Application of Neural Network and Finite Element Method for Multiscale Prediction of Bone Fatigue Crack Growth in Cancellous Bone - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 19

2

1

1

3

2

3

Joint forces
Single-leg stance (1)
Abduction (2)
Abduction (3)
Abductor muscle
forces
Single-leg stance (1)
Abduction (2)
Abduction ( 3)

Fig. 9 Three-dimensional FE model of the femur and boundary conditions

The mean HU number of each element was averaged from the values of the
voxels it contained. The proximal femur was then partitioned into 23 regions with
different values of ash density (23 discrete material groups with an iso-value of
density for each group, thus approximating a continuous distribution) (Fig. 8 ).
Subsequently, the bone volume fraction (BV = TV) and isotropic elastic modulus
(E ) were calculated from q ash based on previously published relations.
The Young's modulus is expressed by [ 11 ]:

1 : 49

E MPa ð Þ¼ 14664 q ð 20 Þ

ash

The bone volume fraction (BV = TV) was calculated using the relationship [ 25 ]:
BV = TV ¼ q ash
q t

ð 21 Þ

where q t is the true tissue density which can be expressed by [ 25 ]:
q t 1 : 41 þ 1 : 29 a

ð 22 Þ

a is the ash function (a ¼ 0 for osteoid and a ¼ 0 : 7 for fully mineralized bone).
The dry tissue densities corresponding to these ash fraction values are 1 : 41 and
2 : 31 g = cm 3 respectively [ 35 ].
To illustrate the capabilities of the FENN multiscale method, the fatigue pro-
cess of the 3D proximal femur was performed. The daily loading history was
simulated consisting of joint reaction and abductor muscle forces similar to those
proposed by Carter et al. [ 5 ] for normal activity (Fig. 9 ).
The model was run in alternating applied loads and unload (F = 0 N) during
1.E5 cycles with a number of cycles in one block set (P ¼ 500) (200 computation