Introduction. Research studies have established mathematical correlations between the lengths of bone segments and the possible biomechanical implications of these correlations. The Lucas sequence comprises a series of integers that adhere to the same recurrence relation as the Fibonacci sequence; it differs in that it can start with any two initial integers. The purpose of this study is to determine whether segmental lengths of the foot height, tibia, femur, and upper body follow a Lucas sequence pattern. Method. This was a retrospective radiographic review of patients who underwent full-body EOS scans. The AP scan was used to measure standing foot height (Ft), tibial length (T), femoral length (Fe), upper body length (UB), and full body length. A linear regression test was performed to determine whether a Lucas sequence-based relationship exists between Ft + T and Fe, and between T + Fe and UB. Result. The regression for the relationship between Ft + T and Fe for the entire cohort (R= 0.82, R2= 0.70), the female subset (R= 0.94, R2= 0.88) and the male subset (R= 0.75, R2= 0.57), all demonstrated a strong positive correlation between Ft + T and Fe and showed that Ft + T is a likely predictor of Fe. The regression test for the entire cohort demonstrated a moderately positive correlation between T + Fe and UB (R= 0.41, R2= 0.17, F(1, 145) = 29.42, p= 2.4E-07). A stronger correlation was found for the relationship between T + Fe and UB (R= 0.57, R2= 0.32, F(1, 35) = 16.64, p= 2.5E-05) for the female subset relative to the male subset (R= 0.20, R2= 0.038, F(1, 35) = 4.37, p= 0.04). Conclusion. This study demonstrates that total height is made up of sequential segments whose lengths approximate a Lucas series. The Fibonacci sequence is therefore once again implicated in human body proportions

The objective of this study was to analyze the biomechanical effect of an implanted ACL graft by determining the tunnel position according to the aspect ratio (ASR) of the distal femur during flexion-extension motion. To analyze biomechanical characteristics according to the ASR of the knee joint, only male samples were selected to exclude the effects of gender and 89 samples were selected for measurement. The mean age was 50.73 years, and the mean height was 165.22 cm. We analyzed tunnel length, graft bending angle, and stress of the graft according to tunnel entry position and aspect ratio (ratio of antero-posterior depth to medio-lateral width) of the articular surface for the distal femur during single-bundle outside-in anterior cruciate ligament reconstruction surgery. We performed multi-flexible-body dynamic analyses with wherein four ASR (98, 105, 111, and 117%) knee models. The various ASRs were associated with approximately 1-mm changes in tunnel length. The graft bending angle increased when the entry point was far from the lateral epicondyle and was larger when the ASR was smaller. The graft was at maximum stress, 117% ASR, when the tunnel entry point was near the lateral epicondyle. The maximum stress value at a 5-mm distance from the lateral epicondyle was 3.5 times higher than the 15-mm entry position and, the cases set to 111% and 105% ASR, showed 1.9 times higher stress values when at a 5-mm distance compared with a 15-mm distance. In the case set at 98% ASR, the low-stress value showed a without-distance difference from the lateral epicondyle. Our results suggest that there is no relationship between the ASR and femoral tunnel length, A smaller ASR causes a higher graft bending angle, and a larger ASR causes greater stress in the graft

The use of retrograde femoral intramedullary nails in children for deformity correction is controversial. It is unknown if the injury to the central part of the growth plate results in premature bony union, leading to limb deformities or discrepancies. The aim of this study was to assess physeal healing and bone growth after insertion of a retrograde femoral nail thorough the centre of the physis in a skeletally immature experimental porcine model. Eleven immature pigs were included in the study. One leg was randomised for operation with a retrograde femoral nail (diameter 10.7 mm), whilst the non-operated contralateral remained as control. All nails were inserted centrally in coronal and sagittal plane under fluoroscopic guidance, and the nails spanned the physis. The nails were removed at 8 weeks. Both femora in all animals underwent MRI at baseline (pre-operatively), 8 weeks (after nail removal) and 16 weeks (before euthanasia). Femoral bone length was measured at 5 sites (anterior, posterior, central, lateral and medial) using 3d T1-weighted MRI. Growth was calculated after 8 weeks (growth with nail) and 16 weeks (growth without nail). Physeal cross-sectional area and percentage violated by the nail was determined on MRI. Operated side was compared to non-operated. Corresponding 95% confidence intervals were calculated. No differences in axial growth were observed between operated and non-operated sides. Mean growth difference was 0,61 mm [−0,78;2,01] whilst the nail was inserted into the bone and 0,72 mm [−1,04;1,65] after nail removal. No signs of angular bone deformities were found when comparing operated side to non-operated side. No premature bony healing at the physis occurred. Histology confirmed fibrous healing. Mean physeal violation was 5.72% [5.51; 5.93] by the femoral nail. The insertion of a retrograde femoral nail through the centre of an open physis might be a safe procedure with no subsequent growth arrest. However, experiments assessing the long term physeal healing and growth are needed

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

Lower limb mal-alignment due to deformity is a significant cause of early degenerative change and dysfunction. Standard techniques are available to determine the centre of rotation of angulation (CORA) and extent of the majority of deformities, however distal femoral deformity is difficult to assess because of the difference between anatomic and mechanical axes. We found the described technique involving constructing a line perpendicular to a line from the tip of the greater trochanter to the centre of the femoral head inaccurate, particularly if the trochanter is abnormal. We devised a novel technique which accurately determines the CORA and extent of distal femoral deformity, allowing accurate correction. Using standard leg alignment views of the normal femur, the distal femoral metaphysis and joint line are stylized as a block. A line bisecting the axis of the proximal femur is then extended distally to intersect the joint. The angle (Θ) between the joint and the proximal femoral axis and the position (p) where the extended proximal femoral axis intersects the joint line are calculated. These measurements can then be reproduced on the abnormal distal femur in order to calculate the CORA and extent of the deformity, permitting accurate correction. We examined the utility and reproducibility of the new method using 100 normal femora. Θ = 81 ± sd 2.5. As expected, Θ correlated with femoral length (r=0.74). P (expressed as the percentage of the distance from the lateral edge of the joint block to the intersection) = 61% ± sd 8%. P was not correlated with Θ. Intra-and inter-observer errors for these measurements are within acceptable limits and observations of 30-paired normal femora demonstrate similar values for Θ and p on the two sides. We have found this technique to be universally applicable and reliable in a variety of distal femoral deformities

Sex hormones play important roles in the regulation of the proliferation, maturation and death of chondrocytes in the epiphyseal growth plate. We have investigated the effects of male castration on the cell kinetics of chondrocytes as defined by the numbers of proliferating and dying cells. The growth plates of normal rabbits and animals castrated at eight weeks of age were obtained at 10, 15, 20 and 25 weeks of age.

Our study suggested that castration led to an increase in apoptosis and a decrease in the proliferation of chondrocytes in the growth plate. In addition, the number of chondrocytes in the castrated rabbits was less than that of normal animals of the same age.