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Micromechanical Modeling of the Effective Mechanical Behavior of Cerebral Cortex Tissue

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

In this paper, a micromechanical approach is employed to propose a cerebral cortex tissue representative volume element (RVE) and simulate the mechanical behavior of this type of tissue in different loadings. In this regard, a MATLAB code is developed to homogenize a random distribution of neurons in the extracellular matrix. To create the RVE, different inputs including the size of RVE, the number of neurons, the radius of the neuron cell body, the coordinates of the axon and dendrites of a neuron, the radius of the axon and dendrites, and the minimum distance between the cellular volumes are considered. Then, a PYTHON code is developed which generates the desired RVE in ABAQUS employing the outputs of the MATLAB code. Also, a viscoelastic material model is considered for material components of the cerebral cortex tissue in this study. To analyze the developed RVE, some relaxation tests are performed on the RVE. Strain rate, neuron volume fraction (NVF), loading time and neuron distribution are investigated in different stress relaxation tests on the developed RVEs. Considering the NVF of 1, 2 and 3%, it is concluded that the maximum tensile and compressive stresses rise by increasing the NVF. Also, the results demonstrate that different irregular distributions of neurons have no effect on the bulk mechanical properties of the tissue for a constant NVF and only affect the distribution of local stresses (and even the maximum stress) in the tissue. Finally, the numerical simulations revealed that the developed RVE is a robust element which can be employed in realistic model of the brain tissue in different loading conditions such as trauma.

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References

  • Abolfathi N et al (2009) A micromechanical procedure for modelling the anisotropic mechanical properties of brain white matter. Comput Methods Biomech Biomed Eng 12(3):249–262

    Article  Google Scholar 

  • Ambrosi D, Beloussov LV, Ciarletta P (2017) Mechanobiology and morphogenesis in living matter: a survey. Meccanica 52(14):3371–3387

    Article  MathSciNet  Google Scholar 

  • Arbogast KB, Margulies SS (1999) A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J Biomech 32(8):865–870

    Article  Google Scholar 

  • Bain AC, Meaney DF (2000) Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. J Biomech Eng 122(6):615–622

    Article  Google Scholar 

  • Bain AC, Shreiber DI, Meaney DF (2003) Modeling of microstructural kinematics during simple elongation of central nervous system tissue. J Biomech Eng 125(6):798–804

    Article  Google Scholar 

  • Boresi AP, Schmidt RJ, Sidebottom OM (1993) Advanced mechanics of materials, vol 6. Wiley, New York

    MATH  Google Scholar 

  • Braitenberg V, Schüz A (2013) Cortex: statistics and geometry of neuronal connectivity. Springer, Berlin

    Google Scholar 

  • Brands DW, Bovendeerd PH, Wismans J (1999) On the potential importance of non-linear viscoelastic material modelling for numerical prediction of brain tissue response: test and application. In: SAE conference proceedings, SAE

  • Budday S et al (2017) Rheological characterization of human brain tissue. Acta Biomater 60:315–329

    Article  Google Scholar 

  • Chatelin S, Deck C, Willinger R (2013) An anisotropic viscous hyperelastic constitutive law for brain material finite-element modeling. J Biorheol 27(1–2):26–37

    Article  Google Scholar 

  • Cloots R, van Dommelen J (2011) Multi-scale mechanics of traumatic brain injury. PhD thesis, Eindhoven University of Technology

  • Cloots R et al (2008) Biomechanics of traumatic brain injury: influences of the morphologic heterogeneities of the cerebral cortex. Ann Biomed Eng 36(7):1203–1215

    Article  Google Scholar 

  • Cloots RJ et al (2011) Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy. Biomech Model Mechanobiol 10(3):413–422

    Article  Google Scholar 

  • Cloots RJ et al (2013) Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads. Biomech Model Mechanobiol 12(1):137–150

    Article  Google Scholar 

  • Cowin SC (1999) Structural change in living tissues. Meccanica 34(5):379–398

    Article  Google Scholar 

  • Documentation A (2010) ABAQUS analysis user’s manual, materials, other plasticity models, concrete

  • Faul M et al (2010) Traumatic brain injury in the United States: national estimates of prevalence and incidence, 2002–2006. Injury Prev 16(Suppl 1):A268–A268

    Article  Google Scholar 

  • Feng Y et al (2013) Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J Mech Behav Biomed Mater 23:117–132

    Article  Google Scholar 

  • Ferrant M et al (2000) Registration of 3D intraoperative MR images of the brain using a finite element biomechanical model. In: Medical image computing and computer-assisted intervention–MICCAI, Springer

  • Garnich MR, Karami G (2004) Finite element micromechanics for stiffness and strength of wavy fiber composites. J Compos Mater 38(4):273–292

