Estimating segment inertial parameters using fan-beam DXA

Body segment inertial parameters are required as input parameters when the kinetics of human motion is to be analyzed. However, owing to interindividual differences in body composition, noninvasive inertial estimates are problematic. Dual-energy x-ray absorptiometry (DXA) is a relatively new imaging approach that can provide cost- and time-effective means for estimating these parameters with minimal exposure to radiation. With the introduction of a new generation of DXA machines, utilizing a fan-beam configuration, this study examined their accuracy as well as a new interpolative data-reduction process for estimating inertial parameters. Specifically, the inertial estimates of two objects (an ultra-high molecular density plastic rod and an animal specimen) and 50 participants were obtained. Results showed that the fan-beam DXA, along with the new interpolative data-reduction process, provided highly accurate estimates (0.10-0.39%). A greater variance was observed in the center of mass location and moment of inertia estimates, likely as a result of the course end-point location (1.31 cm). However, using a midpoint interpolation of the end-point locations, errors in the estimates were greatly reduced for the center of mass location (0.64-0.92%) and moments of inertia (-0.23 to -0.48%).     

The measurement of body segment inertial parameters using dual energy X-ray absorptiometry

Accurate body segment parameter (BSP) information is required for dynamic analyses of motion and the current methods available for obtaining these BSPs have been criticized. The purpose of this study was to determine whether dual energy X-ray absorptiometry (DXA) could accurately measure the BSPs of scanned objects and thus be used as a tool for measuring the BSPs of human subjects. Whole body mass (WBM) of 11 males was measured from a DXA scan and the values were compared to criterion scale-measured values by calculating the mean percent error. Two objects (plastic cylinder, human cadaver leg) were also scanned and DXA measurements of mass, length, centre of mass location (CM) and moment of inertia about the centre of mass (I_CM) were made using custom software. Criterion BSP measurements were then made and compared to DXA BSP values by calculating the percent error. Criterion I_CM measurements of the two objects were made using a pendulum technique and a second criterion I_CM calculation was made for the cylinder using a geometric formula. A mean percent error of −1.05% ±1.32% was found for WBM measurements of the human subjects. Errors for the cylinder and cadaver leg were under 3.2% for all BSPs except for I_CM when DXA was compared to the pendulum method (14.3% and 8.2% for cylinder and leg, respectively). The errors between DXA and the pendulum method were attributed to uncertainty in the pendulum technique (J. Biomech. 2002, in Review). I_CM error of the cylinder when DXA was compared to the geometric calculation was 2.63%. This error, combined with the low errors for all other BSPs, indicated that DXA can be used as a simple and accurate means of obtaining direct BSP information on living humans.     

Influence of body segments' parameters estimation models on inverse dynamics solutions during gait

The purpose of the present study was to examine the influence of anthropometric data on joint kinetics during gait. We particularly focused on the sensitivity of inverse dynamics solutions to the use of models for body segment parameters (BSP) estimation. Six often used estimation models were selected to provide BSP values for the three segments of the lower limb. Kinematics and dynamics were sampled from seven subjects performing barefoot gait at three different speeds. Joint kinetics were estimated with the bottom-up method using BSP values derived from each estimation model as anthropometric inputs. The BSP estimates were highly sensitive to the model used with deviations ranging from at least 9.73% up to 60%. Maximal variations of peak values for the hip joint flexion/extension moment during the swing phase were 20.11%. Hence, our findings suggest that the influence of BSP cannot be neglected. Observed deviations are especially due to the effect of varying simultaneously the mass, moments of inertia and the center of mass location values, according to the underlying relationship of interdependency linking each component. Considering both the differences found in joint kinetics and the level of accuracy of BSP models, evidence is provided that using multiple regression BSP estimation functions derived from Zatsiorsky and Seluyanov should be recommended to assess joint kinetics.     

