Use of uncalibrated biplanar radiography for the measurement of skeletal coordinates around the shoulder girdle

Mechanical modelling of the musculoskeletal system is dependent upon information regarding the bony attachments of the relevant muscles; in order to study the biomechanics of the shoulder girdle the authors have identified the muscle attachments in three embalmed cadavers. A simple biplanar radiographic technique was then used to determine the attachment coordinates using frames of reference defined for each bone. This technique, using hand positioning without special fixtures was believed to be sufficiently accurate, bearing in mind the likely degree of biological variation. In order to test this assumption, the accuracy of the technique has been studied by measuring the agreement between the two measurements of the common coordinate in the pairs of radiographs. it was found that for the trunk, the errors in the common coordinate were always less than the natural variation; for the scapula they were of a similar magnitude but, for the humerus, the measurement errors frequently exceeded the variation in the coordinates of muscle attachments. It was concluded that, in general, uncalibrated biplanar radiography was sufficiently accurate for the determination of the spatial coordinates of muscle attachments.     

Morphometric analysis of Cartesian coordinates of the human skull

A method for locating the three dimensional coordinates of cranial landmarks with respect to the Frankfort, midsagittal, and coronal planes is presented. Sliding calipers were used to obtain the distances from left and right porion and apex to each landmark, except for a few points where spreading calipers are required. In the present example, 35 landmarks (for a total of 105 measurements) were located for each of 35 Peruvian precolumbian skulls. These distances were entered into a program (SKULL) which calculates the Cartesian coordinates of each landmark. The XYZ coordinates of each landmark contain all the information necessary for calculation of the distances between any two landmarks, and these distances may also be obtained as output from program SKULL, if desired (595 distances if all 35 landmarks are used). Reliability of the location of coordinates was determined by comparing computed distances among selected landmarks from program SKULL with traditional anthropometric measurements. Satisfactory agreements were found. Direct multivariate analysis of the coordinates of the landmarks produced insights not available in traditional multivariate analysis of conventional anthropometric measurements.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus.

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

Radiographic estimation of long bone cross-sectional geometric properties

Because of their biomechanical significance, cross-sectional geometric properties of long bone diaphyses (areas, second moments of area) have been increasingly used in a number of form/function studies, e.g., to reconstruct body mass or locomotor mode in fossil primates or to elucidate allometric scaling relationships among extant taxa. In the present study, we test whether these biomechanical section properties can be adequately estimated using biplanar radiographs, as compared to calculations of the same properties from computer digitization of cross-sectional images. We are particularly interested in smaller animals, since the limb bone cortices of these animals may not be resolvable using other alternative noninvasive techniques (computed tomography). The test sample includes limb bones of small (25–5,000 g) relatively generalized quadrupedal mammals—mice, six species of squirrels, and Macaca fascicularis. Results indicate that biplanar radiographs are reasonable substitutes for digitized cross-sectional images for deriving areas and second moments of area of midshaft femora and humeri of mammals in this size range. Potential application to a variety of questions relating to mechanical loading patterns in such animals is diverse. © 1993 Wiley-Liss, Inc.     

Musculotendon parameters and musculoskeletal pathways within the human foot

In order to create a flexible model of the foot for dynamic musculoskeletal models, anthropometric data combined with geometric information describing the intrinsic musculature are needed. In this study, the left feet of two male and two female cadavers were dissected to expose the intrinsic musculotendon pathways. Three-dimensional coordinates of bony landmarks, tendon origins, insertions, and via points were digitized to submillimeter accuracy. Muscle architectural parameters were also measured, including volume, weight, and pennation angle and sarcomere, fascicle, and free tendon lengths. Optimal muscle fascicle lengths, pen-nation angles at optimal length, physiological cross-sectional areas (PCSA), and tendon slack lengths were calculated from the directly measured values. Fascicle length and pennation angle varied greatly within each subject. Average fascicle lengths normalized by optimal fascicle length varied between 0.73 and 1.25, with 75% of the formalin-preserved muscles being found in a shortened state. The muscle volume and PCSA also had a large variability within subjects but less variation between subjects. The ratio of tendon slack length to optimal fascicle length was found to vary between 1.05 and 9.56. Using this data, a deformable model of the foot can now be created. It is envisioned that deformable feet will significantly improve stability and realism in models of gait, posture, and sporting activities.     

Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions.

It is often assumed that moment arms scale with size and can be normalized by body segment lengths or limb circumferences. However, quantitative scaling relationships between moment arms and anthropometric dimensions are generally not available. We hypothesized that peak moment arms of the elbow flexor and extensor muscles scale with the shorter distance (D(s)) between the elbow flexion axis and a muscle's origin and insertion. To test this hypothesis, we estimated moment arms of six muscles that cross the elbow, digitized muscle attachment sites and bone surface geometry, and estimated the location of the elbow flexion axis in 10 upper extremity cadaveric specimens which ranged in size from a 5'0" female to a 6'4" male. D(s) accurately reflected the differences in peak moment arms across different muscles, explaining 93-99% of the variation in peaks between muscles in the same specimen. D(s) also explained between 55% and 88% of the interspecimen variation in peak moment arms for brachioradialis, biceps, and ECRL. Triceps peak moment arm was significantly correlated to the anterior-posterior dimension of the ulna measured at the olecranon (r(2)=0.61, p=0.008). Radius length provides a good measure of the interspecimen variation in peaks for brachioradialis, biceps, and ECRL. However, bone lengths were not significantly correlated to triceps moment arm or anterior-posterior bone dimensions. This work advances our understanding of the variability and scaling dimensions for elbow muscle moment arms across subjects of different sizes.     

Three-dimensional technology for linear morphological studies: a re-examination of cranial variation in four southern African indigenous populations.

In order to compare linear dimensions made by traditional anthropometric techniques, and those obtained from three-dimensional coordinates, samples of four indigenous southern African populations were analysed. Linear measurements were obtained using mathematically transformed, three-dimensional landmark data on 207 male crania of Cape Nguni, Natal Nguni, Sotho and Shangaan. Univariate comparisons for accuracy of the transformed linear data were made with those in a traditional linear study by de Villiers (The Skull of the South African Negro: A Biometrical and Morphological Study. Witwatersrand University Press, Johannesburg) on similar samples and equivalent landmarks. Comparisons were not made with her Penrose (Ann Eugenics 18 (1954) 337) analysis as an apparently anomalous 'shape'-'size' statistic was found. The univariate comparisons demonstrated that accurate linear measurements could be derived from three-dimensional data, showing that it is possible to simultaneously obtain data for three-dimensional geometric 'shape' and linear interlandmark analyses. Using Penrose and canonical variates analyses of the transformed three-dimensional interlandmark measurements, similar population distances were found for the four indigenous southern African populations. The inter-population distance relationships took the form of three separated pairs of distances, with the within-pair distances very similar in size. The cranial features of the four populations were found to be overall very similar morphometrically. However the populations were each shown by CVA to have population specific features, and using discriminant analyses 50% or more of the individual crania (with the exception of the Sotho) could be referred to their correct populations.     

Cranial muscle markers: A preliminary examination of size, sex, and age effects

Most muscle marker research consists of post-cranial analyses, but some researchers examine crania to reconstruct activities. Regardless of bones examined, anthropologists know of some of the complexities surrounding muscle marker development. Here, posterior cranial muscle markers are analyzed to determine whether they are useful in reconstructing activities by examining effects that may hinder reconstructions. Additionally, upper limb muscle markers and humeral cross-sectional robusticity variables are correlated with cranial muscle markers to determine if robust individuals are generally robust due to the synergistic effects of muscle use.Cranial muscle markers of 65 prehistoric California Amerinds are scored using a five-point observer rating scale. Body mass is calculated from femoral head size; maximum cranial length and breadth are measured with a spreading caliper; and age and sex are determined through standard procedures. Upper limb muscle markers are scored on seven sites using two dimensions within a seven-point scale. Cross-sectional properties are calculated from biplanar humeral radiographs. Aggregates are created for cranial muscle markers, upper limb muscle markers, and cross-sectional robusticity.Cranial muscle markers correlate significantly with cranial length, r=0.25 and cross-sectional robusticity of humerus, r=0.29; P’s<0.05. All variables differed between sexes (Mann-Whitney=31.00-307.50, P’s<0.01). Results imply that some differences in cranial muscle markers are related to size; however, individuals with well-developed cranial muscle markers have greater upper limb robusticity possibly due to activity patterns. Sex differences remained after size controls and may relate to activity differences.     

