Constitutive Modeling of Brain Tissue: Current Perspectives

Applied Mechanics Reviews

Volumn 68, Issue 1, 2016, Pages

  De Rooij, Rijk ^a   Kuhl, Ellen ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEHAVIORAL RESEARCH; BRAIN; CONSTITUTIVE MODELS;

CONVOLUTION INTEGRALS; DEPENDENT CONTRIBUTIONS; HYPERELASTIC APPROACH; MULTIPLICATIVE DECOMPOSITION; PATHOLOGICAL CONDITIONS; PHENOMENOLOGICAL MODELING; PHYSIOLOGICAL CONDITION; TIME-DEPENDENT RESPONSE;

TISSUE;

EID: 84955268478     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.4032436     Document Type: Review

References (96)

1. Chatelin, S., Constantinesco, A., and Willinger, R., 2010, "Fifty Years of Brain Tissue Mechanical Testing: From In Vitro to In Vivo Investigations, " Biorheology, 47(5-6), pp. 255-276.
2. Holbourn, A. H. S., 1943, "Mechanics of Head Injury, " Lancet, 242(6267), pp. 438-441.
3. Miller, K., 2011, Biomechanics of the Brain, Springer, New York.
4. Bilston, L. E., 2011, Neural Tissue Biomechanics, Springer, Heidelberg, Germany.
5. Goriely, A., Geers, M. G. D., Holzapfel, G. A., Jayamohan, J., Jerusalem, A., Sivaloganathan, S., Squier, W., van Dommelen, J. A. W., Waters, S., and Kuhl, E., 2015, "Mechanics of the Brain: Perspectives, Challenges, and Opportunities, " Biomech. Model. Mechanobiol., 14(5), pp. 931-965.
6. Bilston, L. E., Liu, Z., and Phan-Thien, N., 1997, "Linear Viscoelastic Properties of Bovine Brain Tissue in Shear, " Biorheology, 34(6), pp. 377-385.
7. Fallenstein, G. T., Hulce, V. D., and Melvin, J. W., 1969, "Dynamic Mechanical Properties of Human Brain Tissue, " J. Biomech., 2(3), pp. 217-226.
8. Holzapfel, G. A., 2000, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Wiley, Chichester, UK.
9. Cheng, S., Clarke, E. C., and Bilston, L. E., 2008, "Rheological Properties of the Tissues of the Central Nervous System: A Review, " Med. Eng. Phys., 30(10), pp. 1318-1337.
10. Goriely, A., Budday, S., and Kuhl, E., 2015, "Neuromechanics: From Neurons to Brain, " Adv. Appl. Mech., 48, pp. 79-139.
11. Franze, K., Janmey, P. A., and Guck, J., 2013, "Mechanics in Neuronal Development and Repair, " Annu. Rev. Biomed. Eng., 15(1), pp. 227-251.
12. Rausch, M. K., and E. K., 2013, "On the Effect of Prestrain and Residual Stress in Thin Biological Membranes, " J. Mech. Phys. Solids, 61(9), pp. 1955-1969.
13. Rausch, M. K., Famaey, N., O'Brien Shultz, T., Bothe, W., Miller, D. C., and Kuhl, E., 2013, "Mechanics of the Mitral Valve: A Critical Review, an In Vivo Parameter Identification, and the Effect of Prestrain, " Biomech. Modell. Mechanobiol., 12(5), pp. 1053-1071.
14. Bilston, L. E., Liu, Z., and Phan-Thien, N., 2001, "Large Strain Behaviour of Brain Tissue in Shear: Some Experimental Data and Differential Constitutive Model, " Biorheology, 28(4), pp. 335-345.
15. Hrapko, M., van Dommelen, J. A. W., Peters, G. W. M., and Wismans, J. S. H. M., 2006, "The Mechanical Behaviour of Brain Tissue: Large Strain Response and Constitutive Modelling, " Biorheology, 43(5), pp. 623-636.
16. Prevost, T. P., Balakrishnan, A., Suresh, S., and Socrate, S., 2011, "Biomechanics of Brain Tissue, " Acta Biomater., 7(1), pp. 83-95.
17. Ogden, R. W., 1984, Non-Linear Elastic Deformations, Wiley, Chichester, UK.
18. Spencer, A. J. M., 1984, "Constitutive Theory of Strongly Anisotropic Solids, " Continuum Theory of the Mechanics of Fibre Reinforced Composites (CISM Courses and Lectures), Vol. 282, A. J. M. Spencer, ed., Springer, Berlin, pp. 1-32.
