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Boundary conditions (BCs) are often simplified in experimental and numerical models simulating distal radius fractures and their treatments. The aim of this study was to investigate the effects of simplified BCs at the radiocarpal joint: (1) on the stress distribution in the intact distal radius, and (2) on the loading of a volar locking plate (VLP) used for distal radius fracture treatment. Finite element models of the distal radius with contact between carpals and cartilage were created as reference models for an intact bone and a fractured bone with VLP treatment. Four models with simplified BCs were compared to these reference models: One with embedding material instead of carpals, one with carpals tied to the radius; each loaded either uniaxially or with statically equivalent loading to the reference model. Differences in distal bone stress distributions and mechanical parameters of the VLP (fracture gap movement, plate peak stresses, distal screw loads) were generally largest for the uniaxially loaded, embedded model (up to 250 % in individual screw loads) and smallest for the model with tied carpals and statically equivalent loads (

Measuring three-dimensional (3D) forearm rotational motion is difficult. We aimed to develop and validate a new method for analyzing 3D forearm rotational motion. We proposed biplane fluoroscopic intensity-based 2D–3D matching, which employs automatic registration processing using the evolutionary optimization strategy. Biplane fluoroscopy was conducted for forearm rotation at 12.5 frames per second along with computed tomography (CT) at one static position. An arm phantom was embedded with eight stainless steel spheres (diameter, 1.5 mm), and forearm rotational motion measurements using the proposed method were compared with those using radiostereometric analysis, which is considered the ground truth. As for the time resolution analysis, we measured radiohumeral joint motion in a patient with posterolateral rotatory instability and compared the 2D–3D matching method with the simulated multiple CT method, which uses CTs at multiple positions and interpolates between the positions. Rotation errors of the radius and ulna between these two methods were 0.31 ± 0.35° and 0.32 ± 0.33°, respectively, translation errors were 0.43 ± 0.35 mm and 0.29 ± 0.25 mm, respectively. Although the 2D–3D method could detect joint dislocation, the multiple CT method could not detect quick motion during joint dislocation. The proposed method enabled high temporal- and spatial-resolution motion analyses with low radiation exposure. Moreover, it enabled the detection of a sudden motion, such as joint dislocation, and may contribute to 3D motion analysis, including joint dislocation, which currently cannot be analyzed using conventional methods.

International audience; Human cortical bone fracture toughness depends on the anatomical locations under quasi-static loading. Recent results also showed that under fall-like loading, cortical bone fracture toughness is similar at different anatomical locations in the same donor. While cortical bone toughening mechanisms are known to be dependent on the tissue architecture under quasi-static loading, the fracture mechanisms during a fall are less studied. In the current study, the structural parameters of eight paired femoral diaphyses, femoral necks and radial diaphyses were mechanically tested under quasi-static and fall-like loading conditions (female donors, 70 ± 14 y.o., [50–91 y.o.]). Synchrotron radiation micro-CT imaging was used to quantify the amount of micro-cracks formed during loading. The volume fraction of these micro-cracks was significantly higher within the specimens loaded under a quasi-static condition than under a loading representative of a fall. Under fall-like loading, there was no difference in crack volume fraction between the different paired anatomical locations. This result shows that the micro-cracking toughening mechanism depends both on the anatomical location and on the loading condition.

The Sneddon formula is conventionally used to calculate the elastic modulus of cell based on atomic force microscope (AFM) experiments. Owing to the disobedience of the formula assumptions, errors exist. Here, the ABAQUS for finite element modeling and analysis was used to simulate the process of compression of cell with a AFM conical probe. It was found that the relative error ranges from 0.094 to 1.455 folds, depending on half angle of the cone, curvature radius at the tip of the cone and the compression depth. By fitting the error data, we proposed a correction factor, which can be multiplied by the Sneddon formula to get a modified formula, providing the more accurate elastic modulus of cell. The experimentally measured elastic moduli of cell and hydrogel are in good agreement with the values obtained using the modified formula.

Optical motion capture (OMC) systems are commonly used to capture in-vivo three-dimensional joint kinematics. However, the skin-based markers may not reflect the underlying bone movement, a source of error known as soft tissue artifact (STA). This study examined STA during wrist motion by evaluating the agreement between OMC and biplanar videoradiography (BVR). Nine subjects completed 7 different wrist motion tasks: doorknob rotation to capture supination and pronation, radial-ulnar deviation, flexion-extension, circumduction, hammering, and pitcher pouring. BVR and OMC captured the motion simultaneously. Wrist kinematics were quantified using helical motion parameters of rotation and translation, and Bland-Altman analysis quantified the mean difference (bias) and 95% limit of agreement (LOA). The rotational bias of doorknob pronation, a median bias of -4.9°, was significantly larger than the flexion-extension (0.7°, p 0.05) and radial-ulnar deviation (1.8°, p 0.01) tasks. The rotational LOA range was significantly smaller in the flexion-extension task (5.9°) compared to pitcher (11.6°, p 0.05) and doorknob pronation (17.9°, p 0.05) tasks. The translation bias did not differ between tasks. The translation LOA range was significantly larger in circumduction (9.8°) compared to the radial-ulnar deviation (6.3°, p 0.05) and pitcher (3.4°, p 0.05) tasks. While OMC technology has a wide-range of successful applications, we demonstrated it has relatively poor agreement with BVR in tracking wrist motion, and that the agreement depends on the nature and direction of wrist motion.