Joint axes of rotation and body segment parameters of pig limbs

To enable a quantification of net joint moments and joint reaction forces, indicators of joint loading, this study aimed to locate the mediolateral joint axes of rotation and establish the body segment parameters of the limbs of pigs (Sus scrofa). To locate the joint axes of rotation the scapulohumeral, humeroradial, carpal complex, metacarpophalangeal, coxofemoral, femorotibial, tarsal, and metatarsophalangeal joints from 12 carcasses were studied. The joints were photographed in three positions, bisecting lines drawn at fixed landmarks with their intersection marking the joint axes of rotation. The body segment parameters, i.e. the segment mass, center of mass and moment of inertia were measured on the humerus, radius/ulna, metacarpus, forepastern, foretoe, femur, tibia, metatarsus, hindpastern, and hindtoe segments from five carcasses. The segments were weighed, and their center of mass was found by balancing them. The moments of inertia of the humerus, radius/ulna, femur and tibia were found by rotating the segments. The moments of inertia of the remaining segments were calculated. Generally, the joint axes of rotation were near the attachment site of the lateral collateral ligaments. The forelimb, with segments taken as one, was significantly lighter and shorter than the hindlimb (P < 0.001). In all segments the center of mass was located 31 to 50% distal to the proximal segment end. The segment mass decreased with distance from the trunk, as did the segment moment of inertia. The results may serve as reference on the location of the joint axes of rotation and on the body segment parameters for inverse dynamic modeling of pigs.     

Age and body mass index associations with body segment parameters

Body segment parameters (BSPs) such as segment mass, center of mass, and radius of gyration are required in many ergonomic tools and biomechanical models to estimate injury risk, and quantify muscle and joint contact forces. Currently, the full effects of age and obesity have not been taken into account when predicting BSPs. The goal of this study is to quantify the impact of body mass index (BMI) and age on BSPs, in order to provide more representative measures necessary for modeling inputs. A whole body dual energy X-ray absorptiometry (DXA) scan was collected for 280 working men and women with a wide range of BMI and aged 21 to 70 years. Established DXA processing methods were used to determine in-vivo estimates of the mass, center of mass, and radius of gyration for the upper arm, forearm, torso, thigh, and shank for males and females. Regression models were used to determine if age and BMI terms, as well as their interactions, were associated with these BSPs. The variability in BSPs explained by BMI alone ranged from 4 to 51%, and age explained an additional 3–19%. Thus, BMI and age are significant correlates of BSPs, and need to be taken into account when predicting certain BSPs in order to obtain accurate and representative results in biomechanical models.     

A comparison between a new model and current models for estimating trunk segment inertial parameters

Modeling of the body segments to estimate segment inertial parameters is required in the kinetic analysis of human motion. A new geometric model for the trunk has been developed that uses various cross-sectional shapes to estimate segment volume and adopts a non-uniform density function that is gender-specific. The goal of this study was to test the accuracy of the new model for estimating the trunk's inertial parameters by comparing it to the more current models used in biomechanical research. Trunk inertial parameters estimated from dual X-ray absorptiometry (DXA) were used as the standard. Twenty-five female and 24 male college-aged participants were recruited for the study. Comparisons of the new model to the accepted models were accomplished by determining the error between the models’ trunk inertial estimates and that from DXA. Results showed that the new model was more accurate across all inertial estimates than the other models. The new model had errors within 6.0% for both genders, whereas the other models had higher average errors ranging from 10% to over 50% and were much more inconsistent between the genders. In addition, there was little consistency in the level of accuracy for the other models when estimating the different inertial parameters. These results suggest that the new model provides more accurate and consistent trunk inertial estimates than the other models for both female and male college-aged individuals. However, similar studies need to be performed using other populations, such as elderly or individuals from a distinct morphology (e.g. obese). In addition, the effect of using different models on the outcome of kinetic parameters, such as joint moments and forces needs to be assessed.     

The use of magnetic resonance imaging for measuring segment inertial properties

The purpose of the study was to determine whether valid measures of segment inertial properties can be generated from a series of cross-sectional tissue scans using magnetic resonance imaging (MRI). The cross-sectional images for eight baboon cadaver segments (four forearms, two upper arms, and two lower legs) were digitized to yield areas of muscle, bone, and fat tissues. These data, along with tissue density values, were used for calculations of segment volume (V), density (D), mass (M), center of mass location (CM), and moment of inertia (Icm) about a transverse axis through the segment center of mass. Criterion measures of these properties were obtained using standard experimental techniques. Close agreement was found between criterion and MRI values for mean segment CM (44.67 vs. 43.36% from proximal end, respectively) while mean segment D was the same (1.124 g.cm-3) for both methods. MRI procedures tended to overestimate segment V(595.3 vs. 633.4 cm3), M(720.0 vs. 769.9 g), and Icm (3.208 vs. 3.332 x 10(-3) kg.m2). It was concluded that MRI represents a promising technique for generating valid measures of segment inertial characteristics as well as other anatomical features.     

