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

estimated the morphological modifications of the breast under gravity loading for
plastic surgery. For that, they proposed that the effect of the gravity in prone position
was compensated by applying the gravity force in the opposite direction. This
approximation has been chosen in this work to study the influence of considering the
prone gravity-loaded breast taken from a MRI as the reference state for the simulation
of a mammographic compression.
In this paper, an approximated of zero-strain state was performed by applying the
gravity force in the opposite direction to the prone position as performed in [9], aimed
to find a reference state to simulate X-ray mammographies. In this work, the
compression force is used to compare two simulations of the X-ray compression, when
gravity is ignored and prone gravity loaded (obtained from MRI) is used as reference
state, and when gravity force is applied and the calculated zero-strain configuration is
used as reference state.
3. MATERIALS AND METHODS
The following four models from literature were used to simulate the breast tissue
biomechanical behavior:
• Linear elastic model: proposed by Kellner et al. in [4] with the following
Young’s modulus for the different tissues Eskin= 88000 Pa, Efat=1000 Pa, and
Egland=10000 Pa and 0.49 for the Poisson's ratios.
• Nonlinear hyperelastic models:
o Neo-Hookean: this model is characterized by its strain energy density
function which is given by Eq. 1:
With the constants provided by Pérez del Palomar et al. in [9]:
C1fat=3000 Pa and C1gland=12000 Pa.
o Mooney-Rivlin: A Money-Rivlin five parameter model is characterized
by its strain energy density function as Eq. 2 shows:
With the constants provided by Tanner et al. in [3]:
- Fat: C10= 46420, C01= -31770, C20= 37070, C11=1960, C02= 1510 Pa.
- Glandular: C10= 42830, C01= -36540, C20=51830, C11=7330, C02=
520 Pa.
o Polynomial: A Polynomial second order model (N=2) is characterized by
its strain energy density function as shown in Eq. 3:
With the constants provided by Samani et al. in [10]:
- Fat: C10= 310, C01= 300, C20=3800, C11=2250, C02= 4700 Pa.
- Glandular: C10= 330, C01= 280, C20=7700, C11=4490, C02= 9400 Pa.
(1)
(2)
(3)