Simulating distal radius fracture strength using biomechanical tests: a modeling study examining the influence of boundary conditions

Distal radius fracture strength has been quantified using in vitro biomechanical testing. These tests are frequently performed using one of two methods: (1) load is applied directly to the embedded isolated radius or (2) load is applied through the hand with the wrist joint intact. Fracture loads established using the isolated radius method are consistently 1.5 to 3 times greater than those for the intact wrist method. To address this discrepancy, a validated finite element modeling procedure was used to predict distal radius fracture strength for 22 female forearms under boundary conditions simulating the isolated radius and intact wrist method. Predicted fracture strength was highly correlated between methods (r = 0.94; p < 0.001); however, intact wrist simulations were characterized by significantly reduced cortical shell load carriage and increased stress and strain concentrations. These changes resulted in fracture strength values less than half those predicted for the isolated radius simulations (2274 ± 824 N for isolated radius, 1124 ± 375 N for intact wrist; p < 0.001). The isolated radius method underestimated the mechanical importance of the trabecular compartment compared to the more physiologically relevant intact wrist scenario. These differences should be borne in mind when interpreting the physiologic importance of mechanical testing and simulation results.     

中医正骨手法改善桡骨远端伸直型骨折患者腕关节功能的临床研究及疗效的影响因素分析

摘要 目的：观察中医正骨手法在桡骨远端伸直型骨折中的临床应用价值,并分析疗效的影响因素。方法：选择四川省骨科医院2020年1月~2022年1月期间收治的桡骨远端伸直型骨折患者152例,按照治疗方式的不同将患者分为对照组（给予石膏固定）和研究组（应用中医正骨手法治疗）,例数分别为77例和75例。对比两组优良率、临床指标、腕关节活动度和X线相关影像学指标。同时采用多因素Logistic回归分析影响研究组腕关节功能疗效的相关因素。结果：治疗后,研究组的优良率明显高于对照组（P<0.05）。研究组手背消肿时间、疼痛缓解时间、骨折愈合时间均短于对照组（P<0.05）。两组治疗后12周掌屈、背伸、桡偏、尺偏、旋前、旋后活动度均扩大,且研究组均大于对照组（P<0.05）。两组治疗后12周掌倾角、尺偏角、桡骨高度均增加,且研究组均大于对照组（P<0.05）。单因素分析显示,研究组腕关节功能优良率与年龄、性别、骨质疏松、功能锻炼、掌倾角、尺偏角、桡骨高度、骨折端稳定性、受伤能量、利手情况有关（P<0.05）,而与体质量指数、就诊时间、基础疾病、骨折类型、固定时间无关（P>0.05）。多因素Logistic回归分析显示：性别为女、骨质疏松、无功能锻炼、掌倾角偏小、桡骨高度偏短、骨折端不稳定、受伤能量为高能量、利手是影响腕关节功能优良率的危险因素（P<0.05）。结论：中医正骨手法可有效改善桡骨远端伸直型骨折患者腕关节功能,减少骨折愈合及疼痛缓解时间。此外,患者腕关节功能的优良率还受到性别、骨质疏松、功能锻炼、掌倾角、桡骨高度、骨折端稳定性、受伤能量、利手情况的影响,值得引起临床重视。     

T型锁定接骨板治疗老年桡骨远端不稳定性骨折的临床疗效

目的:探讨老年桡骨远端不稳定性骨折采用桡骨远端T型锁定接骨板治疗的临床疗效及安全性。方法:选择2013年7月-2015年4月在我院接受治疗的老年桡骨远端不稳定性骨折患者80例,根据手术方式不同分为观察组和对照组。观察组患者采用桡骨远端T型锁定接骨板治疗,对照组采用外固定支架治疗。观察并比较两组患者的临床疗效及手术安全性。结果:观察组骨性愈合时间少于对照组,掌倾角及尺偏角大于对照组,差异有统计学意义(P0.05)。观察组治疗后腕关节功能优于对照组,差异有统计学意义(P0.048)。观察组患者腕关节慢性疼痛、骨折感染的发生率低于对照组,差异有统计学意义(P0.05)。结论:桡骨远端T型锁定接骨板治疗老年桡骨远端不稳定性骨折具有复位效果好、创伤小且安全性高的特点,有一定的临床推广价值。     

