Continuum modeling of biological tissue growth by cell division, and alteration of intracellular osmolytes and extracellular fixed charge density

Journal of Biomechanical Engineering

Volumn 131, Issue 10, 2009, Pages

  Ateshian, Gerard A ^a   Costa, Kevin D ^b   Azeloglu, Evren U ^b   Morrison III, Barclay ^a   Hung, Clark T ^a  

^a Department of Earth and Environmental Sciences   (United States)

^b MOUNT SINAI SCHOOL OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL TISSUES; CELL DIVISIONS; CONTINUUM MODELING; DAUGHTER CELLS; EXTRACELLULAR; EXTRACELLULAR MATRICES; FIXED CHARGE DENSITY; GROWTH MODELS; INTERSTITIAL FLUIDS; MOLECULAR SPECIES; OSMOLYTES; POROUS SOLIDS; PROTEOGLYCANS; SOLID MATRIXES; WATER UPTAKE;

CELL PROLIFERATION; CONTINUUM MECHANICS; ENZYME ACTIVITY; OSMOSIS; WATER CONTENT;

TISSUE;

OSMOLITE; PROTEOGLYCAN; WATER;

ARTICLE; BIOLOGICAL MODEL; CELL DENSITY; CELL DIVISION; CELL VOLUME; DAUGHTER CELL; EXTRACELLULAR MATRIX; FIXED CHARGE DENSITY; HOMOGENATE; INTERSTITIAL FLUID; KINEMATICS; OSMOSIS; OSMOTIC PRESSURE; TISSUE GROWTH; WATER TRANSPORT; ANIMAL; BIOLOGICAL PHENOMENA AND FUNCTIONS CONCERNING THE ENTIRE ORGANISM; BIOMECHANICS; CHEMISTRY; GROWTH; MATHEMATICAL PHENOMENA; MECHANICAL STRESS; MECHANOTRANSDUCTION; PHYSIOLOGY; POROSITY; SOLUTION AND SOLUBILITY;

ANIMALS; BIOLOGICAL PROCESSES; BIOMECHANICS; CELL DIVISION; EXTRACELLULAR MATRIX; GROWTH; MATHEMATICAL CONCEPTS; MECHANOTRANSDUCTION, CELLULAR; MODELS, BIOLOGICAL; OSMOSIS; POROSITY; PROTEOGLYCANS; SOLUTIONS; STRESS, MECHANICAL; WATER;

EID: 73949142001     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.3192138     Document Type: Article

References (54)

