The dispersion of a solute bolus is calculated for cerebrospinal fluid undergoing oscillatory flow in the subarachnoid space of the spine. The fine structure of the subarachnoid space (nerves and trabeculae) enhances both longitudinal and transverse dispersions five to ten times over a simple model with an open annular space. Overall, dispersion is times simple molecular diffusion. The result of enhanced dispersion is rapid spread and dilution of the bolus, effectively stirred by fluid movement around the fine structure.
Issue Section:
Fluids/Heat/Transport
1.
Loth
, F.
, Yardimci
, M. A.
, and Alperin
, N.
, 2001, “Hydrodynamic Modeling of Cerebrospinal Fluid Motion Within the Spinal Cavity
,” ASME J. Biomech. Eng.
0148-0731, 123
, pp. 71
–79
.2.
Stockman
, H. W.
, 2006, “Effect of Anatomical Fine Structure on the Flow of Cerebrospinal Fluid in the Spinal Subarachnoid Space
,” ASME J. Biomech. Eng.
0148-0731, 128
(1
), pp. 106
–114
.3.
Myers
, M. R.
, 1996, “A Numerical Investigation into Factors Affecting Anesthetic Distribution During Spinal Anesthesia
,” J. Biomech.
0021-9290, 29
(2
), pp. 139
–149
.4.
Siegel
, P.
, Mosé
, R.
, Ackerer
, Ph.
, and Jaffré
, J.
, 1997, “Solution of the Advection-Diffusion Equation Using a Combination of Discontinuous and Mixed Finite Elements
,” Int. J. Numer. Methods Fluids
0271-2091, 24
, pp. 595
–613
.5.
Martys
, N.
, and Chen
, H.
, 1996, “Simulation of Multicomponent Fluids in Complex Three-Dimensional Geometries by the Lattice Boltzmann Method
,” Phys. Rev. E
1063-651X, 53
, pp. 743
–750
.6.
Qian
, Y. H.
, d’Humières
, D.
, and Lallemand
, P.
, 1992, “Lattice BGK Models for Navier-Stokes Equation
,” Europhys. Lett.
0295-5075, 17
(6
), pp. 479
–484
.7.
Stockman
, H. W.
, 1999, “A 3D Lattice Boltzmann Code for Modeling Flow and Multi-Component Dispersion
,” Sandia National Laboratories
, Report No. SAND99–0162.8.
Stockman
, H. W.
, Glass
, R. J.
, Cooper
, C.
, and Rajaram
, H.
, 1998, “Accuracy and Computational Efficiency in 3D Dispersion Via Lattice Boltzmann: Models for Dispersion in Rough Fractures and Double-Diffusive Fingering
,” Int. J. Mod. Phys. C
0129-1831, 9
(8
), pp. 1545
–1557
.9.
Porter
, B.
, Zauel
, R.
, Stockman
, H.
, Guldberg
, R.
, and Fyhrie
, D.
, 2004, “3-D Computational Modeling of Media Flow Through Scaffolds in a Perfusion Bioreactor
,” J. Biomech.
0021-9290, 38
(1
), pp. 543
–549
.10.
Stockman
, H. W.
, Johnson
, J. P.
, and Brown
, S. R.
, 2001, “Mixing at Fracture Intersections: Influence of Channel Geometry and the Reynolds and Peclet Numbers
,” Geophys. Res. Lett.
0094-8276, 28
(22
), pp. 4299
–4302
.11.
Flekkøy
, E. G.
, 1993, “Lattice Bhatnagar-Gross-Krook Models for Miscible Fluids
,” Phys. Rev. E
1063-651X, 47
(6
), pp. 4247
–4257
.12.
Aris
, R.
, 1956, “On the Dispersion of a Solute in a Fluid Flowing Through a Tube
,” Proc. R. Soc. London, Ser. A
1364-5021, 235
, pp. 67
–77
.13.
Stepp
, D. W.
, Nishikawa
, Y.
, and Chilian
, W. M.
, 1999, “Regulation of Shear Stress in the Canine Coronary Microcirculation
,” Circulation
0009-7322, 100
(14
), pp. 1555
–1561
.14.
Zacharia
, I. G.
