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 20

Table 3 Selected load conditions that simulate high loads during walking
Cycles/day Joint forces (N) Orientation () Abductor muscle forces (N) Orientation ()

FP SP FP SP

12000 (1) 3244 24 6 (1) 984 28 15

4000 (2) 1621 -15 35 (2) 491 -8 9

4000 (3) 2167 56 -20 (3) 655 35 16

Orientation refers to the frontal (FP) and sagittal (SP) planes [ 5 ]

Table 4 Material properties for bone for the FEM simulation from Hambli [ 20 ]
Parameters

Notation Trabecular

bone
(meso level)

Trabecular
bone
(macro level)

Cortical
bone

General parameters
Elastic modulus

E (MPa) 10000 Eq. ( 20 ) Eq. ( 20 )

Poisson ratio m 0.3 0.3 0.3

q (g/cm 3 )

Bone density 1.2 Eq. ( 19 ) Eq. ( 19 )

Damage law parameters
Fatigue parameter g 0.7 - -

Fatigue exponent b 0.4 - -

Ultimate stress r u (MPa) 120 - -

Fatigue limit r D (MPa) 50 - -

Critical damage value at fracture D c 0.95 - -

Cycles N 1.E5 1.E5 1.E5

Number of cycles in one block set p 500 500

loops), a fixed number of cycles per day and a fixed orientation (Table 3 ). The
transition from the mesoscale to the macroscale was accomplished by employing
the trained NN. The total computation time using the FENN model was about
40 min on 64 GB dual-core computer.
The material properties for bone used for the simulation are given in Table 4 .

6 Results

6.1 Fatigue Cracks Within Trabecular Bone

Figure 10 shows an example of the fatigue damage contour after 1.E5 loading
cycles of the specimen (BV = TV ¼ 26 : 2 %) under excessive cyclic compressive
load (r ¼ 110 MPa). Fatigue damage distribution was found to be highly inho-
mogeneous across the specimen and only a small percentage of trabeculae are
cracked. The ''kill element'' technique was applied to predict the initiation and
growth of the induced fatigue cracks.