Carpal bone maturation assessment by image analysis from computed tomography scans

Bone maturation is the only reliable indicator of growth and its radiologic assessment with or without automated systems is a qualitative method. Image processing allows the study of bone maturation with quantitative data. Carpal bone maturation was studied in 20 children (13 boys and 7 girls, ages ranging from 4 to 15 years) without any clinical evidence of endocrine disease by image analysis from computed tomography (CT) scans. Each wrist CT scan was processed in order to extract the carpal bones and to measure quantitative data regarding volume, axes of inertia and density for each bone. The volumes and the length of the inertia axes were significantly correlated with age. Whatever the age, there were strong correlations between the volume or the length of the main inertia axis of one carpal bone and that of all others. The decrease in the carpal bone volume measured from the processing procedure compared with the theoretical volume of bone defined from the length of the three inertia axes indicated a change in bone shape during growth. Although the mean density was constant, there was an increase in the standard deviation of density with age. Skeletal maturity assessment with image analysis from CT scans seems to be a good complementary investigation to determine bone age in children.     

Cross-sectional structural parameters from densitometry

Bone densitometry has previously been used to obtain cross-sectional properties of bone from a single X-ray projection across the bone width. Using three unique projections, we have extended the method to obtain the principal area moments of inertia and orientations of the principal axes at each scan cross-section along the length of the scan. Various aluminum phantoms were used to examine scanner characteristics to develop the highest accuracy possible for in vitro non-invasive analysis of cross-sectional properties. Factors considered included X-ray photon energy, initial scan orientation, the angle spanned by the three scans (included angle), and I(min)/I(max) ratios. Principal moments of inertia were accurate to within +/-3.1% and principal angles were within +/-1 degrees of the expected value for phantoms scanned with included angles of 60 degrees and 90 degrees at the higher X-ray photon energy (140 kVp). Low standard deviations in the error (0.68-1.84%) also indicate high precision of calculated measurements with these included angles. Accuracy and precision decreased slightly when the included angle was reduced to 30 degrees. The method was then successfully applied to a pair of excised cadaveric tibiae. The accuracy and insensitivity of the algorithms to cross-sectional shape and changing isotropy (I(min)/I(max)) values when various included angles are used make this technique viable for future in vivo studies.     

The effect of swimming activity on bone architecture in growing rats

The effect of non-habitual physical activity on bone architecture in the rat humeral shaft was examined. Two groups of rats were trained to swim for 1 h a day, for 20 weeks, at two training levels. The control group consisted of sedentary rats. Parameters of cross-sectional bone morphology (cross-section areas, principal area moments of inertia and their ratio) were used to evaluate the response of bone architecture to mechanical loading. The strength of bone was assessed by measuring the ultimate compressive force and stress. The cortical cross-section area and principal moments of inertia were found to be significantly higher in the swimming groups than in the controls. Examination of the ratio between the major and minor moments of inertia revealed a pronounced change in the shape of the bone cross-section which became more rounded following swimming training. The ultimate compressive force was significantly higher in the swimming rats while the changes in ultimate stress were not significant. Our results indicate a gain of bone strength due to increased periosteal apposition and modified bone tissue distribution. The marked changes in bone morphology are attributed to the different nature of the forces and moments exerted on the humerus during swimming compared to those prevailing during normal locomotion.     

2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones

A calculation method using the finite element technique is presented. Its main objective was to determine strains, stresses and more particularly stiffnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a non-uniform cross section of a composite beam with arbitrary orientation of fibres. The determination of stresses, strains and stiffnesses within a composite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation with respect to the principal axis of the bone. The comparison of the results, from our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impossible to obtain local stiffnesses by experimentation. The good agreement between the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT scan images with a good accuracy to determine locally the homogenised mechanical characteristics of human tibia in vivo, and particularly to quantify torsional tibial abnormalities of children without approximation of the shape of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values has been emphasised. This 2D method has also allowed to reduce CPU time of the 3D modelling and calculation.     

Prediction of protein-protein interactions based on surface patch comparison

A method to predict if two proteins interact, based on their three-dimensional structures, is presented. It consists of five steps: (i) the surface of each protein, represented by the solvent accessible atoms, is divided into small patches; (ii) the shape of each patch is described by the atom distributions along its principal axes; (iii) the shape complementarity between two patches is estimated by comparing, through contingency table analysis, their atom distributions along their principal axes; (iv) given protein A, with nA surface patches, and protein B, with nB surface patches, nA x nB shape complementarity values are obtained; and (v) the distribution of the latter allows one to discriminate pairs of interacting and of noninteracting proteins. Only a few seconds are necessary to predict if two proteins interact, with accuracy close to 80%, sensitivity over 70% and specificity close to 50%.     