Stochastic-rheological Simulation of Free-fall Arm Impact in Children: Application to Playground Injuries

The aim of this study was to develop and pilot a stochastic-rheological biomechanical model to investigate the mechanics of impact fractures in the upper limbs of children who fall in everyday situations, such as when playing on playground equipment. The rheological aspect of the model characterises musculo-skeletal tissues in terms of inertial, elastic and viscous parameters. The stochastic aspect of the model allows natural variation of children's musculo-skeletal mechanical properties to be accounted for in the analysis. The relationship of risk factors, such as fall height, impact surface, child mass and bone density, to the probability of sustaining an injury in playground equipment falls were examined and found to closely match findings in epidemiological, clinical and biomechanical literature. These results suggest that the stochastic-rheological model is a useful tool for the evaluation of arm fracture risk in children. Once fully developed, information from this model will provide the basis for recommendations for modifications to playground equipment and surface standards.     

Stochastic-rheological simulation of free-fall arm impact in children: application to playground injuries

The aim of this study was to develop and pilot a stochastic-rheological biomechanical model to investigate the mechanics of impact fractures in the upper limbs of children who fall in everyday situations, such as when playing on playground equipment. The rheological aspect of the model characterises musculo-skeletal tissues in terms of inertial, elastic and viscous parameters. The stochastic aspect of the model allows natural variation of children's musculo-skeletal mechanical properties to be accounted for in the analysis. The relationship of risk factors, such as fall height, impact surface, child mass and bone density, to the probability of sustaining an injury in playground equipment falls were examined and found to closely match findings in epidemiological, clinical and biomechanical literature. These results suggest that the stochastic-rheological model is a useful tool for the evaluation of arm fracture risk in children. Once fully developed, information from this model will provide the basis for recommendations for modifications to playground equipment and surface standards.     

Cortical Hand Bone Porosity and Its Association with Distal Radius Fracture in Middle Aged and Elderly Women

Objective

Reduced bone mineral density (BMD), assessed by Dual Energy X-ray absorptiometry (DXA), is a well-known risk factor for fragility fracture. A large proportion of patients with fracture have only slightly reduced BMD. Assessment of other bone structure features than BMD may improve identification of individuals at increased fracture risk. Digital X-ray radiogrammetry (DXR), which is a feasible tool for measurement of metacarpal cortical bone density, also gives an estimate of cortical bone porosity. Our primary aim was to explore the association between cortical porosity in the hand assessed by DXR and distal radius fracture.

Methods

This case-control study included 123 women >50 years with distal radius fracture, and 170 controls. DXR was used to measure metacarpal BMD (DXR-BMD), cortical porosity (DXR-porosity), thickness (DXR-CT) and bone width (DXR-W) of the hand. Femoral neck BMD was measured by DXA.

Results

The fracture group had a statistically significant lower DXR-BMD (0.492 vs. 0.524 g/cm² p<0.001), higher cortical DXR-porosity (0.01256 vs. 0.01093, p<0.001), less DXR-CT (0.148 vs. 0.161cm, p<0.001) and lower femoral neck DXA-BMD (0.789 vs. 0.844 g/cm², p = 0.001) than the controls. In logistic regression analysis adjusted for age, a significant association with distal radius fracture (OR, 95% CI) was found for body mass index (0.930, 0.880–0.983), DXA-BMD (0.996, 0.995–0.999), DXR-BMD (0.990, 0.985–0.998), DXR-porosity (1.468, 1.278–1.687) and DXR-CT (0.997, 0.996–0.999). In an adjusted model, DXR-porosity remained the only variable associated with distal radius fracture (1.415, 1.194–1.677).

