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Is the human acetabulofemoral joint spherical?
Abstract
The human acetabulofemoral joint is commonly modelled as a pure ball-and-socket joint, but there has been no quantitative assessment of this assumption in the literature. Our aim was to test the limits and validity of this hypothesis. We performed experiments on four adult cadavers. Cortical pins, each equipped with a marker cluster, were implanted in the pelvis and the femur. Movements were recorded using stereophotogrammetry while an operator rotated the cadaver’s acetabulofemoral joint, exploiting the widest possible range of movement. The functional consistency of the acetabulofemoral joint as a pure spherical joint was assessed by comparing the magnitude of the translations of the hip joint centre as obtained on cadavers, with the centre of rotation of two metal segments linked through a perfectly spherical hinge. The results showed that the radii of the spheres containing 95% of the positions of the estimated centres of rotation were separated by less than 1 mm for both the acetabulofemoral joint and the mechanical spherical hinge.
Therefore, the acetabulofemoral joint can be modelled as a spherical joint within the considered range of movement (flexion/extension 20° to 70°; abduction/adduction 0° to 45°; internal/external rotation 0° to 30°).
... Andersen et al., 2009;Duprey et al., 2010;Reinbolt et al., 2005) : n'autorise qu'une rotation autour d'un seul axe prédéfini (un degré de liberté) et aucune translation • Rotule à doigt, ellipsoïde et joint de cardan(Andersen et al., 2009;Duprey et al., 2010;Reinbolt et al., 2005) : autorise la rotation autour de deux axes (deux degrés de liberté) et aucune translation.• Rotule ou sphéroïde(Cereatti et al., 2010) : autorise les trois rotations dans l'espace (3 degrés de liberté), mais aucune translation.• Sphère sur plan ou ponctuelle (Parenti-Castelli et al., 2004) : autorise les trois rotations et deux translations sur le plan (cinq degrés de liberté). ...
L’analyse du mouvement humain est un paramètre clé pour comprendre les différentes problématiques de la locomotion humaine. Qui plus est, il est nécessaire que ces analyses soient effectuées au plus proche de la locomotion réelle. L’essor de la miniaturisation des capteurs et des technologies sans fil a permis d’offrir la possibilité d’utiliser les centrales inertielles sur le terrain. Mais différentes problématiques existent encore pour obtenir la cinématique des membres inférieurs avec les centrales inertielles.La première étude de ce manuscrit aborde une comparaison des différents calibrages centrale-à-segment pour définir le passage entre l’orientation de la centrale inertielle et le segment sous-jacent. Nous avons mis en avant une méthode qui valide ces critères au mieux et ne demande que deux postures et un dispositif simple. Mais la cinématique obtenue reste entachée d’erreurs qui pourraient être dues à la présence d’artefacts de tissu mou.C’est pourquoi dans une seconde partie nous étudions la possibilité de diminuer ces effets par l’intermédiaire de l’optimisation multisegmentaire. Ainsi nous avons pu mettre en avant la nécessité de bien paramétrer le modèle derrière l’optimisation sans pour autant présenter un apport significatif. Enfin, en dernière partie, nous proposons d’appliquer la méthodologie de traitement de la cinématique articulaire sur une population pathologique, en collaboration avec le laboratoire de cinésiologie Willy Taillard des HUG et de l’Université de Genève. En conclusion cette thèse propose un processus méthodologique et des recommandations pour développer des analyses de la cinématique en milieu écologique avec des centrales inertielles.
... The joints of a lower limb can be modeled as a spherical joint within the considered range of movement. 36 Referring to the fundamental and basic axes defined in the anatomy, the basic forms of joint motion can be classified into three categories: flexion/extension (FE) around the frontal axis, abduction/adduction (AA) around the sagittal axis, and internal/external (IE) around the vertical axis. Degrees of freedom (DOF) is used as a term to describe the freedom of motion. ...
The lower limb exoskeleton robot is capable of providing assisted walking and enhancing exercise ability of humans. The coupling human–machine model has attracted a lot of research efforts to solve the complex dynamics and nonlinearity within the system. This study focuses on an approach of gait trajectory optimization of lower limb exoskeleton coupled with human through genetic algorithm. The human–machine coupling system is studied in this article through multibody virtual simulation environment. Planning of the motion trajectory is carried out by the genetic algorithm, which is iteratively generated under optimization of a set of specially designed fitness functions. Human motion captured data are used to guide the evolution of gait trajectory generation method based on genetic algorithm. Experiments are carried out using the MATLAB/Simulink Multibody physical simulation engine and genetic algorithm-toolbox to generate a more natural gait trajectory, the results show that the proposed gait trajectory generation method can provide an anthropomorphic gait for lower limb exoskeleton device.
