Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-25T15:08:35.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Computationally Efficient Fluid-Particle Dynamics Simulations of Arterial Systems

Published online by Cambridge University Press:  23 January 2015

Tejas S. Umbarkar  and
Clement Kleinstreuer
Tejas S. Umbarkar
Affiliation:
Mechanical & Aerospace Engineering Department, North Carolina State University, Raleigh, NC 27695, USA
Clement Kleinstreuer*
Affiliation:
Mechanical & Aerospace Engineering Department, North Carolina State University, Raleigh, NC 27695, USA Joint Department of Biomedical Engineering, North Carolina State University and University of North Carolina at Chapel Hill, Raleigh, NC 27695, USA
*
*Email addresses: [email protected] (T. S. Umbarkar), [email protected] (C. Kleinstreuer)
Get access

Abstract

Realistic and accurate computer simulations of the particle-hemodynamics in arterial systems can be a valuable tool for numerous biomedical applications. Examples include optimal by-pass grafting and optimal drug-delivery, as well as best medical management concerning the cardio-vascular system. However, such numerical analyses require large computer resources which may become prohibitive for extended sets of arterial bifurcations. A remedy is to develop a hybrid model where the first few generations of the bifurcating arteries of interest are simulated in full 3-D, while a 1-D model is then coupled for subsequent bifurcations. Alternatively, a 1-D computer model can be directly employed to simulate fluid-particle transport in complex bifurcating networks.

Relying on a representative axial velocity profile, a physiological 1-D model has been developed and validated, which is capable of predicting with reasonable accuracy arterial flow, pressure field and elastic wall interaction as well as particle transport. The usefulness of the novel 1-D simulation approach is demonstrated via a comparison to 3-D blood flow and microsphere transport in a hepatic artery system, featuring as outlets one major branch and four small daughter vessels. Compared to the 3-D simulation, the 1-D analysis requires only about 1% of computational time. The hybrid modeling approach would be also applicable to the human respiratory tract to evaluate the fate of inhaled aerosols.

A simple and cost-effective way to simulate particle-hemodynamics is using a 1-D model for simulating arterial pressures and flow rates as well as microsphere transport, based on assumptions involving the use of a simple algebraic pressure-area relation, an exponential elasticity model for the vessels, and considering only unidirectional flow with a representative skewed velocity profile. In summary, the novel contributions are:

• Particle tracking in arteries via 1-D fluid modeling and selection of an averaged, skewed velocity profile based on 3-D simulation results to provide more realistic friction and inertia term values for modeling a flow system with bifurcations.

• The 1-D model can be coupled to a 3-D model so that simulations can be run for larger regions of vascular or lung-airway systems.