The Pistoia criterion (PC) is widely used to estimate the failure load of distal radius segments based on linear micro Finite Element (μFE) analyses. The advantage of the PC is that a simple strain-threshold and a tissue volume fraction can be used to predict failure properties. In this study, the PC is compared to materially nonlinear μFE analyses, where the bone tissue is modelled as an elastic, damageable material. The goal was to investigate for which outcomes the PC is sufficient and when a nonlinear (NL) simulation is required. Three types of simulation results were compared: (1) prediction of the failure load, (2) load sharing of cortical and trabecular regions, and (3) distribution of local damaged/overstrained tissue at the maximum sustainable load. The failure load obtained experimentally could be predicted well with both the PC and the NL simulations using linear regression. Although the PC strongly overestimated the failure load, it was sufficient to predict adequately normalized apparent results. An optimised PC (oPC) was proposed which uses experimental data to calibrate the individual volume of overstrained tissue. The main areas of local over-straining predicted by the oPC were the same as estimated by the NL simulation, although the oPC predicted more diffuse regions. However, the oPC relied on an individual calibration requiring the experimental failure load while the NL simulation required no a priori knowledge of the experimental failure load.

Distal biceps tendon ruptures have been reported to be associated with narrowing of the proximal radioulnar space. There have been no studies that three-dimensionally measured the distance between the bicipital tuberosity and the proximal ulna during active motion. The purpose of this study was to three-dimensionally measure the proximal radioulnar space during active forearm pronation in healthy subjects. Five healthy volunteers (10 forearms) were recruited for this study. They consisted of all males with a mean age of 37 years (range, 34-46 years). Lateral fluoroscopy of forearm rotation from maximum supination to maximum pronation was recorded for both forearms. Three-dimensional forearm kinematics were determined using model-image registration techniques with fluoroscopic images and CT-derived bone models, and the closest distance between the bicipital tuberosity and the proximal ulna was computed at each 30° increment of radial axial rotation relative to the distal humerus. The distance between the bicipital tuberosity and the proximal ulna decreased with pronation, reaching a minimum value at 90° of radial rotation (average 4.6 ± 1.3 mm), then increased with further rotation to maximum pronation (P = 0.004). The clearance between the proximal radioulnar space and the distal biceps tendon is very small (1mm). Hypertrophy of the bicipital tuberosity or tendon can induce impingement and lead to tendon rupture.

The measurement of wrist passive ranges of motion (ROMs) can provide insight into improvements and allow for effective monitoring during a rehabilitation program. Compared with conventional methods, this study proposed a new robotic assessment technique for measuring passive ROMs of the wrist. The robotic system has a reconfigurable handle structure that allows for multi-dimensional applications of wrist motions. The assessment reliability of this robotic system was analysed on 11 subjects for measuring wrist extension/flexion and radial/ulnar deviation. Preliminary data demonstrated its potential with intraclass correlation coefficient (ICC2,1) all greater than 0.857 and standard error of measurement (SEM) less than 3.38°. Future work will focus on the standardization of the assessment protocol of this robotic system for assessment purposes, paving the way for its clinical application.

During walking, falling is most likely to occur towards the side of the supporting lower limb during the single stance. Timely lateral redirection of the centre of mass (CoM) preceding the no-return position is necessary for balance. We analysed the curvature peaks (the inverse of the radius of curvature) of the three-dimensional path of the CoM during the entire stride. Twelve healthy adults walked on a force-sensorized treadmill at constant velocities from 0.4 to 1.2 m s-1, in 0.2 m s-1 increments. The three-dimensional displacements of the CoM, the muscular power sustaining the CoM motion with respect to the ground, and the efficiency of the pendulum-like transfer of the CoM were computed via the double integration of the ground reaction forces. The curvatures of the CoM trajectory were measured (Frenet– Serret formula). During the single stance, the curvature showed a bell-shaped increment, lasting a few tenths of a millisecond, and peaking at 365–683 m-1 (radius of 2.7–1.4 mm, respectively), the higher the walking velocity. The CoM was redirected towards the swinging lower limb. The curvature increment was sustained by muscle-driven braking of the CoM. Smoother increments of curvature (peaking at approximately 37–150 m-1), further orienting the CoM towards the leading lower limb, were observed during the double stance. The peaks of the curvatures were symmetric between the two sides. The high curvature peaks during the single stance may represent an index of dynamic balance during walking. This index might be useful for both rehabilitation and sports training purposes.