... Hip joint stability is achieved mainly by the contribution of static stabilizers [1]. The high anatomical congruence between the femoral head and the acetabulum has been described as the most important static stabilizer [2]. This bony congruence allows the hip joint to achieve large range of motion in three different axes [3]. ...
Hip joint instability has been targeted as an important issue that affects normal hip function. The diagnosis of hip instability could be very challenging and currently, there is no definitive diagnostic test. Hip instability results in an excessive amount of translation of femoroacetabular articulation, leading to changes on the dynamic loading of the hip. These changes in femoroacetabular translation could be evaluated by human movement analysis methods. The purpose of this study was to describe the triaxial and overall magnitude of acceleration in patients diagnosed with hip instability during gait cycle and compare those results with a control group. Our hypothesis was that acceleration values obtained from the instability group would be higher than asymptomatic controls. Ten patients with previously diagnosed hip instability were included and 10 healthy and asymptomatic subjects were enrolled as control group. Triaxial accelerometers attached bilaterally to the skin over the greater trochanter were used to record acceleration during walking on a treadmill. The overall magnitude of acceleration and the axial, anteroposterior and mediolateral accelerations (x/y/z) were obtained during gait. Mean overall magnitude of acceleration was higher in the hip instability group compared with the control group, 1.51 g (SD: 0.23) versus 1.07 g (SD: 0.16) (P = 0.022). The axial, anteroposterior and mediolateral accelerations significantly differed between the two groups. The axial and mediolateral accelerations showed to be higher for the hip instability group while the anteroposterior axis acceleration was lower.
... The normal hip joint is inherently stable primarily because of the bony anatomy. 6 However, recent studies have highlighted the role of the capsule and labrum as significant contributors to hip stability. 33 Natural history studies have shown that patients with true acetabular dysplasia are predisposed to developing early coxarthrosis. ...
Background:
The arthroscopic management of hip dysplasia has been controversial and has historically demonstrated mixed results. Studies on patients with borderline dysplasia, emphasizing the importance of the labrum and capsule as secondary stabilizers, have shown improvement in patient-reported outcomes (PROs). Purpose/Hypothesis: The purpose was to assess whether the results of hip arthroscopic surgery with labral preservation and concurrent capsular plication in patients with borderline hip dysplasia have lasting, positive outcomes at a minimum 5-year follow-up. It was hypothesized that with careful patient selection, outcomes would be favorable.
Study design:
Case series; Level of evidence, 4.
Methods:
Data were prospectively collected and retrospectively reviewed for patients aged <40 years who underwent hip arthroscopic surgery for intra-articular abnormalities. Inclusion criteria included lateral center-edge angle (LCEA) between 18° and 25°, concurrent capsular plication and labral preservation, and minimum 5-year follow-up. Exclusion criteria were severe dysplasia (LCEA ≤18°), Tönnis grade ≥2, pre-existing childhood hip conditions, or prior hip surgery. PRO scores including the modified Harris Hip Score (mHHS), Non-Arthritic Hip Score (NAHS), and Hip Outcome Score Sport-Specific Subscale (HOS-SSS) and the visual analog scale (VAS) score for pain were collected preoperatively, at 3 months, and annually thereafter. Complications and revisions were recorded.
Results:
Twenty-five hips (24 patients) met the inclusion criteria. Twenty-one hips (19 patients, 84%) were available for follow-up. The mean age at surgery was 22.9 years. The mean preoperative LCEA and Tönnis angle were 21.7° (range, 18° to 24°) and 6.9° (range, -1° to 16°), respectively. The mean follow-up was 68.8 months. The mean mHHS increased from 70.3 to 85.9 ( P < .0001), the mean NAHS from 68.3 to 87.3 ( P < .0001), and the mean HOS-SSS from 52.1 to 70.8 ( P = .0002). The mean VAS score improved from 5.6 to 1.8 ( P < .0001). Four hips (19%) required secondary arthroscopic procedures, all of which resulted in improved PRO scores at latest follow-up. No patient required conversion to total hip arthroplasty.
