Recent advances have enabled a new wave of biomechanics measurements, and have renewed interest in selecting appropriate rheological models for soft tissues such as the liver, thyroid, and prostate. The microchannel flow model was recently introduced to describe the linear response of tissue to stimuli such as stress relaxation or shear wave propagation. This model postulates a power law relaxation spectrum that results from a branching distribution of vessels and channels in normal soft tissue such as liver. In this work, the derivation is extended to determine the explicit link between the distribution of vessels and the relaxation spectrum. In addition, liver tissue is modified by temperature or salinity, and the resulting changes in tissue responses (by factors of 1.5 or greater) are reasonably predicted from the microchannel flow model, simply by considering the changes in fluid flow through the modified samples. The 2 and 4 parameter versions of the model are considered, and it is shown that in some cases the maximum time constant (corresponding to the minimum vessel diameters), could be altered in a way that has major impact on the observed tissue response. This could explain why an inflamed region is palpated as a harder bump compared to surrounding normal tissue.