19. Okamoto, R. J., Feng, Y., Genin, G. M., and Bayly, P. V., 2013, "Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models, " ASME Paper No. SBC2013-14039.
20. Feng, Y., Okamoto, R. J., Namani, R., Genin, G. M., and Bayly, P. V., 2013, "Measurements of Mechanical Anisotropy in Brain Tissue and Implications for Transversely Isotropic Material Models of White Matter, " J. Mech. Behav. Biomed. Mater., 23, pp. 117-132.
21. Tenti, G., Sivaloganathan, S., and Drake, J. M., 1999, "Brain Biomechanics: Steady-State Consolidation Theory of Hydrocephalus, " Can. Appl. Math. Q., 7(1), pp. 111-124.
22. Franceschini, G., Bigoni, D., Regitnig, P., and Holzapfel, G. A., 2006, "Brain Tissue Deforms Similarly to Filled Elastomers and Follows Consolidation Theory, " J. Mech. Phys. Solids, 54(12), pp. 2592-2620.
23. Mihai, L. A., Chin, L. K., Janmey, P. A., and Goriely, A., 2015, "A Hyperelastic Constitutive Model for Compression Stiffening Applicable to Brain and Fat Tissues, " J. R. Soc. Interface, 12(110), p. 20150486.
24. Ogden, R. W., 1972, "Large Deformation Isotropic Elasticity-On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids, " Proc. R. Soc. London A, 326(1567), pp. 565-584.
25. Mooney, M., 1940, "A Theory of Large Elastic Deformation, " J. Appl. Phys., 11(9), pp. 582-592.
26. Rivlin, R. S., 1948, "Large Elastic Deformations of Isotropic Materials. IV. Further Developments of the General Theory, " Philos. Trans. R. Soc. London A, 241(835), pp. 379-397.
27. Rivlin, R. S., and Saunders, D. W., 1951, "Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber, " Philos. Trans. R. Soc. London A, 243(865), pp. 251-288.
28. Gent, A. N., 1996, "A New Constitutive Relation For Rubber, " Rubber Chem. Technol., 69(1), pp. 59-61.
29. Holland, M. A., Miller, K. E., and Kuhl, E., 2015, "Emerging Brain Morphologies From Axonal Elongation, " Ann. Biomed. Eng., 43(7), pp. 1640-1653.
30. Holzapfel, G. A., and Gasser, T. C., 2001, "A Viscoelastic Model for Fiber-Reinforced Composites at Finite Strains: Continuum Basis, Computational Aspects and Applications, " Comput. Methods Appl. Mech. Eng., 190(34), pp. 4379-4403.
31. Gasser, T. C., Ogden, R. W., and Holzapfel, G. A., 2006, "Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations, " J. R. Soc. Interface, 3(6), pp. 15-35.
32. Cloots, R. J. H., van Dommelen, J. A. W., Nyberg, T., Kleiven, S., and Geers, M. G. D., 2011, "Micromechanics of Diffuse Axonal Injury: Influence of Axonal Orientation and Anisotropy, " Biomech. Model. Mechanobiol., 10(3), pp. 413-422.
33. Laksari, K., Shafieian, M., and Darvish, K., 2012, "Constitutive Model for Brain Tissue Under Finite Compression, " J. Biomech., 45(4), pp. 642-646.
34. Simo, J. C., and Miehe, C., 1992, "Associative Coupled Thermoplasticity at Finite Strains: Formulation, Numerical Analysis and Implementation, " Comput. Methods Appl. Mech. Eng., 98(1), pp. 41-104.
35. Ommaya, A. K., 1968, "Mechanical Properties of Tissues of the Nervous System, " J. Biomech., 1(2), pp. 127-136.
36. Galford, J. E., and McElhaney, J. H., 1970, "A Viscoelastic Study of Scalp, Brain, and Dura, " J. Biomech., 3(2), pp. 211-221.
37. Sack, I., Beierbach, B., Hamhaber, U., Klatt, D., and Braun, J., 2008, "Non-Invasive Measurement of Brain Viscoelasticity Using Magnetic Resonance Elastography, " NMR Biomed., 21(3), pp. 265-271.
38. Kruse, S. A., Rose, G. H., Glaser, K. J., Manduca, A., Felmlee, J. P., Jack, C. R., Jr., and Ehman, R. L., 2008, "Magnetic Resonance Elastography of the Brain, " NeuroImage, 39(1), pp. 231-237.