Conclusion:
While periacetabular osteotomy remains the standard for treating true acetabular dysplasia, hip arthroscopy may provide a safe and durable means of managing intra-articular abnormalities in the setting of borderline acetabular dysplasia at midterm follow-up. These procedures should be performed by surgeons with expertise in advanced arthroscopic techniques, using strict patient selection criteria, with emphasis on labral preservation and capsular plication.
... Commonly, human joints are modelled either as spherical or hinge joints. Whereas for the hip joint, the functional consistency between the actual joint and the spherical joint model is almost perfect [90] and therefore a unique centre of rotation exists, this is not true for other human joints. For instance, it was demonstrated that in the knee joint during normal gait the tibiofemoral contact loads contribute substantially to both net extension and adduction moments [5]. ...
Quantitative gait analysis can provide a description of joint kinematics and dynamics, and it is recognized as a clinically useful tool for functional assessment, diagnosis and intervention planning. Clinically interpretable parameters are estimated from quantitative measures (i.e. ground reaction forces, skin marker trajectories, etc.) through biomechanical modelling. In particular, the estimation of joint moments during motion is grounded on several modelling assumptions: (1) body segmental and joint kinematics is derived from the trajectories of markers and by modelling the human body as a kinematic chain; (2) joint resultant (net) loads are, usually, derived from force plate measurements through a model of segmental dynamics. Therefore, both measurement errors and modelling assumptions can affect the results, to an extent that also depends on the characteristics of the motor task analysed (i.e. gait speed). Errors affecting the trajectories of joint centres, the orientation of joint functional axes, the joint angular velocities, the accuracy of inertial parameters and force measurements (concurring to the definition of the dynamic model), can weigh differently in the estimation of clinically interpretable joint moments. Numerous studies addressed all these methodological aspects separately, but a critical analysis of how these aspects may affect the clinical interpretation of joint dynamics is still missing. This article aims at filling this gap through a systematic review of the literature, conducted on Web of Science, Scopus and PubMed. The final objective is hence to provide clear take-home messages to guide laboratories in the estimation of joint moments for the clinical practice.
Electronic supplementary material
The online version of this article (doi:10.1186/s12938-017-0396-x) contains supplementary material, which is available to authorized users.
... In some cases, functionally defined centers and/or axes of rotation can be used as well. This approach is viable when there is a constant and generalizable relationship between anatomy and function among individuals, such as for the hip center of rotation [74,142]. ...
Gait analysis is recognized as a useful assessment tool in the field of human movement research. However, doubts remain on its real effectiveness as a clinical tool, i.e. on its capability to change the diagnostic-therapeutic practice. In particular, the conditions in which evidence of a favorable cost-benefit ratio is found and the methodology for properly conducting and interpreting the exam are not identified clearly. To provide guidelines for the use of Gait Analysis in the context of rehabilitation medicine, SIAMOC (the Italian Society of Clinical Movement Analysis) promoted a National Consensus Conference which was held in Bologna on September 14th, 2013. The resulting recommendations were the result of a three-stage process entailing i) the preparation of working documents on specific open issues, ii) the holding of the consensus meeting, and iii) the drafting of consensus statements by an external Jury. The statements were formulated based on scientific evidence or experts' opinion, when the quality/quantity of the relevant literature was deemed insufficient. The aim of this work is to disseminate the consensus statements. These are divided into 13 questions grouped in three areas of interest: 1) General requirements and management, 2) Methodological and instrumental issues, and 3) Scientific evidence and clinical appropriateness. SIAMOC hopes that this document will contribute to improve clinical practice and help promoting further research in the field.
Purpose:
In the setting of acetabular dysplasia, the increased translational motion of the femur may damage the labrum and cartilage, as well as stretch the capsule. The purpose of the study was to investigate the relationship between the acetabular coverage and the capsular stiffness by assessing the distension of anterior and posterior joint recesses on the hip computed tomography arthrography.
