Skip to main content

Mechanics of Biofluids and Computational Analysis

  • Chapter
  • 1739 Accesses

Part of the book series: A First Course in “In Silico Medicine” ((FCISM,volume 3))

Abstract

The behavior of fluid that accounts for approximately 60% of our body weight obeys the principles of fluid mechanics. A fluid has no preferred shape. It cannot withstand any tendency by applied forces to deform it in a way which leaves the volume unchanged. It may be liquid or gas. Gases can be compressed more readily; motions appreciable pressure results in much larger changes in density than in a liquid.

In order to predict internal and external flows in the field of an interest, we often rely on numerical methods rather than analytical approaches. As the problem is more practical (i.e., three-dimensional, non-Newtonian, unsteady and interaction with solid objects), it becomes more difficult to idealize situations such that analytical approaches can be used. The widespread availability of powerful computers together with efficient solution algorithms and sophisticated pre- and post-processing facilities enable the use of computational fluid dynamics (CFD). In fact, research in the field of biofluid has been highly progressed since the 1990s when computers become available at a low cost. Many investigators including us started from fairly simple objects to quite complicated system and widened the horizon of the computational research not only for fundamental understandings but also for direct or indirect clinical applications.

While the users who started their research career from 1990s had a long learning curve with developments of CFD and are aware of limitations and problems in applying CFD to biofluid problems, new users who just abruptly dived into the highly-developed world of CFD do not always get the sufficient amount of time to obtain the fundamentals of fluid dynamics and of the numerical skills used in CFD. Thus they often face difficulties in applying CFD to biofluid problems. This chapter intends to help those readers understand fundamentals of fluid mechanics and the theoretical background required for the effective use of CFD in biofluid problems. For more advanced readers, this chapter describes issues and problems in dealing with biofluid problems in silico.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Amsden AA, Harlow FH (1970) The SMAC Method: a numerical technique for calculating incompressible fluid flows. LA-4370, Los Alamos Scientific Laboratory, New Mexico

    Google Scholar 

  • Baguchi P (2007) Mesoscale simulation of blood flow in small vessels. Biophys J 92:1858–1877

    Article  Google Scholar 

  • Baguchi P, Johnson PC, Popel AS (2005) Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J Biomech Eng 127:1070–1080

    Article  Google Scholar 

  • Boryczko K, Dzwinel W, Yuen DA (2003) Dynamical clustering of red blood cells in capillary vessels. J Mol Model 9:16–33

    Google Scholar 

  • Buchanan JR Jr, Kleinstreuer C (1998) Simulation of particle-hemodynamics in a partially occluded artery segment with implications to the initiation of microemboli and secondary stenosis. J Biomech Eng 120:446–454

    Article  Google Scholar 

  • Caro CG, Fitz-Gerald JM, Schroter RC (l969) Arterial wall shear and distribution of early atheroma in man. Nature 223:ll59–ll6l

    Google Scholar 

  • Caro CG, Pedley TJ, Schroter RC, Seed WA (2011) The mechanics of the circulation. Cambridge University Press, New York

    Google Scholar 

  • De Mey S, De Sutter J, Vierendeels J, Verdonck P (2001) Diastolic filling and pressure imaging: taking advantage of the information in a colour M-mode Doppler image. Eur J Echocardiogr 12:219–233

    Article  Google Scholar 

  • DeBakey ME, Lawrie GM, Glaeser DH (1985) Patterns of atherosclerosis and their surgical significance. Ann Surg 201:115–131

    Article  Google Scholar 

  • Dzwinel W, Boryczko K, Yuen DA (2003) A discrete-particle model of blood dynamics in capillary vessels. J Colloid Interface Sci 258:163–173

    Article  Google Scholar 

  • Frisch U, d’Humières D, Hasslacher B, Lallemand P, Pomeau Y, Rivet JP (1987) Lattice gas hydrodynamics in two and three dimensions. Complex Syst 1:649–707

    MATH  Google Scholar 

  • Fukui T, Parker KH, Imai Y, Tsubota K, Wada S, Yamaguchi T (2007) Differentiation of stenosed and aneurysmal arteries by pulse wave propagation analysis based on a fluid–solid interaction computational method. Technol Health Care 5:79–90

    Google Scholar 

  • Fung YC (1997) Biomechanics circulation, 2nd edn. Springer, New York, pp 155–159

    Google Scholar 

  • Gonzalez CF, Cho YI, Ortega HV, Moret J (1992) Intracranial aneurysms: flow analysis of their origin and progression. Am J Neuroradiol 13(1):181–188

    Google Scholar 

  • Goto S (2008) Blood constitution: platelet aggregation, bleeding, and involvement of leukocytes. Rev Neurol Dis 5:S22–S27