    Article  Google Scholar 

  • Hashin Z (1966) Viscoelastic fiber reinforced materials. AIAA J 4(8):1411–1417

    Article  Google Scholar 

  • Javid S, Rezaei A, Karami G (2014) A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem. J Mech Behav Biomed Mater 30:290–299

    Article  Google Scholar 

  • Karami G et al (2009) A micromechanical hyperelastic modeling of brain white matter under large deformation. J Mech Behav Biomed Mater 2(3):243–254

    Article  Google Scholar 

  • Laksari K, Shafieian M, Darvish K (2012) Constitutive model for brain tissue under finite compression. J Biomech 45(4):642–646

    Article  Google Scholar 

  • Mazrouei M et al (2014) Evaluating the effect of mechanical loading on the effective thermal conductivity of carbon nanotube reinforced polymers (a Monte-Carlo approach). Studies 22:24

    Google Scholar 

  • Meaney D (2003) Relationship between structural modeling and hyperelastic material behavior: application to CNS white matter. Biomech Model Mechanobiol 1(4):279–293

    Article  Google Scholar 

  • Miller K, Chinzei K (1997) Constitutive modelling of brain tissue: experiment and theory. J Biomech 30(11):1115–1121

    Article  Google Scholar 

  • Nemat-Nasser S, Hori M (2013) Micromechanics: overall properties of heterogeneous materials. Elsevier, Amsterdam

    MATH  Google Scholar 

  • Ning X et al (2006) A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J Biomech Eng 128(6):925–933

    Article  Google Scholar 

  • Oruc-de Leon J (2009) Development of a micromechanical computational finite element model of a brain axon, The University of Texas at San Antonio

  • Pan Y, Shreiber DI, Pelegri AA (2011) A transition model for finite element simulation of kinematics of central nervous system white matter. IEEE Trans Biomed Eng 58(12):3443–3446

    Article  Google Scholar 

  • Park E, Bell JD, Baker AJ (2008) Traumatic brain injury: Can the consequences be stopped? Can Med Assoc J 178(9):1163–1170

    Article  Google Scholar 

  • Pfister BJ et al (2006) Development of transplantable nervous tissue constructs comprised of stretch-grown axons. J Neurosci Methods 153(1):95–103

    Article  Google Scholar 

  • Pierard O, Friebel C, Doghri I (2004) Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation. Compos Sci Technol 64(10):1587–1603

    Article  Google Scholar 

  • Prevost TP et al (2011) Dynamic mechanical response of brain tissue in indentation in vivo, in situ and in vitro. Acta Biomater 7(12):4090–4101

    Article  MathSciNet  Google Scholar 

  • Przekwas A, Somayaji MR, Gupta RK (2016) Synaptic mechanisms of blast-induced brain injury. Front Neurol 7:2

    Article  Google Scholar 

  • Ramo NL et al (2018) Comparison of in vivo and ex vivo viscoelastic behavior of the spinal cord. Acta Biomater 68:78–89

    Article  Google Scholar 

  • Rashid B, Destrade M, Gilchrist MD (2012) Inhomogeneous deformation of brain tissue during tension tests. Comput Mater Sci 64:295–300

    Article  Google Scholar 

  • Shaoning S (2014) Mechanical characterization and modeling of polymer/clay nanocomposites

  • Škrinjar O et al (2001) Steps toward a stereo-camera-guided biomechanical model for brain shift compensation. In: Information processing in medical imaging, Springer

  • Sotudeh-Chafi M et al. (2008) A multi-scale finite element model for shock wave-induced axonal brain injury. In: ASME 2008 summer bioengineering conference, American Society of Mechanical Engineers

  • Valdez M, Balachandran B (2013) Longitudinal nonlinear wave propagation through soft tissue. J Mech Behav Biomed Mater 20:192–208

    Article  Google Scholar 

  • Van Dommelen J et al (2010) Mechanical properties of brain tissue by indentation: interregional variation. J Mech Behav Biomed Mater 3(2):158–166

    Article  Google Scholar 

  • Velardi F, Fraternali F, Angelillo M (2006) Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech Model Mechanobiol 5(1):53–61

    Article  Google Scholar 

  • Wang HC, Wineman AS (1972) A mathematical model for the determination of viscoelastic behavior of brain in vivo—I oscillatory response. J Biomech 5(5):431–446

    Article  Google Scholar 

  • Yves R et al (2016) Applied RVE reconstruction and homogenization of heterogeneous materials. Wiley, New York

    Google Scholar 

Download references

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Correspondence to Majid Baniassadi.

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Shahsavari, H., Jokar, H., Haghighi-yazdi, M. et al. Micromechanical Modeling of the Effective Mechanical Behavior of Cerebral Cortex Tissue. Iran J Sci Technol Trans Mech Eng 44, 273–285 (2020). https://doi.org/10.1007/s40997-018-0267-5

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  • DOI: https://doi.org/10.1007/s40997-018-0267-5

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