Methods:
One hundred thirty-three patients (138 hips) with a median age of 36 years (range 18-50 years) who received the computed tomography arthrography for evaluation of nonarthritic hip pain in our institute between 2015 and 2017 were retrospectively reviewed. The maximal distance between the anterior/posterior capsule and the anterior femoral head-neck junction/posterior femoral head on the axial imaging of computed tomography arthrography was defined as the width of anterior/posterior joint recess. The width of anterior/posterior joint recess was adjusted with the diameter of the femoral head and was then compared between acetabular dysplasia (lateral center-edge angle < 25°), normal acetabulum (lateral center-edge angle between 25 and 39°), and deep acetabulum (lateral center-edge angle > 39°). In addition, the standard univariate linear regression analysis was used to investigate the relationship between the adjusted width of anterior/posterior joint recess and anterior/posterior coverage of the hip, determined by the anterior/posterior wall index.
Results:
The adjusted width of posterior joint recess was significantly greater in the acetabular dysplasia group than the normal acetabulum and deep acetabulum groups (p < 0.01 and p = 0.02, respectively). There was no significant difference of the adjusted width of anterior joint recess between the groups (n.s.). The adjusted width of posterior joint recess had a significant but weak negative correlation with the anterior wall index (r = - 0.25, p < 0.001), and no correlation with the posterior wall index (r = - 0.0004, n.s.). There was no significant correlation between the adjusted width of anterior joint recess and the anterior/posterior wall index (r = 0.05, n.s./r = 0.07, n.s.).
Conclusions:
The distension of posterior capsule on the computed tomography arthrography was significantly greater in acetabular dysplasia. In addition, there was a significant but weak negative correlation between the distension of posterior capsule and the anterior coverage of the hip. It indicated a looser posterior capsule was observed in a dysplastic hip. The relevance of posterior capsular laxity to clinical outcomes warrants further investigation. Given the fact that the distension of anterior capsule was not significantly higher in acetabular dysplasia, the need of anterior capsular plication in a dysplastic hip should be carefully evaluated.
Level of evidence:
Level III.
Purpose:
To elucidate whether capsular closure during hip arthroscopy affected patient outcomes over midterm follow-up.
Methods:
Between 2008 and 2011, data were prospectively collected and retrospectively reviewed on patients who underwent hip arthroscopy. Patients were then matched for age, gender, worker's compensation, body mass index, and acetabular coverage. The inclusion criteria were capsular repair or unrepaired capsulotomy, lateral-center edge angle ≥18°, and minimum 5-year follow-up. The exclusion criteria were previous hip surgery or conditions and Tönnis grade >1. Patient-reported outcome scores (PROs) included modified Harris hip score (mHHS), nonarthritic hip score, hip outcome score sport-specific subscale, and visual analog score for pain, which were collected preoperatively, at 3 months, and annually thereafter. Minimal clinical important difference (MCID) and patient acceptable symptomatic state (PASS) for both groups were analyzed. Patient satisfaction was noted as well as any complications, secondary surgery, and conversion to arthroplasty.
Results:
Minimum 5-year follow-up was available for 82.5% (287 of 348) hips that met the inclusion criteria and were eligible for matching. Ultimately, 65 patients who underwent capsular repair could be matched in a 1:1 ratio to 65 patients with release. Both groups had significant improvements in all mean PROs. The repair group had significant improvement of mean PROs, visual analog score, and patient satisfaction at both 2-year and minimum 5-year follow-up. The unrepaired group had a significant decrease in mHHS (P = .001) and patient satisfaction (P = .01) between 2- and 5-year follow-up. Despite decreasing mHHS in the repair group between 2- and 5-year follow-up, both groups met the MCID and PASS criteria with no significant difference between them. More patients in the release group required conversion to hip arthroplasty (18.5% vs 10.8%). Subgroup analysis considering various perioperative factors confirmed this trend. Rate of revision arthroscopy was the same in both groups (15.4%). Complication rate was low (4.6% vs 6.4%) in both groups.
Conclusions:
Patients undergoing hip arthroscopy and who have minimal or no arthritis have significant short-term improvement, whether the capsule is closed or left unrepaired. However, at midterm follow-up, patients who had unrepaired capsules had deterioration in mHHS as well as a higher rate of conversion to arthroplasty, even when controlling for various perioperative variables. Despite this, patients in both groups met the MCID and PASS criteria. This study suggests that routine capsular closure may lead to more consistently durable outcome in patients undergoing hip arthroscopy, but also that individual patient pathology may dictate capsular management.
Level of evidence:
Level III, retrospective comparative study.