39. Green, M. A., Bilston, L. E., and Sinkus, R., 2008, "In Vivo Brain Viscoelastic Properties Measured by Magnetic Resonance Elastography, " NMR Biomed., 21(7), pp. 755-764.
40. Feng, Y., Clayton, E. H., Chang, Y., Okamoto, R. J., and Bayly, P. V., 2013, "Viscoelastic Properties of the Ferret Brain Measured In Vivo at Multiple Frequencies by Magnetic Resonance Elastography, " J. Biomech., 46(5), pp. 863-870.
41. Sack, I., Beierbach, B., Wuerfel, J., Klatt, D., Hamhaber, U., Papazoglou, S., Martus, P., and Braun, J., 2009, "The Impact of Aging and Gender on Brain Viscoelasticity, " NeuroImage, 46(3), pp. 652-657.
42. Streitberger, K.-J., Sack, I., Krefting, D., Pfuller, C., Braun, J., Paul, F., and Wuerfel, J., 2012, "Brain Viscoelasticity Alteration in Chronic-Progressive Multiple Sclerosis, " PLoS One, 7(1), p. e29888.
43. Mendis, K. K., Stalnaker, R. L., and Advani, S. H., 1995, "A Constitutive Relationship for Large Deformation Finite Element Modeling of Brain Tissue, " ASME J. Biomech. Eng., 117(3), pp. 279-285.
44. Miller, K., and Chinzei, K., 1997, "Constitutive Modelling of Brain Tissue: Experiment and Theory, " J. Biomech., 30(11-12), pp. 1115-1121.
45. Miller, K., 1999, "Constitutive Model of Brain Tissue Suitable for Finite Element Analysis of Surgical Procedures, " J. Biomech., 32(5), pp. 531-537.
46. Miller, K., Chinzei, K., Orssengo, G., and Bednarz, P., 2000, "Mechanical Properties of Brain Tissue In-Vivo: Experiment and Computer Simulation, " J. Biomech., 33(11), pp. 1369-1376.
47. Miller, K., and Chinzei, K., 2002, "Mechanical Properties of Brain Tissue in Tension, " J. Biomech., 35(4), pp. 483-490.
48. Prange, M. T., and Margulies, S. S., 2002, "Regional, Directional, and Age-Dependent Properties of the Brain Undergoing Large Deformation, " ASME J. Biomech. Eng., 124(2), pp. 244-252.
49. Rashid, B., Destrade, M., and Gilchrist, M. D., 2013, "Mechanical Characterization of Brain Tissue in Simple Shear at Dynamic Strain Rates, " J. Mech. Behav. Biomed. Mater., 28, pp. 71-85.
50. Li, K., Zhao, H., Liu, W., and Yin, Z., 2015, "Material Properties and Constitutive Modeling of Infant Porcine Cerebellum Tissue in Tension at High Strain Rate, " PLoS One, 10(4), p. e0123506.
51. Pamidi, M. R., and Advani, S. H., 1978, "Nonlinear Constitutive Relations for Human Brain Tissue, " ASME J. Biomech. Eng., 100(1), pp. 44-48.
52. Budday, S., Raybaud, C., and Kuhl, E., 2014, "A Mechanical Model Predicts Morphological Abnormalities in the Developing Human Brain, " Sci. Rep., 4, p. 5644.
53. Wagner, M. H., 1976, "Analysis of Time-Dependent Non-Linear Stress-Growth Data for Shear and Elongational Flow of a Low-Density Branched Polyethylene Melt, " Rheol. Acta, 15(2), pp. 136-142.
54. Phan-Thien, D. N., Safari-Ardi, M., and Morales-Pati~no, A., 1997, "Oscillatory and Simple Shear Flows of a Flour-Water Dough: A Constitutive Model, " Rheol. Acta, 36(1), pp. 38-48.
55. Arruda, E. M., and Boyce, M. C., 1993, "A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials, " J. Mech. Phys. Solids, 41(2), pp. 389-412.
56. Ahmadzadeh, H., Smith, D. H., and Shenoy, V. B., 2014, "Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules During Axonal Stretch Injury: Predictions From a Mathematical Model, " Biophys. J., 106(5), pp. 1123-1133.
57. van den Bedem, H., and Kuhl, E., 2015, "Tau-ism: The Yin and Yang of the Microtubule Sliding, Detachment, and Rupture, " Biophys. J., 109(11), pp. 2215-2217.