Changes in segmental inertial properties with age

The purpose of this study was to examine how the limb segment inertial parameters vary across the decades from the 1920s to the 1970s. Sixty-six males participated in this study, ranging in age from 20 to 79 years. Pre-screening ensured that all subjects were healthy. The inertial properties of the segments were determined by modeling each segment as series of geometric solids. A multivariate analysis of variance (ANOVA) revealed statistically significant differences between decade age groups for the upper arm, forearm, shank, and thigh (p<0.01). Subsequent ANOVAs revealed statistically significant differences for all the inertial properties for the upper arm, the center of mass location for the forearm, and segment mass for the thigh. Linear regression lines were fit to the data so that each inertial parameter for each segment could be predicted by subject's age, with the slope of this regression line indicating the trend in the data. These trends were statistically significant for all forearm inertial parameters, thigh mass and longitudinal moment of inertia, and forearm center of mass location. The changes for the thigh, upper arm, and forearm were consistent with the changes, which would accompany a change in muscle mass with aging. Resultant joint moments were computed for a set of gait data using inertial properties reflective of the subjects from the age extremes in the study. The resulting differences in the knee and hip moments, young versus old, were all less than 4.5%.     

Scaling segmental moments of inertia for individual subjects

The purpose of this investigation was to validate methods of scaling human segmental moments of inertia for the transverse principal axis. Firstly, two methods of scaling Chandler et al.'s (Pamphlets DOT HS-801 430 and AMRL TR-74-137, Wright Patterson Air Force Base, OH, 1975) mean subject data to estimate the segmental moments of inertia were used. Chandler et al.'s data were scaled using body mass and segment length (formula 1) or body mass and standing height (formula 2). These data were then compared with a procedure of using the cadaver whose anthropometric measurements most closely match those of the subject. The difference between the criterion data (Chandler's subject data) and scaled values were plotted on scatter diagrams with confidence limits of p less than 0.05 at d.f. = 17. For procedure 1, 43% of the scaled values were plotted within the confidence limits using formula (2) (mass and standing height), compared with 26% for formula (1) (mass and segment length). Formula (1) markedly underestimated the tallest and heaviest subjects. In procedure 2, only 16% and 21% of the scaled values, using formula (1) and (2), respectively, fell within the confidence limits. Results suggested that scaling formulae approximate the moment of inertia of body segments with only limited accuracy. However, if scaling was to be adopted then mean moment of inertia data from an appropriate data set, using the formula that incorporates subject mass and standing height, gave results closest to the criterion value.     

A general model for estimating lower extremity inertial properties of individuals with transtibial amputation

Lower extremity joint moment magnitudes during swing are dependent on the inertial properties of the prosthesis and residual limb of individuals with transtibial amputation (TTA). Often, intact limb inertial properties (INTACT) are used for prosthetic limb values in an inverse dynamics model even though these values overestimate the amputated limb’s inertial properties. The purpose of this study was to use subject-specific (SPECIFIC) measures of prosthesis inertial properties to generate a general model (GENERAL) for estimating TTA prosthesis inertial properties. Subject-specific mass, center of mass, and moment of inertia were determined for the shank and foot segments of the prosthesis (n = 11) using an oscillation technique and reaction board. The GENERAL model was derived from the means of the SPECIFIC model. Mass and segment lengths are required GENERAL model inputs. Comparisons of segment inertial properties and joint moments during walking were made using three inertial models (unique sample; n = 9): (1) SPECIFIC, (2) GENERAL, and (3) INTACT. Prosthetic shank inertial properties were significantly smaller with the SPECIFIC and GENERAL model than the INTACT model, but the SPECIFIC and GENERAL model did not statistically differ. Peak knee and hip joint moments during swing were significantly smaller for the SPECIFIC and GENERAL model compared with the INTACT model and were not significantly different between SPECIFIC and GENERAL models. When subject-specific measures are unavailable, using the GENERAL model produces a better estimate of prosthetic side inertial properties resulting in more accurate joint moment measurements for individuals with TTA than the INTACT model.     