The injuries sustained by dance students are mainly the result of overuse (excessive quantity) or abuse (incorrect technique); thus, they could be prevented. The outcome of a dance injury can either affect participation in dance for a given time or bring the student’s potential development as a dancer to an end. In order to predict who is prone to what injuries the medical profession has developed screening processes by which one can draw conclusions for individual dance students regarding their risk factors for certain injuries, and also accumulate data regarding this specific population and establish “norms” and objective parameters to compare between individuals. This chapter will address the differences between specific age groups and describe the correlation between body structure, dance technique, and some pathologies. It should provide tools to empower students and teachers, and enhance medical professionals’ knowledge of the specific issues relevant to dance students.
Hip problems are common in young dancers and often preventable. The extreme ranges of motion demanded of the dancer’s hip without the necessary strength and flexibility to accommodate them create the potential for injury. Additionally, some dancers may have an anatomic makeup that predisposes them to injury, and those with developing musculoskeletal systems may be particularly vulnerable. Pathology about the hip ranges from intra-articular to extra-articular, as well as referred pain from adjacent structures. Diagnosis begins with a history and physical examination to formulate a differential diagnosis, and imaging can be used as an adjunct. Treatment of injuries relies on an understanding of the mechanics of dance, especially as they apply to the dance discipline in question, the associated hip anatomy, and the specific etiology of the injury. When rehabilitation and physical therapy fail, additional interventions such as targeted steroid injections or surgery may be beneficial.
Pre-operative computerised three-dimensional planning was carried out in 223 patients undergoing total hip replacement with a cementless acetabular component and a cementless modular-neck femoral stem. Components were chosen which best restored leg length and femoral offset. The post-operative restoration of the anatomy was assessed by CT and compared with the pre-operative plan.
The component implanted was the same as that planned in 86% of the hips for the acetabular implant, 94% for the stem, and 93% for the neck-shaft angle. The rotational centre of the hip was restored with a mean accuracy of 0.73 mm (sd 3.5) craniocaudally and 1.2 mm (sd 2) laterally. Limb length was restored with a mean accuracy of 0.3 mm (sd 3.3) and femoral offset with a mean accuracy of 0.8 mm (sd 3.1).
This method appears to offer high accuracy in hip reconstruction as the difficulties likely to be encountered when restoring the anatomy can be anticipated and solved pre-operatively by optimising the selection of implants. Modularity of the femoral neck helped to restore the femoral offset and limb length.
Three-dimensional kinematics of the tibiofemoral joint were studied during normal walking. Target markers were fixed to tibia and femur by means of intra-cortical traction pins. Radiographs of the lower limb were obtained to compute the position of the target markers relative to internal anatomical structures. High-speed cine cameras were used to measure three-dimensional coordinates of the target markers in five subjects walking at a speed of 1.2 m s-1. Relative motion between tibia and femur was resolved according to a joint coordinate system (JCS). The measurements have identified that substantial angular and linear motions occur about and along each of the JCS axes during walking. The results do not, however, support the traditional view that the so-called 'screw home' mechanism of the knee joint operates during gait.
This paper reports a discussion on the heuristic and applicative objectives of gait analysis and on the experimental and analytical methods used in this context. In particular, the use of an effective method of description of joint kinematics and kinetics i.e., joint function, as applied to the lower limb joints during normal walking is reported. A methodological hypothesis for the evaluation of gait, as an integrated phenomenon is presented and supported by experimental data concerning normal and pathological walking and sportive gaits.
In a 12- to 18-year radiographic follow-up study of 95 Charnley low-friction total hip arthroplasties (THA), there was a statistically significant correlation between location of the center of rotation of the total hip prosthesis (notably the element horizontal distance cup to tear-drop) and long-term, unfavorable, radiographic signs, such as acetabular and stem demarcation, cup wear, cup migration, subsidence of the stem, and calcar resorption. Small differences, as little as 2 mm, in the placement of the cup in relation to anatomic landmarks were responsible for these findings
The Standardization and Terminology Committee (STC) of the International Society of Biomechanics (ISB) proposes a general reporting standard for joint kinematics based on the Joint Coordinate System (JCS), first proposed by Grood and Suntay for the knee joint in 1983 (J. Biomech. Eng. 105 (1983) 136). There is currently a lack of standard for reporting joint motion in the field of biomechanics for human movement, and the JCS as proposed by Grood and Suntay has the advantage of reporting joint motions in clinically relevant terms.In this communication, the STC proposes definitions of JCS for the ankle, hip, and spine. Definitions for other joints (such as shoulder, elbow, hand and wrist, temporomandibular joint (TMJ), and whole body) will be reported in later parts of the series. The STC is publishing these recommendations so as to encourage their use, to stimulate feedback and discussion, and to facilitate further revisions.For each joint, a standard for the local axis system in each articulating bone is generated. These axes then standardize the JCS. Adopting these standards will lead to better communication among researchers and clinicians.
