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Because fall experiments with volunteers can be both challenging and risky, especially with older volunteers, we wished to develop computer simulations of falls to provide a theoretical framework for understanding and extending experimental results. To perform a preliminary validation of the articulated total body (ATB) model for passive falls, we compared the model predictions of fall direction, impact location, and impact velocity as a function of disturbance type (faint, slip, step down, trip) and gait speed (fast, normal, slow) to experimental results with young adult volunteers. The three-dimensional ATB model had 17 segments and 16 joints. Its physical characteristics, environment definitions, contact functions, and initial conditions were representative of our experiment. For each combination of disturbance and gait speed, the ATB model was left to fall passively under gravity once disturbed, i.e., no joint torques were applied, until impact with the floor occurred. Finally, we also determined the sensitivity of the model predictions to changes in the model's parameters. Our model predictions of fall angles and impact angles were qualitatively in agreement with those observed experimentally for ten and seven of the 12 original simulations, respectively. Quantitatively, the model predictions of fall angles, impact angles, and impact velocities were within one experimental standard deviation for seven, three, and nine of the 12 original simulations, respectively, and within two experimental standard deviations for ten, nine, and 11 of the 12 original simulations, respectively. Finally, the fall angle and impact angle region did not change for 92% and 95% of the 74 input variation simulations, respectively, and the impact velocities were within the experimental standard deviations for 78% of the 74 input variation simulations. Based on our simulations and a sensitivity analysis, we conclude that our preliminary validation of the ATB model for passive falls was successful. In fact, these ATB model simulations represent a significant step forward in fall simulations. We believe that with additional work, the ATB model could be used to accurately simulate a variety of human falls and may be useful in further understanding the etiology and mechanisms of fall injuries such as hip fractures.

Cortical and trabecular bone have similar creep behaviors that have been described by power-law relationships, with increases in temperature resulting in faster creep damage accumulation according to the usual Arrhenius (damage rate approximately exp (-Temp.-1)) relationship. In an attempt to determine the phase (collagen or hydroxyapatite) responsible for these similar creep behaviors, we investigated the creep behavior of demineralized cortical bone, recognizing that the organic (i.e., demineralized) matrix of both cortical and trabecular bone is composed primarily of type I collagen. We prepared waisted specimens of bovine cortical bone and demineralized them according to an established protocol. Creep tests were conducted on 18 specimens at various normalized stresses sigma/E0 and temperatures using a noninvasive optical technique to measure strain. Denaturation tests were also conducted to investigate the effect of temperature on the structure of demineralized bone. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates at all applied normalized stresses and temperatures. Strong (r2 > 0.79) and significant (p < 0.01) power-law relationships were found between the damage accumulation parameters (steady-state creep rate d epsilon/dt and time-to-failure tf) and the applied normalized stress sigma/E0. The creep behavior was also a function of temperature, following an Arrhenius creep relationship with an activation energy Q = 113 kJ/mole, within the range of activation energies for cortical (44 kJ/mole) and trabecular (136 kJ/mole) bone. The denaturation behavior was characterized by axial shrinkage at temperatures greater than approximately 56 degrees C. Lastly an analysis of covariance (ANCOVA) of our demineralized cortical bone regressions with those found in the literature for cortical and trabecular bone indicates than all three tissues creep with the same power-law exponents. These similar creep activation energies and exponents suggest that collagen is the phase responsible for creep in bone.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.

We measured the step response of a surrogate human pelvis/impact pendulum system at force levels between 50 and 350 N. We then fit measured response curves with four different single-degree-of-freedom models, each possessing a single mass, and supports of the following types: standard linear solid, Voigt, Maxwell, and spring. We then compared model predictions of impact force during high-energy collisions (pendulum impact velocity ranging from 1.16 to 2.58 m/s) to force traces from actual impacts to the surrogate pelvis. We found that measured peak impact forces, which ranged from 1700 to 5600 N, were best predicted by the mass-spring, Maxwell, and standard linear solid models, each of which had average errors less than 3 percent. Reduced accuracy was observed for the commonly used Voigt model, which exhibited an average error of 10 percent. Considering that the surrogate pelvis system used in this study exhibited nonlinear stiffness and damping similar to that observed in simulated fall impact experiments with human volunteers, our results suggest that these simple models allow-impact forces in potentially traumatic falls to be predicted to within reasonable accuracy from the measured response of the body in safe, simulated collisions.