58. Hakim, S., Venegas, J. G., and Burton, J. D., 1976, "The Physics of the Cranial Cavity, Hydrocephalus and Normal Pressure Hydrocephalus: Mechanical Interpretation and Mathematical Model, " Surg. Neurol., 5(3), pp. 187-210.
59. Miga, M. I., Paulsen, K. D., Hoopes, P. J., Kennedy, F. E., Hartov, A., and Roberts, D. W., 2000, "in vivo Modeling of Interstitial Pressure in the Brain Under Surgical Load Using Finite Elements, " ASME J. Biomech. Eng., 122(4), pp. 354-363.
60. Shahim, K., Drezet, J. M., Martin, B. A., and Momjian, S., 2012, "Ventricle Equilibrium Position in Healthy and Normal Pressure Hydrocephalus Brains Using an Analytical Model, " ASME J. Biomech. Eng., 134(4), p. 041007.
61. Drapaca, C. S., and Fritz, J. S., 2012, "A Mechano-Electrochemical Model of Brain Neuromechanics: Application to Normal Pressure Hydrocephalus, " Int. J. Numer. Anal. Model., 3(1), pp. 82-93.
62. Garca, J. J., and Smith, J. H., 2008, "A Biphasic Hyperelastic Model for the Analysis of Fluid and Mass Transport in Brain Tissue, " Ann. Biomed. Eng., 37(2), pp. 375-386.
63. Støverud, K. H., Darcis, M., Helmig, R., and Hassanizadeh, S. M., 2011, "Modeling Concentration Distribution and Deformation During Convection-Enhanced Drug Delivery Into Brain Tissue, " Transp. Porous Media, 92(1), pp. 119-143.
64. Biot, M. A., 1941, "General Theory of Three-Dimensional Consolidation, " J. Appl. Phys., 12(2), pp. 155-164.
65. Kaczmarek, M., Subramaniam, R. P., and Neff, S. R., 1997, "The Hydromechanics of Hydrocephalus: Steady-State Solutions for Cylindrical Geometry, " Bull. Math. Biol., 59(2), pp. 295-323.
66. Lang, G. E., Vella, D., Waters, S. L., and Goriely, A., 2015, "Propagation of Damage in Brain Tissue: Coupling the Mechanics of Oedema and Oxygen Delivery, " Biomech. Model. Mechanobiol., 14(6), pp. 1197-1216.
67. Bayly, P. V., Taber, L. A., and Kroenke, C. D., 2014, "Mechanical Forces in Cerebral Cortical Folding: A Review of Measurements and Models, " J. Mech. Behav. Biomed. Mater., 29, pp. 568-581.
68. Kaliske, M., and Rothert, H., 1997, "Formulation and Implementation of Three-Dimensional Viscoelasticity at Small and Finite Strains, " Comput. Mech., 19(3), pp. 228-239.
69. Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., and Kuhl, E., 2015, "Mechanical Properties of Gray and White Matter Brain Tissue by Indentation, " J. Mech. Behav. Biomed. Mater., 46, pp. 318-330.
70. Brands, D. W. A., Peters, G. W. M., and Bovendeerd, P. H. M., 2004, "Design and Numerical Implementation of a 3-D Non-Linear Viscoelastic Constitutive Model for Brain Tissue During Impact, " J. Biomech., 37(1), pp. 127-134.
71. Lee, E. H., 1969, "Elastic-Plastic Deformation at Finite Strains, " ASME J. Appl. Mech., 36(1), pp. 1-6.
72. Sidoroff, F., 1974, "Un Modèle Viscoelastique Non Lineaire Avec Configuration Intermediaire, " J. Mec., 13, pp. 679-713.
73. 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.
74. Nedjar, B., 2002, "Frameworks for Finite Strain Viscoelastic-Plasticity Based on Multiplicative Decompositions. Part I: Continuum Formulations, " Comput. Methods Appl. Mech. Eng., 191(15-16), pp. 1541-1562.
75. Reese, S., and Govindjee, S., 1998, "A Theory of Finite Viscoelasticity and Numerical Aspects, " Int. J. Solids Struct., 35(26-27), pp. 3455-3482.
76. Sadowski, T. J., 1965, "Non-Newtonian Flow Through Porous Media-II: Experimental, " Trans. Soc. Rheol. (1957-1977), 9(2), pp. 251-271.
77. Larson, R. G., and Brenner, H., 1988, Constitutive Equations for Polymer Melts and Solutions, Butterworth-Heinemann, Boston, MA.