Differences in geriatric anthropometric data between DXA-based subject-specific estimates and non-age-specific traditional regression models

Age, obesity, and gender can have a significant impact on the anthropometrics of adults aged 65 and older. The aim of this study was to investigate differences in body segment parameters derived using two methods: (1) a dual-energy x-ray absorptiometry (DXA) subject-specific method (Chambers et al., 2010) and (2) traditional regression models (de Leva, 1996). The impact of aging, gender, and obesity on the potential differences between these methods was examined. Eighty-three healthy older adults were recruited for participation. Participants underwent a whole-body DXA scan (Hologic QDR 1000/W). Mass, length, center of mass, and radius of gyration were determined for each segment. In addition, traditional regressions were used to estimate these parameters (de Leva, 1996). A mixed linear regression model was performed (α = 0.05). Method type was significant in every variable of interest except forearm segment mass. The obesity and gender differences that we observed translate into differences associated with using traditional regressions to predict anthropometric variables in an aging population. Our data point to a need to consider age, obesity, and gender when utilizing anthropometric data sets and to develop regression models that accurately predict body segment parameters in the geriatric population, considering gender and obesity.     

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MS_com,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81 N m for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MS_{mass+com,thigh} is maximally 15.2 N m for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MS_com,shank is maximally 5.01 N m). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.     

Body segment inertial parameter estimation for the general population of older adults

The practical determination of accurate body segment inertial parameters for the general older adult population remains a problem, especially in estimating these parameters for women and accounting for variations in body type. A method is presented for determining the mass and center of mass location of the body segments of individuals within the general population of older adults. Effects of sex and body type on older adult mass distribution are accounted for using 32 easily obtainable body measurements. The method is based on existing results from different data sources and employs a combination of validated estimation approaches, including: body mass and segment length proportions, linear and nonlinear regression equations, and a mathematical model of the trunk. The method was applied to a validation sample of healthy, community-dwelling older adults (29 men, 50 women). Predicted body mass was 96.7+/-4.8% and 95.7+/-3.7% of measured body mass in the men and women, respectively. The estimates of body segment mass and trunk center of mass location for the sample population approximate those reported in the literature, supporting the validity of the described method. By producing practical, subject-specific estimates of body segment inertial parameters, the method should allow more accurate biomechanical analyses of the older adult population.     

Predicting in vivo soft tissue masses of the lower extremity using segment anthropometric measures and DXA

The purpose of this study was to derive and validate regression equations for the prediction of fat mass (FM), lean mass (LM), wobbling mass (WM), and bone mineral content (BMC) of the thigh, leg, and leg + foot segments of living people from easily measured segmental anthropometric measures. The segment masses of 68 university-age participants (26 M, 42 F) were obtained from full-body dual photon x-ray absorptiometry (DXA) scans, and were used as the criterion values against which predicted masses were compared. Comprehensive anthropometric measures (6 lengths, 6 circumferences, 8 breadths, 4 skinfolds) were taken bilaterally for the thigh and leg for each person. Stepwise multiple linear regression was used to derive a prediction equation for each mass type and segment. Prediction equations exhibited high adjusted R2 values in general (0.673 to 0.925), with higher correlations evident for the LM and WM equations than for FM and BMC. Predicted (equations) and measured (DXA) segment LM and WM were also found to be highly correlated (R2 = 0.85 to 0.96), and FM and BMC to a lesser extent (R2 = 0.49 to 0.78). Relative errors between predicted and measured masses ranged between 0.7% and -11.3% for all those in the validation sample (n = 16). These results on university-age men and women are encouraging and suggest that in vivo estimates of the soft tissue masses of the lower extremity can be made fairly accurately from simple segmental anthropometric measures.     

Are fixed limb inertial models valid for dynamic simulations of human movement?

During human movement, muscle activation and limb movement result in subtle changes in muscle mass distribution. Muscle mass redistribution can affect limb inertial properties and limb dynamics, but it is not currently known to what extent. The objectives of this study were to investigate: (1) how physiological alterations of muscle and tendon length affect limb inertial characteristics, and (2) how such changes affect dynamic simulations of human movement. To achieve these objectives, a digital model of a human leg, custom software, and Software for interactive musculoskeletal modeling were used to simulate mass redistribution of muscle–tendon structures within a limb segment during muscle activation and joint movement. Thigh and shank center of mass and moments of inertia for different muscle activation and joint configurations were determined and compared. Limb inertial parameters representing relaxed muscles and fully active muscles were input into a simulated straight-leg movement to evaluate the effect inertial parameter variations could have on movement simulation results. Muscle activation and limb movement altered limb segment center of mass and moments of inertia by less than 0.04 cm and 1.2%, respectively. These variations in limb inertial properties resulted in less than 0.01% change in maximum angular velocity for a simulated straight-leg hip flexion task. These data demonstrate that, for the digital human leg model considered, assuming static quantities for segment center of masses and moments of inertia in movement simulations appear reasonable and induce minimal errors in simulated movement dynamics.     