1. Hsu, F. H., 1968, "The Influences of Mechanical Loads on the Form of a Growing Elastic Body," J. Biomech., 1(4), pp. 303-311.
2. Cowin, S. C., and Hegedus, D. H., 1976, "Bone Remodeling - 1. Theory of Adaptive Elasticity," J. Elast., 6(3), pp. 313-326.
3. Skalak, R., Dasgupta, G., Moss, M., Otten, E., Dullumeijer, P., and Vilmann, H., 1982, "Analytical Description of Growth," J. Theor. Biol., 94(3), pp. 555-577.
4. Rodriguez, E. K., Hoger, A., and McCulloch, A. D., 1994, "Stress-Dependent Finite Growth in Soft Elastic Tissues," J. Biomech., 27(4), pp. 455-467.
5. Epstein, M., and Maugin, G. A., 2000, "Thermomechanics of Volumetric Growth in Uniform Bodies," Int. J. Plast., 16(7-8), pp. 951-978.
6. Klisch, S., Van Dyke, T., and Hoger, A., 2001, "A Theory of Volumetric Growth for Compressible Elastic Biological Materials," Math. Mech. Solids, 6(6), pp. 551-575. (Pubitemid 33120261)
7. Humphrey, J. D., and Rajagopal, K. R., 2002, "A Constrained Mixture Model for Growth and Remodeling of Soft Tissues," Math. Models Meth. Appl. Sci., 12(3), pp. 407-430.
8. Garikipati, K., Arruda, E., Grosh, K., Narayanan, H., and Calve, S., 2004, "A Continuum Treatment of Growth in Biological Tissue: The Coupling of Mass Transport and Mechanics," J. Mech. Phys. Solids, 52(7), pp. 1595-1625.
9. Volokh, K. Y., 2004, "Mathematical Framework for Modeling Tissue Growth," Biorheology, 41(3-4), pp. 263-269.
10. Guillou, A., and Ogden, R. W., 2006, "Growth in Soft Biological Tissue and Residual Stress Development," Mechanics of Biological Tissue, G. A. Holzapfel and R. W. Ogden, eds., Springer, New York, pp. 47-62.
11. Klisch, S. M., Chen, S. S., Sah, R. L., and Hoger, A., 2003, "A Growth Mixture Theory for Cartilage With Application to Growth-Related Experiments on Cartilage Explants," ASME J. Biomech. Eng., 125(2), pp. 169-179. (Pubitemid 36506130)
12. Dimicco, M. A., and Sah, R. L., 2003, "Dependence of Cartilage Matrix Composition on Biosynthesis, Diffusion, and Reaction," Transp. Porous Media, 50(1-2), pp. 57-73.
13. Radisic, M., Deen, W., Langer, R., and Vunjak-Novakovic, G., 2005, "Mathematical Model of Oxygen Distribution in Engineered Cardiac Tissue With Parallel Channel Array Perfused With Culture Medium Containing Oxygen Carriers," Am. J. Physiol. Heart Circ. Physiol., 288(3), pp. H1278-H1289. (Pubitemid 40270035)
14. Lemon, G., King, J. R., Byrne, H. M., Jensen, O. E., and Shakesheff, K. M., 2006, "Mathematical Modelling of Engineered Tissue Growth Using a Multiphase Porous Flow Mixture Theory," J. Math. Biol., 52(5), pp. 571-594.
15. Cosgrove, D., 1986, "Biophysical Control of Plant Cell Growth," Annu. Rev. Plant Physiol., 37, pp. 377-405.
16. Kedem, O., and Katchalsky, A., 1958, "Thermodynamic Analysis of the Permeability of Biological Membranes to Non-Electrolytes," Biochim. Biophys. Acta, 27(2), pp. 229-246.
17. Ateshian, G. A., Likhitpanichkul, M., and Hung, C. T., 2006, "A Mixture Theory Analysis for Passive Transport in Osmotic Loading of Cells," J. Biomech., 39(3), pp. 464-475. (Pubitemid 43028509)
18. Albro, M. B., Chahine, N. O., Caligaris, M., Wei, V. I., Likhitpanichkul, M., Ng, K. W., Hung, C. T., and Ateshian, G. A., 2007, "Osmotic Loading of Spherical Gels: A Biomimetic Study of Hindered Transport in the Cell Protoplasm," ASME J. Biomech. Eng., 129(4), pp. 503-510.
19. Haider, M. A., Schugart, R. C., Setton, L. A., and Guilak, F., 2006, "A Mechano-Chemical Model for the Passive Swelling Response of an Isolated Chondron Under Osmotic Loading," Biomech. Model. Mechanobiol., 5(2-3), pp. 160-171. (Pubitemid 43787099)
20. Lai, W. M., Hou, J. S., and Mow, V. C., 1991, "A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage," ASME J. Biomech. Eng., 113(3), pp. 245-258.
21. Huyghe, J. M., and Janssen, J. D., 1997, "Quadriphasic Mechanics of Swelling Incompressible Porous Media," Int. J. Eng. Sci., 35(8), pp. 793-802.
22. Gu, W. Y., Lai, W. M., and Mow, V. C., 1998, "A Mixture Theory for Charged-Hydrated Soft Tissues Containing Multi-Electrolytes: Passive Transport and Swelling Behaviors," ASME J. Biomech. Eng., 120(2), pp. 169-180.
23. Mauck, R. L., Hung, C. T., and Ateshian, G. A., 2003, "Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering," ASME J. Biomech. Eng., 125(5), pp. 602-614.
24. Truesdell, C., and Toupin, R., 1960. "The Classical Field Theories," Handbuch der Physik, Vol. III/1, S. Flugge, ed., Springer-Verlag, Berlin.
25. Bowen, R. M., 1976, "Theory of Mixtures," Continuum Physics, Vol. 3, A. E. Eringen, ed., Academic, New York, pp. 1-127.
26. Bowen, R. M., 1980, "Incompressible Porous Media Models by Use of the Theory of Mixtures," Int. J. Eng. Sci., 18(9), pp. 1129-1148.
27. Bowen, R. M., 1969, "The Thermochemistry of a Reacting Mixture of Elastic Materials With Diffusion," Arch. Ration. Mech. Anal., 34(2), pp. 97-127.
