David W. Wagner

Deriving tissue density and elastic modulus from microCT bone scans.

Tissue level density and elastic modulus are intrinsic properties that can be used to quantify bone material and analyses incorporating those quantities have been used to evaluate bone on a macroscopic scale. Micro-computed tomography (microCT) technology has been used to construct tissue level finite element models to simulate macroscopic fracture strength, however, a single method for assigning voxel-specific tissue density and elastic modulus based on those data has not been universally accepted. One method prevalent in the literature utilizes an empirical relationship that derives tissue stiffness as a function of bone calcium content weight fraction. To derive calcium content weight fraction from microCT scans, a measure of tissue density is required and a constant value is traditionally used. However, experimental data suggest a non-trivial amount of tissue heterogeneity suggesting a constant tissue density may not be appropriate. A theoretical derivation for determining the relationship between voxel-specific tissue density and microCT scan data (i.e., microCT derived tissue mineral density (TMD), mgHA/cm(3)) and bone constituent properties is proposed. Constant model parameters used in the derivation include the density of water, ash, and organics (i.e., bone constituents) and the volume fraction of the organics constituent. The effect of incorporating the theoretically derived tissue density (instead of a constant value) in determining voxel-specific elastic modulus resulted in a maximum observed increase of 12GPa (5.9GPa versus 17.9GPa, for the constant value and derived tissue density formulations, respectively) for a measured TMD of 1.02gHA/cm(3). Average and bounding quantities for the four constant model parameters were defined from the literature and the influence of those values on the derived tissue density and elastic modulus relationships were also evaluated. The theoretical relationships of tissue density and elastic modulus, with the average constant model parameters applied, were consistent with previously published empirical relationships derived from experimental data. Tissue density as a function of microCT TMD was formulated as a linear relationship and the density of water and ash was shown to solely influence the proportionality (i.e., slope) between those values. The density of water and organics (i.e., collagen) and the volume fraction of the organics constituent were shown to influence the constant offset (intercept) between tissue density and TMD with no influence from ash density. Incorporating tissue density heterogeneity into the derivation of elastic modulus resulted in a significant increase in predicted modulus (for microCT TMD ranges observed for healthy tissue) as compared to when a constant tissue density was used. The presented approach provides a novel method for deriving tissue-level bone material properties and quantifies the effect of assuming tissue homogeneity when calculating elastic modulus (when using a prevalent method in the literature) from microCT scan data.

Consistency Among Musculoskeletal Models: Caveat Utilitor

Musculoskeletal simulation software and model repositories have broadened the user base able to perform musculoskeletal analysis and have facilitated in the sharing of models. As the recognition of musculoskeletal modeling continues to grow as an engineering discipline, the consistency in results derived from different models and software is becoming more critical. The purpose of this study was to compare eight models from three software packages and evaluate differences in quadriceps moment arms, predicted muscle forces, and predicted tibiofemoral contact forces for an idealized knee-extension task spanning −125 to +10° of knee extension. Substantial variation among models was observed for the majority of aspects evaluated. Differences among models were influenced by knee angle, with better agreement of moment arms and tibiofemoral joint contact force occurring at low to moderate knee flexion angles. The results suggest a lack of consistency among models and that output differences are not simply an artifact of naturally occurring inter-individual differences. Although generic musculoskeletal models can easily be scaled to consistent limb lengths and use the same muscle recruitment algorithm, the results suggest those are not sufficient conditions to produce consistent muscle or joint contact forces, even for simplified models with no potential of co-contraction.

Comparison of three methods of calculating strain in the mouse ulna in exogenous loading studies.

