Estudio de Precios de Transferencia

Validation of an FE model is an essential step in confirming that the model is accurately representing a real scenario and thus providing useful results. A common method of model validation is direct comparison with corresponding experimental data, which may demonstrate whether the model can represent the experiment, but the wider clinical application will depend on whether the in vitro simulation is a relatively good representation of the true in vivo scenario. Alternatively, models can be validated by comparison with experimental data or clinical data from the literature but this is usually less robust due to the greater differences in replicating the geometry, material properties and boundary conditions. A summary of the validation process and results reported in finite element studies of vertebrae is presented in Table 2-5.

Table ‎2-5, Validation methods and techniques seen in the literature for a number of modelling approaches, including elastic models, fracture prediction, augmented vertebrae and models of cyclic loading of vertebrae. Showing the level of validation and results.

Author Validation Type Validation Results

FE Vertebrae models

(Erdem et al., 2013)

Validation with experimental and analytical results from the literature of stiffness, displacement, ligament stresses and ROM.

Reported similar values to literature.

al., 2013)

(Li et al., 2014) Qualitative comparison of fracture location (which vertebrae) with clinical results.

FEA results were consistent with clinical observations.

(Lu et al., 2014) Experimental strength comparison in models loaded via PMMA and models loaded via an IVD.

Exp/FE-PMMA: R²=0.68 Exp/FE-IVD: R²=0.71

FE Fracture prediction models

(Silva et al., 1998)

Experimental comparison of yield load. Qualitative comparison of predicted strain with failure pattern.

R2 > 0.86

Some correspondence of strain with fracture patterns.

(Imai et al., 2006)

Comparison with experimental yield loads, fracture loads, minimum principal strains, and fracture sites.

Yield loads r =0.949 Fracture loads r = 0.978 Strain r = 0.838

(Mirzaei et al., 2009)

Experimental comparison of strength Qualitative comparison of augmented vertebrae fracture patterns.

Strength R2 = 0.84 Good failure pattern comparison.

(Dall'Ara et al., 2010)

Experimental comparison with strength prediction

Stiffness R2=0.49 Strength R2=0.79 (Hosseini et al.,

2014)

Qualitative evaluation of fracture locations comparing with

experimental results. Comparison of volumetric strains.

Strain R2 = 0.74

FE Augmented vertebrae models

(Dickey et al., 2012)

Qualitative validation with models in the literature.

‘Showing good agreement’; no evidence given.

(Kinzl et al., 2012)

Experimental comparison of stiffness, strength and loading plate contact pressure.

Stiffness CCC=0.94 low modulus cement and 0.89 standard modulus cement. Strength CCC>0.95 Pressure CCC>0.67 (Liang et al., 2014)

Validation through the use of a previously validated model.

Previous model validated (Purcell et al.,

2014)

Validation through the use of a previously validated full thoracolumbar model.

Previous model validated

(Matsuura et al., 2014)

Experimental comparison of

predicted fracture loads and stiffness.

Failure loads R2=0.78 Stiffness R2=0.39 (Tarsuslugil et

al., 2014)

Experimental comparison of fractured augmented vertebrae stiffness

Stiffness concordance = 0.69

Cyclic Testing Vertebrae

(Schmidt et al., 2010)

Comparison with literature values for axial displacement and pore pressure in IVDs.

Good agreement with literature values.

(Tsouknidas et al., 2013)

Comparison with experimental data from the literature.

Agreement with literature values.

As can be seen from Table 2-5, Validation methods and techniques seen in the literature for a number of modelling approaches, including elastic models, fracture prediction, augmented vertebrae and models of cyclic loading of vertebrae. Table 2-5, there is a wide range of results presented in these validation studies so it is important to consider what level of agreement is sufficient, whether it be with experimental results or literature. This predominantly depends on the application of the model in question. It could be said that the error presented as a result of the non-perfect validation is required to be less than the change seen in the model for any given property. For example, Wijayathunga et al. showed that a large change in cement modulus changed the stiffness of the model by 0.7-3.3% and, if this were within the error value determined by the validation, then the model would not be sufficiently accurate to investigate such changes. So the validation error, along with other likely sources of error, has to be smaller than the size of changes that are likely to be seen in the model as a result of its intended use. It can also be said that the validation accuracy has to be sufficient to determine variations between groups of patients for use in a clinical setting. It can be seen that it is possible to achieve very good agreement for vertebral strength and in some cases for vertebral strain, particularly for fracture prediction models. Stiffness validation is, in general, less robust than strength, however Kinzl et al. have shown excellent agreement (concordance coefficient of 0.94).

When evaluating validation results, it is important to note whether the correlation between model predictions and validation values is given as a Pearson’s correlation coefficient (R2

or r2) or as a concordance coefficient. Concordance evaluates variables with a 1:1 relation which measures degree of linearity between two variables. This is more useful in validating models than linear regression, which only measures the degree of linearity between two variables and not their 1:1 fit.