    Google Scholar 

  • Harlow FH, Welch JE (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8:2182–2189

    Article  MATH  Google Scholar 

  • Hidaka K, Nakamura M, Osuga K, Komizu M, Wada S (2008) Effects of injection position and interval on the fraction of embolic agents at a bifurcation. Trans Jap Soc Med Biol Eng 6:647–654 (in Japanese)

    Google Scholar 

  • Hidaka K, Nakamura M, Osuga K, Komizu M, Miyazaki H, Wada S (2010) Elastic characteristics of microspherical embolic agents used for vascular interventional radiology. J Mech Behav Biomed Mater 3:497–503

    Article  Google Scholar 

  • Kamada H, Tsubota K, Nakamura M, Ishikawa T, Yamaguchi T (2010) A three-dimensional particle simulation of the formation and collapse of a primary thrombus. Int J Numer Meth Biomed Eng 26:488–500

    Article  MathSciNet  MATH  Google Scholar 

  • Kamada H, Tsubota K, Nakamura M, Wada S, Ishikawa T, Yamaguchi T (2011) Computational study on effect of stenosis on primary thrombus formation. Biorheology 48:99–114

    Google Scholar 

  • Kawano Y, Ohmori K, Wada Y, Kondo I, Mizushige K, Senda S, Nozaki S, Kohno M (2000) Anovel color M-mode Doppler echocardiographic index for left ventricular relaxation: depth of the maximal velocity point of left ventricular inflow in early diastole. Heart Vessels 15:205–213

    Article  Google Scholar 

  • Kamiya A, Togawa T (1980) Adaptive regulation of wall shear stress to flow change in the canine carotid artery. Am J Physiol 239:H14–21

    Google Scholar 

  • Kamiya A, Ando J, Shibata M, Masuda H (1988) Roles of fluid shear stress in physiological regulation of vascular structure and function. Biorheology 25:271–278

    Google Scholar 

  • Kleinstreuer C, Hyun S, Buchanan JR Jr, Longest PW, Archie JP Jr, Truskey GA (2001) Hemodynamic parameters and early intimal thickening in branching blood vessels. Crit Rev Biomed Eng 29:1–64

    Article  Google Scholar 

  • Koshizuka S, Oka Y (1996) Moving particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 123:421–434

    Google Scholar 

  • Koshizuka S, Nobe A, Oka Y (1998) Numerical analysis of breaking waves using the moving particle semi-implicit method. Int J Numer Meth Fluid 26:751–769

    Article  MATH  Google Scholar 

  • Ku DN, Giddens DP, Zarins CK, Glagov S (1985) Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis 5:293–302

    Google Scholar 

  • Liu Y, Liu WK (2006) Rheology of red blood cell aggregation by computer simulation. J Comput Phys 220:139–154

    Article  MathSciNet  MATH  Google Scholar 

  • Meng H, Wang Z, Hoi Y, Gao L, Metaxa E, Swartz DD, Kolega J (2007) Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation. Stroke 38:1924–1931

    Google Scholar 

  • Mori D, Yamaguchi T (2002) Computational fluid dynamics modeling and analysis of the effect of 3D distortion of the human aortic arch. Comp Meth Biomech Biomed Eng 5:249–260

    Article  Google Scholar 

  • Morris L, Delassus P, Callanan A, Walsh M, Wallis F, Grace P, McGloughlin T (2005) 3-D numerical simulation of blood flow through models of the human aorta. J Biomech Eng 127:767–775

    Article  Google Scholar 

  • Nakamura M, Wada S (2011) Mesoscopic blood flow simulation considering hematocrit-dependent viscosity. J Biomech Sci Eng 5:578–590

    Article  Google Scholar 

  • Nakamura M, Wada S, Mikami T, Kitabatake A, Karino T (2002) A computational fluid mechanical study on the effects of opening and closing of the mitral orifice on a transmitral flow velocity profile and an early diastolic intraventricular flow. JSME Int J Ser C 45:913–922

    Article  Google Scholar 

  • Nakamura M, Wada S, Mikami T, Kitabatake A, Karino T (2003) Computational study on the evolution of an intraventricular vortical flow during early diastole for the interpretation of color M-mode Doppler echocardiograms. Biomech Model Mechanobiol 2:59–72

    Article  Google Scholar 

  • Nakamura M, Wada S, Mikami T, Kitabatake A, Karino T, Yamaguchi T (2004) Effect of flow disturbances remaining at the beginning of diastole on intraventricular diastolic flow and colour M-mode Doppler echocardiograms. Med Biol Eng Comput 42:509–515

    Article  Google Scholar 

  • Nakamura M, Wada S, Karino T, Yamaguchi T (2005) Effects of a ventricular untwisting on intraventricular diastolic flow and color M-mode Doppler echocardiograms. Technol Health Care 13:269–280