Recent studies suggest that hip padding systems reduce the incidence of hip fractures during falls. However, no data exist on the force attenuating capacity of hip pads under realistic fall impact conditions, and thus it is difficult to compare the protective merit of various pad designs. Our goal is to design a comfortable hip padding system which reduces femoral impact force in a fall below the mean force required to fracture the elderly cadaveric femur. In pursuit of this objective, we designed and constructed a hip pad testing system consisting of an impact pendulum and surrogate human pelvis. We then developed a hip pad containing a shear-thickening material which allows for shunting of the impact energy away from the femur and into the surrounding soft tissue. Finally, we conducted experiments to assess whether the surrogate pelvis accurately represents the impact behavior of the human female pelvis in a fall, and to determine whether our energy-shunting pad attenuates femoral impact force in a fall more effectively than seven available padding systems. We found the surrogate pelvis accurately represented the human female pelvis in regional variation in soft tissue stiffness, total effective stiffness and damping, and impact force attenuation provided by trochanteric soft tissues. We also found that our padding system attenuated femoral impact force by 65 percent, thereby providing two times the force attenuation of the next best system. Moreover, the energy-shunting pad was the only system capable of lowering femoral impact force well below the mean force required to fracture the elderly femur in a fall loading configuration. These results suggest that the force attenuating potential of hip pads which focus on shunting energy away from the femur is superior to those which rely on absorbing energy in the pad material. While these in-vitro results are encouraging, carefully designed prospective clinical trials will be necessary to determine the efficacy of these approaches to hip fracture prevention.

A method for the calculation of translations and Eulerian rotations of an orthogonal axis system with respect to a fixed reference is described with application to the measurement of position in a vertebral motion segment. Kinematic equations were derived to compute the three-dimensional motion of a moving vertebra relative to an adjacent fixed body, without the requirement of a direct physical link between the two bodies. For this calculation, the quadratic error of the lengths of six position vectors was minimized to obtain a mathematically optimal estimate of the translations and rotations. Tests with a rigid model resulted in mean maximum overall system errors of 2.8 percent for the measurement of translation (translations less than 3.5 mm) and 6.1 percent for the measurement of rotations (rotations less than 10 deg) limited by transducer accuracy. The mathematical techniques presented for the quantitative description of rigid body motion, based on the measurement of three reference vectors, may be extended to a broad range of kinematic problems.

Despite our growing understanding of the importance of fall mechanics in the etiology of hip fracture, previous studies have largely ignored the kinematics and dynamics of falls from standing height. Beginning from basic principles, we estimated peak impact force on the greater trochanter in a sideways fall from standing height. Using a one degree-of-freedom impact model, this force is determined by the impact velocity of the hip, the effective mass of that part of the body that is moving prior to impact, and the overall stiffness of the soft tissue overlying the hip. To determine impact velocity and effective mass, three different paradigms of increasing complexity were used: 1) a falling point mass or a rigid bar pivoting at its base; 2) two-link models consisting of a leg segment and a torso; and 3) three-link models including a knee. The total mechanical energy of each model before falling was equated to the total mechanical energy just prior to impact in order to estimate the hip impact velocity. In addition, the configuration of the model just before impact was used to estimate the effective mass. Our model predictions were compared with the results of an earlier experimental study with young subjects falling on a 10-inch thick mattress. Values from literature were used to estimate the soft tissue stiffness. For the models, predicted values for hip impact velocity and effective mass ranged from 2.47 to 4.34 m/s and from 15.9 to 70.0 kg, respectively. Predicted values for the peak force applied to the greater trochanter ranged from 2.90k to 9.99k N. Based on comparisons to the experimental falls, impact velocity and impact force were best predicted by a simple two-link model with the trunk at 45 degrees to the vertical at impact. A three-link model with a quadratic spring incorporated in the knee of the model was the best predictor of effective mass. Using our most accurate model, the peak impact force was 2.90k N for a 5th percentile female and 4.26k N for a 95th percentile female, thereby confirming the widely held perception that "the bigger they are, the harder they fall".

We have reviewed highlights of the research in trabecular bone biomechanics performed over the past 20 years. Results from numerous studies have shown that trabecular bone is an extremely heterogeneous material--modulus can vary 100-fold even within the same metaphysis--with varying degrees of anisotropy. Strictly speaking, descriptions of the mechanical properties of trabecular bone should therefore be accompanied by specification of factors such as anatomic site, loading direction, and age. Research efforts have also been focused on the measurement of mechanical properties for individual trabeculae, improvement of methods for mechanical testing at the continuum level, quantification of the three-dimensional architecture of trabecular bone, and formulation of equations to relate the microstructural and continuum-level mechanical properties. As analysis techniques become more sophisticated, there is now evidence that factors such as anisotropy and heterogeneity of individual trabeculae might also have a significant effect on the continuum-level properties, suggesting new directions for future research. Other areas requiring further research are the time-dependent and multiaxial failure properties at the continuum level, and the stiffness and failure properties at the lamellar level. Continued research in these areas should enhance our understanding of issues such as age-related bone fracture, prosthesis loosening, and bone remodeling.

In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.

