ARTICLE
Pulse wave propagation along human aorta: a model study
1, 2
,
3
,
4
| 1 | Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics |
| 2 | V.N. Karazin Kharkov National University, Kharkov |
| 3 | Provincial Hospital in Zamość, Zamość |
| 4 | Kharkov National Technical University, Kharkov |
Online publication date: 2020-01-15
Publication date: 2020-01-15
Submission date: 2018-12-03
Acceptance date: 2019-06-10
Journal of Theoretical and Applied Mechanics 2020;58(1):17–34
KEYWORDS
ABSTRACT
In the study, wave propagation along aorta is studied for different normal and pathological
conditions in distal arteries. The mathematical model is based on the axisymmetric incompressible
Navier-Stokes equations for blood and momentum equations for an incompressible
viscoelastic arterial wall. The solution has been found as a superposition of forward and backward
running waves. The blood pressure and flow curves measured by ultrasound in larger
systemic arteries of ten healthy volunteers have been used for identification of the model
parameters. It is shown that individual geometry plays an essential role in the location of
positive and negative wave reflection sites along the aorta and, thus, in the pressure and
flow patterns as well as blood distribution into the side branches. The model is validated by
comparative study with the same dependencies computed previously on a 55-tube model as
well as on the measurement data. The model can be used for determination of the individual
parameters for patient-specific cardiovascular models and further in silico modeling of the
outcomes of surgical and therapeutic procedures.
REFERENCES (32)
1.
Alastruey J., Parker K.H., Peiró J., Byrd S.M., Sherwin S.J., 2007, Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows, Journal of Biomechanics, 40, 1794-1805, DOI: 10.1016/j.jbiomech.2006.07.008.
2.
Alastruey J., Parker K.H., Peiró J., Sherwin S.J., 2006, Can the modified Allen’s test always detect sufficient collateral flow in the hand? A computational study, Computer Methods in Biomechanics and Biomedical Engineering, 9, 353-361.
3.
Baksi A.J., Davies J.E., Hadjiloizou N., Baruah R., Unsworth B., Foale R.A., Korolkova O., Siggers J.H., Francis D.P., Mayet J., Parker K.H., Hughes A.D., 2019, Attenuation of reflected waves in man during retrograde propagation from femoral artery to proximal aorta, International Journal of Cardiology, 202, 441-445, DOI: 10.1016/j.ijcard.2015.09.064.
4.
Díaz-Zuccarini V., Narracott A.J., Burriesci G., Zervides C., Rafiroiu D., Jones B., Hose D.R., Lawford P.V., 2006, Adaptation and development of software simulation methodologies for cardiovascular engineering: present and future challenges from an end-user perspective, Philosophical Transactions of the Royal Society A, 367, 2655-2666, DOI: 10.1098/rsta.2009.0052.
5.
Epstein S., Willemet M., Chowienczyk P.J., Alastruey J., 2015, Reducing the numer of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations, American Journal of Physiology, 309, H222-H234.
6.
Formaggia L., Gerbeau J.-F., Nobile F., Quarteroni A., 2002, On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels, Computer Methods in Applied Mechanics and Engineering, 191, 561-582.
7.
Hall D.C., Ba Le Q., 2015, Monitoring and evaluation of one health projects; lessons from Southeast Asia, Procedia – Social and Behavioral Sciences, 186, 681-683, DOI: 10.1016/j.sbspro.2015.04.070.
8.
Hollander E.H., Wang J.J., Dobson G.M., Parker K.H., Tyberg J.V., 2001, Negative wave reflections in pulmonary arteries, American Journal of Physiology, 281, 895-902, DOI: 10.1152/ajpheart.2001.281.2.H895.
9.
Hughes A.D., Davies J.E., Parker K.H., 2013, The importance of wave reflection: a comparison of wave intensity analysis and separation of pressure into forward and backward components, Conference of the IEEE Engineering in Medicine and Biology Society, 229-232.
10.
Karamanoglu M., Gallagher D.E., Avolio A.P., O’Rourke M.F., 1995, Pressure wave propagation in a multibranched model of the human upper limb, American Journal of Physiology, 269, H1363-H1369.
11.
Kassab G.S., 2006, Biomechanics of the cardiovascular system: the aorta as an illustratory example, Journal of the Royal Society Interface, 3, 719-740.
12.
Kizilova N.N., 2006, Pressure wave propagation in liquid-filled tubes of viscoelastic material, Fluid Dymanics, 41, 434-446.
13.
Kizilova N., Mizerski J., 2018, Validation of numerical models for flow simulation and wave propagation along human aorta, Journal of Physics: Conference Series, 1101, 012014.
14.
