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Research Papers

Poro-Viscoelastic Behavior of Gelatin Hydrogels Under Compression-Implications for Bioelasticity Imaging

[+] Author and Article Information
Sureshkumar Kalyanam, Rebecca D. Yapp

Beckman Institute for Advanced Science & Technology, Department of Bioengineering, University of Illinois at Urbana-Champaign Urbana, IL 61801

Michael F. Insana

Beckman Institute for Advanced Science & Technology, Department of Bioengineering, University of Illinois at Urbana-Champaign Urbana, IL 61801mfi@uiuc.edu

J Biomech Eng 131(8), 081005 (Jul 02, 2009) (13 pages) doi:10.1115/1.3127250 History: Received June 13, 2008; Revised March 23, 2009; Published July 02, 2009

Ultrasonic elasticity imaging enables visualization of soft tissue deformation for medical diagnosis. Our aim is to understand the role of flow-dependent and flow-independent viscoelastic mechanisms in the response of biphasic polymeric media, including biological tissues and hydrogels, to low-frequency forces. Combining the results of confined and unconfined compression experiments on gelatin hydrogels with finite element analysis (FEA) simulations of the experiments, we explore the role of polymer structure, loading, and boundary conditions in generating contrast for viscoelastic features. Feature estimation is based on comparisons between the biphasic poro-elastic and biphasic poro-viscoelastic (BPVE) material models, where the latter adds the viscoelastic response of the solid polymer matrix. The approach is to develop a consistent FEA material model (BPVE) from confined compression-stress relaxation measurements to extract the strain dependent hydraulic permeability variation and cone-plate rheometer measurements to obtain the flow-independent viscoelastic constants for the solid-matrix phase. The model is then applied to simulate the unconfined compression experiment to explore the mechanics of hydropolymers under conditions of quasi-static elasticity imaging. The spatiotemporal distributions of fluid and solid-matrix behavior within the hydrogel are studied to propose explanations for strain patterns that arise during the elasticity imaging of heterogeneous media.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Shear-creep-strain experiment performed using a cone-plate rheometer. (a) Shear-creep strain γ12(t) is measured with an applied step stress of σa=40 Pa. (b) Shear compliance J(t) estimates versus time are obtained from creep-strain data.

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Figure 2

(a) Schematic of the confined compression-force relaxation experiment. (b) Finite element model of the hydrogel specimen under confined compression.

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Figure 3

(a) Schematic of the unconfined compression-creep strain experiment. (b) Finite element model used for simulating the unconfined compression experiment.

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Figure 4

Preconditioning of the hydrogel under unconfined compression (a) Stress versus time (cyclic engineering strain of 0–10%). (b) Stress-strain curves from the loading part of the 40th cycle.

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Figure 5

Confined compression-force relaxation experiment. (a) Force measured with applied uni-axial step strain of ϵa=2%. (b) Loss spectra obtained from force versus time experimental data for the hydrogel. Two measurements for each pore sizes 35 μm and 120 μm are shown.

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Figure 6

Comparison of predicted and observed confined compression-force relaxation behavior. Compressive force F(t) is predicted from FEA (a) using constant values of hydraulic permeability, k(x,t)=k0, and (b) using different biphasic models for k(x,t)=k0=3×10−11 m/s. The shaded region indicates the range of measured values; see Fig. 5.

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Figure 14

Unconfined compression-creep strain. Predicted (a) void ratio e(x,t) and (b) radial strain ϵr(x,t) variations with time from FEA using BPVE model. Locations A–D are illustrated in Fig. 1.

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Figure 15

Unconfined compression-creep strain. Predicted (a) pore pressure p(x,t) and (b) magnitude of solid-matrix stress σz(x,t) variations with time in the radial r-direction (at specimen height h=H/2=22.225 mm) from FEA using the BPVE material model.

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Figure 13

Unconfined compression-creep strain. (a) Locations along the radial r-direction chosen for showing variations in field quantities. (b) Predicted pore pressure p(x,t) and magnitude of the solid stress σz(x,t) variations with time from FEA using BPVE material model.

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Figure 12

FEA predictions for confined compression-force relaxation using the BPVE material model. (a) Pore pressure p(t) and magnitude of the solid-matrix stress |σz(t)| variation with time. (b) Void ratio e(t) variation with time. Locations I-M are illustrated in Fig. 1.

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Figure 11

FEA predictions of pore pressure variations during confined compression-force relaxation experiments. (a) Locations are identified along the central z-axis of the cylindrical specimen. (b) Pore pressure variation with time and position (I-M).

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Figure 10

Comparison of experimentally observed and predicted (FEA) creep strain, ϵz(t) of the hydrogel specimen under unconfined compression. Creep strain is predicted from FEA using BPVE material model by varying solid-matrix properties: (a) elastic modulus Em and (b) Poisson’s ratio νm. The shaded region indicates the range of experimentally measured values.

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Figure 9

Comparison of unconfined compression-creep strain ϵz(t), measured experimentally for 6% gelatin hydrogel (σa=638 Pa) and obtained from FEA using BPVE material model with material constants Em=3650 Pa, νm=0.47, and e0=9.0. (a) Hydraulic permeability of Eq. 15 is used with k0=3×10−10 m/s, M=4.25 that also predicts the confined compression-force relaxation data (Fig. 8). (b) Variation with k0 from Eq. 15. The shaded region indicates the range of measured values.

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Figure 8

Confined compression-force relaxation experiment. (a) Time-averaged error (T=3000 s) is estimated by comparing experimentally measured and predicted compressive forces while varying M values for each of the models Eqs. 12,13,14,15 depicting hydraulic permeability. (b) F(t) versus time predicted from FEA performed using various models using the minimum M value obtained for each model from Fig. 8. The shaded region indicates the range of measured values; see Fig. 5.

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Figure 7

Comparison of experimentally observed and predicted (FEA) confined compression-force relaxation behavior. Compressive force F(t) is predicted from FEA using BPVE material model and constant hydraulic permeability k(x,t)=k0=3.0×10−11 m/s by varying solid-matrix properties (a) elastic modulus Em and (b) Poisson’s ratio νm. The shaded region indicates the range of measured values; see Fig. 5.

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