A major determinant of the risk of hip fracture in a fall from standing height is the force applied to the femur at impact. This force is determined by the impact velocity of the hip and the effective mass, stiffness, and damping of the body at the moment of contact. We have developed a simple experiment (the pelvis release experiment) to measure the effective stiffness and damping of the body when a step change in force is applied to the lateral aspect of the hip. Results from pelvis release experiments with 14 human subjects suggest that both increased soft tissue thickness over the hip and impacting the ground in a relaxed state can decrease the effective stiffness of the body, and subsequently reduce peak impact forces. Comparison between our fall impact force predictions and in-vitro measures of femoral fracture strength suggest that any fall from standing height producing direct, lateral impact on the greater trochanter can fracture the elderly hip.

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region.(ABSTRACT TRUNCATED AT 250 WORDS)

A three-dimensional, linear finite element model was generated for an intact plexiglass tube with an attached six-hole stainless steel compression plate. We examined external forces representing axial, off-center axial, and four-point bending, along with superimposed plate and screw pretension. Strain gage experiments were conducted to test model validity and the finite element results were contrasted to a composite beam theory solution. Excellent correspondence was observed between finite element and strain gage data for the most significant strain components. Composite beam theory tended to overestimate the neutral axis shift which results from plate application. The model also demonstrated fracture site distraction due to plate pretension, and the tendency for outer screw failure for the combination of bending-closed with a preload in the plate and screws.

Stable internal fixation usually results in a unique histological healing pattern which involves direct cortical reconstruction and an absence of periosteal bridging callus. While it has been suggested that longitudinal interfragmentary strain levels control this healing pattern, the complex, multiaxial strain fields in the interfragmentary region are not well understood. Based on an in-vivo study of gap healing in the sheep tibia by Mansmann et al., we used several finite element models of simplified geometry to: explore modeling assumptions on material linearity and deformation kinematics, and examine the strain distribution in a healing fracture gap subjected to known levels of interfragmentary strain. We found that a general nonlinear material, nonlinear geometric analysis is necessary to model an osteotomy gap subjected to a maximum longitudinal strain of 100 percent. The large displacement, large strain conditions which were used in the in-vivo study result in complex, multiaxial strain fields in the gap. Restricting the maximum longitudinal strain to 10 percent allows use of a linear geometric formulation without compromising the numerical results. At this reduced strain level a linear material model can be used to examine the extent of material yielding within a homogeneous osteotomy gap. Severe local strain variations occurred both through the thickness of the gap and radially from the endosteal to periosteal gap surfaces. The bone/gap interface represented a critical plane of high distortional and volumetric change and principal strain magnitudes exceeded the maximum longitudinal strains.

Mechanical studies of the Functional Spinal Unit (FSU) in-vitro have shown that the slopes of the load-displacement curves increase with load. This nonlinearity implies that the stiffness of the FSU is not constant over the range of physiologic loads, and that measurements obtained for FSU specimens through the application of individual loads cannot be summed to predict the response of the specimens to combined loads. Both experimental and analytical methods were developed in the present study to better quantify the nonlinear FSU load-displacement response and to calculate the coupled stiffness of FSU specimens at combined states of load reflecting in-vivo conditions. Results referenced to the center of the vertebral body indicate that lumbar FSU specimens are stiffer in flexion than in extension, and that FSU specimens loaded in flexion are stiffer at high loads than at low loads. The importance of combined load testing and a nonlinear interpretation of load-displacement data is demonstrated.

An in-vitro system has been devised to monitor the properties of an idealized fracture site immobilized with a Hoffman-Vidal external fixator. A dial gage was used to measure the relative pin displacements under controlled axial loading. The displacement measurements were then used in conjunction with a finite element model to predict the modulus of an idealized fracture site. Five fracture sites made of neoprene disks of different mechanical properties were monitored in order to simulate the increasing modulus of a healing fracture. Good agreement was observed between directly measured mechanical properties of the neoprene and those inferred from the combined finite element and pin displacement tests.

Based on a regular array of cubic unit cells, each containing a body-centered spherical void, we created an idealized three-dimensional model for both subchondral trabecular bone and a class of porous foams. By considering only face-to-face stacking of unit cells, the inherent symmetry was such that, except at the surface, the displacements and stresses within any one unit cell were representative of the entire porous structure. Using prescribed displacements the model was loaded in both uniaxial compressive strain and uniaxial shear strain. Based on the response to these loads, we found the tensor of elastic constants for an equivalent homogeneous elastic solid with cubic symmetry. We then compared the predicted modulus with our experimental values for bovine trabecular bone and literature values for an open-celled latex rubber foam.

A theoretical formulation for studying limb motions and joint kinetics by multiaxial accelerometry is developed. The technique is designed to study the swing phase of human gait, modeling the lower leg as a rigid body. Major advantages of the approach are that acceleration information needed for the calculation of forces and moments is generated directly, and that the method automatically generates its own initial conditions. Results of validation experiments using both artificial and experimental data demonstrate that the method is theoretically valid, but that it taxes available instrumentation and requires further development before it can be applied in a clinical setting.