Soft Tissue Nonlinear Elasticity

Increased hepatic venous pressure can be observed in patients with advanced liver disease and congestive heart failure. This elevated portal pressure also leads to variation in acoustic radiation-force derived shear wave based liver stiffness estimates. These changes in stiffness metrics with hepatic interstitial pressure may confound stiffness-based predictions of liver ?brosis tage. The underlying mechanism for this observed stiffening behavior with pressurization is not well understood, and is not explained with commonly-used linear elastic mechanical models. Our efforts have been devoted to exploring the mechanical nonlinearity exhibited in hepatic pressurization using shear wave speed stiffness metrics.

 

Preliminary results suggest that the increase in shear wave speeds observed with increased portal hepatic pressure is a strain-dependent phenomenon. This suggests that mechanical nonlinear theories such as hyperelasticity will play an important role in understanding and predicting hepatic pressurization behavior moving forward. 

 

Experimental Results

 

 

 Comparison between pressurization and shear wave speed (SWS) for constrained (shown with circles) and unconstrained (shown with boxes) cases from independent measures taken in six ex-vivo canine livers. Standard deviation between the experiments in pressure and SWS are shown as horizontal and vertical errorbars respectively. The * represent groups for which the p-value was less than 0.01. Shear Wave Speed vs. Portal Venous Pressure

SWS vs. Portal Venous Pressure

Shear wave speed increases observed with increasing portal venous pressure across 6 excised canine livers (differentiated by color). Errorbars shown represent the standard deviation of 6 shear wave speed datasets acquired in the same location at each pressure.

 

Axial Strain vs. Portal Venous Pressure

Axial Strain vs. Portal Venous Pressure

Percent axial strain increases observed as a function of increasing portal venous pressure for 6 excised canine livers (differentiated by color). Errorbars shown represent the accumulated 95% confidence interval on the strain estimate.

 

Shear Wave Speed vs. Axial Strain

Axial Strain vs. Portal Venous Pressure

Shear wave speed compared with percent axial strain across 6 excised canine livers (differentiated by color). Because the six SWS estimates were in the same region of interest, the errorbars (which represent the standard deviation of the six SWS estimates) do not show potential tissue heterogeneity but rather the limits of system precision on SWS estimates.

Related publications

The impact of hepatic pressurization on liver shear wave speed estimates in constrained versus unconstrained conditions. Rotemberg V, Palmeri M, Nightingale R, Rouze N, Nightingale K. Phys Med Biol. 2012 Jan 21;57(2):329-41. Epub 2011 Dec 14.