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Characterizing the Nonlinear Mechanical Response of Liver to Surgical Manipulation

A.E. Kerdok*, S. Socrate**, M. Ottensmeyer***, S. Dawson***, R.D. Howe*
*Biorobotics Laboratory, Harvard University
**Department of Mechanical Engineering, Massachusetts Institute of Technology
***CIMIT Simulations Group, Massachusetts General Hospital

Support provided by United States Army Medical Research and Material Command
Graduate Student Support provided by the Whitaker Foundation

For in-depth information regarding this work please refer to Amy Kerdok's PhD Thesis (2006).


Motivation
Computer-aided medical technologies such as simulators for surgical training, planning, and assessment, are currently limited by the inability to realistically portray the behavior of the involved tissues. The goal of this work is to accurately characterize the mechanical behavior of liver under large deformations typical of surgical manipulation.

Three steps are required for this characterization. First, the effect of testing conditions on the sought-after behavior is identified. A study that evaluated the effects of perfusion on the viscoelastic response of liver resulted in the development of an ex vivo perfusion system that nearly approximates the in vivo condition. Second, a mathematical model is derived that is capable of capturing the liver's nonlinear, viscoelastic response based on the physical make-up of the tissue. Third, using the perfusion apparatus, indentation tests are performed to identify and validate the models parameters by solving the inverse problem using an iterative approach.

Ex Vivo Liver Testing
In the initial phase of the project, we identified the effect of perfusion on mechanical behavior. Creep experiments conducted on porcine livers across four conditions (in vivo, ex vivo perfused, ex vivo post perfused, and an excised section) suggested that perfusion affects the viscoelastic response, two time constants were needed to characterize the response, and an ex vivo perfusion system can nearly approximate the in vivo response.

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 Nonlinear Poro-viscoelastic Liver Model
A constitutive model based on the combined contributions of individual tissue components was then developed. The model is comprised of three networks working in parallel: a modified 8-chain hyperelastic network represents the elastic response of the tissue's collagenous structure, a nonlinear viscoelastic network represents both the elastic and time response from the parenchyma, and a porous network represents the time response from extracellular fluid flow.

Material Parameter Estimation
Using the perfusion apparatus, indentation tests were performed to identify and validate the model's parameters by solving the inverse problem using an iterative approach. An axisymmetric finite element indentation model has been developed to identify the model's parameters from load/unload experiments, and validated using data from stress relaxation, and creep experiments.

Conclusions
The effects of perfusion on the viscoelastic response of liver were identified, and a perfusion apparatus was created that approximates the in vivo condition. Indentation tests measuring the response of whole, perfused, porcine livers under finite deformations (~30% nominal strain) were conducted. Results indicate a time dependent, nonlinear, viscoelastic, force-displacement behavior. A constitutive model describes the time varying response through the combined contributions of three subsystems: collagenous capsule, parenchyma, and fluid filled vessels. Solving the inverse problem through iterative finite element modeling identifies the seven independent material parameters. The model is capable of capturing the salient features of the data.


Validation and Standards
We are developing a silicone rubber model that will serve as the foundation on which new models of soft tissues will be validated. A 10 x 10 x 10 cm cube with CT fiducial markers is being developed for testing in indentation, compression, shear, tension, and rotation. The resulting force, strain and displacement fields will be made available via the web and will serve as a standard over which soft tissue models can be compared and validated.

Access to the physical standard database for validating real-time simulation of soft tissues: Truth Cube

Related Research

Karol Miller from the University of Western Australia and his research on very soft tissue mechanical properties .

Frank Tendick from the University of California at San Francisco and his research on surgical robotics and abdominal organ tissue measurements.

Stanford University Medical Center's National Biocomputation Center

Stanford University Center for Advanced Technology in Surgery (CATSS)

University of Teubingen Germany lab



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