Subject-specific musculoskeletal model of the lower limb in a lying and standing position

Accurate estimation of joint loads implies using subject-specific musculoskeletal models. Moreover, as the lines of action of the muscles are dictated by the soft tissues, which are in turn influenced by gravitational forces, we developed a method to build subject-specific models of the lower limb in a functional standing position. Bones and skin envelope were obtained in a standing position, whereas muscles and a set of bony landmarks were obtained from conventional magnetic resonance images in a lying position. These muscles were merged with the subject-specific skeletal model using a nonlinear transformation, taking into account soft tissue movements and gravitational effects. Seven asymptomatic lower limbs were modelled using this method, and results showed realistic deformations. Comparing the subject-specific skeletal model to a scaled reference model rendered differences in terms of muscle length up to 4% and in terms of moment arm for adductor muscles up to 30%. These preliminary findings enlightened the importance of subject-specific modelling in a functional position.     

Prediction of the hip joint centre in adults, children, and patients with cerebral palsy based on magnetic resonance imaging

The location of the hip joint centre (HJC) is required for calculations of hip moments, the location and orientation of the femur, and muscle lengths and lever arms. In clinical gait analysis, the HJC is normally estimated using regression equations based on normative data obtained from adult populations. There is limited relevant anthropometric data available for children, despite the fact that clinical gait analysis is predominantly used for the assessment of children with cerebral palsy. In this study, pelvic MRI scans were taken of eight adults (ages 23-40), 14 healthy children (ages 5-13) and 10 children with spastic diplegic cerebral palsy (ages 6-13). Relevant anatomical landmarks were located in the scans, and the HJC location in pelvic coordinates was found by fitting a sphere to points identified on the femoral head. The predictions of three common regression equations for HJC location were compared to those found directly from MRI. Maximum absolute errors of 31 mm were found in adults, 26 mm in children, and 31 mm in the cerebral palsy group. Results from regression analysis and leave-one-out cross-validation techniques on the MRI data suggested that the best predictors of HJC location were: pelvic depth for the antero-posterior direction; pelvic width and leg length for the supero-inferior direction; and pelvic depth and pelvic width for the medio-lateral direction. For single-variable regression, the exclusion of leg length and pelvic depth from the latter two regression equations is proposed. Regression equations could be generalised across adults, children and the cerebral palsy group.     

A biplanar reconstruction method based on 2D and 3D contours: application to the distal femur

A three-dimensional (3D) reconstruction algorithm based on contours identification from biplanar radiographs is presented. It requires, as technical prerequisites, a method to calibrate the biplanar radiographic environment and a surface generic object (anatomic atlas model) representing the structure to be reconstructed. The reconstruction steps consist of: the definition of anatomical regions, the identification of 2D contours associated to these regions, the calculation of 3D contours and projection onto the radiographs, the associations between points of the X-rays contours and points of the projected 3D contours, the optimization of the initial solution and the optimized object deformation to minimize the distance between X-rays contours and projected 3D contours. The evaluation was performed on 8 distal femurs comparing the 3D models obtained to CT-scan reconstructions. Mean error for each distal femur was 1 mm.     

The role of grafted skin in the regeneration of X-irradiated axolotl limbs

The primary aim of these experiments was to follow the cells descended from limb skin through the process of limb regeneration to determine what range of differentiations these cells may assume. Triploid hindlimb or forelimb skin was grafted to the denuded thighs of diploid host axolotls that had previously received 3000 R of X irradiation across both hindlimbs and the intervening pelvic area. The host limbs were then amputated through their grafts and permitted to regenerate. Cartilage, perichondrium, joint connective tissue, general connective tissue, dermis, and epidermis were present in all the regenerated limbs, but only 10% of the regenerates contained muscle. Tabulation of nucleolar numbers showed that the majority of cells in each regenerated tissue originated from the grafted skin. A strong correlation was demonstrated between the forelimb or hindlimb origin of the skin grafts and the number of digits regenerated.     

