New Perspectives in Biological Fluid Dynamics

  • T. J. Pedley


The subject of biological fluid dynamics is divided into two major parts, internal or physiological fluid dynamics and external fluid dynamics (e. g. swimming and flying) or the interaction of living organisms with their fluid environment. This review will discuss several topics in each category, surveying recent progress and indicating probable growth areas in the near future. The emphasis will be on mechanisms and scientific understanding rather than clinical results. Disproportionately little attention will be paid to cardiovascular fluid dynamics because a disproportionately large number of papers were devoted to it at the World Congress. Otherwise the major topics to be considered are:
  1. (i)

    Respiratory fluid dynamics — energy loss and pressure drop in airways; forced expiration; gas mixing in airways, especially during high frequency ventilation; surface tension effects in airway closure.

  2. (ii)

    Peristaltic pumping in the ureter — the conventional concentration on flow within the ureter is now being supplemented by detailed modelling of the contraction of ureteral smooth muscle, against the loads provided by the hydrodynamics, in response to the propagating activation signal.

  3. (iii)

    Fish swimming — a similar development is taking place in this area: observations of the motion of a fish body can be used not only to compute the time-dependent hydrodynamic forces acting on it, but also to infer the distribution of bending moment along the fish and, with data on the mechanical properties of the tissues, to calculate the forces and rates of contraction of the swimming muscles. The results can be compared with new measurements of muscle properties at different distances along the fish.

  4. (iv)

    Bioconvection, or spontaneous pattern — formation in dense populations of swimming micro-organisms (certain algae and bacteria in particular). Intriguing experimental observations will be shown and a qualitative explanation given. The need for a stochastic model of random changes in a cell’s swimming trajectory will be emphasised.



