Poroviscoelastic modeling of stress relaxation of porcine liver to investigate injury response

Highly vascular tissue is a combination of solid and fluid components. The interaction between these two phases during deformation creates a viscoelastic or rate-dependent behavior. To understand how fluid and solid components contribute to the injury response of liver tissue, a constitutive model is needed which reflects the biphasic nature of the material. This study aims to capture the stress relaxation response of porcine liver in unconfined compression using biphasic poroviscoelastic (PVE) modeling. Seventeen fresh porcine liver specimens (19mm diameter, 10mm thick) were compressed to 5% strain at varying strain rates (.001s, .01s, .1s) using a Bose Electroforce Test Instrument. Relaxation response was monitored for 2000 seconds until equilibrium was achieved. Abaqus (v6.8-2, Simulia) SOIL analysis was used to create a PVE axisymmetric finite element model for each strain rate group. Rate dependent and independent responses of the solid phase were modeled with a three-term Prony series and a hyperelastic material model respectively. Best fit parameters were determined using nonlinear least-squares algorithms. Poisson’s ratio was selected as 0.49, the initial void ratio 0.2, and material permeability 3.09x10m/Ns. Compression data showed rate dependence of the peak reaction force. Best fit Prony series parameters were g1=0.5026, g2=. 1848, g3=0.1418, τ1=2.1s, τ2=47.1s, τ3=380.1s and the initial shear modulus was 795Pa. Linear regression analysis between model and experiment resulted in R values of 0.997, 0.988, and 0.989 for 0.001s, 0.01s and 0.1s respectively (p<0.05). The PVE model accurately predicted the stress relaxation behavior of porcine liver tissue. Advantages of the PVE model include the ability to simulate both the overall mechanical response and the fluid pressure changes in response to loading. Future studies will validate pore fluid pressure model predictions and incorporate higher strain rates to examine interstitial fluid pressure as an injury severity indicator. INTRODUCTION Liver injuries account for one-third of all abdominal injuries, with 5% of trauma cases pertaining to liver injury (Moore, 2004). The most common source of blunt liver injury arises from motor vehicle crashes (Moore, 2004). Computational models created from an understanding of the biomechanics of blunt liver injury can aid in evaluating the risk of liver injury. Data from these models may be valuable in progressing vehicle safety. Previous studies have modeled the mechanical response of liver tissue in high rate loading typical of impact trauma, using phenomenological models such as quasilinear viscoelasticity (QLV) (Miller, 2000; Tamura et al., 2002; Sparks and Dupaix, 2008). In contrast to these studies, the current study adopts a more mechanistic model of liver tissue, basing model design on material structure. The benefit of this approach is the ability to study the interaction between solid and fluid phases of the material. Vascular tissues such as liver are made up of a combination of solid matrix and fluid from arterial, venous, lymphatic and interstitial sources. This allows the characterization of this tissue as biphasic, or a combination of solid and fluid phases (Mow, 1980). A biphasic poroviscoelastic model allows the rate dependence of the tissue to stem from both intrinsic properties of the solid matrix as well as the interaction between solid and fluid phases. This type of analysis has been used considerably to characterize cartilage and intervertebral discs, and more recently visceral organs (Cheng and Bilston, 2007; Ng et al.; 2005, Ford et al., 1991). An extensive literature search revealed no characterization of liver tissue in this manner. The objective of this study is to characterize the behavior of porcine liver tissue in unconfined compression through biphasic poroviscoelastic modeling. Strain rates will be varied in order to determine model capability to predict rate-dependence.