Facial asymmetry: three-dimensional analysis using laser surface scanning

This study evaluates six different techniques with respect to their ability to quantitatively describe facial asymmetry in three dimensions. Three-dimensional facial images were acquired using a Cyberware 3030RGB laser surface scanner. Image processing was performed on a Silicon Graphics Indigo computer workstation. The following techniques for facial asymmetry analysis were developed: asymmetry in the location of anthropometric landmarks, Euclidean distance matrix analysis (EDMA), scalar measurement of the lower ciliary margin and palpebral fissure area, clearance vector mapping, and determination of the volume of asymmetry. Techniques were applied and validated in three anthropometric models: a perfectly symmetrical plastic head model and a plaster head model with and without a unilateral cheek augmentation. In each of the anthropometric test models, each analytical technique was validated by means of static anthropometric facial models and was evaluated for intraobserver and interobserver reliability. Asymmetries in the location of anthropometric landmarks can be accurately determined to within 2 mm in x, y, and z directions of the Cartesian space. EDMA is a useful technique in describing both size and shape changes of discrete areas of the face. Measurement of the lower ciliary margin and palpebral fissure area is reliable. Clearance vector mapping is especially useful in quantifying facial surface asymmetries in facial areas where anthropometric landmarks are scarce. Volume of asymmetry is potentially useful in those patients for whom the use of injections or implants of known volume may be helpful in correcting unilateral facial deficiencies.     

A three-dimensional musculoskeletal model for gait analysis. Anatomical variability estimates

Three-dimensional coordinates defining the origin and insertion of 40 muscle units, and bony landmarks for osteometric scaling were identified on dry bone specimens. Interspecimen coordinate differences along the anterior-posterior axis of the pelvis and the long bone axes of the pelvis, femur and leg were reduced by scaling but landmark differences along the other axes were not. The coordinates were mapped to living subjects using close-range photogrammetry to locate superficial reference markers. The error of predicting the positions of internal coordinates was assessed by comparing joint centre locations calculated from local axes defining the orientation of segments superior and inferior to a joint. A difference was attributed to: anatomical variability not accounted for by scaling; errors in identifying and placing reference landmarks; the accuracy of locating markers using photogrammetry and error introduced by marker oscillation during movement. Anatomical differences between specimens are one source of error in defining a musculoskeletal model but larger errors are introduced when such models are mapped to living subjects.     

Simultaneous induction of ectopic pelvic zone and duplication of regenerated limbs in tadpoles of Polypedates maculatus by vitamin A

With a view to determine ectopic limb developing capacity along with normal hind limb regeneration in response to vitamin A palmitate in well-differentiated hind limb stage tadpoles of P. maculatus, higher doses of vitamin A (30 IU/ml and 20 IU/ml) were administered for a longer period (120 hr) to the tadpoles following tail amputation through middle and hind limb amputation through middle of thigh. Simultaneous development of ectopic pelvic zone was observed along with hind limbs from the cut end of tail and duplication of regenerated hind limbs in the same tadpole for the first time. Besides, development of double ectopic pelvic girdle was also reported in one case. Results also indicate that induction of pelvic zone and duplication of regenerated limbs are concentration dependent.     

Mass, center of mass, and moment of inertia estimates for infant limb segments.

To quantify limb dynamics, accurate estimates are needed of anthropometric inertia parameters (mass, center-of-mass location, and moments of inertia). These estimates, however, are not available for human infants; therefore, the movement dynamics of infants have not been studied extensively. Here, regression equations for the masses, center-of-mass locations, and transverse moments of inertia of upper and lower limb segments (upper arm, forearm, and hand; thigh, leg, and foot) of 0.04 to 1.50 yr old infants are provided. A mathematical model of the human body was used to determine the anthropometric inertia parameters for upper limbs in 44 infants and for lower limbs in 70 infants. Stepwise linear regressions were used to fit the distributions of the anthropometric inertia parameters. The regression equations accounted for significant amounts of the variance (64-98%), and the R2-values compared favorably when our equations were cross-validated. Consequently, these regression equations can provide, for infants of similar ages, reasonable estimates of upper and lower limb anthropometric inertia parameters, suitable for equations of motion in the analysis of limb dynamics in human infants.     

