Microfluidics and Nanofluidics

, Volume 4, Issue 3, pp 193–204 | Cite as

Pairing computational and scaled physical models to determine permeability as a measure of cellular communication in micro- and nano-scale pericellular spaces

  • Eric J. Anderson
  • Steven M. Kreuzer
  • Oliver Small
  • Melissa L. Knothe Tate
Research Paper


Cells, the living components of tissues, bathe in fluid. The pericellular fluid environment is a challenge to study due to the remoteness and complexity of its nanoscale fluid pathways. The degree to which the pericellular fluid environment modulates the transport of mechanical and molecular signals between cells and across tissues is unknown. As a consequence, experimental and computational studies have been limited and/or highly idealized. In this study we apply a fundamental fluid dynamics technique to measure pericellular permeability through scaled-up physical models obtained from high resolution microscopy. We assess permeability of physiologic tissue by tying together data from parallel experimental and computational models that account for specific structures of the flow cavities and cellular structures therein (cell body, cell process, pericellular matrix). A healthy cellular network devoid of cellular structure is shown to exhibit permeability on the order of 2.8 × 10−16 m2; inclusion of cellular structures reduces permeability to the order of 10−17 to 10−18 m2. These permeability studies provide not only unprecedented quantitative experimental measures of the pericellular fluid environment but also provide a novel measure of “infrastructural integrity” that likely influences the efficiency of the cellular communication network across the tissue.


Scaling Permeability Pericellular Cell Tissue Signal transmission efficiency 

List of symbols


viscosity of fluid


density of fluid


intrinsic permeability of specimen


hydraulic conductivity


volume flow rate


length of specimen


permeation/diffusion time


gravitational constant


height above specimen surface




inlet pressure


fluid pressure


characteristic pore/channel dimension


Reynolds number

\( \dot{m} \)

