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

C10, C01 and d were taken from [10] (C10=9850 Pa, C01=26290 Pa and K0=10 7
Pa).
The following two cases were used to find a parameter of each model:
Case 1: A linear elastic model for a cube where a force of 4.9 N was applied
perpendicular to one of its surfaces. The Poisson’s ratio was fixed with a value from the
literature and Young’s modulus was found using the GSF and ISA.
Case 2: A Mooney-Rivlin’s model for the human liver. A displacement of 15 mm was
applied to the top part of the liver similar to the movement of the diaphragm due
to the patient breathing [2]. Both parameters, C10 and C01, were estimated
separately. First C01 was fixed and C10 estimated and vice versa.
To estimate the parameters of the biomechanical models, an ex-vivo human liver
supplied by Unidad de Cirugía y Trasplante Hepático from the Hospital Universitari i
Politècnic La Fe was scanned with the Brillance iCT from Philips. The scan parameters
were 80 KVp and 100 mAs. CT images of the liver were acquired in DICOM format
with a size of 323x125x289 pixels. The voxel size was 1.08555x1.08555x0.80 mm. The
DICOM images were processed in order to obtain a Finite Element (FE) mesh. The
commercial software Simpleware 4.2 was used to segment the liver and generate the 3D
model of the liver. A smoothing Gaussian filter was used to get a more realistic and
continuous 3D model. Finally Simpleware 4.2 was used again to obtain a FE mesh
which was exported to the commercial package ANSYS 13.0 for the simulations.
3.2. Computational estimation of the model parameters.
A Geometric Similarity Function (GSF) was formulated in order to compare the liver
volume after the simulation using the selected parameter in the iteration n with the liver
volume of the reference deformation. To formulate GSF, two similarity coefficients
typically used in validation of medical image segmentation was used [14]:
• Jaccard Coefficient: This coefficient measures the overlap between two volumes
providing a value between 0 and 1 where 1 means total overlap and 0 means that
there is no overlap at all.
= | ∩ |
| ∪ |
• Hausdorff Coefficient: This coefficient uses the distance between the voxel i and
the closest voxel of a volume V denoted as . In this work, a modified
Hausdorff coefficient was used, as Eq. 3 shows:
= max , "
For each border voxel from the volume V1, Ɓ (the voxels which have at least one
neighbor that does not belong to V1), the mean of the distances to the closest voxel i
from Ɓ to the volume V2, , is used. The process is computed analogously
from V2 to V1. Both mean distances are stored and the maximum is taken.
#
(2)
(3)