Introduction

Unicompartmental Knee Replacement Arthroplasty (UKA) is a treatment option for early knee OA that appears under-utilised, partly because of a lack of clear guidance on how to best restore lasting knee function using such devices. Computational tools can help consider inherent uncertainty in patient anatomy, implant positioning and loading when predicting the performance of any implant. In the present research an approach for creating patient-specific finite element models (FEM) incorporating joint and muscle loads was developed to assess the response of the underlying bone to UKA implantation.

Inter-subject variability is inherently present in patient anatomy and is apparent in differences in shape, size and relative alignment of the bony structures. Understanding the variability in patient anatomy is useful for distinguishing between pathologies and to assist in surgical planning. With the aim of supporting the development of stratified orthopaedic interventions, this work introduces an Articulated Statistical Shape Model (ASSM) of the lower limb. The model captures inter-subject variability and allows reconstructing ‘virtual’ knee joints of the lower limb shape while considering pose.

A training dataset consisting of 173 lower limbs from CT scans of 110 subjects (77 male, 33 female) was used to construct the ASSM of the lower limb. Each bone of the lower limb was segmented using ScanIP (Simpleware Ltd., UK), reconstructed into 3D surface meshes, and a SSM of each bone was created. A series of sizing and positioning procedures were carried out to ensure all the lower limbs were in full extension, had the same femoral length and that the femora were aligned with a coincident centre. All articulated lower limbs were represented as: (femur scale factor) × (full extension articulated lower limb + relative transformation of tibia, fibula and patella to femur). Articulated lower limbs were in full extension were used to construct a statistical shape model, representing the variance of lower limb morphology. Relative transformations of the tibia, fibula and patella versus the femur were used to form a statistical pose model. Principal component analysis (PCA) was used to extract the modes of changes in the model.

The first 30 modes of the shape model covered 90% of the variance in shape and the first 10 modes of the pose model covered 90% of the pose variance. The first mode captures changes of the femoral CCD angle and the varus/valgus alignment of the knee. The second mode represents the changes in the ratio of femur to tibia length. The third mode reflects change of femoral shaft diameter and patella size. The first mode characterising pose captures the medial/lateral translation between femur and tibia. The second mode represents variation in knee flexion. The third mode reflects variation in tibio-femoral joint space.

An articulated statistical modelling approach was developed to characterize inter-subject variability in lower limb morphology for a set of training specimens. This model can generate large sets of lower limbs to systematically study the effect of anatomical variability on joint replacement performance. Moreover, if a series of images of the lower limb during a dynamic activity are used as training data, this method can be applied to analyse variance of lower limb motion across a population.

There is a large variability associated with hip stem designs, patient anatomy, bone mechanical property, surgical procedure, loading, etc. Designers and orthopaedists aim at improving the performance of hip stems and reducing their sensitivity to this variability. This study focuses on the primary stability of a cementless short stem across the spectrum of patient morphology using a total of 109 femoral reconstructions, based on segmentation of patient CT scan data. A statistical approach is proposed for assessing the variability in bone shape and density [Blanc, 2012]. For each gender, a thousand new femur geometries were generated using a subset of principal components required to capture 95% of the variance in both female and male training datasets [Bah, 2013]. A computational tool (Figure 1) is then developed that automatically selects and positions the most suitable implant (distal diameter 6–17 mm, low and high offset, 126° and 133° CCD angle) to best match each CT-based 3D femur model (75 males and 34 females), following detailed measurements of key anatomical parameters. Finite Element contact models of reconstructed hips, subjected to physiologically-based boundary constraints and peak loads of walking mode [Speirs, 2007] were simulated using a coefficient of fricition of 0.4 and an interference-fit of 50μm [Abdul-Kadir, 2008]. Results showed that the maximum and average implant micromotions across the subpopulation were 100±7μm and 7±5μm with ranges [15μm, 350μm] and [1μm, 25μm], respectively. The computed percentage of implant area with micromotions greater than reported critical values of 50μm, 100μm and 150μm never exceeded 14%, 8% and 7%, respectively. To explore the possible correlations between anatomy and implant performance, response surface models for micromotion metrics were constructed using the so-called Kriging regression methodology, based on Gaussian processes. A clear nonlinear decreasing trend was revealed between implant average micromotion and the metaphyseal canal flare indexes (MCFI) measured in the medial-lateral (ML), anterio-posterior (AP) and femoral neck-oriented directions but also the average bone density in each Gruen zone. In contrast, no clear influence of the remaining clinically important parameters (neck length and offsets, femoral anteversion and CCD angle, standard canal flares, patient BMI and weight or stem size) to implant average micromotion was found. In conclusion, the present study demonstrates that the primary stability and tolerance of the short stem to variability in patient anatomy were high, suggesting no need for patient stratification. The developed methodology, based on detailed morphological analysis, accurate implant selection and positioning, prediction of implant micromotion and primary stability, is a novel and valuable tool to support implant design and planning of femoral reconstructive surgery.