Bone alignment using the iterative closest point algorithm

Computer assisted surgical interventions and research in joint kinematics rely heavily on the accurate registration of three-dimensional bone surface models reconstructed from various imaging technologies. Anomalous results were seen in a kinematic study of carpal bones using a principal axes alignment approach for the registration. The study was repeated using an iterative closest point algorithm, which is more accurate, but also more demanding to apply. The principal axes method showed errors between 0.35 mm and 0.49 mm for the scaphoid, and between 0.40 mm and 1.22 mm for the pisiform. The iterative closest point method produced errors of less than 0.4 mm. These results show that while the principal axes method approached the accuracy of the iterative closest point algorithm in asymmetrical bones, there were more pronounced errors in bones with some symmetry. Principal axes registration for carpal bones should be avoided.     

Comparison of the hindfoot axes of a multi-segment foot model to the underlying bony anatomy

Musculoskeletal models used in gait analysis require coordinate systems to be identified for the body segments of interest. It is not obvious how hindfoot (or rearfoot) axes defined by skin-mounted markers relate to the anatomy of the underlying bones. The aim of this study was to compare the marker-based axes of the hindfoot in a multi-segment foot model to the orientations of the talus and calcaneus as characterized by their principal axes of inertia. Twenty adult females with no known foot deformities had radio-opaque markers placed on their feet and ankles at the foot model marker locations. CT images of the feet were acquired as the participants lay supine with their feet in a semi-weight bearing posture. The spatial coordinates of the markers were obtained from the images and used to define the foot model axes. Segmented masks of the tali and calcanei were used to create 3D bone models, from which the principal axes of the bones were obtained. The orientations of the principal axes were either within the range of typical values reported in the imaging literature or differed in ways that could be explained by variations in how the angles were defined. The model hindfoot axis orientations relative to the principal axes of the bones had little bias but were highly variable. Consideration of coronal plane hindfoot alignment as measured clinically and radiographically suggested that the model hindfoot coordinate system represents the posterior calcaneal tuberosity, rather than the calcaneus as a whole.     

Use of a natural hybrid zone for genomewide association mapping of craniofacial traits in the house mouse

The identification of the genes involved in morphological variation in nature is still a major challenge. Here, we explore a new approach: we combine 178 samples from a natural hybrid zone between two subspecies of the house mouse (Mus musculus domesticus and Mus musculus musculus), and high coverage of the genome (~ 145K SNPs) to identify loci underlying craniofacial shape variation. Due to the long history of recombination in the hybrid zone, high mapping resolution is anticipated. The combination of genomes from subspecies allows the mapping of both, variation within subspecies and inter‐subspecific differences, thereby increasing the overall amount of causal genetic variation that can be detected. Skull and mandible shape were measured using 3D landmarks and geometric morphometrics. Using principal component axes as phenotypes, and a linear mixed model accounting for genetic relatedness in the mapping populations, we identified nine genomic regions associated with skull shape and 10 with mandible shape. High mapping resolution (median size of significant regions = 148 kb) enabled identification of single or few candidate genes in most cases. Some of the genes act as regulators or modifiers of signalling pathways relevant for morphological development and bone formation, including several with known craniofacial phenotypes in mice and humans. The significant associations combined explain 13% and 7% of the skull and mandible shape variation, respectively. In addition, a positive correlation was found between chromosomal length and proportion of variation explained. Our results suggest a complex genetic architecture for shape traits and support a polygenic model.     

Adjustments to McConville et al. and Young et al. body segment inertial parameters

Body segment inertial parameters (BSIPs) are important data in biomechanics. They are usually estimated from predictive equations reported in the literature. However, most of the predictive equations are ambiguously applicable in the conventional 3D segment coordinate systems (SCSs). Also, the predictive equations reported in the literature all include two assumptions: the centre of mass and the proximal and distal endpoints are assumed to be aligned, and the inertia tensor is assumed to be principal in the segment axes. These predictive equations, restraining both position of the centre of mass and orientation of the principal axes of inertia, become restrictive when computing 3D inverse dynamics, when analyzing the influence of BSIP estimations on joint forces and moments and when evaluating personalized 3D BSIPs obtained from medical imaging. In the current study, the extensive data from McConville et al. (1980. Anthropometric relationships of body and body segment moments of inertia. AFAMRL-TR-80-119, Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio) and from Young et al. (1983. Anthropometric and mass distribution characteristics of the adults female. Technical Report AFAMRL-TR-80-119, FAA Civil Aeromedical Institute, Oklaoma City, Oklaoma) are adjusted in order to correspond to joint centres and to conventional segment axes. In this way, scaling equations are obtained for both males and females that provide BSIPs which are directly applicable in the conventional SCSs and do not restrain the position of the centre of mass and the orientation of the principal axes. These adjusted scaling equations may be useful for researchers who wish to use appropriate 3D BSIPs for posture and movement analysis.     