28. Ateshian, G. A., 2007, "On the Theory of Reactive Mixtures for Modeling Biological Growth," Biomech. Model. Mechanobiol., 6(6), pp. 423-445.
29. Katzir-Katchalsky, A., and Curran, P. F., 1965, "Nonequilibrium Thermodynamics in Biophysics," Harvard Books in Biophysics, Vol. 1, Harvard University Press, Cambridge.
30. Tinoco, I., Jr., Sauer, K., and Wang, J. C., 1995, Physical Chemistry: Principles and Applications in Biological Sciences, Prentice-Hall, Englewood Cliffs, NJ.
31. Nobel, P. S., 1969, "The Boyle-Van't Hoff Relation," J. Theor. Biol., 23(3), pp. 375-379.
32. Weiss, T. F., 1996, Cellular Biophysics, MIT, Cambridge, MA.
33. McManus, M. L., Churchwell, K. B., and Strange, K., 1995, "Regulation of Cell Volume in Health and Disease," N. Engl. J. Med., 333(19), pp. 1260-1266.
34. Delesse, A., 1847, "Procédé Mécanique pour Déterminer la Composition des Roches," C.R. [Hebd. Séanc.] Acad. Sci., Paris, 4, pp. 544-545.
35. Bonet, J., and Wood, R. D., 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge.
36. Azeloglu, E. U., Albro, M. B., Thimmappa, V. A., Ateshian, G. A., and Costa, K. D., 2008, "Heterogeneous Transmural Proteoglycan Distribution Provides a Mechanism for Regulating Residual Stresses in the Aorta," Am. J. Physiol. Heart Circ. Physiol., 294(3), pp. H1197-H205.
37. Carter, D. R., and Hayes, W. C., 1976, "Bone Compressive Strength: The Influence of Density and Strain Rate," Science, 194(4270), pp. 1174-1176.
38. Gibson, L. J., and Ashby, M. F., 1997. Cellular Solids: Structure and Properties (Cambridge Solid State Science Series), 2nd ed., Cambridge University Press, Cambridge.
39. Mow, V. C., and Huiskes, R., 2005, Basic Orthopaedic Biomechanics & Mechano-Biology, 3rd ed., Lippincott Williams & Wilkins, Philadelphia, PA.
40. Wight, T. N., and Ross, R., 1975, "Proteoglycans in Primate Arteries. I. Ultrastructural Localization and Distribution in the Intima," J. Cell Biol., 67(3), pp. 660-674.
41. Yao, L. Y., Moody, C., Schonherr, E., Wight, T. N., and Sandell, L. J., 1994, "Identification of the Proteoglycan Versican in Aorta and Smooth Muscle Cells by DNA Sequence Analysis, In Situ Hybridization and Immunohistochemistry," Matrix Biol., 14(3), pp. 213-225. (Pubitemid 24136381)
42. Chuong, C. J., and Fung, Y. C., 1986, "On Residual Stresses in Arteries," ASME J. Biomech. Eng., 108(2), pp. 189-192.
43. Porterfield, S. P., Calhoon, T. B., and Weiss, H. S., 1968, "Changes in Connective Tissue Colloidal Charge Density With Atherosclerosis and Age," Am. J. Physiol., 215(2), pp. 324-329.
44. Volker, W., Schmidt, A., Oortmann, W., Broszey, T., Faber, V., and Buddecke, E., 1990, "Mapping of Proteoglycans in Atherosclerotic Lesions," Eur. Heart J., 11, pp. 29-40.
45. Evanko, S. P., Raines, E. W., Ross, R., Gold, L. I., and Wight, T. N., 1998, "Proteoglycan Distribution in Lesions of Atherosclerosis Depends on Lesion Severity, Structural Characteristics, and the Proximity of Platelet-Derived Growth Factor and Transforming Growth Factor-Beta," Am. J. Pathol., 152(2), pp. 533-546. (Pubitemid 28106400)
46. Matsumoto, T., Hayashi, K., and Ide, K., 1995, "Residual Strain and Local Strain Distributions in the Rabbit Atherosclerotic Aorta," J. Biomech., 28(10), pp. 1207-1217.
47. Valenta, J., Svoboda, J., Valerianova, D., and Vitek, K., 1999, "Residual Strain in Human Atherosclerotic Coronary Arteries and Age Related Geometrical Changes," Biomed. Mater. Eng., 9(5-6), pp. 311-317. (Pubitemid 30194145)
48. Gregersen, H., Zhao, J., Lu, X., Zhou, J., and Falk, E., 2007, "Remodelling of the Zero-Stress State and Residual Strains in apoE-Deficient Mouse Aorta," Biorheology, 44(2), pp. 75-89. (Pubitemid 47356402)
49. Treggiari, M. M., Schutz, N., Yanez, N. D., and Romand, J. A., 2007, "Role of Intracranial Pressure Values and Patterns in Predicting Outcome in Traumatic Brain Injury: A Systematic Review," Neurocrit. Care, 6(2), pp. 104-112. (Pubitemid 46934020)
50. Humphrey, J. D., and Rajagopal, K. R., 2003, "A Constrained Mixture Model for Arterial Adaptations to a Sustained Step Change in Blood Flow," Biomech. Model. Mechanobiol., 2(2), pp. 109-126.
51. Guo, X., Lanir, Y., and Kassab, G. S., 2007, "Effect of Osmolarity on the Zero-Stress State and Mechanical Properties of Aorta," Am. J. Physiol. Heart Circ. Physiol., 293(4), pp. H2328-H2334. (Pubitemid 47605878)
52. Guilak, F., and Mow, V. C., 2000, "The Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions in Articular Cartilage," J. Biomech., 33(12), pp. 1663-1673.
53. Rangel-Castilla, L., Gopinath, S., and Robertson, C. S., 2008, "Management of Intracranial Hypertension," Neurol. Clin., 26(2), pp. 521-541.
54. Skalak, R., Farrow, D. A., and Hoger, A., 1997, "Kinematics of Surface Growth," J. Math. Biol., 35(8), pp. 869-907.