Conclusion

DXR derived porosity is associated with fracture at distal radius and might be a sensitive marker for skeletal fragility.     

中西医结合治疗桡骨远端骨折的临床分析

目的:探讨中西医结合治疗桡骨远端骨折的临床治疗效果。方法:选取本院收治的桡骨远端骨折患者60例,将其随机分为对照组和实验组,每组30例。对照组采用切开复位钢板螺钉固定方法治疗,实验组采用切开复位钢板螺钉固定加局部中药外敷治疗。观察和比较两组患者的骨折愈合时间、腕部功能恢复情况以及临床疗效。结果:与对照组比较,实验组患者的骨折愈合时间明显缩短,患肢腕部功能明显改善,差异具有统计学意义(P0.05);实验组的临床总有效率(76.66%)明显高于对照组(65.00%),差异具有统计学意义(P0.05)。结论:中西医结合治疗桡骨远端骨折能够有效缩短骨折愈合时间,明显改善患者的腕部功能,值得临床推广。     

The epidemiology of low- and high-energy distal radius fracture in middle-aged and elderly men and women in southern norway

Background

Distal radius is one of the most frequent sites for fractures in the elderly population. Despite this, there is a paucity of epidemiological data for distal radius fracture, in particular, distinguishing between high- and low-energy fractures. Our aim was to study the epidemiology of high- and low-energy distal radius fracture in middle-aged and elderly men and women in Southern Norway, and search for associates with high- or low-energy distal radius fracture in this population.

Methodology/Principal Findings

Patients with distal radius fractures aged ≥50 years were identified from all four hospitals in Southern Norway between 2004 and 2005. Age-adjusted and age-specific incidence rates for men and women were calculated, and potential associates with high- and low-energy distal radius fracture were explored both in univariate and multivariate analyses. A total of 799 individuals (118 men and 681 women) aged ≥50 years with low-energy and 84 (48 men and 36 women) with high-energy distal radius fracture were identified. The overall age-adjusted incidence rate per 10,000 person-years was 18.9 for men (low energy, 12.8 vs. high-energy, 6.1) and 75.1 for women (low energy, 71.1 vs. high energy, 4.0). In multivariate model, younger age, male gender, summer season, and living in a rural area were independently associated with an increased risk of high-energy fracture.

Conclusion

An approximately fourfold higher age-adjusted incidence rate for distal radius fracture was found among women, when compared with men. However, the proportion of patients with high-energy distal radius fracture was approximately fivefold higher in men than in women. Our data suggest that younger age, male gender, summer seasons, and living in rural areas are independent risk factors for increased risk of high-energy distal radius fracture.     

Prediction of Colles’ fracture load in human radius using cohesive finite element modeling

Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles’ fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731–6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4–5% per decade based only on material level changes and by 6–20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r²=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.     

Replicating a Colles fracture in an excised radius: revisiting testing protocols

A distal radius fracture in middle-age and older adults is often considered a sentinel indicator of osteoporosis. Mechanical testing of cadaveric specimens is often used to quantify bone strength and develop insight for relating in-vivo measures to fracture force. Mechanical testing protocols using an intact forearm have been successful at replicating a Colles fracture, however, excised isolated radius protocols based on the intact forearm testing protocol have not been as successful. One protocol originally designed to replicate the physiological condition of a fall on an outstretched hand was reproduced in our laboratory, yet surprisingly the produced distal radius fracture patterns were not consistent among specimens nor was dorsal angulation of the distal fragment that is characteristic of a Colles fracture observed. The purpose of this study was to perform a mechanics-based analysis of the excised radius loading protocol in order to quantify the imposed and internal forces on the radius. An idealized beam model of the excised radius revealed that in the area of the distal radius where Colles fractures occur, 99.99% of the maximum strain on the bone outer surface was the result of pure compressive loading. This loading condition is in direct contrast to the accepted mechanics of a Colles fracture, which is characterized as a metaphyseal bending fracture with the volar cortex failing due to tensile stresses and the dorsal cortex exhibiting compression and comminution. The results suggest that additional research, particularly related to overcoming the difficulties of reliably supporting and applying a force to the distal end of the radius, is necessary for clinical fracture patterns to be reliably reproduced with an excised radius mechanical testing protocol.     