Predicting the shapes of bones at a joint: application to the shoulder

This paper presents a novel method to explore the intrinsic morphological correlation between the bones of a shoulder joint (humerus and scapula). To model this correlation, canonical correlation analysis (CCA) is used. We also propose a technique to predict a three-dimensional (3D) bone shape from its adjoining segment at a joint based on partial least squares regression (PLS). The high dimensional 3D surface information of a bone is represented by a few variables using principal component analysis, which also captures the pattern of variability of the shapes in our datasets. Our results show that the humerus set and scapula set have highly linear morphological relationship and that the correlation information can be used as a classifier. In this study, primate shoulder bone datasets were categorised into two clusters: great apes (including humans) and monkeys. A leave one out experiment was performed to test the robustness of this prediction method. The prediction behaviour using this method shows statistically significantly better results than using the mean shape from the training set.     

Automatic construction of an anatomical coordinate system for three-dimensional bone models of the lower extremities – Pelvis,femur, and tibia

Automated methods for constructing patient-specific anatomical coordinate systems (ACSs) for the pelvis, femur and tibia were developed based on the bony geometry of each, derived from computed tomography (CT). The methods used principal axes of inertia, principal component analysis (PCA), cross-sectional area, and spherical and ellipsoidal surface fitting to eliminate the influence of rater's bias on reference landmark selection. Automatic ACSs for the pelvis, femur, and tibia were successfully constructed on each 3D bone model using the developed algorithm. All constructions were performed within 30 s; furthermore, between- and within- rater errors were zero for a given CT-based 3D bone model, owing to the automated nature of the algorithm. ACSs recommended by the International Society of Biomechanics (ISB) were compared with the automatically constructed ACS, to evaluate the potential differences caused by the selection of the coordinate system. The pelvis ACSs constructed using the ISB-recommended system were tilted significantly more anteriorly than those constructed automatically (range, 9.6–18.8°). There were no significant differences between the two methods for the femur. For the tibia, significant differences were found in the direction of the anteroposterior axis; the anteroposterior axes identified by ISB were more external than those in the automatic ACS (range, 17.5–25.0°).     

Mechanism of local anesthesia: long-range orientation effects

The orientation interaction of a molecule of a local anesthetic with a biomembrane and cell-like liquid was studied, based on the model of adsorption of the anesthetic from a cell-like solution on the surface of a biomembrane for compounds of the trimecaine series. A statistically significant correlation equation was obtained, which relates the minimum blocking concentration to the projection of the dipole moment of the anesthetic on the plane X(1)0X2 of the principal axes of inertia. A model is prosed according to which the "anesthetic-biomembrane" interaction is most effective the molecule of the anesthetic rotates around the axis of the maximum moment of inertia.     

Porosity-geometry interaction in the conservation of bone strength

Automated image analysis of a small sample of femoral cross-section radiographs has revealed a consistent difference in bone porosity relative to geometry. Two sub-periosteal fields were assessed microscopically, with field location determined with reference to the principal moment axes (Imax, Imin). The data indicate that: (1) porosity is greatest in the direction of maximum geometric resistance to bending, along the Imin axis; and (2) porosity differences between the Imax and Imin fields decrease as the bone becomes more circular in cross-sectional shape.     

On the variation explained by ordination and constrained ordination axes

Abstract. Total inertia (TI), the sum of eigenvalues for all ordination axes, is often used as a measure of total variation in a data set. By use of simulated data sets, I demonstrate that lack-of-fit of data to the response model implicit in any eigenvector ordination method results in polynomial distortion ordination axes, with eigenvalues that normally contribute 30–70% to TI (depending on data set properties). The amount of compositional variation extracted on ecologically interpretable ordination axes (structure axes) is thus underestimated by the eigenvalue-to-total-inertia ratio. I recommend that the current use of total inertia as a measure of compositional variation is discontinued. Eigenvalues of structure axes can, however, be used with some caution to indicate their relative importance. I also demonstrate that when the total inertia is partitioned on different sets of explanatory variables and unexplained variation by use of (partial) constrained ordination, (35) 50–85% of the variation ‘unexplained’ by the supplied explanatory variables represents lack-of-fit of data to model. Thus, the common interpretation of ‘unexplained variation’ as random variation (‘noise’) or coenoclinal variation caused by unmeasured explanatory variables, is generally inappropriate. I recommend a change of focus from the variation-explained-to-total inertia ratio and ‘unexplained’ variation to relative amounts of variation explained by different sets of explanatory variables.     

