Fig 1.
Liver samples were cut to a diameter of 20 mm and placed on a parallel plate rheometer with an upper platen of 25 mm. Tension and compression were generated by applying force in a direction perpendicular to the sample. Shear forces were applied by rotating the bottom plate in a direction parallel to the sample. Values derived from compression and tension studies were corrected to account for the difference in size between the sample and the top platen, and for narrowing at the waist of the sample in tension (see methods).
Fig 2.
G', G'', and axial stress increase with fibrosis and with compression.
(A-C) Normal and fibrotic livers (2 and 6 weeks of CCl4 treatment) were subject to varying degrees of axial strain (compression, from 0–25%) as indicated. G' (A), G'' (B) and axial stress (C) were measured over 120 s after each incremental increase in compression. Curves shown are from single livers and are representative of results generated from 3–5 independent livers. (Mean curves +/- SD, representing results from all livers tested, are shown in S2 Fig).
Fig 3.
The relationship between G' and E in compression.
(A) Normal and fibrotic (2 and 6 weeks of CCl4) livers underwent shear rheometry with measurement of G’ under varying degrees of compression. G’ shown here was taken at 120 s from the start of compression, approximating equilibrium values after viscous effects have largely dissipated. (B) E was determined by calculating the slope from the stress-strain curve, where stress (calculated from the normal force) was taken at 120 s from the start of compression. The slope was determined in between two neighboring points – 0 and 10, 10 and 15, 15 and 20, 20 and 25 for compression. (C) G' and E for normal livers were calculated as described above in both tension and compression and normalized with respect to initial G’ and E values at no compression. For all cases, 3–5 livers were analyzed for each condition and curves represent the mean +/- SD. By two-way ANOVA, G’ for both 2 and 6 week CCl4 livers are significantly higher than for normal livers (p≤ 0.002) pink *; E for 6 week CCl4 livers is significantly higher than for normal and 2 weeks CCl4 livers (p≤ 0.02) blue *.
Fig 4.
Normal and fibrotic livers demonstrate strain softening and compression stiffening.
(A-C) G' was measured for normal and fibrotic (after 2 and 6 weeks of CCl4) livers by shear rheometry under increasing strain and under variable degrees of compression ranging from 0–25%. Note that the y-axes scales are the same and that G' values increase significantly as fibrosis progresses. Curves are mean +/- SD for 3–5 livers tested for each condition. (D) Normal liver subjected to three rounds of shear rheometry, each round with increasing, then decreasing strain. Livers demonstrated no evidence of significant tissue damage due to measurements. Representative liver of 3 tested is shown. (See S3 Fig for mean curves +/- SD for all three livers tested.)
Fig 5.
G’ increases linearly with compressional stress, while stress increases nonlinearly with compressional strain for normal and fibrotic liver.
Normal and fibrotic (2 and 6 weeks of CCl4) livers were subjected to shear rheometry under various degrees of compression. Compressional stress was calculated in mm Hg and plotted against G' or compressional strain (% compression). (A) G' vs. compressional stress, showing a nearly linear relationship between the two conditions in both normal and fibrotic livers. Lines were fit to each curve (in red) and are shown in the graph. (B) Compressional stress vs. compressional strain, shown for normal and fibrotic livers. G’ and compressional stress values are after 120 s of relaxation. Curves reflect mean +/- SD for 3–5 livers per condition.
Fig 6.
Poroelasticity plays little role in normal liver mechanics.
8 and 20 mm diameter samples were taken from normal liver and subjected to (A) 25% compression or (B) 25% shear strain. Normal force and G' were measured for 1200 s. Stress was subsequently calculated from normal force. There is no statistically significant difference between the curves for the 8 and 20 mm samples for either condition (for the means of 3 samples each) at time points beyond 5 s (which takes into account differences between the initiation of manual compression and the initiation of measurements), suggesting that tissue poroelasticity contributes little to liver mechanics. Curves shown are from a single liver, representative of 3; curves for the remaining 2 livers are shown in S4 Fig.
Fig 7.
The impact of tissue manipulations on liver mechanics.
Normal livers were subject to the manipulations indicated, and then G' was measured under various strains. (A) G' as a function of compression for treated livers. (B) Strain sweeps of normal liver, disintegrin-treated, amylase-treated, and permeabilized livers at 0% compression. Key as in (A). (C) Strain sweeps of decellularized normal and fibrotic (2 weeks CCl4) livers at 0% compression, compared to a curve for normal liver (the same as shown in (B)). Note the different shape of the curves for decellularized compared to normal liver. (D) G' measured under 2% oscillatory shear for livers at either 0% or 25% compression. G’ values are after 120 s of relaxation. By two-way ANOVA for the data plotted in (A), G’ for amylase treated livers was significantly reduced from normal and permeabilized livers (brown *, p≤0.02). Disintegrin treatment significantly reduced G’ of normal liver (green *, p = 0) and G’ of decellularized livers was significantly reduced from normal and all other manipulated livers (green *, p = 0). Two-way ANOVA of the data in (D) showed that G’ compared between 0% and 25% compression was significantly different only for normal livers (blue ***, p≤0.001) and permeabilized livers (green ***, p = 0). G’ values at 25% compression were significantly different between normal livers and α-Amylase (*, p≤0.05), VLO4-treated (brown **, p = 0.059), and decellularized livers (brown ***, p = 0). For all graphs, data represent the mean of 3 independent livers +/- SD per condition.
Fig 8.
A) Schematic for liver tissue, consisting of cells and ECM. B) When under compression, cells maintain the same volume but begin to contact each other and generate strong resistance, resulting in compression stiffening. C) We propose that there are two kinds of cell-ECM connections: strong connections that sustain large loads and re-formable connections that break under large loads and re-form when there is no external load. When under shear, the re-formable connections break, which results in shear softening.