Cellular contribution to symmetrical forelimbs from triploid-marked "polarizing region" in the embryo of axolotl, Ambystoma mexicanum

Grafts of posterior tissue placed anterior to the limb bud in the salamander embryo exert a polarizing influence. To explain this result, the idea that the anteroposterior axis of the developing forelimb is polarized by a diffusible morphogen has been proposed. An alternative hypothesis, and the working hypothesis of the present study, is that the polarization of the developing salamander forelimb is accomplished by short-range cellular interactions resulting in intercalation rather than by the more global influence of a diffusible morphogen. One prediction of this intercalation hypothesis is that cells will be contributed to the limb from the "polarizing tissue." To test this idea, grafts of triploid marked polarizing tissue were implanted anterior to the limb bud in 82 diploid axolotl embryos at stages 32-34 of development. A total of 27 (33%) of the limbs that resulted were symmetrical and ranged in complexity from one to seven digits. Histological analysis of a subgroup of the original symmetrical limbs revealed that mesodermally derived tissues in the anterior side of these limbs (the side which formed as a duplication in response to the influence of the graft) contained high percentages of trinucleolate cells (muscle, 12.1%; connective tissue tissue, 12.5%; and cartilage, 13.4%) when compared to similar tissues in the posterior side of the same symmetrical limbs (muscle, 1.8%; connective tissue , 0.7%; and cartilage, 0.6%). When symmetrical limbs were amputated, 73% regenerated symmetrical limbs. When these regenerated limbs were again amputated, 63% formed symmetrical secondary regenerates. Histological analysis of the first generation of regenerated limbs revealed that the pattern of distribution of trinucleolate cells in each regenerate was similar to the pattern seen in the original symmetrical limb. These results indicate that there is considerable cellular contribution to the anterior side of the symmetrical forelimb from the mesoderm of grafted "polarizing tissue." This result supports the idea that short-range cellular interaction are sufficient for formation of symmetrical forelimbs in salamander embryos.     

Pelvic growth: ontogeny of size and shape sexual dimorphism in rat pelves

The mammalian pelvis is sexually dimorphic with respect to both size and shape. Yet little is known about the differences in postnatal growth and bone remodeling that generate adult sexual dimorphism in pelvic bones. We used Sprague-Dawley laboratory rats (Rattus norvegicus), a species that exhibits gross pelvic size and shape dimorphism, as a model to quantify pelvic morphology throughout ontogeny. We employed landmark-based geometric morphometrics methodology on digitized landmarks from radiographs to test for sexual dimorphism in size and shape, and to examine differences in the rates, magnitudes, and directional patterns of shape change during growth. On the basis of statistical significance testing, the sexes became different with respect to pelvic shape by 36 days of age, earlier than the onset of size dimorphism (45 days), although visible shape differences were observed as early as at 22 days. Males achieved larger pelvic sizes by growing faster throughout ontogeny. However, the rates of shape change in the pelvis were greater in females for nearly all time intervals scrutinized. We found that trajectories of shape change were parallel in the two sexes until age of 45 days, suggesting that both sexes underwent similar bone remodeling until puberty. After 45 days, but before reproductive maturity, shape change trajectories diverged because of specific changes in the female pelvic shape, possibly due to the influence of estrogens. Pattern of male pelvic bone remodeling remained the same throughout ontogeny, suggesting that androgen effects on male pelvic morphology were constant and did not contribute to specific shape changes at puberty. These results could be used to direct additional research on the mechanisms that generate skeletal dimorphisms at different levels of biological organization.     

Three-dimensional model of the feline hindlimb

This article describes a three-dimensional musculoskeletal model of the feline hindlimb based on digitized musculoskeletal anatomy. The model consists of seven degrees of freedom: three at the hip and two each at the knee and ankle. Lines of action and via points for 32 major muscles of the limb are described. Interspecimen variability of muscle paths was surprisingly low; most via points displayed a scatter of only a few millimeters. Joint axes identified by mechanical techniques as noncoincident and nonorthogonal were further honed to yield moment arms consistent with previous reports. Interspecimen variability in joint axes was greater than that of muscle paths and highlights the importance of joint axes in kinematic models. The contribution of specific muscles to the direction of endpoint force generation is discussed.