Three-dimensional computer simulation of radiostereometric analysis (RSA) in distal radius fractures

Physical phantom models have conventionally been used to determine the accuracy and precision of radiostereometric analysis (RSA) in various orthopaedic applications. Using a phantom model of a fracture of the distal radius it has previously been shown that RSA is a highly accurate and precise method for measuring both translation and rotation in three-dimensions (3-D). The main shortcoming of a physical phantom model is its inability to mimic complex 3-D motion. The goal of this study was to create a realistic computer model for preoperative planning of RSA studies and to test the accuracy of RSA in measuring complex movements in fractures of the distal radius using this new model. The 3-D computer model was created from a set of tomographic scans. The simulation of the radiographic imaging was performed using ray-tracing software (POV-Ray). RSA measurements were performed according to standard protocol. Using a two-part fracture model (AO/ASIF type A2), it was found that for simple movements in one axis, translations in the range of 25microm-2mm could be measured with an accuracy of +/-2microm. Rotations ranging from 16 degrees to 2 degrees could be measured with an accuracy of +/-0.015 degrees . Using a three-part fracture model the corresponding values of accuracy were found to be +/-4microm and +/-0.031 degrees for translation and rotation, respectively. For complex 3-D motion in a three-part fracture model (AO/ASIF type C1) the accuracy was +/-6microm for translation and +/-0.120 degrees for rotation. The use of 3-D computer modelling can provide a method for preoperative planning of RSA studies in complex fractures of the distal radius and in other clinical situations in which the RSA method is applicable.     

Variations in morphological and biomechanical indices at the distal radius in subjects with identical BMD

Determination of osteoporotic status is based primarily on areal bone mineral density (aBMD) obtained through dual X-ray absorptiometry (DXA). However, many fractures occur in patients with T-scores above the WHO threshold of osteoporosis, in part because DXA measures are insensitive to biomechanically important alterations in bone quality. The goal of this study was to determine--within groups of subjects with identical radius aBMD values--the extant variation in densitometric, geometric, microstructural, and biomechanical parameters. High resolution peripheral quantitative computed tomography (HR-pQCT) and DXA radius data from males and females spanning large ranges in age, osteoporotic status, and anthropometrics were compiled. 262 distal radius datasets were processed for this study. HR-pQCT scans were analyzed according to the manufacturer's standard clinical protocol to quantify densitometric, geometric, and microstructural indices. Micro-finite element analysis was performed to calculate biomechanical indices. Factor of risk of wrist fracture was calculated. Simulated aBMD calculated from HR-pQCT data was used to group scans for evaluation of variation in quantified indices. Indices reflecting the greatest variation within aBMD level were BMD in the central portion of the trabecular compartment (max CV 142), trabecular heterogeneity (max CV 90), and intra-cortical porosity (max CV 151). Of the biomechanical indices, cortical load fraction had the greatest variation (max CV 38). Substantial variations in indices reflecting density, structure, and biomechanical competence exist among subjects with identical aBMD levels. Overlap of these indices among osteoporotic status groups reflects the reported incidence of osteoporotic fracture in subjects classified as osteopenic or normal.     