A common method used to study tibiofemoral joint biomechanics following total knee arthroplasty (TKA) is the lowest point method, which finds the lowest points of each femoral condyle in relation to the plane of the resected tibia. The objectives of this paper were twofold: 1) to use a circle-based model to demonstrate the large inherent error introduced when the lowest points are used to indicate anterior-posterior (AP) positions of contact by the femur on the tibial insert, 2) to use the circle-based model to estimate the magnitude of error. A circle-based model was created to simulate articular surfaces of the tibial insert and condyles of the femoral component and to demonstrate the error. Equations relating the error to radii of tibial and femoral articular surfaces were derived. The magnitude of the error was estimated for common low-conforming TKA components by determining radii using best-fit circles to approximate curvature of articular surfaces. Error in AP tibial insert contact locations is caused by the slope of the tibial articular surface and the magnitude increases with increasing slope and increasing radius of the femoral condyle. For radii approximating articular surfaces of common low-conforming components, relative errors range from 45% to 109%. The circle-based model effectively demonstrates the cause of the large error in using lowest points to indicate AP tibial insert contact locations and enables an estimate of relative error. Because relative error exceeds 45%, the lowest point method should not be used to indicate the AP tibial insert contact locations.

Total wrist arthroplasty (TWA) designs suffer from relatively high complication rates when compared to other arthroplasties. Understanding the contact pattern of hip and knee replacement has improved their design and function; however, the in vivo contact pattern of TWA has not yet been examined and is thus the aim of this study. We hypothesized that the center of contact (CoC) is located at the geometric centers of the carpal component and radial component in the neutral posture and that the CoC moves along the principal arcs of curvature throughout primary anatomical motions. Wrist motion and implant kinematics of six patients with the Freedom® total wrist implant were studied during various tasks using biplanar videoradiography. The location of the CoC of the components was investigated by calculating distance fields between the articular surfaces. We found the CoC at the neutral posture was not at the geometric centers but was located 3.5 mm radially on the carpal component and 1.2 mm ulnarly on the radial component. From extension to flexion, the CoC moved 10.8 mm from dorsal to volar side on the carpal component (p 0.0001) and 7.2 mm from volar to dorsal on the radial component (p = 0.0009). From radial to ulnar deviation, the CoC moved 12.4 mm from radial to ulnar on the carpal component (p 0.0001), and 5.6 mm from ulnar to radial on the radial component (p = 0.009). The findings of this study may eventually improve TWA success by advancing future designs through a more accurate understating of their kinematic performance in vivo.

We present a method for the statistical modeling of the displacements of wrist bones during the performance of coordinated maneuvers, such as radial-ulnar deviation (RUD). In our approach, we decompose bone displacement via a set of basis functions, identified via principal component analysis (PCA). We utilized MRI wrist scans acquired at multiple static positions for deriving these basis functions. We then utilized these basis functions to compare the displacements undergone by the bones of the left versus right wrist in the same individual, and between bones of the wrists of men and women, during the performance of the coordinated RUD maneuver. Our results show that the complex displacements of the wrist bones during RUD can be modeled with high reliability with just 5 basis functions, that captured over 91% of variation across individuals. The basis functions were able to predict intermediate wrist bone poses with an overall high accuracy (mean error of 0.26 mm). Our proposed approach found statistically significant differences between bone displacement trajectories in women versus men, however, did not find significant differences in those of the left versus right wrist in the same individual. Our proposed method has the potential to enable detailed analysis of wrist kinematics for each sex, and provide a robust framework for characterizing the normal and pathologic displacement of the wrist bones, such as in the context of wrist instability.

Erosion of articular cartilage is a concern following distal humeral hemiarthroplasty, because native cartilage surfaces are placed in contact with stiff metallic implant components, which causes decreases in contact area and increases in contact stresses. Recently, reverse engineered implants have been proposed which are intended to promote more natural contact mechanics by reproducing the native bone or cartilage shape. In this study, finite element modeling is used in order to calculate changes in cartilage contact areas and stresses following distal humeral hemiarthroplasty with commercially available and reverse engineered implant designs. At the ulna, decreases in contact area were -34±3% (p=0.002), -27±1% (p0.001) and -14±2% (p=0.008) using commercially available, bone reverse engineered and cartilage reverse engineered designs, respectively. Peak contact stresses increased by 461±57% (p=0.008), 387±127% (p=0.229) and 165±16% (p=0.003). At the radius, decreases in contact area were -21±3% (p=0.013), -13±2% (p0.006) and -6±1% (p=0.020), and peak contact stresses increased by 75±52% (p0.999), 241±32% (p=0.010) and 61±10% (p=0.021). Between the three different implant designs, the cartilage reverse engineered design yielded the largest contact areas and lowest contact stresses, but was still unable to reproduce the contact mechanics of the native joint. These findings align with a growing body of evidence indicating that although reverse engineered hemiarthroplasty implants can provide small improvements in contact mechanics when compared with commercially available designs, further optimization of shape and material properties is required in order reproduce native joint contact mechanics.

Micro-Finite Element (micro-FE) analysis is now widely used in biomedical research as a tool to derive bone mechanical properties as they relate to its microstructure. With the development of in vivo high-resolution peripheral quantitative CT (HR-pQCT) scanners, it can now be applied to analyze bone in-vivo in the peripheral skeleton. In this survey, the results of several experimental and clinical studies are summarized that addressed the feasibility of this approach to predict bone strength in-vivo. Specific questions that will be addressed are: how accurate are strength predictions based on micro-FE; how reproducible are the results; and, is it a better predictor of bone fracture risk than DXA based measures? Based on results of experimental studies, it is first concluded that micro-FE based on HR-pQCT images can accurately predict the strength of the distal radius during a fall on the outstretched hand using either linear elastic analysis, implementing a 'Pistoia criterion' or similar criterion in combination with an 'effective' Young's modulus or using non-linear analyses. When evaluating results of clinical reproducibility studies, it is concluded that for single-center studies, errors at the radius are less than 4.4% and 3.7% and at the tibia less than 3.6% and 2.3% for stiffness and strength, respectively. In multicenter trials, however, these errors can be increased by some 1.8% and 1.4% for stiffness and strength, respectively. Finally, based on the results of large cohort studies, it is concluded that micro-FE calculated stiffness better separates cases from controls than bone density parameters for subjects with fragility fractures at any site, but not for subjects with only radius fractures. In this latter case, however, combinations of micro-FE derived parameters can significantly improve the separation.

