Characteristic time demonstrates similar viscous relaxation behavior of normal brain and brain tumors.

<p>Graph depicts the characteristic time, τ, of potential mechanical surrogates for brain tissue and tumors. τ is determined from fitting the calculated effective modulus (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.e002" target="_blank">Eq 2</a>) during stress relaxation to the SLS model of viscoelasticity (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.e003" target="_blank">Eq 3</a>). Similar relaxation behavior can be seen between potential surrogates, and based on recent studies, capturing the viscous behavior of biomimetic materials is equally important as elastic behavior.</p

Mechanical characterization of human brain tumors from patients and comparison to potential surgical phantoms

<div><p>While mechanical properties of the brain have been investigated thoroughly, the mechanical properties of human brain tumors rarely have been directly quantified due to the complexities of acquiring human tissue. Quantifying the mechanical properties of brain tumors is a necessary prerequisite, though, to identify appropriate materials for surgical tool testing and to define target parameters for cell biology and tissue engineering applications. Since characterization methods vary widely for soft biological and synthetic materials, here, we have developed a characterization method compatible with abnormally shaped human brain tumors, mouse tumors, animal tissue and common hydrogels, which enables direct comparison among samples. Samples were tested using a custom-built millimeter-scale indenter, and resulting force-displacement data is analyzed to quantify the steady-state modulus of each sample. We have directly quantified the quasi-static mechanical properties of human brain tumors with effective moduli ranging from 0.17–16.06 kPa for various pathologies. Of the readily available and inexpensive animal tissues tested, chicken liver (steady-state modulus 0.44 ± 0.13 kPa) has similar mechanical properties to normal human brain tissue while chicken crassus gizzard muscle (steady-state modulus 3.00 ± 0.65 kPa) has similar mechanical properties to human brain tumors. Other materials frequently used to mimic brain tissue in mechanical tests, like ballistic gel and chicken breast, were found to be significantly stiffer than both normal and diseased brain tissue. We have directly compared quasi-static properties of brain tissue, brain tumors, and common mechanical surrogates, though additional tests would be required to determine more complex constitutive models.</p></div

Readily-available store-bought meats are reasonable mechanical surrogates of soft tissues.

<p>Chicken breast, liver, and tenuis and crassus muscle of the gizzard were indented to determine the steady-state properties (n = 4 indentations of 4 samples for each tissue type). Mean (red bar) of pooled indentations are shown along with resulting steady-state modulus from each indentation performed. Chicken breast and tenuis muscle of the gizzard had significantly higher steady-state moduli than the mouse brain and human brain tumors (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.g004" target="_blank">Fig 4</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.t001" target="_blank">Table 1</a>), compared to the liver and crassus muscle of the gizzard. The liver and crassus muscle showed similar mechanical properties to normal brain tissue and human brain tumor samples, respectively. Given the low cost and low regulatory burden of obtaining these samples, they may be reasonable mechanical surrogates for brain tissue and tumors in certain testing applications.</p

Steady-state mechanical properties are independent of initial strain rate.

<p>Samples of (A) meningioma and (B) 0.4% agarose hydrogel were indented with our MSI to 10% of sample thickness (3 mm sample thickness, 300 μm indentation depth) at 15, 30, 50, and 75 <i>μ</i>m/s and subsequently allowed to undergo stress relaxation. Given adequate relaxation time, samples relaxed and converged to a similar steady-state modulus. This robust quasi-static property of tissues allows us to use the steady-state modulus as a simple metric for direct comparison of brain tissue and hydrogels. N.B. Scales of the effective modulus axes are different to allow clear visualization of stress-relaxation behavior.</p

Human brain tumors are approximately twice as stiff as normal brain tissue.

<p>Mean (red bar) of pooled indentations show glioma (n = 8 indentations from 1 sample), meningioma (n = 118 indentations from 18 samples), and mouse tumors implanted in mice (n = 31 indentations from 9 samples) are stiffer and more heterogeneous than normal mouse brain tissue (n = 50 from 11 samples) tested in our lab and as previously reported in literature (grey box). In contrast, metastatic lymphomas (n = 14 indentations from 3 samples from one patient) showed no significant difference between the SSM of normal brain tissue and were not as stiff as other tumors. Grey box reflects values for normal brain modulus reported in the literature using unconfined compression [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref040" target="_blank">40</a>] and indentation methods [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref007" target="_blank">7</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref041" target="_blank">41</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref043" target="_blank">43</a>].</p

A wide variety of commercially available materials can serve as mechanical surrogates for human brain tissue and tumors.

<p>(A) SSM mean for each tissue (as an average of each sample mean) with the corresponding standard deviation; samples with the same letter and color are <b>not</b> statistically different from each other based on a multiple comparison Wilcoxon test (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.t001" target="_blank">Table 1</a>). (B) Readily obtainable chicken liver shows similar steady-state moduli to normal mouse brain. (C) The crassus muscle of the chicken gizzard is mechanically similar to both human meningiomas and mouse tumors, and non-living hydrogels can be fabricated with concentrations similar to tumors.</p

Multi-scale indenter can quantify quasi-static properties of arbitrarily shaped soft matter and biological tissue samples.

<p>A capacitive probe (A) measures capacitive changes due to the deflection of a titanium cantilever (B) as a sample is indented. A 4 mm-diameter ruby tip (C) at the free end of the cantilever comes into contact with the sample (D). The image depicts a posterior coronal cross-section of a mouse brain sample being indented. Capacitive probe is able to measure deflections on the order of 10 nm, allowing for quantification of μN-level forces.</p

Agarose hydrogels and ballistic gel are stiffer than normal brain tissue.

<p>Mean (red bar) of pooled indentations are shown along with resulting steady-state modulus from each indentation performed. Despite being used frequently as mechanical surrogates for healthy brain tissue, low concentration agarose samples and a ballistic gel were stiffer than tested normal mouse brain samples. Store-bought Knox® Gelatin samples were also stiffer than normal brain tissue yet similar to the agarose hydrogels tested. Grey box reflects values for normal brain modulus reported in the literature using unconfined compression [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref040" target="_blank">40</a>] and indentation methods [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref041" target="_blank">41</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.ref042" target="_blank">42</a>].</p

Results of multiple comparisons of characteristic time of potential surrogates.

<p>Results of multiple comparisons of characteristic time of potential surrogates.</p

Effective modulus of a 0.4% agarose gel sample is determined by a time-dependent rearrangement of the Hertz contact model.

<p>Force displacement data (lower orange curve) is converted to the effective modulus (upper blue curve) using the Hertz contact model for a sphere and a half space (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0177561#pone.0177561.e002" target="_blank">Eq 2</a>, inset). Samples were indented at a rate of 15 <i>μ</i>m/s followed by a stress-relaxation phase where the base of the cantilever is held at a constant strain until the tissue fully relaxes.</p