the trasnsition to turbulence in a pipe. Nonlinearity 18, R17\u2013R44. https:\/\/doi.org\/10.1088\/0951-7715\/18\/6\/r01 (2005).","journal-title":"Nonlinearity"},{"key":"72309_CR31","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1017\/S0022112095001248","volume":"289","author":"AG Darbyshire","year":"1995","unstructured":"Darbyshire, A. G. & Mullin, T. Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83\u2013114 (1995).","journal-title":"J. Fluid Mech."},{"key":"72309_CR32","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1115\/1.2895504","volume":"115","author":"S Einav","year":"1993","unstructured":"Einav, S. & Sokolov, M. An experimental study of pulsatile pipe flow in the transition range. J. Biomech. Eng. 115, 404\u2013411. https:\/\/doi.org\/10.1115\/1.2895504 (1993).","journal-title":"J. Biomech. Eng."},{"key":"72309_CR33","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/S0955-5986(01)00020-6","volume":"12","author":"M \u00d6zdin\u00e7 \u00c7arpinlio\u01e7lu","year":"2001","unstructured":"\u00d6zdin\u00e7 \u00c7arpinlio\u01e7lu, M. & Ya\u015far G\u00fcndo\u01e7du, M. A critical review on pulsatile pipe flow studies directing towards future research topics. Flow Meas. Instrum. 12, 163\u2013174. https:\/\/doi.org\/10.1016\/S0955-5986(01)00020-6 (2001).","journal-title":"Flow Meas. Instrum."},{"key":"72309_CR34","doi-asserted-by":"publisher","first-page":"014103","DOI":"10.1063\/1.3673611","volume":"24","author":"R Trip","year":"2012","unstructured":"Trip, R., Kuik, D. J., Westerweel, J. & Poelma, C. An experimental study of transitional pulsatile pipe flow. Phys. Fluids 24, 014103. https:\/\/doi.org\/10.1063\/1.3673611 (2012).","journal-title":"Phys. Fluids"},{"key":"72309_CR35","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1017\/jfm.2017.58","volume":"815","author":"B Pier","year":"2017","unstructured":"Pier, B. & Schmid, P. J. Linear and nonlinear dynamics of pulsatile channel flow. J. Fluid Mech. 815, 435\u2013480. https:\/\/doi.org\/10.1017\/jfm.2017.58 (2017).","journal-title":"J. Fluid Mech."},{"key":"72309_CR36","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1017\/jfm.2018.789","volume":"857","author":"D Xu","year":"2018","unstructured":"Xu, D. & Avila, M. The effect of pulsation frequency on transition in pulsatile pipe flow. J. Fluid Mech. 857, 937\u2013951. https:\/\/doi.org\/10.1017\/jfm.2018.789 (2018).","journal-title":"J. Fluid Mech."},{"key":"72309_CR37","unstructured":"Stribling, B. E., Welsh, B. M. & Roggemann, M. C. in Atmospheric Propagation and Remote Sensing IV. 181\u2013197 (International Society for Optics and Photonics)."},{"key":"72309_CR38","unstructured":"Belen'kii, M. S., Karis, S. J., Osmon, C. L., Brown, J. M. & Fugate, R. Q. in 18th Congress of the International Commission for Optics. 50\u201352 (International Society for Optics and Photonics)."},{"key":"72309_CR39","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/0021-9150(94)90207-0","volume":"110","author":"JE Moore Jr","year":"1994","unstructured":"Moore, J. E. Jr., Xu, C., Glagov, S., Zarins, C. K. & Ku, D. N. Fluid wall shear stress measurements in a model of the human abdominal aorta: Oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 110, 225\u2013240. https:\/\/doi.org\/10.1016\/0021-9150(94)90207-0 (1994).","journal-title":"Atherosclerosis"},{"key":"72309_CR40","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1146\/annurev.fluid.29.1.399","volume":"29","author":"DN Ku","year":"1997","unstructured":"Ku, D. N. Blood flow in arteries. Annu. Rev. Fluid Mech. 29, 399\u2013434. https:\/\/doi.org\/10.1146\/annurev.fluid.29.1.399 (1997).","journal-title":"Annu. Rev. Fluid Mech."