Although high-impact hemodynamic forces are thought to lead to cerebral aneurysmal change, little is known about the aneurysm formation on the inner aspect of vascular bends such as the internal carotid artery (ICA) siphon where wall shear stress (WSS) is expected to be low. This study evaluates the effect of vessel curvature and hemodynamics on aneurysm formation along the inner carotid siphon. Catheter 3D-rotational angiographic volumes of 35 ICA (10 aneurysms, 25 controls) were evaluated in 3D for radius of curvature and peak curvature of the siphon bend, followed by univariate statistical analysis. Computational fluid dynamic (CFD) simulations were performed on patient-derived models after aneurysm removal and on synthetic variants of increasing curvature. Peak focal siphon curvature was significantly higher in aneurysm bearing ICAs (0.36 ± 0.045 vs. 0.30 ± 0.048 mm(-1), p=0.003), with no difference in global radius of curvature (p=0.36). In CFD simulations, increasing parametric curvature tightness (from 5 to 3mm radius) resulted in dramatic increase of WSS and WSS gradient magnitude (WSSG) on the inner wall of the bend. In patient-derived data, the location of aneurysms coincided with regions of low WSS (

Bone strains resulting from physical activity are thought to be a primary driver of bone adaptation, but cannot be directly noninvasively measured. Because bone adapts nonuniformly, physical activity may make an important independent structural contribution to bone strength that is independent of bone mass and density. Our objective was to create and validate methods for subject-specific finite element (FE) model generation that would accurately predict the surface strains experienced by the distal radius during an in vivo loading task, and to apply these methods to a group of 23 women age 23-35 to examine variations in strain, bone mass and density, and physical activity. Four cadaveric specimens were experimentally tested and specimen-specific FE models were developed to accurately predict periosteal surface strains (Root mean square error=16.3%). In the living subjects, when a 300 N load was simulated, mean strains were significantly inversely correlated with BMC (r=−0.893), BMD (r=−0.892) and physical activity level (r=−0.470). Although the group of subjects was relatively homogenous, BMD varied by two-fold (range: 0.19 – 0.40 g/cm3) and mean energy-equivalent strain varied by almost six-fold (range: 226.79 – 1328.41 με) with a simulated 300 N load. In summary, we have validated methods for estimating surface strains in the distal radius that occur while leaning onto the palm of the hand. In our subjects, strain varied widely across individuals, and was inversely related to bone parameters that can be measured using clinical CT, and inversely related to physical activity history.

The 16-station RandomPOD wear test system, previously validated for prosthetic hip wear, was used in the simulation of knee wear mechanisms with a ball-on-flat test configuration. This consisted of a CoCr pin with a ground and polished spherical bearing surface (radius 28 mm) against a conventional, gamma-sterilized UHMWPE disk in serum lubrication. The biaxial motion, consisting of x and y translations, and the load was non-cyclic. Relative to the disk, the center of contact wandered within a circle of 10mm diameter, and the average sliding velocity was 15.5mm/s (ranging from 0 to 31 mm/s). The load varied non-cyclically between 0 and 142 N (average 73 N). In the 60-day test with 16 similar wear couples, moderate adhesive wear, the principal wear mechanism of a well-functioning prosthetic knee, dominated. This showed as a burnished, circular wear mark (diameter 13.2mm, area 137 mm(2)). The wear factor was 2.04 ± 0.03 × 10(-6)mm(3)/Nm (mean ± 95 percent confidence limit). For the first time a truly multidirectional, realistic and uniform, large capacity pin-on-disk simulation of knee wear mechanisms was implemented.

The distal radius fracture (DRF) is a particularly dominant injury of the wrist, commonly resulting from a forward fall on an outstretched hand. In an attempt to reduce the prevalence, costs, and potential long-term pain/deformities associated with this injury, in vivo and in vitro investigations have sought to classify the kinematics and kinetics of DRFs. In vivo forward fall work has identified a preparatory muscle contraction that occurs in the upper extremity prior to peak impact force. The present investigation constitutes the first attempt to systematically determine the effect of static muscle forces on the fracture threshold of the distal radius in vitro. Paired human cadaveric forearm specimens were divided into two groups, one that had no muscle forces applied (i.e., right arms) and the other that had muscle forces applied to ECU, ECRL, FCU and FCR (i.e., left arms), with magnitudes based on peak muscle forces and in vivo lower bound forward fall activation patterns. The specimens were secured in a custom-built pneumatic impact loading device and subjected to incremental impacts at pre-fracture (25 J) and fracture (150 J) levels. Similar fracture forces (6565 (866)N and 8665 (5133)N), impulses (47 (6)Ns and 57 (30)Ns), and energies (152 (38)J and 144 (45)J) were observed for both groups of specimens (p>0.05). Accordingly, it is suggested that, at the magnitudes presently simulated, muscle forces have little effect on the way the distal radius responds to forward fall initiated impact loading.