The human hip joint is normally represented as a spherical hinge and its centre of rotation is used to construct femoral anatomical axes and to calculate hip joint moments. The estimate of the hip joint centre (HJC) position using a functional approach is affected by stereophotogrammetric errors and soft tissue artefacts. The aims of this study were (1) to assess the accuracy with which the HJC position can be located using stereophotogrammetry and (2) to investigate the effects of hip motion amplitude on this accuracy. Experiments were conducted on four adult cadavers. Cortical pins, each equipped with a marker cluster, were implanted in the pelvis and femur, and eight skin markers were attached to the thigh. Recordings were made while an operator rotated the hip joint exploiting the widest possible range of motion. For HJC determination, a proximal and a distal thigh skin marker cluster and two recent analytical methods, the quartic sphere fit (QFS) method and the symmetrical centre of rotation estimation (SCoRE) method, were used. Results showed that, when only stereophotogrammetric errors were taken into account, the analytical methods performed equally well. In presence of soft tissue artefacts, HJC errors highly varied among subjects, methods, and skin marker clusters (between 1.4 and 38.5 mm). As expected, larger errors were found in the subject with larger soft tissue artefacts. The QFS method and the distal cluster performed generally better and showed a mean HJC location accuracy better than 10mm over all subjects. The analysis on the effect of hip movement amplitude revealed that a reduction of the amplitude does not improve the HJC location accuracy despite a decrease of the artefact amplitude.
Hip resurfacing is a technically demanding procedure in which accurate positioning of the femoral component is critical to the avoidance of early implant failures. The purpose of this study was to assess the accuracy of computer-assisted placement of the femoral component and to evaluate the impact of computer-assisted surgery on the learning curve associated with this procedure.
The accuracy of positioning the femoral component was analyzed radiographically in hips undergoing resurfacing procedures performed by surgeons assigned to four different study groups: Group 1, in which the operations were performed with use of computer-assisted surgery by a fellowship-trained surgeon who was experienced in performing resurfacing arthroplasty (surgical experience, more than 250 hip resurfacings); Group 2, in which the operations were performed with use of computer-assisted surgery by senior residents who were inexperienced in performing resurfacing arthroplasty and who were closely supervised by faculty; Group 3, in which the operations were performed with use of conventional instruments by fellowship-trained faculty members; and Group 4, in which the operations were performed with use of computer-assisted surgery by a lesser experienced fellowship-trained faculty member (surgical experience, more than forty but less than seventy-five hip resurfacings) from Group 3.
The range of error in varus or valgus angulation that was observed for navigated procedures was 6 degrees in Group 1, 7 degrees in Group 2, and 5 degrees in Group 4. Compared with the preoperative neck-shaft angle value, the mean postoperative stem-shaft angle value increased by a mean of 4.7 degrees in Group 1, 7.2 degrees in Group 2, 6.5 degrees in Group 3, and 11.6 degrees in Group 4. When compared with the use of standard instrumentation, the use of computer-assisted surgery reduced the number of outliers and facilitated valgus insertion.
In the present study, computer-assisted surgery resulted in improved accuracy and precision in positioning the femoral component. In addition, computer-assisted surgery led to a reduction in the length of the learning curve for beginners in hip resurfacing and improved the surgeon's ability to perform this procedure safely.
The sphericity of a limited area of the surface of the human femoral head has been assessed using the Talyrond roundness-measuring
instrument. It is argued that this area approximates sufficiently closely to the load-bearing surface during standing and
walking to allow conclusions to be drawn as to the sphericity of the whole head. The degree of sphericity is less than that
reported byWalmsley (1928), but asphericity does frequently exist. The exis of any ovality is highly variable in this range of specimens, and
the significance of this in relation to other published work is briefly discussed.