Smoothing of displacements allowed for the computer of strains.

<p>Absolute precision of both displacement (top) and strain (bottom) measurements is improved with more smoothing cycles. Across all spatial resolutions (<i>A</i>) and gradient moments (<i>B</i>), imaging parameters that show better precision in raw displacement data require fewer smoothing cycles before reaching a plateau in the precision of smoothed displacement data.</p

Effects of spatial resolution, slice thickness, gradient moment, and averaging.

<p>Displacement precision depends strongly on SNR of the displacement-encoded image. Finer in-plane spatial resolutions required increased NA or slice thickness (from 1.76 mm (dark blue) to 3.52–3.84 mm (light red)) to improve mean (± standard deviation) SNR (<i>A</i>) and precision (<i>B</i>). Increasing the gradient moment from 0.23π/mm (dark blue) to 0.65π/mm (light red) has no effect on SNR (<i>D</i>) but improves precision (<i>E</i>). Complementary NA = 4 acquisitions (phase advance = 60°, 180°, 300°) did not significantly affect SNR and do not show improvements to precision compared to NA = 4 scans (phase advance = 180°). SNR and precision show an exponential relationship (<i>C</i>, <i>F</i>) that can inform the choice of imaging parameters for DENSE-FISP.</p

DENSE-FISP for displacements and strains in a complex system inclusive of broad <i>T₂</i> materials.

<p>A human cadaveric tibiofemoral joint was cyclically loaded in the inferior-to-superior direction for DENSE-FISP imaging of a coronal slice (<i>A</i>). Displacements (<i>B</i>) and strains (<i>C</i>) in human tibiofemoral joint show non-homogeneous behavior in the articular cartilage, meniscus, and ligament. DENSE-FISP measures displacements in tissues that range in <i>T₂</i> values (<i>D</i>). Cartilage sections stained with Safranin-O depict some histological signs of degeneration on the medial and lateral femoral condyles (<i>E</i>).</p

Displacements and strains determined by noninvasive DENSE-FISP.

<p>An MRI-compatible loading apparatus cyclically loads a silicone gel phantom within a 9.4T MRI system by compressing the phantom against a fixed platform and then retracting after the load plateau (<i>A</i>). The unloaded phantom was imaged using standard MRI (<i>B</i>) prior to displacement-encoded MRI. In the representative images, displacements (<i>C</i>) and strains computed from smoothed displacements, after 25 smoothing cycles, (<i>D</i>) were found to be heterogeneous.</p

DENSE-FISP of transient mechanical behavior.

<p>High temporal resolution displacement-encoded MRI nondestructively measured displacements and strains at a sampling rate of 444 Hz (TR = 2.25 ms). Cyclic compression was applied to a silicone gel using a rounded indenter, and a 100-frame cine DENSE-FISP image was acquired during a transient portion of the loading curve (<i>A</i>). In-plane displacements (<i>B</i>) and strains (<i>C</i>) shown for frame numbers 10, 11, and 100 demonstrate that DENSE-FISP is capable of measuring transient mechanical behaviors at high temporal resolution (<i>B</i>).</p

Synchronized loading and imaging for the calculation of displacements and strains using displacement-encoded MRI.

<p>Various cyclic loading regimes, including a plateau of constant load (Case 1 – long dashed green line) and a time-transient loading scheme (Case 2 – short dashed orange line) are synchronized with displacement-encoded MRI actions (<i>A</i>). Within each loading and imaging cycle, the reference configuration is encoded using radiofrequency (RF) excitation and a linear magnetic gradient (<i>B</i>). In the current deformed configuration, the new position of the material is decoded by applying another linear magnetic gradient, and signal encoded with the change in position is acquired (<i>C</i>). For Case 1, position decoding and acquisition occurs throughout the load plateau. For Case 2, decoding and partial acquisitions occur during shorter time periods within the loading scheme to produce time-resolved frames of MRI data. This acquisition scheme requires many more loading cycles but produces MRI data at frame rates limited only by TR. The spatial resolution, Δ<i>x</i> (<i>D</i>) determines the volume over which displacements (<i>E</i>) and strains (<i>F</i>) are computed for each pixel.</p

High resolution imaging of cartilage reveals evidence of connectivity between individual chondrocytes.

<p>Interactions between individual chondrocytes within bovine articular cartilage can be resolved throughout the entire 307 μm–thick <i>z</i>-stack (arrowheads). The same <i>z</i>-stack shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116662#pone.0116662.g002" target="_blank">Fig. 2C’</a>was bleached corrected and rendered in 3D using FIJI. The top of the volume was imaged just below the articular surface and goes deeper into the cartilage as <i>z</i> increases. Cartilage was stained with DiI, cleared with SeeDB and imaged using a Nikon A1R microscope, with a PlanFluor 20× multi-immersion objective, NA = 0.75, 3× confocal zoom. The depth of the image stack was limited by the working distance of the objective. Tick marks on isolated cell volumes = 10 μm. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116662#pone.0116662.s003" target="_blank">S1</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116662#pone.0116662.s006" target="_blank">S4</a>Movies.</p

Optical clearing of ECM-rich bovine musculoskeletal tissues.

<p>Equilibration to concentrated fructose solutions that closely match the refractive index of biological tissue substantially enhances the macroscopic transmission of light though 2.5 mm thick samples of cartilage (top row) and ligament (bottom row). While the transparency of light was greater in cleared meniscus (middle row, see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116662#pone.0116662.g002" target="_blank">Fig. 2</a>), the background grid pattern was not easily visualized. Control and cleared samples were imaged using the same acquisition parameters on a Leica MZ80 stereomicroscope. Grid spacing = 2.1 mm.</p

<i>In Vivo</i> Multiscale and Spatially-Dependent Biomechanics Reveals Differential Strain Transfer Hierarchy in Skeletal Muscle

Biological tissues have a complex hierarchical architecture that spans organ to subcellular scales and comprises interconnected biophysical and biochemical machinery. Mechanotransduction, gene regulation, gene protection, and structure–function relationships in tissues depend on how force and strain are modulated from macro to microscales, and <i>vice versa</i>. Traditionally, computational and experimental techniques have been used in common model systems (e.g., embryos), and simple strain measures were applied. However, the hierarchical transfer of mechanical parameters like strain in mammalian systems is largely unexplored <i>in vivo</i>. Here, we experimentally probed complex strain transfer processes in mammalian skeletal muscle tissue over multiple biological scales using complementary <i>in vivo</i> ultrasound and optical imaging approaches. An iterative hyperelastic warping technique quantified the spatially dependent strain distributions in tissue, matrix, and subcellular (nuclear) structures, and revealed a surprising increase in strain magnitude and heterogeneity in active muscle as the spatial scale also increased. The multiscale strain heterogeneity indicates tight regulation of mechanical signals to the nuclei of individual cells in active muscle and an emergent behavior appearing at larger (e.g., tissue) scales characterized by dramatically increased strain complexity