},{"key":"72309_CR41","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1161\/01.RES.76.4.536","volume":"76","author":"M Noris","year":"1995","unstructured":"Noris, M. et al. Nitric oxide synthesis by cultured endothelial cells is modulated by flow conditions. Circ. Res. 76, 536\u2013543. https:\/\/doi.org\/10.1161\/01.RES.76.4.536 (1995).","journal-title":"Circ. Res."},{"key":"72309_CR42","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1161\/01.RES.82.10.1094","volume":"82","author":"GW De Keulenaer","year":"1998","unstructured":"De Keulenaer, G. W. et al. Oscillatory and steady laminar shear stress differentially affect human endothelial redox state: Role of a superoxide-producing NADH oxidase. Circ. Res. 82, 1094\u20131101. https:\/\/doi.org\/10.1161\/01.RES.82.10.1094 (1998).","journal-title":"Circ. Res."},{"key":"72309_CR43","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1161\/hh0901.090440","volume":"88","author":"A Tedgui","year":"2001","unstructured":"Tedgui, A. & Mallat, Z. Anti-inflammatory mechanisms in the vascular wall. Circ. Res. 88, 877\u2013887. https:\/\/doi.org\/10.1161\/hh0901.090440 (2001).","journal-title":"Circ. Res."},{"key":"72309_CR44","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1161\/01.RES.0000038487.19924.18","volume":"91","author":"JYJ Shyy","year":"2002","unstructured":"Shyy, J. Y. J. & Chien, S. Role of integrins in endothelial mechanosensing of shear stress. Circ. Res. 91, 769\u2013775. https:\/\/doi.org\/10.1161\/01.RES.0000038487.19924.18 (2002).","journal-title":"Circ. Res."},{"key":"72309_CR45","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.yjmcc.2018.08.004","volume":"122","author":"CJ Donaldson","year":"2018","unstructured":"Donaldson, C. J., Lao, K. H. & Zeng, L. The salient role of microRNAs in atherogenesis. J. Mol. Cell. Cardiol. 122, 98\u2013113. https:\/\/doi.org\/10.1016\/j.yjmcc.2018.08.004 (2018).","journal-title":"J. Mol. Cell. Cardiol."},{"key":"72309_CR46","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1146\/annurev.fluid.39.050905.110241","volume":"39","author":"D Jackson","year":"2007","unstructured":"Jackson, D. & Launder, B. Osborne Reynolds and the publication of his papers on turbulent flow. Annu. Rev. Fluid Mech. 39, 19\u201335. https:\/\/doi.org\/10.1146\/annurev.fluid.39.050905.110241 (2007).","journal-title":"Annu. Rev. Fluid Mech."},{"key":"72309_CR47","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1098\/rstl.1883.0029","volume":"174","author":"OXXIX Reynolds","year":"1883","unstructured":"Reynolds, O. X. X. I. X. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos. Trans. R. Soc. A. 174, 935\u2013982. https:\/\/doi.org\/10.1098\/rstl.1883.0029 (1883).","journal-title":"Philos. Trans. R. Soc. A."},{"key":"72309_CR48","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1017\/S0022112062000518","volume":"13","author":"AN Kolmogorov","year":"2006","unstructured":"Kolmogorov, A. N. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82\u201385. https:\/\/doi.org\/10.1017\/S0022112062000518 (2006).","journal-title":"J. Fluid Mech."},{"key":"72309_CR49","first-page":"16","volume":"32","author":"AN Kolmogorov","year":"1991","unstructured":"Kolmogorov, A. N. Dissipation of energy in locally isotropic turbulence. Akad. Nauk SSSR Doklady. 32, 16 (1991).","journal-title":"Akad. Nauk SSSR Doklady."},{"key":"72309_CR50","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1017\/S0022112062000506","volume":"13","author":"AM Oboukhov","year":"1962","unstructured":"Oboukhov, A. M. Some specific features of atmospheric tubulence. J. Fluid Mech. 13, 77\u201381. https:\/\/doi.org\/10.1017\/S0022112062000506 (1962).","journal-title":"J. Fluid Mech."},{"key":"72309_CR51","first-page":"453","volume":"5","author":"A Obukhov","year":"1941","unstructured":"Obukhov, A. On the distribution of energy in the spectrum of turbulent flow. Bull. Acad. Sci. USSR Geog. Geophys. 