两种方法治疗桡骨远端骨折的疗效比较研究

目的:比较采用T形钢板内固定和闭合复位石膏外固定这两种方法治疗桡骨远端骨折的疗效研究。方法:选取我院2008年3月至2011年12月间的76例桡骨远端骨折患者,并按照治疗方法不同分为2组,41例患者进行T形钢板内固定,其余35例患者进行复位后石膏外固定。并借助X线对比分析桡骨远端骨折复位前后及临床愈合时桡骨腕关节的掌倾角、尺偏角及桡骨轴向缩短长度变化等数据,并根据改良的Shea评定法对临床疗效进行比较。结果:针对桡骨远端不稳定型骨折的患者,T形钢板内固定组的优良率要优于石膏外固定组的疗效(P<0.05);而对于稳定性桡骨远端骨折的患者,两组之间的优良率没有明显差异(P>0.05)。结论:对于桡骨远端不稳定骨折的患者,应优先选择T形钢板内固定手术方法,而对于稳定性骨折患者这两种治疗方法均可采用。     

In Process Citation]

Abstract Introduction: The aim of the present study was to develop a test setup with continuous angle alteration to imitate elbow joint motion for the mechanical evaluation of tension band wiring and a newly designed intramedullary nail. Materials and methods: The servo-pneumatical test stand worked with a rotational angle-adjusted and a linear force-adjusted engine. The fracture model was dynamically tested under cyclic loading imitating elbow joint motion. In total, 14 fresh cadaver upper extremities underwent olecranon fracture by means of transverse osteotomy and were assigned to two groups: tension band wiring and intramedullary nailing. There was a continuous angle alteration between 0 and 100 degrees of flexion, with continuous changing pull force between 25 N and 150 N. Two steel pins were placed in the proximal, two in the distal olecranon fragment for video analysis of the motion between the two pairs of pins. Displacement in the fracture gap was determined after 4 and 300 cycles. Results: After 300 cycles, the displacement in the fracture fixation model was significantly higher in the tension band wiring group than in the intramedullary nailing group. Discussion: Other studies evaluating biomechanical properties of olecranon osteosyntheses with joint involvement did not change the force direction dynamically. We introduced a test setup with continuous angle alteration to imitate joint motion. This is an important step for accurate biomechanical evaluation of the treatment of different fixation methods in olecranon fractures. The tested nailing system showed significant advantages in loosening under cyclic loading compared to tension band wiring.     

Personalized loading conditions for homogenized finite element analysis of the distal sections of the radius

The microstructure of trabecular bone is known to adapt its morphology in response to mechanical loads for achieving a biomechanical homeostasis. Based on this form–function relationship, previous investigators either simulated the remodeling of bone to predict the resulting density and architecture for a specific loading or retraced physiological loading conditions from local density and architecture. The latter inverse approach includes quantifying bone morphology using computed tomography and calculating the relative importance of selected load cases by minimizing the fluctuation of a tissue loading level metric. Along this concept, the present study aims at identifying an optimal, personalized, multiaxial load case at the distal section of the human radius using in vivo HR-pQCT-based isotropic, homogenized finite element (hFE) analysis. The dataset consisted of HR-pQCT reconstructions of the 20 mm most distal section of 21 human fresh-frozen radii. We simulated six different unit canonical load cases (FX palmar–dorsal force, FY ulnar–radial force, FZ distal–proximal force, MX moment about palmar–dorsal, MY moment about ulnar–radial, MZ moment about distal–proximal) using a simplified and efficient hFE method based on a single isotropic bone phase. Once we used a homogeneous mean density (shape model) and once the original heterogeneous density distribution (shape + density model). Using an analytical formulation, we minimized the deviation of the resulting strain tensors ε(x) to a hydrostatic compressive reference strain ε₀, once for the 6 degrees of freedom (DOF) optimal (OPT) load case and for all individual 1 DOF load cases (FX, FY, FZ, MX, MY, MZ). All seven load cases were then extended in the nonlinear regime using the scaled displacements of the linear load cases as loading boundary conditions (MAX). We then compared the load cases and models for their objective function (OF) values, the stored energies and their ultimate strength using a specific torsor norm. Both shape and shape + density linear-optimized OPT models were dominated by a positive force in the z-direction (FZ). Transversal force DOFs were close to zero and mean moment DOFs were different depending on the model type. The inclusion of density distribution increased the influence and changed direction of MX and MY, while MZ was small in both models. The OPT load case had 12–15% lower objective function (OF) values than the FZ load case, depending on the model. Stored energies at the optimum were consistently 142–178% higher for the OPT load case than for the FZ load case. Differences in the nonlinear response maximum torsor norm ‖t‖ were heterogeneous, but consistently higher for OPT_MAX than FZ_MAX. We presented the proof of concept of an optimization procedure to estimate patient-specific loading conditions for hFE methods. In contrast to similar models, we included canonical load cases in all six DOFs and used a strain metric that favors hydrostatic compression. Based on a biomechanical analysis of the distal joint surfaces at the radius, the estimated load directions are plausible. For our dataset, the resulting OPT load case is close to the standard axial compression boundary conditions, usually used in HR-pQCT-based FE analysis today. But even using the present simplified hFE model, the optimized linear six DOF load case achieves a more homogeneous tissue loading and can absorb more than twice the energy than the standard uniaxial load case. The ultimate strength calculated with a torsor norm was consistently higher for the 6-DOF nonlinear model (OPT_MAX) than for the 1-DOF nonlinear uniaxial model (FZ_MAX). Defining patient-specific boundary conditions may decrease angulation errors during CT measurements and improve repeatability as well as reproducibility of bone stiffness and strength estimated by HR-pQCT-based hFE analysis. These results encourage the extension of the present method to anisotropic hFE models and their application to repeatability data sets to test the hypothesis of reduced angulation errors during measurement.