Wall Shear Stress Liquid Bridge Oscillatory Flow Surface Tension Effect Secondary Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altringham, J.D., Wardle, C.S. & Smith, C.L., 1993, Myotomal muscle function at different locations in the body of a swimming fish, J. Exp.Biol., 182: 191–206.Google Scholar
  2. Aris, R., 1956, On the dispersion of a solute in a fluid flowing through a tube, Proc. R. Soc. Lond., Ser. A, 235: 67–77.CrossRefGoogle Scholar
  3. Bertram, C.D., 1995, The dynamics of collapsible tubes, in Biological Fluid Dynamics, S.E.B. Symposium 49, ed. by C.P. Ellington & T.J. Pedley, London, Company of Biologists.Google Scholar
  4. Borgas, M.S. & Pedley, T.J., 1990, Non-uniqueness and bifurcation in annular and planar channel flows, J. Fluid Mech., 214: 229–250.CrossRefGoogle Scholar
  5. Bowtell, G. & Williams, T.L., 1993, Anguilliform body dynamics: a continuum model for the interaction between muscle activation and body curvature, J. Math. Biol., 32: 83–92.CrossRefGoogle Scholar
  6. Caro, C.G., Fitz-Gerald, J.M. & Schroter, R.C., 1971, Atheroma and arterial wall shear: observation, correlation and proposal for a shear dependent mass transfer mechanism for atherogenesis, Proc. R. Soc. Lond., Ser. B., 177: 109–159.CrossRefGoogle Scholar
  7. Chang, H.K., 1989, Flow dynamics in the respiratory tract, in Respiratory Physiology, an Analytical Approach, ed. by H.K. Chang & M. Paiva, New York, Marcel Dekker, 57–138.Google Scholar
  8. Cheng, J. Blickhan, R., 1994, Bending moment distribution along swimming fish calculated by waving plate theory, J. Theor. Biol., 168: 337–348.CrossRefGoogle Scholar
  9. Cheng, J., Pedley, T.J. & Altringham, 1995, A continuous dynamic beam model for swimming fish, in preparation.Google Scholar
  10. Cheng, J., Zhuang, L.-X., & Tong, B.-G., 1991, Analysis of swimming three-dimensional waving plates, J. Fluid Mech., 232: 341–355.CrossRefGoogle Scholar
  11. Collins, J.M., Shapiro, A.H., Kimmel, E. & Kamm, R.D., 1993, The steady expiratory pressure-flow relation in a model pulmonary bifurcation, J. Biomech. Eng., 115: 299–305.PubMedCrossRefGoogle Scholar
  12. Daniel, T.L., 1995, Invertebrate swimming: integrating internal and external mechanics, in Biological Fluid Dynamics, SEB Symposium 49, ed. by C.P. Ellington & T.J. Pedley, London, Company of Biologists.Google Scholar
  13. Daskopoulos, P. & Lenhoff, A.M., 1989, Flow in curved ducts: bifurcation structure for stationary ducts, J. Fluid Mech., 203:125–148.CrossRefGoogle Scholar
  14. Eckmann, D.M. & Grotberg, J.B., 1988, Oscillatory flow and mass transport in a curved tube, J. Fluid Mech., 188: 509–527.CrossRefGoogle Scholar
  15. Elad, D. & Kamm, R.D., 1991, Modelling a forced expiration, Comments Theor. Biol., 2: 239–260.Google Scholar
  16. Ellington, C.P., 1995, Unsteady aerodynamics of insect flight, in Biological Fluid Dynamics, SEB Symposium 49, ed. by C.P. Ellington & T.J. Pedley, London, Company of Biologists.Google Scholar
  17. Ellington, C.P. & Pedley, T.J., eds, Biological Fluid Dynamics, SEB Symposium 49, London, Company of Biologists.Google Scholar
  18. Friedman, M.H., 1993, Atherosclerosis research using vascular flow models: from 2-D branches to compliant replicas, J. Biomech. Eng., 115: 595–601.PubMedCrossRefGoogle Scholar
  19. Fry, D.L., 1987, Mass transport, atherogenesis and risk, Arteriosclerosis, 7: 88–100.PubMedCrossRefGoogle Scholar
  20. Fukushima, T. & Azuma, T., 1982, The horseshoe vortex: a secondary flow generated in arteries with stenosis, bifurcations and branchings, Biorheology, 19 1: 143–154.PubMedGoogle Scholar
  21. Fung, Y.C., 1971, Peristaltic pumping: a bioengineering model, in Urodynamics: hydrodynamics of the ureter and renal pelvis, ed. by S. Boyarsky, C.W. Gottschalk, E.A. Tanago & P.D. Zimsking, New York, Academic Press, 177–198.Google Scholar