5, 453\u2013466 (1941).","journal-title":"Bull. Acad. Sci. USSR Geog. Geophys."},{"key":"72309_CR52","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s00332-012-9164-z","volume":"23","author":"B Birnir","year":"2013","unstructured":"Birnir, B. The Kolmogorov\u2013Obukhov statistical theory of turbulence. J. Nonlinear Sci. 23, 657\u2013688. https:\/\/doi.org\/10.1007\/s00332-012-9164-z (2013).","journal-title":"J. Nonlinear Sci."},{"key":"72309_CR53","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1098\/rspa.1938.0032","volume":"164","author":"GI Taylor","year":"1938","unstructured":"Taylor, G. I. The spectrum of turbulence. Proc. R. Soc. A. 164, 476\u2013490 (1938).","journal-title":"Proc. R. Soc. A."},{"key":"72309_CR54","doi-asserted-by":"crossref","unstructured":"Belen'kii, M., Karis, S., Osmon, C., Brown, J. & Fugate, R. Experimental Evidence of the Effects of Non-Kolmogorov Turbulence and Anisotropy of Turbulence. Vol. 3749 ICO (SPIE, 1999).","DOI":"10.1117\/12.354860"},{"key":"72309_CR55","doi-asserted-by":"publisher","first-page":"026003","DOI":"10.1117\/1.2870113","volume":"47","author":"I Toselli","year":"2008","unstructured":"Toselli, I., Andrews, L. C., Phillips, R. L. & Ferrero, V. Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence. Opt. Eng. 47, 026003 (2008).","journal-title":"Opt. Eng."},{"key":"72309_CR56","volume-title":"The Essence of Turbulence as a Physical Phenomenon: With Emphasis on Issues of Paradigmatic Nature","author":"A Tsinober","year":"2013","unstructured":"Tsinober, A. The Essence of Turbulence as a Physical Phenomenon: With Emphasis on Issues of Paradigmatic Nature (Springer, Netherlands, 2013)."},{"key":"72309_CR57","volume-title":"Instabilities, Chaos And Turbulence","author":"M Paul","year":"2010","unstructured":"Paul, M. Instabilities, Chaos And Turbulence 2nd edn. (World Scientific Publishing Company, Singapore, 2010).","edition":"2"},{"key":"72309_CR58","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1002\/9781118032534","volume-title":"Theoretical Fluid Dynamics","author":"BK Shivamoggi","year":"1998","unstructured":"Shivamoggi, B. K. Theoretical Fluid Dynamics 489\u2013495 (Wiley, New York, 1998)."},{"key":"72309_CR59","doi-asserted-by":"publisher","first-page":"164501","DOI":"10.1103\/PhysRevLett.108.164501","volume":"108","author":"L Biferale","year":"2012","unstructured":"Biferale, L., Musacchio, S. & Toschi, F. Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108, 164501 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"72309_CR60","volume-title":"The Essence of Turbulence as a Physical Phenomenon: With Emphasis on Issues of Paradigmatic Nature","author":"A Tsinober","year":"2018","unstructured":"Tsinober, A. The Essence of Turbulence as a Physical Phenomenon: With Emphasis on Issues of Paradigmatic Nature (Springer, Berlin, 2018)."},{"key":"72309_CR61","doi-asserted-by":"publisher","DOI":"10.1007\/978-90-481-3174-7","volume-title":"An Informal Conceptual Introduction to Turbulence: Second Edition of An Informal Introduction to Turbulence","author":"A Tsinober","year":"2009","unstructured":"Tsinober, A. An Informal Conceptual Introduction to Turbulence: Second Edition of An Informal Introduction to Turbulence (Springer, Netherlands, 2009)."},{"key":"72309_CR62","first-page":"867","volume":"20","author":"B Dubrulle","year":"2019","unstructured":"Dubrulle, B. Beyond kolmogorov cascades. J. Fluid Mech. 20, 867 (2019).","journal-title":"J. Fluid Mech."},{"key":"72309_CR63","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1103\/PhysRevLett.72.336","volume":"72","author":"Z-S She","year":"1994","unstructured":"She, Z.-S. & Leveque, E. Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336 (1994).","journal-title":"Phys. Rev. Lett."},{"key":"72309_CR64","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1017\/S0022112075000298","volume":"67","author":"A Perry","year":"1975","unstructured":"Perry, A. & Abell, C. Scaling laws for pipe-flow turbulence. J. Fluid Mech. 67, 257\u2013271 (1975).","journal-title":"J. Fluid Mech."},{"key":"72309_CR65","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1002\/cnm.2868","volume":"33","author":"RM Lancellotti","year":"2017","unstructured":"Lancellotti, R. M., Vergara, C., Valdettaro, L., Bose, S. & Quarteroni, A. Large eddy simulations for blood dynamics in realistic stenotic carotids. Int. J. Numer. Method. Biomed. Eng. 33, 20. https:\/\/doi.org\/10.1002\/cnm.2868 (2017).","journal-title":"Int. J. Numer. Method. Biomed. Eng."},{"key":"72309_CR66","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s13239-019-00410-9","volume":"10","author":"V Mancini","year":"2019","unstructured":"Mancini, V., Bergersen, A. W., Vierendeels, J., Segers, P. & Valen-Sendstad, K. High-frequency fluctuations in post-stenotic patient specific carotid stenosis fluid dynamics: A computational fluid dynamics strategy study. Cardiovasc. Eng. Technol. 10, 277\u2013298. https:\/\/doi.org\/10.1007\/s13239-019-00410-9 (2019).","journal-title":"Cardiovasc. Eng. Technol."},{"key":"72309_CR67","doi-asserted-by":"publisher","first-page":"F400","DOI":"10.1152\/ajprenal.1991.261.3.F400","volume":"261","author":"KP Yip","year":"1991","unstructured":"Yip, K. P., Holstein-Rathlou, N. H. & Marsh, D. J. Chaos in blood flow control in genetic and renovascular hypertensive rats. Am. J. Physiol. Renal. Physiol. 261, F400\u2013F408 (1991).","journal-title":"Am. J. Physiol. Renal. Physiol."},{"key":"72309_CR68","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1111\/j.1525-1594.1994.tb03391.x","volume":"18","author":"T Yambe","year":"1994","unstructured":"Yambe, T. et al. Chaotic hemodynamics during oscillated blood flow. Artif. Organs 18, 633\u2013637. https:\/\/doi.org\/10.1111\/j.1525-1594.1994.tb03391.x (1994).","journal-title":"Artif. Organs"},{"key":"72309_CR69","unstructured":"Bracic, M. & Stefanovska, A. in Annual International Conference of the IEEE Engineering in Medicine and Biology\u2014Proceedings. 1740\u20131741."},{"key":"72309_CR70","first-page":"29","volume":"63","author":"M Bra\u010di\u010d","year":"1996","unstructured":"Bra\u010di\u010d, M. & Stefanovska, A. Lyapunov exponents of quasi-periodic flows. Electrotech. Rev. 63, 29\u201337 (1996).","journal-title":"Electrotech. Rev."},{"key":"72309_CR71","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1080\/01616412.1995.11740347","volume":"17","author":"HF Visee","year":"1995","unstructured":"Visee, H. F. et al. The physiological and clinical significance of nonlinear TCD waveform analysis in occlusive cerebrovascular disease. Neurol. Res. 17, 384\u2013388 (1995).","journal-title":"Neurol. Res."},{"key":"#cr-split#-72309_CR72.1","unstructured":"Ozturk, A. in BIOSIGNALS 2016 - 9th International Conference on Bio-Inspired Systems and Signal Processing, Proceedings"},{"key":"#cr-split#-72309_CR72.2","unstructured":"Part of 9th International Joint Conference on Biomedical Engineering Systems and Technologies, BIOSTEC 2016. 168-174."},{"key":"72309_CR73","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.cmpb.2007.02.004","volume":"86","author":"A Ozturk","year":"2007","unstructured":"Ozturk, A. & Arslan, A. Classification of transcranial Doppler signals using their chaotic invariant measures. Comput. Methods Programs Biomed. 86, 171\u2013180. https:\/\/doi.org\/10.1016\/j.cmpb.2007.02.004 (2007).","journal-title":"Comput. Methods Programs Biomed."