     

Fluoride and Children’s Intelligence: A Meta-analysis

This paper presents a systematic review of the literature concerning fluoride that was carried out to investigate whether fluoride exposure increases the risk of low intelligence quotient (IQ) in China over the past 20 years. MEDLINE, SCI, and CNKI search were organized for all documents published, in English and Chinese, between 1988 and 2008 using the following keywords: fluorosis, fluoride, intelligence, and IQ. Further search was undertaken in the website www.fluorideresearch.org because this is a professional website concerning research on fluoride. Sixteen case-control studies that assessed the development of low IQ in children who had been exposed to fluoride earlier in their life were included in this review. A qualitative review of the studies found a consistent and strong association between the exposure to fluoride and low IQ. The meta-analyses of the case-control studies estimated that the odds ratio of IQ in endemic fluoride areas compared with nonfluoride areas or slight fluoride areas. The summarized weighted mean difference is -4.97 (95%confidence interval [CI] = -5.58 to -4.36; p < 0.01) using a fixed-effect model and -5.03 (95%CI = -6.51 to 3.55; p < 0.01) using a random-effect model, which means that children who live in a fluorosis area have five times higher odds of developing low IQ than those who live in a nonfluorosis area or a slight fluorosis area.     

Peripheral quantitative computed tomography at the distal radius: cross-calibration between two scanners

Peripheral quantitative computed tomography (pQCT) is an important technique to study the interaction between the muscle and bone systems. We have recently established pQCT reference ranges for children, adolescents and young adults using a recent version (XCT 2000) of the Stratec scanners (Stratec Inc., Pforzheim, Germany). However, the previous version of this type of scanner (XCT 900) is still widely used and cross-calibration is needed to use these reference data. Therefore, both distal radii of 19 healthy subjects (age 21 to 59 years; 11 women) were analyzed at the "4% site" using both the XCT 900 and the XCT 2000. Cross-sectional area, total and trabecular bone mineral density (BMD), total bone mineral content (BMC) and polar Strength-Strain Index (SSI) results from the two scanners were compared using linear regression analysis. To achieve scanner calibration we used the intercept and slope of the correlations. The correlation coefficients between the two devices were 0.82 for the cross-sectional area, 0.81 for total BMD, 0.97 for trabecular BMD, 0.99 for total BMC and 0.86 for polar SSI. In conclusion, these data allow for the conversion of XCT 900 results at the distal radius to XCT 2000 values and vice versa.     