Axial compression of mouse limbs is commonly used to induce bone formation in a controlled, non-invasive manner. Determination of peak strains caused by loading is central to interpreting results. Load-strain calibration is typically performed using uniaxial strain gauges attached to the diaphyseal, periosteal surface of a small number of sacrificed animals. Strain is measured as the limb is loaded to a range of physiological loads known to be anabolic to bone. The load-strain relationship determined by this subgroup is then extrapolated to a larger group of experimental mice. This method of strain calculation requires the challenging process of strain gauging very small bones which is subject to variability in placement of the strain gauge. We previously developed a method to estimate animal-specific periosteal strain during axial ulnar loading using an image-based computational approach that does not require strain gauges. The purpose of this study was to compare the relationship between load-induced bone formation rates and periosteal strain at ulnar midshaft using three different methods to estimate strain: (A) Nominal strain values based solely on load-strain calibration; (B) Strains calculated from load-strain calibration, but scaled for differences in mid-shaft cross-sectional geometry among animals; and (C) An alternative image-based computational method for calculating strains based on beam theory and animal-specific bone geometry. Our results show that the alternative method (C) provides comparable correlation between strain and bone formation rates in the mouse ulna relative to the strain gauge-dependent methods (A and B), while avoiding the need to use strain gauges.

Geometric mouse variation: Implications to the axial ulnar loading protocol and animal specific calibration

Large variations in axial ulnar load strain calibration results suggest that animal-specific calibrations may be necessary. However, the optimal set of geometric measures for performing an animal-specific calibration are not known, potentially as a result of confounding effects associated with experimentally introduced variation. The purpose of this study was to characterize the inherent variability of ulnar geometric measures known to influence periosteal midshaft strain during axial ulnar exogenous loading, and to further quantify the relationship between the variance of those geometric measures and periosteal strain during axial loading. Thirty-nine right mouse forelimbs were scanned with microCT. Seven geometric measures that influence periosteal strain resulting from a combined axial and bending loading were computed and used to estimate animal-specific strains on the periosteal midshaft. Animal specific strains were estimated using a theoretical model based on the generalized flexure formula. The predicted mean and standard deviation of the simulated midshaft strain gauge measurement resulting from the inter-animal geometric differences was -985 ± 148 με/N. The complete beam bending term associated with bending about the I(min) axis accounted for 89% of the variance and reduced the residual RMSE to 50.4 με. Eccentricity associated with the axial loading contributed a substantial portion of variation to the computed strain suggesting that calibration procedures to account for animal differences should incorporate that variable. The method developed in this study provides a relatively simple procedure for computing animal-specific strains using microCT scan data, without the need of a load/strain calibration study or computationally intensive finite element models.

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.

Dynamic Force Response of Human Legs due to Vertical Jumps

Jumping is a natural exertion that occurs during a variety of human activities including playing sports, working, skateboarding, dancing, escaping from hazardous events, rescue activities, and many others. During jumping, the ankles in particular are expected to support the entire body weight of the jumper and that may lead to ankle injuries. Each year hundreds of patients are treated for ankle sprains/strains with ankle fractures as one of the most common injuries treated by orthopedists and podiatrists. The knee joint is also considered the most-often injured joint in the entire human body. Although the general anatomy of the lower extremities is fairly well understood, an understanding of the injury mechanism during these jumping tasks is not well understood. The aim of this study is to determine the reaction forces exerted on legs and joints due to vertical jumps, through musculoskeletal simulation and experimental studies to better understand the dynamic jump process and the injury mechanism. The joint reaction forces and moments exerted on the ankle, knee and hip joint during takeoff and extreme squat landing of a vertical jump were determined through the application of musculoskeletal simulation. It is concluded that during extreme squat landing of a vertical jump, joint reaction forces and moments were highest in proximal/distal and anteroposterior direction may cause most likely injury to the hip joint ligaments, ankle fracture and knee joint, respectively.Copyright

Reply to “Letter to the Editor: Consistency Among Musculoskeletal Models: Caveat Utilitor”

DAVID W. WAGNER, VAHAGN STEPANYAN, JAMES M. SHIPPEN, MATTHEW S. DEMERS, ROBIN S. GIBBONS, BRIAN J. ANDREWS, GRAHAM H. CREASEY, and GARY S. BEAUPRE Center for Tissue Regeneration, Repair, and Restoration, VA Palo Alto Health Care System, 3801 Miranda Ave, Palo Alto, CA 94304, USA; Department of Mechanical Engineering, Stanford University, Stanford, CA, USA; Industrial Design, Coventry University, Worcestershire, UK; School of Sport and Education, Brunel University, Middlesex, UK; Nuffield Department of Surgical Sciences, Oxford University, Oxford, UK; and Spinal Cord Injury Service, VA Palo Alto Health Care System, Palo Alto, CA, USA.