This work was motivated by the need to capture the spectrum of anatomical shape variability rather than relying on analyses of single bones. A novel tool was developed that combines image-based modelling with statistical shape analysis to automatically generate new femur geometries and measure anatomical parameters to capture the variability across the population. To demonstrate the feasibility of the approach, the study used data from 62 Caucasian subjects (31 female and 31 male) aged between 43 and 106 years, with CT voxel size ranging 0.488 × 0.488 × 1.5 mm to 0.7422 × 0.7422 × 0.97 mm.

The scans were divided into female and male subgroups and high-quality subject-specific tetrahedral finite element (FE) meshes resulting from segmented femurs formed the so-called training samples. A source mesh of a segmented femur (25580 nodes, 51156 triangles) from the Visible Human dataset [Spitzer, 1996] was used for elastic surface registration of each considered target male and female subjects, followed by applying a mesh morphing strategy.

To represent the variations in bone morphology across the population, gender-based Statistical Shape Models (SSM) were developed, using Principal Component Analysis. These were then sampled using the principal components required to capture 95% of the variance in each training dataset to generate 1000 new anatomical shapes [Bryan, 2010; Blanc, 2012] and to automatically measure key anatomical parameters known to critically influence the biomechanics after hip replacement (Figure 1).

Analysis of the female and male training datasets revealed the following data for the five considered anatomical parameters: anteversion angle (12.6 ± 6.4° vs. 6.2 ± 7.5°), CCD angle (124.8 ± 4.7° vs. 126.3 ± 4.6°), femoral neck length (48.7 ± 3.8 mm vs. 52 ± 5 mm), femoral head radius (21.5 ± 1.3 mm vs. 24.9 ± 1.5 mm) and femur length (431.0 ± 17.6 mm vs. 474.5 ± 26.3 mm). However, using the SSM generated pool of 1000 femurs, the following data were computed for females against males: anteversion angle (10.5 ± 14.3° vs. 7.6 ± 7.2°), CCD angle (123.9 ± 5.8° vs. 126.7 ± 4°), femoral neck length (46.7 ± 7.7 mm vs. 51.5 ± 4.4 mm), femoral head radius (21.4 ± 1.2 mm vs. 24.9 ± 1.4 mm) and femur length (430.2 ± 16.1 mm vs. 473.9 ± 25.9 mm).

The highest variability was found in the anteversion of the females where the standard deviation in the SSM-based sample was increased to 14.3° from 6.4° in the original training dataset (Figures 2 & 3). The mean values for both females (10.5°) and males (7.6 °) were found close to the values of 10° and 7° reported in [Mishra, 2009] in 31 females and 112 males with a [2°, 25°] and [2°, 35°] range, respectively.

Femoral neck length of the female (male) subjects was 47.3 ± 6.2 mm (51.8 ± 4.1 mm) compared to 48.7 ± 3.8 mm (52 ± 5 mm) in the training dataset and 63.65 ± 5.15 mm in [Blanc, 2012] with n = 142, 54% female, 46% male and a [50.32–75.50 mm] range. For the measured CCD angle in both female (123.9 ± 5.8°) and male (126.7 ± 4°) subjects, a good correlation was found with reported values of 128.4 ± 4.75° [Atilla, 2007], 124.7 ± 7.4° [Noble, 1988] and 129.82 + 5.37° [Blanc, 2012].

In conclusion, the present study demonstrates that the proposed methodology based on gender-specific statistical shape modelling can be a valuable tool for automatically generating a large specific population of femurs to support implant design and planning of femoral reconstructive surgery.