Biomedical Engineering Reference
In-Depth Information
accumulation can be assessed. Second, a trained NN is able to generalize the
acquired data. Third, the NN model can be incorporated into an FE multiscale
simulation procedure as a material formulation on the integration point level at
every FE iteration—e.g. the behaviour law needed to compute the outputs at the
mesoscale is substituted by the trained neural network.
The potential of the proposed FENN method is its ability to incorporate local
trabecular information with physical meaning at the continuum whole femur level.
This is beneficial for investigating for example the role of damage accumulation
on femoral neck fractures. The NN approach is beneficial if the numerical analysis
of the complex model is time-consuming or even unfeasible [ 3 , 17 , 21 , 33 , 44 ].
A further advantage of the method is that the training data can be directly extracted
from experimental data. The development of a multiscale procedure coupling FE
and NN computation is also motivated by the need in the field of bone biome-
chanics for an efficient coupling between scales in a multiscale approach for bone
analysis. Such detailed numerical simulations on the mesoscale can capture many
of the relevant bone features. Performing FE analysis at the entire femur level with
its trabecular architecture generates a complete mesh composed of some millions
of FE which requires a huge computational time.
2 Hybrid Finite Element and Neural Network
Multiscale Concept
The proposed hybrid FENN method is a simulation procedure to link multiscale
simulations. From a numerical point of view, the macro scale passes information to
the mesoscale in the form of macroscopic variables and boundary conditions
obtained at each FE of the mesh after solving the macroscopic analysis using FE
simulation. At the mesoscopic scale, the local boundary conditions (derived from
the macro FE results) are applied to the mesoscopic bone model and the trained
NN allows for the rapid computation of the meso model responses. And finally, the
mesoscale passes information to the macroscale in the form of averaged updated
outputs (Cr.Dn and Cr.Le) (Fig. 2 ). Changes in the material distribution of the
continuum model will have an effect on the stress/strain field, thus affecting the
mechanical state of the bone in the subsequent iteration. At the completion of
every iteration, a new FE analysis is performed to update the Cr.Dn and Cr.Le
distribution in the continuum model at the macro level. The proposed methodology
follows this iterative procedure until convergence is achieved.
From a practical point of view, the following five steps summarize the appli-
cation of the proposed FENN approach (Fig. 3 ):
Search WWH ::




Custom Search