Step scaling and behaviour selection in a constrained set of manual material handling transfers

Predictive biomechanical analysis of manual material handling (MMH) transfers is dependent on accurate prediction of foot locations relative to the task. Previous studies have classified common acyclic stepping patterns used during those transfer tasks, but the influence of walking distance prior to the transfer is not well understood. Twenty men and women performed transfers for a minimum of six different delivery distance conditions. The number of steps used by the participants ranged from two to seven. A theoretical framework for idealised step-scaling strategies is proposed and compared with the experimental data. The maximum observed increase in step length prior to delivery was 1.43 times the nominal step length calculated for each participant. The data suggest that although participants can scale their steps to facilitate the use of a single terminal stance at the transfer, the majority of participants chose to utilise a combination of stepping strategies if the preferred contralateral lead foot strategy could not be easily implemented. Practitioner summary: Accurate foot placements are needed for predictive biomechanical analysis of MMH. A laboratory study investigated the influence of previous step positions on MMH. A flexible step-scaling strategy, in which step lengths and strategy were varied, suggests that analysis based on simulated movements should consider multiple lifting postures.

Factors Contributing to Spiral Humerus Fracture During Muscle-Up Exercise

Spiral humerus fractures associated with extreme muscular torsion loading have been well documented in literature. Throwing motions and arm wrestling are the two causes most often researched, while spiral fractures associated with gymnastics have received less attention. The purpose of this study is to explore the factors that may contribute to torsional failure of the humerus while performing a gymnastics move known as a muscle-up. Primary motivation for this study was the result of the author sustaining a spiral fracture to the distal aspect of her left humerus while attempting a muscle-up. To the author’s knowledge, no previous studies analyzing the forces imposed on the upper extremities during a muscle-up have been conducted.Utilizing the author’s estimated anthropometric measurements and the kinematic and kinetic constraints of the muscle-up activity, the torque acting about the long axis of the humerus was determined in two ways. First, an analytical approach was used to calculate the forces and moments within a simplified linkage representation of the upper extremity for several representative muscle-up postures. The second method was a computer simulation that modeled the entire body with muscles in several different kinematic positions and outputted internal body elbow joint net moments.The analytical approach resulted in torques between 12.0 N·m and 29.3 N·m. The kinetics derived with the computer simulation revealed joint reaction torques between 13 N·m and 38 N·m and net axial torques between 29.1 N·m and 69.1 N·m acting on the left humerus. The internal moments predicted using the computer simulation were above the author’s minimum predicted torque, 53 N·m, associated with humerus fracture initiation.Although there may be many factors that contribute to spiral humerus fracture, in this study, it was determined that the kinematic positions of the muscle-up movement are sufficiently extreme so as to produce torques capable of resulting in spiral humerus fracture.Copyright

Dynamic Response of Human Legs due to Horizontal Jump

Jumping is a coordinated extension of the human body through combined strength and agility to perform a leap motion far enough for the feet to land on the ground. However, the repeated reaction forces and the resulting stresses on the ankle, knee and hip joints may cause injuries to a person. A primary mechanism of such injuries is suggested to be the acute high impact loads experienced during the landing in a horizontal jump. The goal of this study is to determine the reaction force distribution at the joints in the lower extremities during the horizontal jump. A detailed biomechanical system was constructed to calculate the reaction forces generated during the horizontal jump. The horizontal jump kinematics of a participant was measured using a three-dimensional motion capture system and the landing forces were measured using two force plates. Biomechanical simulation software was used to calculate the internal joint reaction forces at the ankle, knee, and hip. It was determined that the maximum reaction forces primarily occurred in the proximo/distal direction of the hip, 2,300 N; and ankle, 2,700 N. However, at the knee joint, the maximum reaction force was determined to be in antero/posterior direction, at 2,000 N; and proximo/distal direction, at 2,100 N, respectively.Copyright