  22. Gavriely, N., Shee, T.R., Cugell, D.W. & Grotberg, J.B., 1989, Flutter in flow-limited collapsible tubes: a mechanism for generation of wheezes. J. Appl. Physiol. 66: 2251–2261.Google Scholar
  23. Giddens, D.P, Zarins, C.K. & Glagov, S., 1993, The role of fluid mechanics in the localization and detection of atherosclerosis, J. Biomech. Eng., 115: 588–594.PubMedCrossRefGoogle Scholar
  24. Greenough, A. & Milner, A.D., 1987, High frequency ventilation in the neonatal period, Eur. J. Pediatr., 146: 446–449.PubMedCrossRefGoogle Scholar
  25. Griffiths, D.J., 1983, The mechanics of urine transport in the upper urinary tract. II. The discharge of the bolus into the bladder anddynamics at high rates of flow. Neurourol. Urodynam. 2: 167–173.CrossRefGoogle Scholar
  26. Griffiths, D.J., 1989, Flow of urine through the ureter: acollapsible, muscular tube undergoing peristalsis. J. Biomech. Eng., 111: 206–211.PubMedCrossRefGoogle Scholar
  27. Grotberg, J.B., 1994, Pulmonary flow and transport phenomena, Annu. Rev. Fluid Mech., 26: 529–571.CrossRefGoogle Scholar
  28. Grotberg, J.B. & Gavriely, N., 1989, Flutter in collapsible tubes: a theoretical model and wheezes, J. Appl. Physiol., 66: 2262–2273.PubMedGoogle Scholar
  29. Halpern, D. & Grotberg, J.B., 1992, Fluid-elastic instabilities of liquid-lined flexible tubes,. J. Fluid Mech., 244:615–632.CrossRefGoogle Scholar
  30. Halpern, D. & Grotberg, J.B., 1993, Surfactant effects on fluid-elastic instabilities of liquid-lined flexible tubes: a model of airway closure. J. Biomech. Eng., 115: 271–277.PubMedCrossRefGoogle Scholar
  31. Heil, M. & Pedley, T.J., 1995, Post-buckling deformations of a cylindrical shell conveying a viscous flow, in preparation for J. Fluids Structures.Google Scholar
  32. Hess, F. & Videler, J.J., 1984, Fast continuous swimming of saithe (Pollachius virens): a dynamic analysis of bending moments and muscle power, J. Exp. Biol., 109: 229–251.Google Scholar
  33. Hillesdon, J. A., Pedley, T.J. & Kessler, J.O., 1995, The development of concentration gradients in a suspension of chemotactic bacteria, Bull. Math. Biol., (in press).Google Scholar
  34. Hyatt, R.E. & Flath, R.E., 1966, Relationship of air flow to pressure during maximal respiratory effort in man. J. Appl. Physiol., 21: 477–482.PubMedGoogle Scholar
  35. Hydon, P.E., 1994a Resonant and chaotic advection in a curved pipe, Chaos, Solitons & Fractals, 4: 941–954.CrossRefGoogle Scholar
  36. Hydon, P.E., 1994b, Resonant advection by oscillatory flow in a curved pipe, Physica D, 76: 44–54.CrossRefGoogle Scholar
  37. Isabey, D. & Chang, H.K., 1981, Steady and unsteady pressure-flow relationships in central airways, J. Appl. Physiol., 51: 1338–1348.PubMedGoogle Scholar
  38. Jaffrin, M.-Y. & Kesic, P., 1974, Airway resistance: a fluid mechanical approach, J. Appl. Physiol, 36: 354–361.PubMedGoogle Scholar
  39. Jaffrin, M.-Y. & Shapiro, A.H., 1971, Peristaltic pumping, Annu. Rev. Fluid Mech., 3: 13–36.CrossRefGoogle Scholar
  40. Jan, D.L., Shapiro, A.H. & Kamm, R.D., 1989, Some features of oscillatory flow in the lung, J. Appl. Physiol., 67: 147–159.PubMedGoogle Scholar
  41. Jensen, O.E. & Grotberg, J.B., 1992, Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture, J. Fluid Mech., 240: 259–288.CrossRefGoogle Scholar
  42. Johnson, M. & Kamm, R.D., 1986, Numerical studies of steady flow dispersion at low Dean number in a gently curving tube, J. Fluid Mech., 172: 329–345.CrossRefGoogle Scholar
  43. Johnson, M., Kamm, R.D., Ho, L.W., Shapiro, A.H. & Pedley, T.J., 1991, The nonlinear growth of surface-tension driven instabilities of a thin annular film, J. Fluid Mech., 233: 141–156.CrossRefGoogle Scholar
