On nonlinear viscoelastic properties of arterial tissue

A novel method to make viscoelastic polyacrylamide gels for cell culture and traction force microscopy

Polyacrylamide hydrogels are commonly used in cell biology, notably to cultivate cells on soft surfaces. Polyacrylamide gels are purely elastic and well adapted to cell culture as they are inert and can be conjugated with adhesion proteins. Here, we report a method to make viscoelastic polyacrylamide gels with mechanical properties more closely resembling biological tissues and suitable for cell culture in vitro. We demonstrate that these gels can be used for traction force microscopy experiments. We also show that multiple cell types respond to the viscoelasticity of their substrate and that viscous dissipation has an influence on cell spreading, contractility, and motility. This new material provides new opportunities for investigating how normal or malignant cells sense and respond to viscous dissipation within the extra-cellular matrix.

Control of cell morphology and differentiation by substrates with independently tunable elasticity and viscous dissipation

The mechanical properties of extracellular matrices can control the function of cells. Studies of cellular responses to biomimetic soft materials have been largely restricted to hydrogels and elastomers that have stiffness values independent of time and extent of deformation, so the substrate stiffness can be unambiguously related to its effect on cells. Real tissues, however, often have loss moduli that are 10 to 20% of their elastic moduli and behave as viscoelastic solids. The response of cells to a time-dependent viscous loss is largely uncharacterized because appropriate viscoelastic materials are lacking for quantitative studies. Here we report the synthesis of soft viscoelastic solids in which the elastic and viscous moduli can be independently tuned to produce gels with viscoelastic properties that closely resemble those of soft tissues. Systematic alteration of the hydrogel viscosity demonstrates the time dependence of cellular mechanosensing and the influence of viscous dissipation on cell phenotype.

Quasi-linear viscoelastic modeling of arterial wall for surgical simulation

PURPOSE

Realistic soft tissue deformation modeling and haptic rendering for surgical simulation require accurate knowledge of tissue material characteristics. Biomechanical experiments on porcine tissue were performed, and a reduced quasi-linear viscoelastic model was developed to describe the strain-dependent relaxation behavior of the arterial wall. This information is used in surgical simulation to provide a realistic sensation of reduction in strength when the user holds a virtual blood vessel strained at different levels.

MATERIALS AND METHODS

Twelve pieces of porcine abdominal artery were tested with uniaxial elongation and relaxation test in both circumferential and longitudinal directions. The mechanical property testing system consists of automated environment control, testing, and data collection mechanism. A combined logarithm and polynomial strain energy equation was applied to model the elastic response of the specimens. The reduced relaxation function was modified by integrating a rational equation as a corrective factor to precisely describe the strain-dependent relaxation effects.

RESULTS

The experiments revealed that (1) stress is insensitive to strain rate in arterial tissue when the loading rate is low, and (2) the rate of stress relaxation of arterial wall is highly strain dependent. The proposed model can accurately represent the experimental data. Stress-strain function derived from the combined strain energy function is able to fit the tensile experimental data with R(2) equals to 0.9995 in circumferential direction and 0.999 in longitudinal direction. Modified reduced relaxation function is able to model the strain-dependent relaxation with R(2) equals to 0.9686 in circumferential direction and 0.988 in longitudinal direction.

CONCLUSION

The proposed model, based on extensive biomechanical experiments, can be used for accurate simulation of arterial deformation and haptic rendering in surgical simulation. The resultant model enables stress relaxation status to be determined when subjected to different strain levels.

A quasi-linear constitutive relation for arterial wall materials

In this work, considering that under physiological conditions the arteries are subjected to a large initial static deformation and additional small dynamical displacements are superimposed on this initial field, a Boltzman type of constitutive relation is presented for arterial wall materials. For its simplicity in the analysis, the material under investigation is assumed to be isotropic, incompressible and constitutionally nonlinear in Green deformation tensor but linear in the history of deformation tensor. The numerical values of elastic coefficients are obtained by comparing the analytical results with experiments by Simon et al. [Circ. Res. 30, 491-500 (1972)]. For the determination of viscoelastic coefficients we studied the propagation of torsional waves in a prestressed thin cylindrical tube and proposed a method of determining the viscoelastic coefficients.