A quantitative comparison of soft tissue compressive viscoelastic model accuracy

Viscoelastic models are generally considered a good option for modeling biological tissue due to tissue time-dependency. However, although various forms of viscoelastic models have been developed, only a few have shown a good balance between model mathematical simplicity and experimental fit accuracy. Starting from a basic Standard Linear Solid (SLS) model, a systematic modification of the viscoelastic model leading to a more accurate tissue model is presented. A five-element model family, with a Double Maxwell-arm Wiechert (DMW) representative model, is selected for its mathematical simplicity and mathematical loading accuracy. This DMW model is then used to fit experimental data collected from stress relaxation indentation tests performed on fresh porcine liver and spleen. The results show that this DMW model provides a closer fit with the experimental liver (SLS R2=0.731, DMW R2=0.991) and spleen (SLS R2=0.720, DMW R2=0.981) data, compared to an SLS model, while maintaining appreciable mathematical simplicity by using only five model elements, compared to seven-element models. Thus, any model from this five-element model family can be used as a base compressive model for complex soft tissue with an approximate 35% improved model fit over SLS. Finally, model element parameters for in vitro fresh porcine liver and spleen are determined from the associated indentation tests.