Automatic determination of anatomical coordinate systems for three-dimensional bone models of the isolated human knee

The combination of three-dimensional (3-D) models with dual fluoroscopy is increasingly popular for evaluating joint function in vivo. Applying these modalities to study knee motion with high accuracy requires reliable anatomical coordinate systems (ACSs) for the femur and tibia. Therefore, a robust method for creating ACSs from 3-D models of the femur and tibia is required. We present and evaluate an automated method for constructing ACSs for the distal femur and proximal tibia based solely on 3-D bone models. The algorithm requires no observer interactions and uses model cross-sectional area, center of mass, principal axes of inertia, and cylindrical surface fitting to construct the ACSs. The algorithm was applied to the femur and tibia of 10 (unpaired) human cadaveric knees. Due to the automated nature of the algorithm, the within specimen variability is zero for a given bone model. The algorithm’s repeatability was evaluated by calculating variability in ACS location and orientation across specimens. Differences in ACS location and orientation between specimens were low (<1.5 mm and <2.5°). Variability arose primarily from natural anatomical and morphological differences between specimens. The presented algorithm provides an alternative method for automatically determining subject-specific ACSs from the distal femur and proximal tibia.     

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three "non-orthogonal effective axes" that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90 degrees was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.     

A Morphospace for Reef Fishes: Elongation Is the Dominant Axis of Body Shape Evolution

Tropical reef fishes are widely regarded as being perhaps the most morphologically diverse vertebrate assemblage on earth, yet much remains to be discovered about the scope and patterns of this diversity. We created a morphospace of 2,939 species spanning 56 families of tropical Indo-Pacific reef fishes and established the primary axes of body shape variation, the phylogenetic consistency of these patterns, and whether dominant patterns of shape change can be accomplished by diverse underlying changes. Principal component analysis showed a major axis of shape variation that contrasts deep-bodied species with slender, elongate forms. Furthermore, using custom methods to compare the elongation vector (axis that maximizes elongation deformation) and the main vector of shape variation (first principal component) for each family in the morphospace, we showed that two thirds of the families diversify along an axis of body elongation. Finally, a comparative analysis using a principal coordinate analysis based on the angles among first principal component vectors of each family shape showed that families accomplish changes in elongation with a wide range of underlying modifications. Some groups such as Pomacentridae and Lethrinidae undergo decreases in body depth with proportional increases in all body regions, while other families show disproportionate changes in the length of the head (e.g., Labridae), the trunk or caudal region in all combinations (e.g., Pempheridae and Pinguipedidae). In conclusion, we found that evolutionary changes in body shape along an axis of elongation dominates diversification in reef fishes. Changes in shape on this axis are thought to have immediate implications for swimming performance, defense from gape limited predators, suction feeding performance and access to some highly specialized habitats. The morphological modifications that underlie changes in elongation are highly diverse, suggesting a role for a range of developmental processes and functional consequences.     

Reorienting in Virtual 3D Environments: Do Adult Humans Use Principal Axes,Medial Axes or Local Geometry?

Studies have shown that animals, including humans, use the geometric properties of environments to orient. It has been proposed that orientation is accomplished primarily by encoding the principal axes (i.e., global geometry) of an environment. However, recent research has shown that animals use local information such as wall length and corner angles as well as local shape parameters (i.e., medial axes) to orient. The goal of the current study was to determine whether adult humans reorient according to global geometry based on principal axes or whether reliance is on local geometry such as wall length and sense information or medial axes. Using a virtual environment task, participants were trained to select a response box located at one of two geometrically identical corners within a featureless rectangular-shaped environment. Participants were subsequently tested in a transformed L-shaped environment that allowed for a dissociation of strategies based on principal axes, medial axes and local geometry. Results showed that participants relied primarily on a medial axes strategy to reorient in the L-shaped test environment. Importantly, the search behaviour of participants could not be explained by a principal axes-based strategy.     

Accuracy of elastic property measurement in mandibular cortical bone is improved by using cylindrical specimens

Ultrasonic determination of elastic properties in human craniofacial cortical bone is problematic because of a lack of information about the principal material axes, and because the cortex is often thinner than in long bones. This study investigated solutions that permit reasonable determination of elastic properties in the human mandible. We tested whether ultrasonic velocities could be reliably measured in cylindrical samples of aluminum and mandibular bone, and the effects of reduced specimen thickness. Results indicted that (1) varying shape had minimal effects on ultrasonic velocities or derived elastic properties, and (2) ultrasonic velocities have relatively increased measurement error as propagation distances decreased. The increased error in velocity measurements of mandibular cortical specimens of less than 1.2 mm in thickness should be considered when assessing the reliability of single measurements.