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A narrow-band ultrasonic shear-wave imaging technique for estimating phase speed was applied to fresh and thermally damaged porcine liver in vitro. Two constitutive models were applied to the measurements to represent rheological behavior of the tissue and estimate the complex shear modulus at frequencies between 50 and 300 Hz. Our results were compared to similar values from the literature to assess how well models represent liver measurements over a range of shear-wave frequencies, experimental conditions and mammalian species. We found remarkable consistency in some parameters but not in others, suggesting that the Kelvin-Voigt model commonly applied in elasticity-imaging situations is representative of tissue dispersion but the description it offers is incomplete. Data are consistent with the theory that viscoelastic contrast is more likely due to changes in protein and other biomolecular-scale structures than from tissue anatomy larger than a cell. Dispersion measurements at frequencies between 0.5-1000 kHz are needed to more completely evaluate models for the viscoelastic behavior liver.