The purpose of this study was to develop a multivariate distal radius injury risk prediction model that incorporates dynamic loading variables in multiple directions, and interpret the distal radius failure data in order to establish injury probability thresholds. Repeated impacts with increasing intensity were applied to the distal third of eight human cadaveric radius specimens (mean (SD) age=61.9 (9.7)) until injury occurred. Crack (non-propagating damage) and fracture (specimen separated into at least two fragments) injury events were recorded. Best subsets analysis was performed to find the best multivariate injury risk model. Force-only risk models were also determined for comparison. Cumulative distribution functions were developed from the parameters of a Weibull analysis and the forces and risk scores (i.e., values calculated from the injury risk models) from 10% to 90% probability were calculated. According to the adjusted R(2), variance inflation factor and p-values, the model that best predicted the crack event included medial/lateral impulse, Fz load rate, impact velocity and the natural logarithm of Fz (Adj. R(2)=0.698), while the best predictive model of the fracture event included medial/lateral impulse, impact velocity and peak Fz (Adj. R(2)=0.845). The multivariate models predicted injury risk better than both the Fz-only crack (Adj. R(2)=0.551) and fracture (Adj. R(2)=0.293) models. Risk scores of 0.5 and 0.6 corresponded to 10% failure probability for the crack and fracture events, respectively. The inclusion of medial/lateral impulse and impact velocity in both crack and fracture models, and Fz load rate in the crack model, underscores the dynamic nature of these events. This study presents a method capable of developing a set of distal radius fracture prediction models that can be used in the assessment and development of distal radius injury prevention interventions.

High-resolution in vivo bone micro-architecture assessment, as possible now for the distal forearm, in combination with bone remodelling simulation algorithms could, eventually, predict patient-specific bone morphology changes. To simulate load-adaptive bone remodelling, however, physiological loading conditions must be defined. In this paper we test a previously developed algorithm to estimate such physiological loading conditions from the bone micro-architecture. The aims of this study were to investigate if realistic boundary forces and moments are predicted for the scanned distal radius section and how these predicted forces and moments should be distributed to the scanned section in order to obtain a load transfer similar to that in situ. Images at in vivo resolution were generated for the clinically measured section of nine distal radius cadaver bones, converted to micro-finite element models and used for load estimation. Models of the full distal radius were created to analyse tissue loading distributions of the sections in situ. It was found that predicted forces and moments at the boundaries of the scanned region varied considerably but, when translated to equivalent radiocarpal joint forces, agreed well with values reported in the literature. Bone tissue loading distribution was in best agreement with in situ distributions when loading was applied to an extra layer of material at both ends of the clinical scan region. The agreement of the predicted loading to previous studies and the wide range of predicted loading values indicate that subject-specific bone loading estimation is possible and necessary.

Dual energy X-ray absorptiometry (DXA) is the standard for assessing fragility fracture risk using areal bone mineral density (aBMD), but only explains 60-70% of the variation in bone strength. High-resolution peripheral quantitative computed tomography (HR-pQCT) provides 3D-measures of bone microarchitecture and volumetric bone mineral density (vBMD), but only at the wrist and ankle. Finite element (FE) models can estimate bone strength with 86-95% precision. The purpose of this study is to determine how well vBMD and FE bone strength at the wrist and ankle relate to fracture strength at the hip and spine, and to compare these relationships with DXA measured directly at those axial sites. Cadaveric samples (radius, tibia, femur and L4 vertebra) were compared within the same body. The radius and tibia specimens were assessed using HR-pQCT to determine vBMD and FE failure load. aBMD from DXA was measured at the femur and L4 vertebra. The femur and L4 vertebra specimens were biomechanically tested to determine failure load. aBMD measures of the axial skeletal sites strongly correlated with the biomechanical strength for the L4 vertebra (r=0.77) and proximal femur (r=0.89). The radius correlated significantly with biomechanical strength of the L4 vertebra for vBMD (r=0.85) and FE-derived strength (r=0.72), but not with femur strength. vBMD at the tibia correlated significantly with femoral biomechanical strength (r=0.74) and FE-estimated strength (r=0.83), and vertebral biomechanical strength for vBMD (r=0.97) and FE-estimated strength (r=0.91). The higher correlations at the tibia compared to radius are likely due to the tibia's weight-bearing function.