78. Bergstrom, J. S., and Boyce, M. C., 2001, "Constitutive Modeling of the Time-Dependent and Cyclic Loading of Elastomers and Application to Soft Biological Tissues, " Mech. Mater., 33(9), pp. 523-530.
79. Diani, J., Fayolle, B., and Gilormini, P., 2009, "A Review on the Mullins Effect, " Eur. Polym. J., 45(3), pp. 601-612.
80. Mullins, L., 1969, "Softening of Rubber by Deformation, " Rubber Chem. Technol., 42(1), pp. 339-362.
81. Chagnon, G., Verron, E., Gornet, L., Marckmann, G., and Charrier, P., 2004, "On the Relevance of Continuum Damage Mechanics as Applied to the Mullins Effect in Elastomers, " J. Mech. Phys. Solids, 52(7), pp. 1627-1650.
82. Simo, J. C., 1987, "On a Fully Three-Dimensional Finite-Strain Viscoelastic Damage Model: Formulation and Computational Aspects, " Comput. Methods Appl. Mech. Eng., 60(2), pp. 153-173.
83. Dorfmann, A., and Ogden, R. W., 2004, "A Constitutive Model for the Mullins Effect With Permanent Set in Particle-Reinforced Rubber, " Int. J. Solids Struct., 41(7), pp. 1855-1878.
84. El Sayed, T., Mota, A., Fraternali, F., and Ortiz, M., 2008, "A Variational Constitutive Model for Soft Biological Tissues, " J. Biomech., 41(7), pp. 1458-1466.
85. Taylor, D. W., 1948, Fundamentals of Soil Mechanics, Wiley, New York.
86. Koeneman, J. B., 1966, "Viscoelastic Properties of Brain Tissue, " M. S. Thesis, Case Institute of Technology, Cleveland, OH.
87. Christ, A. F., Franze, K., Gautier, H., Moshayedi, P., Fawcett, J., Franklin, R. J. M., Karadottir, R. T., and Guck, J., 2010, "Mechanical Difference Between White and Gray Matter in the Rat Cerebellum Measured by Scanning Force Microscopy, " J. Biomech., 43(15), pp. 2986-2992.
88. Gefen, A., and Margulies, S. S., 2004, "Are In Vivo and In Situ Brain Tissues Mechanically Similar?" J. Biomech., 37(9), pp. 1339-1352.
89. Zhang, J., Green, M. A., Sinkus, R., and Bilston, L. E., 2011, "Viscoelastic Properties of Human Cerebellum Using Magnetic Resonance Elastography, " J. Biomech., 44(10), pp. 1909-1913.
90. Genet, M., Lee, L. C., Baillargeon, B., Guccione, J. M., and Kuhl, E., 2016, "Modeling Pathologies of Systolic and Diastolic Heart Failure, " Ann. Biomed. Eng., 44(1), pp. 112-127.
91. Budday, S., Steinmann, P., and Kuhl, E., 2014, "The Role of Mechanics During Brain Development, " J. Mech. Phys. Solids, 72, pp. 75-92.
92. Budday, S., Steinmann, P., and Kuhl, E., 2015, "Physical Biology of Human Brain Development, " Front. Cell. Neurosci., 9, pp. 257. 1-257. 17.
93. Budday, S., Kuhl, E., and Hutchinson, J. W., 2015, "Period-Doubling and Period-Tripling in Growing Bilayered Systems, " Philos. Mag., 95(28-30), pp. 3208-3224.
94. Songbai, J., Ghadyani, H., Bolander, R., Beckwith, J. G., Ford, J. C., McAllister, T. W., Flashman, L. A., Paulsen, K. D., Ernstrom, K., Jain, S., Raman, R., Zhang, L., and Greenwald, R. M., 2014, "Parametric Comparisons of Inter Cranial Mechanical Responses From Three Validated Finite Element Models for the Human Head, " Ann. Biomed. Eng., 42(1), pp. 11-24.
95. Mazumder, M. M. G., Miller, K., Bunt, S., Mostayed, A., Joldes, G., Day, R., Hart, R., and Wittek, A., 2013, "Mechanical Properties of the Brain-Skull Interface, " Acta Bioeng. Biomech., 15(2), pp. 3-11.
96. Bayly, P. V., Clayton, E. H., and Genin, G. M., 2012, "Quantitative Imaging Methods for the Development and Validation of Brain Biomechanics Models, " Annu. Rev. Biomed. Eng., 14(1), pp. 369-396.