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

The combination of JC and H allows more information about the fit between two
volumes than by considering only one of them [15]. Fig. 1 shows an example of four
volume comparisons.
(a) (b) (c) (d)
Fig. 1: In (a) and (b) JC provides the same value for both cases; however H differs
between both deformations. In (c) and (d) H provides the same value while JC differs
now between both deformations.
Given the above, a combination of both coefficients called Geometric Similarity
Function was formulated as Eq. 4 indicates:
%&' = 2
The value of GSF is lower when the similarity between two volumes is better.
The Iterative Search Algorithm (ISA) evaluates GSF in each iterate. A search range is
given to the ISA and a step that is half of the range is defined. This step is divided by
two in each iterate till its value is 1, which is the stop condition of the algorithm.
The ISA starts simulating the liver deformation in ANSYS with the first parameter of
the range. The initial search direction is from the lower limit to the upper limit of the
range. After that, ISA voxelizes the FE mesh of the simulated liver and the FE mesh of
the reference simulation and calculates the GSF. Based on the value of the step, the
parameter is updated and GSF is calculated again. In each iterate, the value of GSF is
compared with its value in the previous iteration. Thus holding the search direction if
GSF is getting better and changing it otherwise. This criterion is held till the step is
equal to one, what means that ISA stops. The Fig. 2 shows the block diagram of the
entire method.
Fig. 1: Block diagram of the entire process of the computational method to estimate the
parameters of the biomechanical model of the liver.
2
(4)