Abstract
Iterative finite element (FE) models are used to simulate bone remodelling that takes place due to the surgical insertion of an implant or to simulate fracture healing. In such simulations element material properties are calculated after each iteration of solving the model. New material properties are calculated based on the results derived by the model during the last iteration. Once the FE model has gone through a number of such iterations it is often necessary to assess the remodelling that has taken place. The method widely used to do this is to analyse element Young's modulus plots taken at particular sections through the model. Although this method gives relevant information which is often helpful when comparing different implants, the information is rather abstract and is difficult to compare with patient data which is commonly in the form of radiographs.
The authors suggest a simple technique that can be used to generate synthetic radiograph images from FE models. These images allow relatively easy comparisons of FE derived information with patient radiographs. Another clear advantage of this technique is that clinicians (who are familiar with reading radiographs) are able to understand and interpret them readily.
To demonstrate the technique a three dimensional (3D) model of the proximal tibia implanted with an Oxford Unicompartmental Knee replacement was created based on CT data obtained from a cadaveric tibia. The model's initial element material properties were calculated from the same CT data set using a relationship between radiographic density and Young's modulus.
The model was subject to simplified loading conditions and solved over 365 iterations representing one year of in vivo remodelling. After each iteration the element material properties were recalculated based on previously published remodelling rules. Next, synthetic anteroposterior radiographs were generated by back calculating radiographic densities from material properties of the model after 365 iterations. A 3D rectangular grid of sampling points which encapsulated the model was defined. For each of the elements in the FE model radiographic densities were back calculated based on the same relationships used to calculate material properties from radiographic densities. The radiographic density of each element was assigned to all the sampling grid points within the element. The 3D array of radiographic densities was summed in the anteroposterior direction thereby creating a 2D array of radiographic densities. This 2D array was plotted giving an image analogous to anteroposterior patient radiographs. Similar to a patient radiograph denser material appeared lighter while less dense material appeared darker.
The resulting synthetic radiographs were compared to patient radiographs and found to have similar patterns of dark and light regions.
The synthetic radiographs were relatively easy to produce based on the FE model results, represented FE results in a manner easily comparable to patient radiographs, and represented FE results in a clinician friendly manner.
