Three-dimensional modeling of the brain's ECS by minimum configurational energy packing of fluid vesicles

Biophysical Journal

Volumn 92, Issue 10, 2007, Pages 3368-3378

  Nandigam, Ravi K ^a   Kroll, Daniel M ^b  

^a PURDUE UNIVERSITY   (United States)

^b NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; BRAIN CELL; CELL SHAPE; COMPARATIVE STUDY; ENERGY; EXTRACELLULAR SPACE; GEOMETRY; MATHEMATICAL COMPUTING; MEMBRANE VESICLE; MONTE CARLO METHOD; SIMULATION;

EID: 34247882027     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1529/biophysj.106.095547     Document Type: Article

References (48)

1. Nicholson, C. 2001. Diffusion and related transport mechanisms in brain tissue. Rep. Prog. Phys. 64:815-884.
2. Nicholls, J. G., A. R. Martin, and B. G. Wallace. 1992. From Neuron to Brain: A Cellular Approach To The Function of The Nervous System, 3rd Ed. Sinauer Associates, Sunderland, MA.
3. Villegas, G. M., and J. Fernández. 1966. Permeability to thorium dioxide of the intercellular space of frog cerebral hemisphere. Exp. Neurol. 15:18-36.
4. Ruoslahti, E. 1996. Brain extracellular matrix. Glycobiology. 6:489-492.
5. Harris, E. J., and G. P. Burn. 1949. The transfer of sodium and potassium ions between muscle and the surrounding medium. Trans. Faraday Soc. 45:508-528.
6. Rusakov, D. A., and D. M. Kullmann. 1998. Geometric and viscous components of the tortuosity of the extracellular space in the brain. Proc. Natl. Acad. Sci. USA. 95:8975-8980.
7. El-Kareh, A. W., S. L. Braunstein, and T. W. Secomb. 1993. Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue. Biophys. J. 64:1638-1646.
8. Tao, L. 1999. Effects of osmotic stress on dextran diffusion in rat neocortex studied with integrative optical imaging. J. Neurophysiol. 81:2501-2507.
9. Krizaj, D., M. E. Rice, R. A. Wardle, and C. Nicholson. 1996. Water compartmentalization and extracellular tortuosity after osmotic challenge in cerebellum of Trachemys scripta. J. Physiol. 492:887-896.
10. Kume-Kick, J., T. Mazel, I. Voříšek, S. H. L. Tao, and C. Nicholson. 2002. Independence of extracellular tortuosity and volume fraction during osmotic challenge in rat neocortex. J. Physiol. 542:515-527.
11. Chen, K. C., and C. Nicholson. 2000. Changes in brain cell shape create residual extracellular space volume and explain tortuosity behavior during osmotic challenge. Proc. Natl. Acad. Sci. USA. 97:8306-8311.
12. Bensoussan, A., J. L. Lions, and G. Papanicolaou. 1978. Asymptotic Analysis for Periodic Structures. North Holland Science Publishers, New York.
13. Tao, L., and C. Nicholson. 2004. Maximum geometrical hindrance to Diffusion in brain extracellular space surrounding uniformly spaced convex cells. J. Theor. Biol. 229:59-68.
14. Crank, J. 1975. The Mathematics of Diffusion, 2nd Ed. Clarendon Press, Oxford, UK.
15. Tao, A., L. Tao, and C. Nicholson. 2005. Cell cavities increase tortuosity in brain extracellular space. J. Theor. Biol. 234:525-536.
16. Hrabe, J., S. Hrabětová, and K. Segeth. 2004. A model of effective diffusion and tortuosity in the extracellular space of the brain. Biophys. J. 87:1606-1617.
17. Hrabětová, S., and C. Nicholson. 2004. Contribution of dead-space microdomains to tortuosity of brain extracellular space. Neurochem. Int. 45:467-477.
18. Nicholson, C. 2005. Factors governing diffusing molecular signals in brain extracellular space. J. Neural Transm. 112:29-44.
19. Hrabětová, S., J. Hrabe, and C. Nicholson. 2003. Dead-space microdomains hinder extracellular diffusion in rat neocortex during ischemia. J. Neurosci. 23:8351-8359.
20. Maier, R. S., D. M. Kroll, H. T. Davis, and R. S. Bernard. 1999. Simulation of flow in bidisperse sphere packings. J. Colloid Interface Sci. 217:341-347.