mass flow rate


cross-sectional area of specimen


axial pipe velocity


radius of pericellular channel


axial pipe coordinate


radial pipe coordinate




diffusion coefficient


  1. Ackroyd JAD (2002) Sir George Cayley, the father of aeronautics. Part 1. The invention of the airplane. Notes Rec R Soc Lond 56:167–181CrossRefMathSciNetGoogle Scholar
  2. Alexopoulos LG, Setton LA, Guilak F (2005) The biomechanical role of the chondrocyte pericellular matrix in articular cartilage. Acta Biomater 1:317–325CrossRefGoogle Scholar
  3. Anderson EJ, Kaliyamoorthy S, Alexander JID, Knothe Tate ML (2005) Nano-micro scale models of periosteocytic flow show differences in stresses imparted to cell body and processes. Ann Biom Eng 33:52–62CrossRefGoogle Scholar
  4. Anderson EJ, Falls TD, Sorkin AM, Knothe Tate ML (2006) The imperative for controlled mechanical stresses in unraveling cellular mechanisms of mechanotransduction. Biomed Eng Online 5:27CrossRefGoogle Scholar
  5. Astarita G (1997) Dimensional analysis, scaling, and orders of magnitude. Chem Eng Sci 52:4681–98CrossRefGoogle Scholar
  6. Baals DD, Corliss WR (1981) Wind tunnels of NASA. Scientific and technical branch, National Aeronautics and Space Administration, SP-440, Washington, D.CGoogle Scholar
  7. Bardet JP (1997) Experimental Soil Mechanics. Prentice-Hall, New JerseyGoogle Scholar
  8. Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155–64CrossRefGoogle Scholar
  9. Bridgman P (1922) Dimensional analysis. Yale University Press, New HavenGoogle Scholar
  10. Chang J, Poole CA (1996) Sequestion of type VI collagen in the pericellular microenvironment of adult chrondrocytes [sic] cultured in agarose. Osteoarthritis Cartilage 4:275–285CrossRefGoogle Scholar
  11. Coleman HW, Steele WG (1999) Experimentation and uncertainty analysis for engineers. Wiley, New YorkGoogle Scholar
  12. Dillaman RM, Roer RD, Gay DM (1991) Fluid movement in bone: theoretical and empirical. J Biomech 24:163–177CrossRefGoogle Scholar
  13. Einstein A (1911) Elementare Betrachtungen ueber die thermische Molekularbewegung in festen Koerpern. Ann Phys 35:679–94Google Scholar
  14. Fleury ME, Boardman KC, Swartz MA (2006) Autologous morphogen gradients by subtle interstitial flow and matrix interactions. Biophys J 91:113–121CrossRefGoogle Scholar
  15. Goldstein RJ (1996) Fluid mechanics measurements. Taylor & Francis, Washington, D.CGoogle Scholar
  16. Gupta T, Haut Donahue TL (2006) Role of cell location and morphology in the mechanical environment around meniscal cells. Acta Biomater 2:483–492CrossRefGoogle Scholar
  17. Han Y, Cowin SC, Schaffler MB, Weinbaum S (2004) Mechanotransduction and strain amplification in osteocyte cell processes. Proc Natl Acad Sci 101:16689–16694CrossRefGoogle Scholar
  18. Johnson MW, Chakkalakal DA, Harper RA, Katz JL (1980) Comparison of the electromechanical effects in wet and dry bone. J Biomech 13:437–442CrossRefGoogle Scholar
  19. Knothe Tate ML (2001) Mixing mechanisms and net solute transport in bone. Ann Biomed Eng 29:810–11CrossRefGoogle Scholar
  20. Knothe Tate ML (2002) Micropathoanatomy of osteoporosis—indications for a cellular basis of bone disease. Adv Osteoporotic Fract Mgmt 2:9–14Google Scholar
  21. Knothe Tate ML (2003) “Whither flows the fluid in bone?” An osteocyte’s perspective. J Biomech 36:1409–1424CrossRefGoogle Scholar
  22. Knothe Tate ML (2007) Multiscale computational engineering of bones: state-of-the-art insights for the future. In: Bronner F, Farach-Carson MC, Mikos AG (eds) Engineering of Skeletal Tissues, vol 3 Springer, London, p 143Google Scholar
  23. Knothe Tate ML, Knothe U (2000) An ex vivo model to study transport processes and fluid flow in loaded bone. J Biomech 33:247–254CrossRefGoogle Scholar
  24. Knothe Tate ML, Niederer P, Knothe U (1998) In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading. Bone 22:107–117CrossRefGoogle Scholar
  25. Korhonen RK, Julkunen P, Rieppo J, Lappalainen R, Konttinen YT, Jurvelin JS (2006) Collagen network of articular cartilage modulates fluid flow and mechanical stresses in chondrocyte, Biomech Model Mechanobiol 5:150–159CrossRefGoogle Scholar
  26. Liebschner M, Keller T (1998) Hydraulic strengthening affects the stiffness and strength of cortical bone. Comput Meth Bioeng 20:761–762Google Scholar
  27. Maroudas A (1976) Transport of solutes through cartilage: permeability to large molecules. J Anat 122:335–347Google Scholar
  28. Means RE, Parcher JV (1963) Physical properties of soils. Charles E. Merrill Books, ColumbusGoogle Scholar
  29. Mishra S, Knothe Tate ML (2003) Effect of lacunocanalicular architecture on hydraulic conductance in bone tissue: implications for bone health and evolution. Anat Rec A Discov Mol Cell Evol Biol 273:752–762CrossRefGoogle Scholar
  30. Nicholson C (1988–1989) Issues involved in the transmission of chemical signals through the brain extracellular space. Acta Morphol Neeri Scand 26:69–80Google Scholar
  31. Patel RB, O’Leary JM, Bhatt SJ, Vasanja A, Knothe Tate ML (2005). Determining the permeability of cortical bone at multiple length scales using fluorescence recovery after photobleaching techniques. Proceedings of the Orthopaedic Research SocietyGoogle Scholar
  32. Rayleigh L (1892) On the question of the stability of the flow of fluids. Philos Mag 34:59–70Google Scholar
  33. Rayleigh L (1904) Fluid friction on even surfaces. Philos Mag 8:66–67Google Scholar
  34. Rayleigh L (1915) The principle of similitude. Nature 95:66–68Google Scholar
  35. Reynolds O (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos Trans R Soc Lond 174:935–982CrossRefGoogle Scholar
  36. Reynolds O (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos Trans R Soc Lond 186:123–164CrossRefGoogle Scholar
  37. Sorkin AM, Knothe Tate ML (2004) “Culture shock” from the bone cell’s perspective: emulating physiological conditions for mechanobiological investigations. Am J Physiol Cell Physiol 287:C1527–C1536CrossRefGoogle Scholar
  38. Steck R, Niederer P, Knothe Tate ML (2003) A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone. J Theor Biol 220:249–259CrossRefGoogle Scholar
  39. Steck R, Knothe Tate ML (2005) In silico stochastic network models that emulate the molecular sieving characteristics of bone. Ann Biomed Eng 33:87–94CrossRefGoogle Scholar
  40. da Vinci L (1508) Ms. F. In: Johnstone RE, Thring MW (eds) Pilot plants, models, and scale-up methods in chemical engineering. McGraw-Hill, New YorkGoogle Scholar
  41. Wang L, Wang Y, Han Y, Henderson SC, Majeska RJ, Weinbaum S, Schaffler MB (2005) In situ measurement of solute transport in the bone lacunar-canalicular system. Proc Natl Acad Sci 102:11911–11916CrossRefGoogle Scholar
  42. Wehrli FW, Fernández-Seara MA (2005) Nuclear magnetic resonance studies of bone water. Ann Biomed Eng 33:79–86CrossRefGoogle Scholar
  43. Weinbaum S, Cowin SC, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J Biomech 27:339–360CrossRefGoogle Scholar
  44. You L, Cowin SC, Schaffler MB, Weinbaum S (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J Biomech 34:1375–1386CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Eric J. Anderson
    • 1
  • Steven M. Kreuzer
    • 1
  • Oliver Small
    • 2
  • Melissa L. Knothe Tate
    • 1
    • 2
  1. 1.Department of Mechanical and Aerospace EngineeringCase Western Reserve UniversityClevelandUSA
  2. 2.Department of Biomedical EngineeringCase Western Reserve UniversityClevelandUSA

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