The use of sparse CT datasets for auto-generating accurate FE models of the femur and pelvis

Two types of grids used in our mesh generation. The grid on the left was used for the pelvis and the one on the right was used for the femur. Arrows show that directions are kept consistent.

Fitting of a lattice to a given boundary. The flowchart on the left shows the steps in our mesh generation method and the pictures on the right explain the steps. (1) Shows cross sections and their initial boundaries. Images are from the illium of the pelvis, the shaft of the femur and the bottom condyle of the femur. Note that different types of grids were used for each case and for the hole boundary. The rows have been moved to coincide with the start and end of the hole. (2) Shows how grids are fitted and nodes are distributed. For simple cross-sections like the illium in 2.1, nodes are evenly distributed. However, for hole and bifurcation, rows are placed at their boundaries and additional nodes are introduced to accommodate geometry change. In 2.2, the number of columns given is two and the hole inside the object cannot be described with two columns. Hence additional nodes are introduced. In 2.3, the number of rows given is 6 and the gap between the two objects cannot be described accurately with 6 rows. Hence additional nodes are introduced. (3) Shows the 3D elements formed by connecting two neighbouring grids. Since the initial grid over the whole area is covered by object and only non-empty nodes are used in forming an element holes and bifurcations are created. (a) Mesh generation flow chart. (b) Examples of each step in mesh generation.

Initial linear mesh and final fitted mesh. The left column shows linear meshes generated from our automatic mesh generation method. The right column shows the final fitted meshes resulting from the least-squares fitting. (a) Linear mesh before fitting. (b) Cubic mesh after fitting.

Steps in skeletonization to extract landmark points from a boundary. (a) The boundary of a section in the acetabulum; (b) the skeleton of the boundary in dotted line; (c) the boundary, skeleton and landmark points found. The solid lines drawn from the skeleton to the boundary are rays. The points where rays meet with the boundary are landmark points.

Pelvic regions and the way that extra slices were placed. Extra slices are shown as lines. (a) Four principal pelvis regions assumed in our study. Those four regions are the blade region comprising the wide section of the illium just above the greater sciatic notch, the isthmus region from the greater sciatic notch to just above the acetabulum, the acetabulum region, and the foramen obturatum region surrounded by the pubis and the ischium. (b) A case where the foramen obturatum region was divided into two. Note that two extra slices were used; one at the start of the blade and the other at the middle of the foramen obturatum region. The isthmus region was described by the last slice of the acetabulum. (c) A case where the foramen obturatum and the blade regions were divided into two. Note that three extra slices were used. (d) A case where the foramen obturatum region is divided into two and the blade was divided into three. Four extra slices were used.

Overall process of generating a hybrid dataset composed of Visible Human CT slices as well as patient CT slices. The flow chart on the left shows the overall steps in the method and the one on the right shows how the matching Visible Human slices were selected.

Final fitted meshes generated. (a) Mesh 1 (7 slices); (b) mesh 2 (9 slices); (c) mesh 3 (11 slices); (d) mesh 4 (17 slices); (e) mesh 5 (22 slices). The bottom row shows the error plot where the maximum error was depicted both in colour and with the length of the error bar. Maximum error is indicated by red lines and the colour scale is on the bottom right corner.

Error vs number of slices used in mesh generation.

Comparison of resulting meshes from the hybrid dataset as described in Section 2.3 to the one generated with the full patient dataset. (a) Mesh generated with 11 CT slices; (b) mesh generated with all of the available CT slices (27 slices).

Pelvic meshes generated from three patient datasets and the locations of the maximum errors. Note that the maximum error is denoted as red on the mesh and the scale bars on the bottom right corner shows the colour scales.

Error vs number of slices used in mesh generation.