, and Deen
, W. M.
, 2005, “Diffusivity and Solubility of Nitric Oxide in Water and Saline
,” Ann. Biomed. Eng.
0090-6964, 33
(2
), pp. 214
–222
.15.
Watson
, E. J.
, 1983, “Diffusion in Oscillatory Pipe Flow
,” J. Fluid Mech.
0022-1120, 133
, pp. 233
–244
.16.
Joshi
, C. H.
, Kamm
, R. D.
, Drazen
, J. M.
, and Slutsky
, A. S.
, 1983, “An Experimental Study of Gas Exchange in Laminar Oscillatory Flow
,” J. Fluid Mech.
0022-1120, 133
, pp. 245
–254
.17.
Kurzweg
, U. H.
, Howell
, G.
, and Jaeger
, M. J.
, 1984, “Enhanced Dispersion in Oscillatory Flows
,” Phys. Fluids
0031-9171, 27
(5
), pp. 1046
–1048
.18.
Tsangaris
, S.
, and Athanassiadis
, N.
, 1985, “Diffusion in Oscillatory Flow in an Annular Pipe
,” Z. Angew. Math. Mech.
0044-2267, 65
(4
), pp. T253
–T254
.19.
Weast
, R. C.
, 1978, CRC Handbook of Chemistry and Physics
, 59th ed., CRC
, Boca Raton, FL
, pp. F
-51
and F
-62
.20.
Bloomfield
, I. G.
, Johnston
, I. H.
, and Bilston
, I. E.
, 1998, “Effects of Proteins, Blood Cells and Glucose on the Viscosity of Cerebrospinal Fluid
,” Pediatr. Neurosurg.
1016-2291, 28
, pp. 246
–251
.21.
Kutcuoglu
, V.
, Poulikakos
, D.
, and Ventikos
, Y.
, 2005, “Computational Modeling of the Mechanical Behavior of the Cerebrospinal Fluid System
,” ASME J. Biomech. Eng.
0148-0731, 127
, pp. 264
–269
.22.
Smillie
, A.
, Sobey
, I.
, and Molnar
, Z.
, 2005, “A Hydroelastic Model of Hydrocephalus
,” J. Fluid Mech.
0022-1120, 539
, pp. 417
–443
.23.
Nilson
, R. H.
, Peterson
, E. W.
, Lie
, K. H.
, Burkhard
, N. R.
, and Hearst
, J. R.
, 1991, “Atmospheric Pumping: A Mechanism Causing Vertical Transport of Contaminated Gases Through Fractured Permeable Media
,” J. Geophys. Res.
0148-0227, 96
(B13
), pp. 21933
–21948
.24.
Stockman
, H. W.
, 1997, “A Lattice-Gas Study of Retardation and Dispersion in Fractures: Assessment of Errors From Desorption Kinetics and Buoyancy
,” Water Resour. Res.
0043-1397, 33
(8
), pp. 1823
–1832
.25.
Myers
, M. R.
, 1997, “First Ever Computer Simulation of Spinal Anesthesia Highlights Potential Dangers
,” Simulation
0037-5497, 69
(2
), pp. 111
–113
.26.
Myers
, M. R.
, and Malinauskas
, R. A.
, 1998, “Effect of Orifice-Area Reduction on Flow Characteristics During Injection Through Spinal Needles
,” Anaesthesia
0003-2409, 53
(2
), pp. 151
–156
.27.
Robinson
, R. A.
, Stewart
, S. F. C.
, Myers
, M. R.
, Lien
, L. F.
, Rinaldi
, J. R.
, Swisher
, J. L.
, and Drasner
, K.
, 1994, “In Vitro Modeling of Spinal Anesthesia: A Digital Video Imaging Technique and Its Application to Catheter Characterization
,” Anesthesiology
0003-3022, 81
(4
), pp. 1053
–1060
.28.
Eisenach
, J. C.
, Hood
, D. D.
, Curry
, R.
, and Shafer
, S. L.
, 2002, “Cephalad Movement of Morphine and Fentanylin in Humans After Intrathecal Injection
,” Anesthesiology
0003-3022, 99
(1
), pp. 166
–173
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