Colles’ fracture, a transverse fracture of the distal radius bone, is one of the most frequently observed osteoporotic fractures resulting from low energy or traumatic events, associated with low and high strain rates, respectively. Although experimental studies on Colles’ fracture were carried out at various loading rates ranging from static to impact loading, there is no systematic study in the literature that isolates the influence of strain rate on Colles’ fracture load. In order to provide a better understanding of fracture risk, the current study combines experimental material property measurements under varying strain rates with computational modeling and presents new information on the effect of strain rate on Colles’ fracture. The simulation results showed that the Colles’ fracture load decreased with increasing strain rate with a steeper change in lower strain rates. Specifically, strain rate values (0.29 s−1) associated with controlled falling without fracture corresponded to a 3.7% reduction in the fracture load. On the other hand, the reduction in the fracture load was 34% for strain rate of 3.7 s−1 reported in fracture inducing impact cadaver experiments. Further increase in the strain rate up to 18 s−1 lead to an additional 22% reduction. The most drastic reduction in fracture load occurs at strain rates corresponding to the transition from controlled to impact falling. These results are particularly important for the improvement of fracture risk assessment in the elderly because they identify a critical range of loading rates (10–50 mm/s) that can dramatically increase the risk of Colles’ fracture.

Total disc arthroplasty (TDA) can be used to replace a degenerated intervertebral disc in the spine. There are different designs of prosthetic discs, but one of the most common is a ball-and-socket combination. Contact between the bearing surfaces can result in high frictional torque, which can then result in wear and implant loosening. This study was designed to determine the effects of ball radius on friction. Generic models of metal-on-metal TDA were manufactured with ball radii of 10, 12, 14 and 16 mm, with a radial clearance of 0.015 mm. A simulator was used to test each sample in flexion–extension, lateral bending and axial rotation at frequencies of 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 Hz under loads of 50, 600, 1200 and 2000 N, in new born calf serum. Frictional torque was measured and Stribeck curves were plotted to illustrate the lubrication regime in each case. It was observed that implants with a smaller ball radius showed lower friction and showed boundary and mixed lubrication regimes, whereas implants with larger ball radius showed boundary lubrication only. This study suggests designing metal-on-metal TDAs with ball radius of 10 or 12 mm, in order to reduce wear and implant loosening.

Type 1 Gaucher disease (GD) is an autosomal recessive lysosomal storage disease, affecting bone metabolism, structure and strength. Current bone assessment methods are not ideal. Semi-quantitative MRI scoring is unreliable, not standardized, and only evaluates bone marrow. DXA BMD is also used but is a limited predictor of bone fragility/fracture risk. Our purpose was to measure trabecular bone microarchitecture, as a biomarker of bone disease severity, in type 1 GD individuals with different GD genotypes and to apply machine learning based analytics to discriminate between GD patients and healthy individuals. Micro-MR imaging of the distal radius was performed on 20 type 1 GD patients and 10 healthy controls (HC). Fifteen stereological and textural measures (STM) were calculated from the MR images. General linear models demonstrated significant differences between GD and HC, and GD genotypes. Stereological measures, main contributors to the first two principal components (PCs), explained ~50% of data variation and were significantly different between males and females. Subsequent PCs textural measures were significantly different between GD patients and HC individuals. Textural measures also significantly differed between GD genotypes, and distinguished between GD patients with normal and pathologic DXA scores. PCA and SVM predictive analyses discriminated between GD and HC with maximum accuracy of 73% and area under ROC curve of 0.79. Trabecular STM differences can be quantified between GD patients and HC, and GD sub-types using micro-MRI and machine learning based analytics. Work is underway to expand this approach to evaluate GD disease burden and treatment efficacy.

Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical–experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young’s modulus for cortex, density–modulus relationship for trabecular bone and Poisson’s ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R2 values of the measured strains versus load under three-point bending and torsion were 0.96–0.99 and 0.61–0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from −6% to 7% under bending and from −37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P

Nanoindentation has been widely used as a means to measure the micro-mechanical properties of bone and to predict the macroscopic properties. The role of indent depth and indenter tip geometry in measuring the hierarchical properties of bone tissue was explored experimentally using a range of spherical indenter tips of R=5, 25, 65, and 200 μm. Nanoindentation arrays, not targeted to fall on specific structures or locations, enabled statistical sampling of osteons within PMMA-embedded, bovine, cortical bone on a single sample to a range of maximum displacements (minimum of 100 nm and maximum of 2000 nm). Elastic finite element models were then utilized to isolate the contributions of indenter tip radius, contact area, and position within the lamellar structure in comparison to the experimental results. For a small, R=5 μm indenter tip, indentation modulus consistently increased with contact depth and increased plastic deformation, resulting in an artificial increase in elastic properties. While larger radius tips (R=25, 65, and 200 μm) did not enable evaluation of a high spatial resolution on the surface, they produced data that was representative of the lower load and contact depth measurements with the smaller tip. However the sensitivity to mechanical property variations across the 2-D surface of the material was lost with increase in indenter tip size. Correspondingly, measurement variance was also decreased as the volume contributing to the indent response represented an average of surface roughness, varying mineral content, defects, and underlying tissue type and structure.

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 data sets 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.

A simple model of the bicycle drive system with a non-circular front chain ring is proposed and an algorithm is devised for calculation of the corresponding Gear Ratio As a Function Of Crank Angle (GRAFOCA). It is shown that the true effective radius of the chain ring is always the perpendicular distance between the crank axis and the line through the chain segment between the chain ring and the cog. It is illustrated that the true effective radius of the chain ring at any crank angle may differ substantially from the maximum vertical distance between the crank axis and the chain ring circumference that is used as a proxy for the effective chain ring radius in several studies; in particular, the crank angle at which the effective chain ring radius is maximal as predicted from the latter approach may deviate by as much as 0.30. rad from the true value. The algorithm proposed may help in designing chain rings that achieve the desired GRAFOCA. © 2013 Elsevier Ltd.