Kizilova N., Philippova H., Zenin O., 2010, A realistic model of human arterial system: blood flow distribution, pulse wave propagation and modeling of pathology, [In:] Mechanika w Medycynie, Korzynski M., Cwanka J. (Edit.), 10, Rzeszow University Press, 103-118.
15.
Kizilova N., Solovyova H., Mizerski J., 2019, Modeling of pulse wave propagation and reflection along human aorta, [In:] Biomechanics in Medicine and Biology, K. Arkusz, R.Będziński, T. Klekiel, S. Piszczatowski (Edit.), Springer Series “Advances in Intelligent Systems and Computing”, 831, 23-35.
16.
Lighthill M.J., 1978, Waves in Fluids, Cambridge: Cambridge University Press.
17.
Michail M., Davies J.E.R., Cameron J.D., Parker K.H., Brown A.J., 2018, Pathophysiological coronary and microcirculatory flow alterations in aortic stenosis, Nature Reviews Cardiology, 15, 420-431, DOI: 10.1038/s41569-018-0011-2.
18.
Narayan O., Parker K.H., Davies J.E., Hughes A.D., Meredith I.T., Cameron1 J.D., 2017, Reservoir pressure analysis of aortic blood pressure: An in-vivo study at five locations in humans, Journal of Hypertension, 35, 2025-2033, DOI: 10.1097/HJH.0000000000001424.
19.
Negoita M., Hughes A.D., Parker K.H., Khir A.W., 2017, Non-invasive technique for determining local pulse wave velocity in humans ascending aorta, Computing in Cardiology, 44, 1-4.
20.
NicholsW., O’Rourke M., 2005,McDonald’s, Blood Flow in Arteries. Theoretical, Experimental and Clinical Principles, Oxford: Oxford University Press.
21.
Quarteroni A., 2001, Modeling the Cardiovascular System: A Mathematical Challenge, Mathematics Unlimited and Beyond, Springer, Berlin, 961-970.
22.
Quarteroni A., Tuveri M., Veneziani A., 2000, Computational vascular fluid dynamics: Problems, models and methods, Computer Visualization Sciences, 2, 163-197.
23.
Raphael C.E., Cooper R., Parker K.H., Collinson J., Vassiliou V., Pennell D.J., de Silva R., Hsu L.Y., Greve A.M., Nijjer S., Broyd C., Ali A., Keegan J., Francis D.P., Davies J.E., Hughes A.D., Arai A., Frenneaux M., Stables R.H., Di Mario C., Prasad S.K., 2016, Mechanisms of myocardial ischemia in hypertrophic cardiomyopathy. Insights from wave intensity analysis and magnetic resonance, Journal of American College of Cardiology, 68, 1651-1660, DOI: 10.1016/j.jacc.2016.07.751.
24.
Salvi P., 2017, Pulse Waves. How Vascular Hemodynamics Affects Blood Pressure, 2nd ed. Springer.
25.
Shipkowitz T., Rodgers V.G.J., Frazin L.J., Chandran K.B., 2000, Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches, Journal of Biomechanics, 33, 717-728.
26.
Sun Y.-H., Anderson T.J., Parker K.H., Tyberg J.V., 2000, Wave-intensity analysis: a new approach to coronary hemodynamic, Journal of Applied Physiology, 89, 1636-1644.
27.
Takach T., Reul G., Cooley D., Duncan J.M., Livesay J.J., Ottet D.A., 2006, Myocardial thievery: the coronary-subclavian steal syndrome, Annals of Thoracic Surgery, 81, 386-392, DOI: 10.1016/j.athoracsur.2005.05.071.
28.
Wang J.J., Parker K.H., 2004, Wave propagation in a model of the arterial circulation, Journal of Biomechanics, 37, 4, 457-470. DOI: 10.1016/j.jbiomech.2003.09.007.
29.
Westerhof N., Bosman F., de Vries C.J., Noordergraaf A., 1969, Analog studies of the human systemic arterial tree, Journal of Biomechanics, 2, 121-143.
30.
Westerhof B.E., Guelen I.,Westerhof N., Karemaker J.M., Avolioet A., 2006, Quantification of wave reflection in the human aorta from pressure alone: a proof of principle, Hypertension, 48, 4, 595-601, DOI: 10.1161/01.HYP.0000238330.08894.17.
31.
Willemet M., Chowienczyk P., Alastruey J., 2015, A database of virtual healthy subjects to assess the accuracy of foot-to-foot pulse wave velocities for estimation of aortic stiffness, American Journal of Physiology, 309, H663-H675.
32.
Zenin O.K., Kizilova N.N., Filippova E.N., 2007, Studies on the structure of human coronary vasculature, Biophysics, 52, 499–503.
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