Trunk density profile estimates from dual X-ray absorptiometry

Accurate body segment parameters are necessary to estimate joint loads when using biomechanical models. Geometric methods can provide individualized data for these models but the accuracy of the geometric methods depends on accurate segment density estimates. The trunk, which is important in many biomechanical models, has the largest variability in density along its length. Therefore, the objectives of this study were to: (1) develop a new method for modeling trunk density profiles based on dual X-ray absorptiometry (DXA) and (2) develop a trunk density function for college-aged females and males that can be used in geometric methods. To this end, the density profiles of 25 females and 24 males were determined by combining the measurements from a photogrammetric method and DXA readings. A discrete Fourier transformation was then used to develop the density functions for each sex. The individual density and average density profiles compare well with the literature. There were distinct differences between the profiles of two of participants (one female and one male), and the average for their sex. It is believed that the variations in these two participants' density profiles were a result of the amount and distribution of fat they possessed. Further studies are needed to support this possibility. The new density functions eliminate the uniform density assumption associated with some geometric models thus providing more accurate trunk segment parameter estimates. In turn, more accurate moments and forces can be estimated for the kinetic analyses of certain human movements.     

A new method for the simultaneous measurement of the movement of inertia, the damping coefficient and the location of the centre of mass of a body segment in situ.

A new method which permits, in a single measurement, the determination of the moment of inertia, the angular damping coefficient of the joint and the location of the centre of mass of a body segment in situ is presented. The underlying principle is the theory of small, damped oscillations of a system about its equilibrium position. The fact that the oscillogram contains information about certain parameters of the oscillating system is used to find these parameters. The application of the method is simple and does not require highly sophisticated instrumentation. The results are very reproducable and immediately available.     

Hydrodynamic Analysis of C-start in Crucian Carp

The kinematics of turning maneuvers of startled Crucian Carp (Carassius auratus) are presented. All escape response observed are C-type fast-starts. The position of the center of mass and the me,merit of inertia of the fish are calculated. The results show that the position of the center of mass is always at 35% of the length of the fish from the head and the position of the center of mass and rroment of inertia can be considered unchanged during C-start of Crucian Carp. Hydro-dynamic analysis of the C-start is given based on the kinematics data from our experiments. The C-start consists of three stages. In stage 1, the tail fin of fish rapidly flaps in one direction, and a large moment acts on the fish‘s body, which rotates around the center of mass with an angular acceleration. In stage 2, the tail fin flaps more slowly in the opposite direction at slower speed, the fish‘s body rotates around the center of mass with angular deceleration and the center of mass of the fish moves along an are. In stage 3, the moment approximately equals zero, the fish‘s body stops rotating and the center of mass the moves along a straight line.     

Bioimpedance analysis: a useful technique for assessing appendicular lean soft tissue mass and distribution.

The present study was aimed at evaluating the feasibility and reliability of lower limb skeletal muscle (SM) mass estimates obtained by bioimpedance analysis (BIA). BIA estimates were compared with the estimates obtained by dual-energy X-ray absorptiometry (DXA). Ten normal weight and 10 obese women had BIA and DXA evaluations. Lower limb SM mass was then derived from DXA appendicular lean soft tissue estimates. Lower limb SM mass and SM distribution were also estimated from BIA modeling that fits measured resistance values along the leg. SM mass (mean +/- SD) was 5.8 +/- 1.0 kg by BIA vs. 5.8 +/- 1.1 kg by DXA in normal weight subjects and 7.2 +/- 1.4 kg by BIA vs. 7.2 +/- 1.2 kg by DXA in obese subjects. Mean +/- SD of the absolute value of the relative error was 7.0 +/- 3.4 and 5.9 +/- 3.4% in the two groups, respectively. Similar results were obtained by using five resistance values for the analysis. In conclusion, the proposed BIA model provides an adequate means of evaluating appendicular SM mass.