    Google Scholar 

  • Nakamura M, Wada S, Yamaguchi T (2006) Influence of the opening mode of the mitral valve orifice on intraventricular hemodynamics. Ann Biomed Eng 34:927–935

    Article  Google Scholar 

  • Nerem RM (1993) Hemodynamics and the vascular endothelium. J Biomech Eng 115:510–514

    Article  Google Scholar 

  • Niwa K, Kado T, Sakai J, Karino T (2004) The effects of a shear flow on the uptake of LDL and acetylated LDL by an EC monoculture and an EC-SMC coculture. Ann Biomed Eng 32:537–543

    Article  Google Scholar 

  • Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, Taylor & Francis Group, New York

    MATH  Google Scholar 

  • Patankar SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transfer 15:1787–1806

    Article  MATH  Google Scholar 

  • Poleur H, Hanet C, Gurne O, Rousseau MF (1989) Focus on diastolic dysfunction: a new approach to heart failure therapy. Br J Clin Pharmacol 28(Suppl 1):41S–52S

    Article  Google Scholar 

  • Rossitti S (1998) Shear stress in cerebral arteries carrying saccular aneurysms. A preliminary study. Acta Radiol 39:711–717

    Google Scholar 

  • Ruggeri ZM, Dent JA, Saldiver E (1999) Contribution of distinct adhesive interactions to platelet aggregation in flowing blood. Blood 94:172–178

    Google Scholar 

  • Sabbah HN, Stein PD (1981) Pressure-diameter relations during early diastole in dogs. Incompatibility with the concept of passive left ventricular filling. Circ Res 48:357–365

    Article  Google Scholar 

  • Sakariassen KS, Barstad RM (1993) Mechanisms of thromboembolism at arterial plaques. Blood Coagul Fibrinolysis 4:615–625

    Article  Google Scholar 

  • Schmugge M, Rand ML, Freedman J (2003) Platelets and von Willebrand factor. Transfus Apher Sci 28:269–277

    Article  Google Scholar 

  • Secomb TW (1991) Red blood cell mechanics and capillary blood rheology. Cell Biophys 18:231–251

    Google Scholar 

  • Shimogonya Y, Ishikawa T, Imai Y, Matsuki N, Yamaguchi T (2009) Can temporal fluctuation in spatial wall shear stress gradient initiate a cerebral aneurysm? A proposed novel hemodynamic index, the gradient oscillatory number (GON). J Biomech 42:550–554

    Google Scholar 

  • Sun C, Munn LL (2005) Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis. Biophys J 88:1635–1645

    Article  Google Scholar 

  • Takatsuji H, Mikami T, Urasawa K, Teranishi J, Onozuka H, Takagi C, Makita Y, Matsuo H, Kusuoka H, Kitabatake A (1996) A new approach for evaluation of left ventricular diastolic function: spatial and temporal analysis of left ventricular filling flow propagation by color M-mode Doppler echocardiography. J Am Coll Cardiol 27:365–371

    Article  Google Scholar 

  • Thubrikar MJ, Labrosse M, Robicsek F, Al-Soudi J, Fowler B (2001) Mechanical properties of abdominal aortic aneurysm wall. J Med Eng Technol 25:133–142

    Article  Google Scholar 

  • Ting CT, Chou CY, Chang MS, Wang SP, Chiang BN, Yin FC (1991) Arterial hemodynamics in human hypertension. Effects of adrenergic blockade. Circulation 84:1049–1057

    Article  Google Scholar 

  • Van Doormal JP, Raithby GD (1984) Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer Heat Transfer 7:147–163

    Google Scholar 

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

    Google Scholar 

  • Yokosawa S, Nakamura M, Wada S, Isoda H, Takeda H, Yamaguchi T (2005) Quantitative measurements on the human ascending aortic flow using 2D cine phase-contrast magnetic resonance imaging. JSME Int J Ser C 48:459–467

    Article  Google Scholar 

  • Zhang J, Johnson PC, Popel AS (2007) An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Phys Biol 4:285–295

    Article  Google Scholar 

  • Zhang J, Johnson PC, Popel AS (2008) Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. J Biomech 41:47–55

    Article  Google Scholar 

  • Zhang J, Johnson PC, Popel AS (2009) Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc Res 77:265–272

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Masao Tanaka .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer

About this chapter

Cite this chapter

Tanaka, M., Wada, S., Nakamura, M. (2012). Mechanics of Biofluids and Computational Analysis. In: Computational Biomechanics. A First Course in “In Silico Medicine”, vol 3. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54073-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-54073-1_3

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-54072-4

  • Online ISBN: 978-4-431-54073-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics