Identifying a minimal rheological configuration: a tool for effective and efficient constitutive modeling of soft tissues.

We describe a modeling methodology intended as a preliminary step in the identification of appropriate constitutive frameworks for the time-dependent response of biological tissues. The modeling approach comprises a customizable rheological network of viscous and elastic elements governed by user-defined 1D constitutive relationships. The model parameters are identified by iterative nonlinear optimization, minimizing the error between experimental and model-predicted structural (load-displacement) tissue response under a specific mode of deformation. We demonstrate the use of this methodology by determining the minimal rheological arrangement, constitutive relationships, and model parameters for the structural response of various soft tissues, including ex vivo perfused porcine liver in indentation, ex vivo porcine brain cortical tissue in indentation, and ex vivo human cervical tissue in unconfined compression. Our results indicate that the identified rheological configurations provide good agreement with experimental data, including multiple constant strain rate load/unload tests and stress relaxation tests. Our experience suggests that the described modeling framework is an efficient tool for exploring a wide array of constitutive relationships and rheological arrangements, which can subsequently serve as a basis for 3D constitutive model development and finite-element implementations. The proposed approach can also be employed as a self-contained tool to obtain simplified 1D phenomenological models of the structural response of biological tissue to single-axis manipulations for applications in haptic technologies.

Effects of perfusion on the viscoelastic characteristics of liver.

Accurate characterization of soft tissue material properties is required to enable new computer-aided medical technologies such as surgical training and planning. The current means of acquiring these properties in the in vivo and ex vivo states is fraught with problems, including limited accessibility and unknown boundary conditions in the former, and unnatural behavior in the latter. This paper presents a new testing method where a whole porcine liver is perfused under physiologic conditions and tested in an ex vivo setting. To characterize the effects of perfusion on the viscoelastic response of liver, indentation devices made force and displacement measurements across four conditions: in vivo, ex vivo perfused, ex vivo post perfused, and in vitro on an excised section. One device imposed cyclic perturbations on the liver's surface, inducing nominal strains up to 5% at frequencies from 0.1 to 200 Hz. The other device measured 300 s of the organ's creep response to applied loads, inducing nominal surface stresses of 6.9-34.7 kPa and nominal strains up to 50%. Results from empirical models indicate that the viscoelastic properties of liver change with perfusion and that two time constants on the order of 1.86 and 51.3s can characterize the liver under large strains typical of surgical manipulation across time periods up to 300 s. Unperfused conditions were stiffer and more viscous than the in vivo state, resulting in permanent strain deformation with repeated indentations. Conversely, the responses from the ex vivo perfusion condition closely approximated the in vivo response.

Truth cube: establishing physical standards for soft tissue simulation.

Accurate real-time models of soft tissue behavior are key elements in medical simulation systems. The need for fast computation in these simulations, however, often requires simplifications that limit deformation accuracy. Validation of these simplified models remains a challenge. Currently, real-time modeling is at best validated against finite element models that have their own intrinsic limitations. This study develops a physical standard to validate real-time soft tissue deformation models. We took CT images of a cube of silicone rubber with a pattern of embedded Teflon spheres that underwent uniaxial compression and spherical indentation tests. The known material properties, geometry and controlled boundary conditions resulted in a complete set of volumetric displacement data. The results were compared to a finite element model analysis of identical situations. This work has served as a proof of concept for a robust physical standard for use in validating soft tissue models. A web site has been created to provide access to our database: http://biorobotics.harvard.edu/truthcube/ (soon to be http://www.truthcube.org).

Energetics and mechanics of human running on surfaces of different stiffnesses.

Mammals use the elastic components in their legs (principally tendons, ligaments, and muscles) to run economically, while maintaining consistent support mechanics across various surfaces. To examine how leg stiffness and metabolic cost are affected by changes in substrate stiffness, we built experimental platforms with adjustable stiffness to fit on a force-plate-fitted treadmill. Eight male subjects [mean body mass: 74.4 +/- 7.1 (SD) kg; leg length: 0.96 +/- 0.05 m] ran at 3.7 m/s over five different surface stiffnesses (75.4, 97.5, 216.8, 454.2, and 945.7 kN/m). Metabolic, ground-reaction force, and kinematic data were collected. The 12.5-fold decrease in surface stiffness resulted in a 12% decrease in the runner's metabolic rate and a 29% increase in their leg stiffness. The runner's support mechanics remained essentially unchanged. These results indicate that surface stiffness affects running economy without affecting running support mechanics. We postulate that an increased energy rebound from the compliant surfaces studied contributes to the enhanced running economy.