Recent studies have determined a seemingly consistent feature of able-bodied level ground walking termed the roll-over shape, which is the effective rocker (cam) shape that the lower limb system conforms to between heel contact and contralateral heel contact during walking (first half of the gait cycle). The roll-over shape has been found to be largely unaffected by changes in walking speed, load carriage, and shoe heel height. However, it is unclear from previous studies whether persons are controlling their lower limb systems to maintain a consistent roll-over shape or whether this finding is a byproduct of their attempt to keep ankle kinematic patterns similar during the first half of the gait cycle. We measured the ankle-foot roll-over shapes and ankle kinematics of eleven able-bodied subjects while walking on rocker shoes of different radii. We hypothesized that the ankle flexion patterns during single support would change to maintain a similar roll-over shape. We also hypothesized that with decreasing rocker shoe radii, the difference in ankle flexion between the end and beginning of single support would decrease. Our results supported these hypotheses. Ankle kinematics were changed significantly during walking with the different rocker shoe radii (p < 0.001), while ankle-foot roll-over shape radii (p = 0.146) and fore-aft position (p = 0.132) were not significantly affected. The results of this study have direct implications for designers of ankle-foot prostheses, orthoses, walking casts/boots, and rocker shoes. The results may also be relevant to researchers studying control of human movements.

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 (r(2)=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.

Knowledge of internal stress-strain in bone tissue is important for clinical diagnosis and remedies. The inorganic mineral phase of apatite crystals in bone composite, because of its crystalline nature, provides a reliable way of measurement through X-ray diffraction system. Use of a two-dimensional detector, imaging plate, is considered to expedite the process with much more information, hence, is widely applied in the study of organization, stress, strain, etc for crystalline substance. The distortion of Debye rings in the image obtained by imaging plate can be directly related to the deformation in lattice plane of the crystals. Since X-ray diffraction method involves measurement at nano-level, proper focus on the extraction of data and corresponding analysis is needed. In the current work, we considered weighted average value of intensity to locate radius vectors along azimuthal direction in the diffracted rings from the primary array of digital data in steps of pixels. The widely applied approaches for profile shift measurement - peak-shift and full width at half maximum (FWHM) of a peak, and shift of centre of gravity of profile – were compared with a new concept of segmental-shift (SS) proposed previously by the authors. We observed reliable and effective outcomes with higher precision in the consideration of SS while using imaging plate as a detector. Our approach in this work for intensity integration and radius vector positioning especially add precision in such applications.

Body segment parameters are required when researching joint kinetics using inverse dynamics models. However, the only regression equations for estimating pediatric body segment parameters across a wide age range were developed, using photogrammetry, based on 12 boys and have not been validated to date (Jensen, R.K., 1986. Body segment mass, radius and radius of gyration proportions of children. Journal of Biomechanics 19, 359–368). To assess whether these equations could validly be applied to girls, we asked whether body segment parameters estimated by the equations differ from parameters measured using a validated magnetic resonance imaging (MRI) method. If so, do the differences cause significant differences in joint kinetics during normal gait? Body segment parameters were estimated from axial MRIs of the left thigh and shank of 10 healthy girls (9.6±0.9 years) and compared to those from Jensen's equations. Kinematics and kinetics were collected for 10 walking trials. Extrema in hip and knee moments and powers were compared between the two sets of body segment parameters. With the exception of the shank mass center and radius of gyration, body segment parameters measured using MRI were significantly different from those estimated using regression equations. These systematic differences in body segment parameters resulted in significant differences in sagittal-plane joint moments and powers during gait. Nevertheless, it is doubtful that even the greatest differences in kinetics are practically meaningful (0.3%BW×HT and 0.7%BW×HT/s for moments and power at the hip, respectively). Therefore, body segment parameters estimated using Jensen's regression equations are a suitable substitute for more detailed anatomical imaging of 8–10-year-old girls when quantifying joint kinetics during gait.

The Leap Motion Controller (LMC) is a low-cost, markerless motion capture device that tracks hand, wrist and forearm position. Integration of this technology into healthcare applications has begun to occur rapidly, making validation of the LMC׳s data output an important research goal. Here, we perform a detailed evaluation of the kinematic data output from the LMC, and validate this output against gold-standard, markered motion capture technology. We instructed subjects to perform three clinically-relevant wrist (flexion/extension, radial/ulnar deviation) and forearm (pronation/supination) movements. The movements were simultaneously tracked using both the LMC and a marker-based motion capture system from Motion Analysis Corporation (MAC). Adjusting for known inconsistencies in the LMC sampling frequency, we compared simultaneously acquired LMC and MAC data by performing Pearson׳s correlation (r) and root mean square error (RMSE). Wrist flexion/extension and radial/ulnar deviation showed good overall agreement (r=0.95; RMSE=11.6°, and r=0.92; RMSE=12.4°, respectively) with the MAC system. However, when tracking forearm pronation/supination, there were serious inconsistencies in reported joint angles (r=0.79; RMSE=38.4°). Hand posture significantly influenced the quality of wrist deviation (P