  44. Kamm, R.D., 1987, Flow through collapsible tubes, in Handbook of Bioengineering, ed. by R. Skalak & S. Chien, New York, McGraw Hill, chap. 23.Google Scholar
  45. Kamm, R.D. 1995, Shear-augmented dispersion in the respiratory system, in Biological Fluid Dynamics, SEB Symposium 49, ed. by C.P. Ellington & T.J. Pedley, London, Company of Biologists.Google Scholar
  46. Kamm, R.D. & Pedley, T.J., 1989, Flow in collapsible tubes: a brief review,. J. Biomech. Eng., 111: 177–179.PubMedCrossRefGoogle Scholar
  47. Keller, E.F. & Segel, L., 1971, Model for Chemotaxis, J. Theor. Biol, 30: 225–234.PubMedCrossRefGoogle Scholar
  48. Kessler, J.O., 1985, Hydrodynamic focussing of motile algal cells, Nature, 313: 218–220.CrossRefGoogle Scholar
  49. Kessler, J.O., 1986, The external dynamics of swimming micro-organisms, in Progress in Phycological Research, Vol 4. ed. by F.E. Round, Bristol, Bristol Biopress, 257–307.Google Scholar
  50. Kessler, J.O., Hoelzer, M.A., Pedley, T.J. & Hill, N.A., 1994, Functional patterns of swimming bacteria, in Mechanics and Physiology of Animal Swimming, ed. by L. Maddock, Q. Bone & J.M.V. Rayner, Cambridge, Cambridge University Press, 3–12.CrossRefGoogle Scholar
  51. Ku, D.N., Giddens, D.P., Zarins, C.K. & Glagov, S., 1985, Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque localization and low and oscillating shear stress, Arteriosclerosis, 5: 293–302.PubMedCrossRefGoogle Scholar
  52. Li, M. & Brasseur, J.G., 1993, Nonsteady peristaltic transport in finite-length tubes, J. Fluid Mech., 248: 129–151.CrossRefGoogle Scholar
  53. Lighthill, M.J., 1970, Aquatic animal propulsion of high hydromechanical efficiency, J. Fluid Mech., 44: 265–301.CrossRefGoogle Scholar
  54. Lighthill, M.J., 1971, Large-amplitude elongated-body theory of fish locomotion, Proc. R. Soc. Lond., Ser. B, 179: 125–138.CrossRefGoogle Scholar
  55. Lighthill, J., 1975, Mathematical Biofluiddynamics, Philadelphia, S.I.A.M.Google Scholar
  56. Luo, X.-Y. & Pedley, T.J., 1995, A numerical simulation of steady flow in a 2-D collapsible channel, J. Fluids Structures, 9: 149–175.CrossRefGoogle Scholar
  57. Miftakhov, R. & Wingate, D., 1994, Numerical simulation of the peristaltic reflex of the small bowel, Biorheology, 31: 309–325.PubMedGoogle Scholar
  58. Otis, D.R., Johnson, M., Pedley, T.J. & Kamm, R.D., 1993, The role of pulmonary surfactant in airway closure: a computational study, J. Appl. Physiol., 75: 1323–1333.PubMedGoogle Scholar
  59. Pedley, T.J., 1995, High Reynolds numberflow in tubes of complex geometry with application to wall shear stress in arteries, in Biological Fluid Dynamics, SEB Symposium 49, ed. by C.P. Ellington & T.J. Pedley, London, Company of Biologists.Google Scholar
  60. Pedley, T.J. & Kamm, R.D., 1988, The effect of secondary motion on axial transport in oscillatory tube flow, J. Fluid Mech., 193: 347–367.CrossRefGoogle Scholar
  61. Pedley, T.J. & Kamm, R.D., 1991, Dynamics of gas flow and pressure-flow relationships, in The Lung: Scientific Foundations, ed. by R.G. Crystal & J.B. West, New York, Raven Press, Vol. 1, 995–1010.Google Scholar
  62. Pedley, T.J. & Kessler, J.O., 1990, A new continuum model for suspensions of gyrotactic micro-organisms, J. Fluid Mech., 212: 155.PubMedCrossRefGoogle Scholar
  63. Pedley, T.J. & Kessler, J.O., 1992a, Hydrodynamic phenomena in suspensions of swimming micro-organisms, Annu. Rev. Fluid Mech., 24: 313–358.CrossRefGoogle Scholar
  64. Pedley, T.J. & Kessler, J.O., 1992b, Bioconvection, Sci. Progress, 76: 105–123.Google Scholar
  65. Pedley, T.J., Schröter, R.C. & Sudlow, M.F., 1970a, Energy losses and pressure drop in models of human airways. Respir. Physiol., 9: 371–386.PubMedCrossRefGoogle Scholar