21. Maier, R. S., D. M. Kroll, R. S. Bernard, S. E. Howington, J. F. Peters, and H. T. Davis. 2000. Pore-scale simulation of dispersion. Phys. Fluids. 12:2065-2079.
22. Maier, R. S., D. M. Kroll, R. S. Bernard, S. E. Howington, J. F. Peters, and H. T. Davis. 2003. Hydrodynamic dispersion in confined packed beds. Phys. Fluids. 15:3795-3815.
23. Canham, P. B. 1970. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theor. Biol. 26:61-81.
24. Helfrich, W. 1973. Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28c:693-703.
25. Evans, E. A. 1974. Bending resistance and chemically induced moments in membranes bilayers. Biophys. J. 14:923-931.
26. Morse, D. C., and S. T. Milner. 1995. Statistical mechanics of closed fluid membranes. Phys. Rev. E. 52:5918-5945.
27. Gompper, G., and D. Kroll. 2004. Triangulated-surface models of fluctuating membranes. In Statistical Mechanics of Membranes and Surfaces. D. Nelson, T. Piram, and S. Weinberg, editors. World Scientific, Singapore.
28. Kazakov, V. A., I. K. Kostov, and A. A. Migdal. 1985. Critical properties of randomly triangulated planar random surfaces. Phys. Lett. B. 157:295-300.
29. Boulatov, D. V., V. A. Kazakov, I. K. Kostov, and A. A. Migdal. 1986. Analytical and numerical study of a model of dynamically triangulated random surfaces. Nucl. Phys. B. 275:641-686.
30. Billoire, A., and F. David. 1986. Scaling properties of randomly triangulated planar random surfaces: a numerical study. Nucl. Phys. B. 275:617-640.
31. Ho, J. S., and A. Baumgärtner. 1990. Simulations of fluid self-avoiding membranes. Europhys. Lett. 12:295-300.
32. Kroll, D. M., and G. Gompper. 1992. The conformation of fluid membranes: Monte Carlo simulations. Science. 255:968-971.
33. Boal, D. H., and M. Rao. 1992. Scaling behavior of fluid membranes in three dimensions. Phys. Rev. A. 45:R6947-R6950.
34. Itzykson, C. 1986.Proceedings of the GIFT Seminar, Jaca 85. J. Abad, M. Asorey, and A. Cruz, editors. World Scientific, Singapore.
35. Espriu, D. 1987. Triangulated random surfaces. Phys. Lett. B. 194:271-276.
36. Szymczak, P., and A. J. C. Ladd. 2003. Boundary conditions for stochastic solutions of the convection-diffusion equation. Phys. Rev. E. 68:036704-1-036704-12.
37. Drazer, G., and J. Koplik. 2001. Tracer dispersion in two-dimensional rough fractures. Phys. Rev. E. 63:056104.
38. Kurowski, P., I. Ippolito, J. P. Hulin, J. Koplik, and E. J. Hinch. 1994. Anomalous dispersion in a dipole flow geometry. Phys. Fluids. 6:108-117.
39. Rage, T. 1996. Studies of Tracer Dispersion and Fluid Flow in Porous Media. PhD thesis, University of Oslo, Oslo, Norway.
40. Salles, J., J. F. Thovert, R. Delannay, L. Prevors, J. L. Auriault, and P. M. Adler. 1993. Taylor dispersion in porous media. Determination of the dispersion tensor. Phys. Fluids A. 5:2348-2376.
41. Reference deleted in proof.
42. Reference deleted in proof.
43. Mathias, R. T. 1983. Effect of tortuous extracellular pathways on resistance measurements. Biophys. J. 42:55-59.
44. Kloeden, P. E., and E. Platen. 1992. Numerical solution of stochastic differential equations. In Applications of Mathematics Series, Vol. 23. Springer-Verlag, Heidelberg.
45. Marsaglia, G. 1972. Choosing a point from the surface of a sphere. Ann. Math. Stat. 43:645-646.
46. Allen, M., and D. Tildesley. 1987. Computer Simulation of Fluids. Clarendon Press, Oxford, UK.
47. Maier, R. S., D. M. Kroll, Y. E. Kutsovsky, H. T. Davis, and R. S. Bernard. 1998. Simulation of flow through bead packs using lattice Boltzmann method. Phys. Fluids. 10:60-74.
48. Mair, R., G. Wong, D. Hoffmann, M. Hürlimann, S. Patz, L. Schwartz, and R. Walsworth. 1999. Probing porous media with gas diffusion NMR. Phys. Rev. Lett. 83:3324-3327.