Keywords

70-081-D modelingskewed representative velocity profilefluid-structure interactionparticle tracking
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015 , pp. 401 - 423
Copyright
Copyright © Global Science Press Limited 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Kleinstreuer, C., Basciano, C.A., Childress, E.M., Kennedy, A.S., A new catheter for tumor-targeting with radioactive microspheres in representative hepatic artery systems. Part I: Impact of catheter presence on local blood flow and microsphere delivery, Journal of Biome-chanical Engineering, 134:051004–10,2012.CrossRefGoogle ScholarPubMed
[2]Childress, E.M., Kleinstreuer, C., Kennedy, A.S., A new catheter for tumor-targeting with radioactive microspheres in representative hepatic artery systems. Part II: Solid tumor-targeting in a patient-inspired hepatic artery system, Journal of Biomechanical Engineering, 134:051005–10,2012.Google Scholar
[3]Lin, C.-L., Tawhai, M.H., McLennan, G, Hoffman, E.A., Multiscale simulation of gas flow in subject-specific models of the human lung, IEEE Engineering in Medicine and Biology Magazine, 28(3):25–33,2009.Google Scholar
[4]Formaggia, L., Gerbeau, J.F., Nobile, F., Quarteroni, A., On the coupling of 3D and 1D Navier Stokes equations for flow problems in compliant vessels, Computer Methods in Applied Mechanics and Engineering, 191(6–7):561–582,2001.Google Scholar
[5]Olufsen, M.S., Modeling the Arterial System with Reference to an Anesthesia Simulator, Ph.D. Thesis, 1998.Google Scholar
[6]Formaggia, L., Lamponi, D., Quarteroni, A., One dimensional models for blood flow in arteries, Journal of Engineering Mathematics, 47:251–276,2003.Google Scholar
[7]Alastruey, J., Parker, K.H., Peiro, J., Byrd, S.M., Sherwin, S.J., Modeling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows, Journal of Biomechanics, 40:1794–1805,2007.CrossRefGoogle ScholarPubMed
[8]van de Vosse, F.N., Stergiopulos, N., Pulse wave propagation in the arterial tree, Annual Review of Fluid Mechanics, 43:467–499,2011.CrossRefGoogle Scholar
[9]Kung, E., Les, A., Figueroa, A., Medina, F., Arcaute, K., Wicker, R., McConnell, M., Taylor, C., In vitro validation of finite element analysis of blood flow in deformable models, Annals of Biomedical Engineering, 39(7):1947–1960,2011.Google Scholar
[10]Matthys, K.S., Alastruey, J., Peiró, J., Khir, A.W., Segers, P., Verdonck, P.R., Parker, K.H., Sherwin, S.J., Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements, Journal of Biomechanics, 40(15):3476–86, 2007.CrossRefGoogle Scholar
[11]Segers, P., Duboins, F., De Wachter, D., Verdonck, P., Role and relevancy of a cardiovascular simulator, Journal for Extracorporeal Circulation, 3(1):48–56,1998.Google Scholar
[12]Sherwin, S., Franke, V., Peiro, J., Parker, K., One-dimensional modeling of a vascular network in space-time variables, Journal of Engineering Mathematics, 47(3–4):217–250,2003.CrossRefGoogle Scholar
[13]Alastruey, J., Numerical modeling of pulse wave propagation in the cardiovascular system: development, validations and clinical applications, Ph.D. Thesis, Imperial College London, London, UK, 2006.Google Scholar
[14]Olufsen, M.S., Peskin, C.S., Kim, W.Y., Pedersen, E., Nadim, A., Larsen, J., Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions, Annals of Biomedical Engineering, 28:1281–1299,2000.Google Scholar
[15]Smith, N.P., Pullan, A.J., Hunter, P.J., An anatomically based model of transient coronary blood flow in the heart, SIAM Journal of Applied Mathematics, 62:990–1018,2002.Google Scholar
[16]Ho, H., Sands, G., Schmid, H., Mithraratne, K., Mallinson, G., Hunter, P., A hybrid 1D and 3D approach to hemodynamics modelling for a patient-specific cerebral vasculature and aneurysm, Medical Image Computing and Computer-Assisted Intervention - MICCAI Part II Lecture Notes in Computer Science, 5762:323–30,2009.Google Scholar
[17]Reymond, P., Merenda, F., Perren, F., Rufenacht, D., Stergiopulos, N., Validation of a one-dimensional model of the systemic arterial tree, American Journal of Physiology-Heart and Circulatory Physiology, 297:H208-H222,2009.Google Scholar
[18]Wang, J.J., Parker, K.H., Wave propagation in a model of the arterial circulation, Journal of Biomechanics, 37:457–470, 2004.Google Scholar
[19]Umbarkar, T., Computationally Efficient Simulation of Fluid-Particle Flow in Elastic Bifurcating Systems, MS Thesis, NC State University, Raleigh, NC, 2013.Google Scholar
[20]Bushi, D., Grad, Y., Einav, S., Yodfat, O., Nishri, B., Tanne, D., Hemodynamic evaluation of em-bolic trajectory in an arterial bifurcation: An in-vitro experimental model, Stroke, 36:2696–2700, 2005.Google Scholar
[21]Pedley, T.J., Schroter, R.C., Sudlow, M.F., Flow and pressure drop in systems of repeatedly branching tubes, Journal of Fluid Mechanics, 46:365–383, 1971.Google Scholar
[22]Stergiopulos, N., Young, D.F., Rogge, T.R., Computer simulation of arterial flow with application to arterial and aortic stenoses, Journal of Biomechanics, 25(12):1477–1488,1992.CrossRefGoogle ScholarPubMed
[23]Olufsen, M.S., Structured tree outflow condition for blood flow in larger systemic arteries, American Journal of Physiology, Heart and Circulatory Physiology, 276:H257-268, 1999.Google Scholar
[24]Basciano, C., Computational Particle-Hemodynamics Analysis Applied to an Abdominal Aortic Aneurysm with Thrombus and Microsphere-Targeting of Liver Tumors, Ph.D. Thesis, NC State University, Raleigh, NC, USA, 2010.Google Scholar
[25]Schiller, L., Naumann, A., Über die grundlegenden Berechnungen bei der Schwerkraftauf bereitung, z. Ver. Deut. Ing. 77:318–320,1933.Google Scholar
[26]Childress, E.M., Kleinstreuer, C., Impact of fluid-structure interaction on direct tumortargeting in a representative hepatic artery system, Annals of Biomedical Engineering (in press), 2013.Google Scholar
[27]Marchandise, E., Willemet, M., Lacroix, V., A numerical hemodynamic tool for predicative vascular surgery, Medical and Engineering Physics, 31:131–144,2009.Google Scholar
[28]Müller, L.O., Parés, C., Toro, E.F., Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties, Journal of Computational Physics, 242:53–85, 2013.Google Scholar
[29]Basciano, C.A., Kleinstreuer, C., Kennedy, A.S., Dezarn, W.A., Childress, E., Computer modeling of controlled microsphere release and targeting in a representative hepatic artery system, Annals of Biomedical Engineering, 38(5):1862–79,2010.CrossRefGoogle Scholar
[30]Waite, L., Fine, J., Applied Biofluid Mechanics, The McGraw-Hill Companies,Inc., ISBN 9780071472173,2007.Google Scholar
[31]Brown, R.H., Mitzner, W., Effect of lung inflation and airway muscle tone on airway diameter in vivo, Journal of Applied Physiology, 80:1581–1588, 1996.Google Scholar
[32]Alhamadi, E.S., 1D Model for Flow in the Pulmonary Airway System, Ph.D. Thesis, The University of Manchester, Manchester, UK, 2012.Google Scholar
[33]Martin, V., Clement, F., Decoene, A., Gerbeau, J-F., Parameter identification for a one-dimensional blood flow model, ESIAM: Proceedings, 14:174–200,2005.Google Scholar
[34]Quarteroni, A., Formaggia, L., Veneziani, A., Cardiovascular Mathematics, Springer-Verlag, Italia, Milano, 2009.Google Scholar
[35]Loth, E. and Dorgan, A.J., An equation of motion for particles of finite Reynolds number and size, Environ. Fluid Mechanics, 9(2):187–206,2009.Google Scholar