  66. Pedley, T.J., Schröter, R.C. & Sudlow, M.F., 1970b, The prediction of pressure drop and variation of resistance within the human bronchial airways, Respir. Physiol., 9: 387–405.PubMedCrossRefGoogle Scholar
  67. Pedley, T.J., Schröter, R.C. & Sudlow, M.F., 1971, Flow and pressure drop in systems of repeatedly branching tubes, J. Fluid Mech., 46: 365–383.CrossRefGoogle Scholar
  68. Pedley, T.J. & Stephanoff, K.D., 1985, Flow along a channel with a time-dependent indentation in one wall: the generation of vorticity waves, J. Fluid Mech., 160: 337–367.CrossRefGoogle Scholar
  69. Perun, M.L. & Gaver, D.P., 1995, An experimental model investigation of the opening of a collapsed untethered pulmonary airway, J. Biomech. Eng. 117: 245–253.PubMedCrossRefGoogle Scholar
  70. Platt, J.R., 1961, ‘Bioconvection patterns’ in cultures of free-swimming organisms, Science, 133: 1766–1767.PubMedCrossRefGoogle Scholar
  71. Ralph, M.E. & Pedley, T.J., 1988, Flow I a channel with a moving indentation, J. Fluid Mech., 190: 87–112.CrossRefGoogle Scholar
  72. Shapiro, A.H., 1977, Steady flow in collapsible tubes, J. Biomech. Eng., 99: 126–147.CrossRefGoogle Scholar
  73. Sharp, M.K., Kamm, R.D., Shapiro, A.H., Kimmel, E. & Karniadakis, G.E., 1991, Dispersion in a curved tube during oscillatory flow, J. Fluid Mech., 223: 537–563.CrossRefGoogle Scholar
  74. Shin, J. J., Kamm, R.D. & Elad, D., 1995, Simulation of forced breathing maneuvers, Chapter-15 in this volume.Google Scholar
  75. Snyder, B., Olson, D.E., Hammersley, J.R., Peterson, C.V. & Jaeger, M.J., 1987, Reversible and irreversible components of central-airway flow resistance, J. Biomech. Eng., 109: 154–159.PubMedCrossRefGoogle Scholar
  76. Taylor, G.I., 1953, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Ro. Soc. Lond., Ser. A., 219: 186–203.CrossRefGoogle Scholar
  77. Tutty, O.R. & Pedley, T.J., 1993, Oscillatory flow in a stepped channel, J. Fluid Mech., 247: 179–204.CrossRefGoogle Scholar
  78. Wager, H., 1911, On the effect of gravity upon the movements and aggregation of Euglena viridis, Ehrb., and other micro-organisms. Phil. Trans. R. Soc. Lond., Ser. B., 201: 333–390.CrossRefGoogle Scholar
  79. Wardle, C.S. & Videler, J.J., 1993, The timing of the electromyogram in the lateral myotomes of mackerel and saithe at different swimming speeds, J. Fish Biol., 42: 347–359.CrossRefGoogle Scholar
  80. Wardle, C.S. & Videler, J. J., 1994, The timing of lateral muscle train and EMG activity in different species of steadily swimming fish, in MMechanics and Physiology of Animal Swimming, ed. by L. Maddock, Q. Bone & M.V. Rayner, Cambridge, Cambridge University Press, 111–118.CrossRefGoogle Scholar
  81. Weihs, D., 1972, A hydrodynamic analysis of fish turning manoeuvres, Proc. R. Soc. Lond., Ser. B., 182: 59–72.CrossRefGoogle Scholar
  82. Weihs, D., 1973, The mechanism of rapid starting of slender fish, Biorheology, 10: 343–350.PubMedGoogle Scholar
  83. Williams, T.L., Bowtell, G., Carling, J.C, Sigvardt, K.A. & Curtin, N.A., 1995, Interactions between muscle activation, body curvature and the water in the swimming lamprey, in Biological Fluid Dynamics, SEB Symposium 49, ed. by C.P. Ellington & T.J. Pedley, London, Company of Biologists.Google Scholar
  84. Zarins, C.K., Giddens, D.P., Bharodvaj, B.K., Sottiurai, V.S., Mabon, R.F. & Glagov, S., 1983, Carotid bifurcation atherosclerosis: quantitative correlation of plaque localization with flow velocity profiles and wall shear stress, Circ. Res., 53: 502–514.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • T. J. Pedley
    • 1
  1. 1.Department of Applied Mathematical StudiesUniversity of LeedsLeedsUK

Personalised recommendations