},{"key":"72309_CR74","doi-asserted-by":"crossref","unstructured":"Swinney, H. L. & Gollub, J. P. Hydrodynamic instabilities and the transition to turbulence. Hydrodynamic instabilities and the transition to turbulence (1981).","DOI":"10.1007\/978-3-662-02330-3"},{"key":"72309_CR75","doi-asserted-by":"publisher","DOI":"10.1017\/9781108566834","volume-title":"Theory and Computation in Hydrodynamic Stability","author":"WO Criminale","year":"2018","unstructured":"Criminale, W. O., Jackson, T. L. & Joslin, R. D. Theory and Computation in Hydrodynamic Stability (Cambridge University Press, Cambridge, 2018)."},{"key":"72309_CR76","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1016\/0020-7225(73)90014-1","volume":"11","author":"JH Ginsberg","year":"1973","unstructured":"Ginsberg, J. H. The dynamic stability of a pipe conveying a pulsatile flow. Int. J. Eng. Sci. 11, 1013\u20131024. https:\/\/doi.org\/10.1016\/0020-7225(73)90014-1 (1973).","journal-title":"Int. J. Eng. Sci."},{"key":"72309_CR77","doi-asserted-by":"publisher","first-page":"1938","DOI":"10.1063\/1.1476673","volume":"14","author":"AG Straatman","year":"2002","unstructured":"Straatman, A. G., Khayat, R. E., Haj-Qasem, E. & Steinman, D. A. On the hydrodynamic stability of pulsatile flow in a plane channel. Phys. Fluids 14, 1938\u20131944. https:\/\/doi.org\/10.1063\/1.1476673 (2002).","journal-title":"Phys. Fluids"},{"key":"72309_CR78","unstructured":"Isler, J. A. & Carmo, B. S. in Procedia IUTAM. 580\u2013589."},{"key":"72309_CR79","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1017\/jfm.2017.163","volume":"820","author":"K Tsigklifis","year":"2017","unstructured":"Tsigklifis, K. & Lucey, A. D. Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel. J. Fluid Mech. 820, 370\u2013399. https:\/\/doi.org\/10.1017\/jfm.2017.163 (2017).","journal-title":"J. Fluid Mech."},{"key":"72309_CR80","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/bf00284160","volume":"3","author":"J Serrin","year":"1959","unstructured":"Serrin, J. On the stability of viscous fluid motions. Arch. Ration. Mech. Anal. 3, 1\u201313. https:\/\/doi.org\/10.1007\/bf00284160 (1959).","journal-title":"Arch. Ration. Mech. Anal."},{"key":"72309_CR81","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1016\/j.tcb.2016.07.005","volume":"26","author":"A Freikamp","year":"2016","unstructured":"Freikamp, A., Cost, A. L. & Grashoff, C. The piconewton force awakens: Quantifying mechanics in cells. Trends Cell Biol. 26, 838\u2013847. https:\/\/doi.org\/10.1016\/j.tcb.2016.07.005 (2016).","journal-title":"Trends Cell Biol."},{"key":"72309_CR82","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.jbiomech.2016.11.015","volume":"50","author":"M Epshtein","year":"2017","unstructured":"Epshtein, M. & Korin, N. Shear targeted drug delivery to stenotic blood vessels. J. Biomech. 50, 217\u2013221. https:\/\/doi.org\/10.1016\/j.jbiomech.2016.11.015 (2017).","journal-title":"J. Biomech."},{"key":"72309_CR83","doi-asserted-by":"publisher","first-page":"2541","DOI":"10.1161\/strokeaha.116.013555","volume":"47","author":"S Sugiyama","year":"2016","unstructured":"Sugiyama, S. et al. Blood flow into basilar tip aneurysms: A predictor for recanalization after coil embolization. Stroke 47, 2541\u20132547. https:\/\/doi.org\/10.1161\/strokeaha.116.013555 (2016).","journal-title":"Stroke"},{"key":"72309_CR84","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1016\/j.molmed.2017.07.007","volume":"23","author":"S Baratchi","year":"2017","unstructured":"Baratchi, S. et al. Molecular sensors of blood flow in endothelial cells. Trends Mol. Med. 23, 850\u2013868. https:\/\/doi.org\/10.1016\/j.molmed.2017.07.007 (2017).","journal-title":"Trends Mol. Med."