ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

ehavior. Other researchers have measured the mechanical response of in-vivo liver
tissue [9-11]. However, they do it by means of invasive or open surgery.
In this situation, the use of Medical Image Techniques can play an important role to
estimate the parameters of biomechanical models since they can be obtained through
non-invasive methods avoiding surgery. Some researchers have used Elasticity Imaging
Techniques as Magnetic Resonance Elastography (MRE) [12-13]. MRE uses
propagating acoustic shear waves to measure the stiffness of the soft tissue.
Nevertheless MRE only allows the estimation of the Young’s modulus and viscous
effects, so parameters of non-linear elastic models cannot be estimated. Furthermore,
this technique requires additional and complex hardware to measure and create the
mechanical wave.
Therefore, the similarity coefficients commonly used for segmentation validation in
Medical Image can be quite suitable used over liver volumes reconstructed from
Computer Tomography (CT). They can be used to estimate how accurate are the
parameters comparing a real deformed liver volume with the liver volume of the
simulated deformation. This method allows estimating the parameter of any model and
only using a CT Machine, that is, no additional hardware is needed in the Hospital.
Inside this framework, this paper takes the last approach to estimate the parameters of
several biomechanical models. An Iterative Search Algorithm (ISA) is used to find the
optimum parameter of each model where the results of the Geometric Similarity
Function (GSF), based on similarity coefficients, provides information to the ISA about
the direction of the search.
3. MATERIALS AND METHODS
This section is divided in two subsections. The first one explains everything related to
obtain the model geometry of the liver and the simulation of its deformation due to the
patient breathing using biomechanical models. The second subsection explains the
method used to estimate the models parameters based on a Geometric Similarity
Function (GSF) and an iterative search algorithm (ISA).
3.1. Simulation of the human liver deformation due to the breathing.
The biomechanical models used for the simulations were two:
• Linear elastic model: Two parameters characterize the behavior of the material,
Young’s modulus E and Poisson’s ratio υ. These two parameters were taken
from the literature for the reference deformation [1], which would be equivalent
to the real deformation (E=7800 Pa and υ=0.3).
̅ ̅
• Mooney-Rivlin’s model: The strain energy potential for this model with two
parameters is defined as Eq. 1 indicates:
= − 3 + − 3 +
2
− 1
(1)
Where C10 and C01 are material constants, ̅ and ̅ are the first and second
deviatoric strain invariant respectively, K0 is the Bulk modulus and J is the
determinant of the elastic deformation gradient. For the reference deformation