Characterisation of three-dimensional anatomic shapes using principal components: application to the proximal tibia

The objective of the research is to determine if principal component analys is (PCA) provides an efficient method to characterise the normative shape o f the proximal tibia. Bone surface data, converted to analytical surface de scriptions, are aligned, and an auto-associative memory matrix is generated . A limited subset of the matrix principal components is used to reconstruc t the bone surfaces, and the reconstruction error is assessed. Surface reco nstructions based on just six (of 1452) principal components have a mean ro ot-mean-square (RMS) reconstruction error of 1.05% of the mean maximum radi al distance at the tibial plateau. Surface reconstruction of bones not incl uded in the auto-associative memory matrix have a mean RMS error of 2.90%. The first principal component represents the average shape of the sample po pulation. Addition of subsequent principal components represents the shape variations most prevalent in the sample and can be visualised in a geometri cally meaningful manner. PCA offers an efficient method to characterise the normative shape of the proximal tibia with a high degree of dimensionality reduction.