},{"key":"72309_CR85","doi-asserted-by":"publisher","first-page":"81","DOI":"10.3389\/fbioe.2019.00081","volume":"7","author":"F Tovar-Lopez","year":"2019","unstructured":"Tovar-Lopez, F. et al. A microfluidic system for studying the effects of disturbed flow on endothelial cells. Front. Bioeng. Biotechnol. 7, 81. https:\/\/doi.org\/10.3389\/fbioe.2019.00081 (2019).","journal-title":"Front. Bioeng. Biotechnol."},{"key":"72309_CR86","doi-asserted-by":"publisher","first-page":"2114","DOI":"10.1073\/pnas.83.7.2114","volume":"83","author":"PF Davies","year":"1986","unstructured":"Davies, P. F., Remuzzi, A., Gordon, E. J., Dewey, C. F. Jr. & Gimbrone, M. A. Jr. Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro. Proc. Natl. Acad. Sci. USA 83, 2114\u20132117. https:\/\/doi.org\/10.1073\/pnas.83.7.2114 (1986).","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"72309_CR87","doi-asserted-by":"publisher","first-page":"2114","DOI":"10.1073\/pnas.83.7.2114","volume":"83","author":"PF Davies","year":"1986","unstructured":"Davies, P. F., Remuzzi, A., Gordon, E. J., Dewey, C. F. & Gimbrone, M. A. Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro. Proc. Natl. Acad. Sci. 83, 2114. https:\/\/doi.org\/10.1073\/pnas.83.7.2114 (1986).","journal-title":"Proc. Natl. Acad. Sci."},{"key":"72309_CR88","volume-title":"The Physics of Pulsatile Flow","author":"EL Ritman","year":"2012","unstructured":"Ritman, E. L. & Zamir, M. The Physics of Pulsatile Flow (Springer, New York, 2012)."},{"key":"72309_CR89","unstructured":"A Matlab version of the Lyapunov exponent estimation algorithm of Wolf et al. Physica 16D, 1985. (Mathworks, https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/48084-lyapunov-exponent-estimation-from-a-time-series-documentation-added, 2016)."},{"key":"72309_CR90","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0185-1","volume-title":"Stability and Transition in Shear Flows","author":"PJ Schmid","year":"2001","unstructured":"Schmid, P. J. & Henningson, D. S. Stability and Transition in Shear Flows (Springer, Berlin, 2001)."},{"key":"72309_CR91","volume-title":"Mathematical New Series","author":"TY Thomas","year":"1941","unstructured":"Thomas, T. Y. Mathematical New Series (University of California Publications, California, 1941)."},{"key":"72309_CR92","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1073\/pnas.29.8.243","volume":"29","author":"T Thomas","year":"1943","unstructured":"Thomas, T. On the uniform convergence of the solutions of the Navier-Stokes equations. Proc. Natl. Acad. Sci. USA 29, 243 (1943).","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"72309_CR93","unstructured":"Hopf, E. in Lecture Series of the Symposium on Partial Differential Equations, Berkeley. 1\u201329."},{"key":"72309_CR94","volume-title":"Procedure for determining turbulence length scales using hotwire anemometry","author":"LA El-Gabry","year":"2014","unstructured":"El-Gabry, L. A., Thurman, D. R. & Poinsatte, P. E. Procedure for determining turbulence length scales using hotwire anemometry (NASA Glenn Research Center, Cleveland, 2014)."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-020-72309-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-020-72309-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-020-72309-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T18:58:39Z","timestamp":1670353119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-020-72309-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,23]]},"references-count":95,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["72309"],"URL":"https:\/\/doi.org\/10.1038\/s41598-020-72309-8","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,23]]},"assertion":[{"value":"17 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 August 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"15492"}}