Maternal age at last birth in Egypt

To assess the effects of women's education, residence, and marital experience on their age at the birth of their last child, a proportional hazards regression model was applied to 1980 Egyptian Fertility Survey (EFS) data. The detailed data include the date of birth of each child for every women interviewed, and the woman's date of birth and age at interview. Age at last birth was examined by regression analysis on birth history and socioeconomic information. 4 hypotheses were tested: women who are well educated have a greater probability of ending childbearing earlier than women with less education; women in rural areas have a higher probability of having their last child at older ages than urban women; marital disruption without remarriage lowers the probability of older maternal age at last birth; and marital disruption with remarriage increases the probability that a woman stops reproducing at an older age. The overall chi-square indicates a significant regression. All coefficients were significant, except the coefficient for women with intact 1st marriages. Women with more education had a greater probability of ending childbearing earlier than women with less education. Rural women tended to have their last children at ages significantly older than overall age at last birth. Current residence in urban areas had the opposite effect. The coefficient for those with intact 1st marriages was insignificant, meaning that the mean age at last birth for this group of women was not much different from the overall mean. Remarried women tended to end childbearing at ages significantly older than the overall average age at last birth, suggesting that these women tended to have children by their new husbands. Those with dissolved 1st marriages who had not remarried had a higher probability of ending childbearing earlier than did older women. Marriage age and final parity had highly significant negative coefficients; as marriage age and number of children born increased, so did the "survival" time or the age at last birth. Results from the hazards model indicate that the effects were as anticipated. The median age at last birth for the total sample of women aged 45-49 was 45-49 years. The median age at last birth was about 2 years older for rural compared to urban women. Illiterate women had the oldest median age at last birth of the education groups. There was little differences between median ages at last birth for women with intact 1st marriages and those whose 1st unions were dissolved and who had remarried. The median age at last birth increased with final parity.     

Masses, centers-of-gravity, and moments-of-inertia of the body segments of the rhesus monkey (Macaca mulatta).

Segmental parameters (mass, center-of-gravity, and moment-of-inertia) are necessary for biomechanical analyses of a species' locomotor behavior. Seven male and eight female adult rhesus monkey cadavers were dismembered in order to determine segmental parameters. Mean values for the segment masses and moments-of-inertia are presented for males and females, separately and together. Statistical tests revealed significant differences between the sexes for these parameters. Regression equations for predicting segment masses and moments-on-inertia were developed for the sexes separately and pooled. For most segments the male and female equations did not differ significantly in slope or y-intercept. The center-of-gravity for each segment is presented as a mean percentage of the distance between the proximal and distal joint centers. The regression equations and center-of-gravity locations presented here permit biomechanical investigations of rhesus monkey locomotion without the necessity of subsequent sacrifice. The segmental parameter values determined for the rhesus monkey are compared with available data for other primate and mammalian species and the biomechanical and adaptive implications of such comparisons are discussed.     

Moment arms and musculotendon lengths estimation for a three-dimensional lower-limb model

This paper presents a set of polynomial expressions that can be used as regression equations to estimate length and three-dimensional moment arms of 43 lower-limb musculotendon actuators. These equations allow one to find, at a low computational cost, the musculotendon geometric parameters required for numerical simulation of large musculoskeletal models. Nominal values for these biomechanical parameters were established using a public-domain musculoskeletal model of the lower limb (IEEE Trans. Biomed. Eng. 37 (1990) 757). To fit these nominal values, regression equations with different levels of complexity were generated, based on the number of generalized coordinates of the joints spanned by each musculotendon actuator. Least squares fitting was used to identify regression equation coefficients. The goodness of the fit and confidence intervals were assessed, and the best fitting equations selected.