Research Papers

An Indirect Indentation Method for Evaluating the Linear Viscoelastic Properties of the Brain Tissue

[+] Author and Article Information
Aref Samadi-Dooki

Computational Solid Mechanics Laboratory,
Department of Civil and Environmental
Louisiana State University,
Baton Rouge, LA 70803
e-mail: asamad3@lsu.edu

George Z. Voyiadjis

Boyd Professor
Computational Solid Mechanics Laboratory,
Department of Civil and Environmental
Louisiana State University,
Baton Rouge, LA 70803
e-mail: voyiadjis@eng.lsu.edu

Rhett W. Stout

Pathobiological Sciences Department,
School of Veterinary Medicine,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: rstout1@lsu.edu

1Corresponding author.

Manuscript received February 3, 2017; final manuscript received April 8, 2017; published online April 26, 2017. Assoc. Editor: Barclay Morrison.

J Biomech Eng 139(6), 061007 (Apr 26, 2017) (12 pages) Paper No: BIO-17-1042; doi: 10.1115/1.4036486 History: Received February 03, 2017; Revised April 08, 2017

Indentation experiments offer a robust, fast, and repeatable testing method for evaluating the mechanical properties of the solid-state materials in a wide stiffness range. With the advantage of requiring a minimal sample preparation and multiple tests on a small piece of specimen, this method has recently become a popular technique for measuring the elastic properties of the biological materials, especially the brain tissue whose ultrasoft nature makes its mechanical characterization very challenging. Nevertheless, some limitations are associated with the indentation of the brain tissue, such as improper surface detection, negative initial contact force due to tip-tissue moisture interaction, and partial contact between the tip and the sample. In this study, an indirect indentation scheme is proposed to overcome the aforementioned difficulties. In this way, the indentation force is transferred from a sharp tip to the surface of the tissue slices via a rigid coverslip. To demonstrate the accuracy of this method, the linear viscoelastic properties of the white and gray matters of the bovine brain samples are measured by imposing small cyclic loads at different frequencies. The rate, regional, directional, and postmortem time dependence of the viscoelastic moduli are investigated and compared with the previous results from cyclic shear and monotonic experiments on the brain tissue. While findings of this research present a comprehensive set of information for the viscoelastic properties of the brain at a wide frequency range, the central goal of this paper is to introduce a novel experimentation technique with noticeable advantages for biomechanical characterization of the soft tissue.

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Fig. 1

(a) Slicing directions for testing the anisotropy of the mechanical properties of the brain tissue and (b) sagittal section of the brain indicating 1: posterior, 2: superior, 3: anterior, and 4: thalamus regions (based on Van Dommelen et al. [38])

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Fig. 2

A pictorial representation of the viscoelasticity of (a) the nanoindenter instrument and (b) the whole indentation and contact system, based on Oliver and Pharr [40] and Herbert et al. [41]

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Fig. 3

Samples mounted in cylindrical cups for tests on: (a) cortical GM in the radial direction and (b) WM and GM of a sagittal slice

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Fig. 4

Indirect application of the load from the indenter tip to the tissue surface through a rigid coverslip

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Fig. 5

Effect of the precompression on dynamic shear moduli of the posterior WM brain tissue in the horizontal plane. The frequency and oscillation amplitude are set to 110 Hz and 1 μm, respectively (error bars represent the standard deviation).

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Fig. 6

Effect of the oscillation amplitude on dynamic shear moduli of the posterior WM brain tissue in the horizontal plane. The frequency and precompression are set at 110 Hz and 5 μm, respectively (error bars represent the standard deviation).

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Fig. 7

Analyzing the symmetricity of cyclic: (a) displacement and (b) load response graphs of a test for WM at the frequency of 2 Hz

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Fig. 8

Variation of the shear storage modulus in the anterior (a) and posterior (b) regions, shear loss modulus in the anterior (c) and posterior (d) regions, and absolute shear complex modulus in the anterior (e) and posterior (f) regions of the WM brain tissue with loading frequency at different directions. (g) The variation of the phase shift angle of the WM brain tissue (average of all directions and regions) with loading frequency. Abbreviations used are defined as follows: first character: “W” white matter; second character: “C” coronal direction, “H” horizontal direction, and “S” sagittal direction; third character: “A” anterior region and “P” posterior region (error bars represent the standard deviation).

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Fig. 9

Variation of the (a) shear storage modulus, (b) shear loss modulus, (c) absolute shear complex modulus, and (d) average phase shift angle of the cortical GM brain tissue with loading frequency at different regions and directions. Abbreviations used are defined as follows: first character: “G” cortical gray matter; second character: “C” coronal direction, “R” radial direction, and “S” sagittal direction; third character: “A” anterior region and “S” superior region (error bars represent the standard deviation). (Reproduced with permission from Catani et al. [54]. Copyright 2008 by Elsevier.)

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Fig. 10

Average reduction of the absolute complex shear modulus of the coronal slices of anterior WM tissue tested 48 h postmortem

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Fig. 11

Comparison of the average WM brain tissue storage (circles) and loss (triangles) moduli based on 1. Bilston et al. [51], 2. Shuck and Advani [52], 3. Nicolle et al. [26], 4. Arbogast and Margulies [23], and 5. Hrapko et al. [53] with the current study 6

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Fig. 12

Projection of the fibers that stem from the corpus callosum and extend into the white matter (Reproduced with permission from Catani and De Schotten [54] Copyright 2008 by Elsevier). The same pattern exists for the fiber orientation of corona radiata (see Fig. 9 of the same reference).

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Fig. 13

Variation of the (a) shear storage modulus, (b) shear loss modulus, and (c) absolute shear complex modulus of the average cortical GM, average WM, and thalamic GM in the sagittal direction with loading frequency (error bars represent the standard deviation)

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Fig. 14

Illustrative axisymmetric finite element simulation of the indirect indentation of the brain tissue for investigating the rigid behavior of the coverslip



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