Laboratory mice provide a versatile experimental model for studies of skeletal biomechanics. In order to determine the strength of the mouse skeleton, mechanical testing has been performed on a variety of bones using several procedures. Because of differences in testing methods, the data from previous studies are not comparable. The purpose of this study was to determine which long bone provides the values closest to the published material properties of bone, while also providing reliable and reproducible results. To do this, the femur, humerus, third metatarsal, radius, and tibia of both the low bone mass C57BL/6H (B6) and high bone mass C3H/HeJ (C3H) mice were mechanically tested under three-point bending. The biomechanical tests showed significant differences between the bones and between mouse strains for the five bones tested (p0.05). Computational models of the femur, metatarsal, and radius were developed to visualize the types of measurement error inherent in the three-point bending tests. The models demonstrated that measurement error arose from local deformation at the loading point, shear deformation and ring-type deformation of the cylindrical cross-section. Increasing the aspect ratio (bone length/width) improved the measurement of Young's modulus of the bone for both mouse strains (p0.01). Bones with the highest aspect ratio and largest cortical thickness to radius ratio were better for bending tests since less measurement error was observed in the computational models. Of the bones tested, the radius was preferred for mechanical testing because of its high aspect ratio, minimal measurement error, and low variability.

The objective of this work was to determine bone loading conditions that, when applied to a finite element model, would best reproduce the in vivo strain field as measured by surface-mounted strain rosettes. The present study adopts the basic mathematical approach to load reconstruction introduced by Weinans and Blankevoort (J. Biomech. 28 (1995) 739) who determined the relationship between applied loads and bone strain distribution using ex vivo calibration testing. Our method eliminates the need for subsequent ex vivo calibration tests by instead substituting a computational calibration procedure. This first application of the method is with in vivo strains on the canine forelimb during gait (Coleman et al., J. Biomech. 35 (2002) 1677), but with further refinements the method could be used to reconstruct the in vivo loading conditions in living subjects.

The capitate is often considered the "keystone" of the carpus, not simply because of its central and prominent position in the wrist, but also because of its mechanical interactions with neighboring bones. The purpose of this study was to determine in vivo three-dimensional capitate kinematics. Twenty uninjured wrists were investigated using a recently developed, non-invasive markerless bone registration (MBR) technique. Surface contours of the capitate, third metacarpal and radius were extracted from computed tomography images of seven wrist positions and the three-dimensional motions of the capitate and third metacarpal were calculated with respect to the radius in wrist flexion-extension and radio-ulnar deviation. We found that in vivo capitate motion does not simply occur about a single pivot point like a universal joint, as demonstrated by non-intersecting rotation axes for different capitate motions. The distance between flexion and ulnar deviation axes was 3.9+/-2.0 mm, and the distance between extension and ulnar deviation axes was 3.9+/-1.4 mm. Furthermore, capitate axes for males tended to be located more distally than axes for females. However, we believe that this result is related to subject size and not to gender. We also found that there is minimal relative motion between the capitate and third metacarpal during these in vivo wrist motions. These findings demonstrate the complexity of capitate kinematics, as well as the different mechanisms through which wrist flexion, extension, radial deviation and ulnar deviation occur.

The purpose of this study was to estimate the relation of some noninvasively derived mechanical characteristics of radial bone including architectural parameters for bone strength to grip strength and muscle cross-section. Sixty-three males between 21 and 78yr of age and 101 females between 18 and 80yr of age were measured at the nondominant forearm using peripheral quantitative computed tomography (pQCT). We assessed the integral bone mineral density (BMD(I)) and content (BMC(I)) by pQCT at the distal and at the mid-shaft radius. Integral bone area (Area(I)), cortical thickness (C-th), and a newly proposed index for bone strength; the stress-strain index (SSI) were also calculated. The dynamometrically measured maximum grip strength was taken as a mechanical loading parameter and muscle cross-section as a substitute for it. Sex, grip strength, BMC(I) and BMD(I) (distal radius) were identified in a multiple regression analysis to significantly predict bone strength as expressed by SSI, after adjusting for all other independent variables, including age and sex (p0.0001). Grip strength was closest related to age, sex, BMD(I) and SSI(p) of the distal radius. The cross-sectional area of muscle was not significantly determining the grip strength within the analysis model. In conclusion, our results suggested that architectural parameters at the distal radius were better related to grip strength than to cross-sectional muscle area in both males and females. Maximum muscle strength as estimated by grip strength might be a stronger determinant of mechanical characteristics of bones as compared with cross-sectional muscle area.

A method for measuring three-dimensional kinematics that incorporates the direct cross-registration of experimental kinematics with anatomic geometry from Computed Tomography (CT) data has been developed. Plexiglas registration blocks were attached to the bones of interest and the specimen was CT scanned. Computer models of the bone surface were developed from the CT image data. Determination of discrete kinematics was accomplished by digitizing three pre-selected contiguous surfaces of each registration block using a three-dimensional point digitization system. Cross-registration of bone surface models from the CT data was accomplished by identifying the registration block surfaces within the CT images. Kinematics measured during a biomechanical experiment were applied to the computer models of the bone surface. The overall accuracy of the method was shown to be at or below the accuracy of the digitization system used. For this experimental application, the accuracy was better than +/-0.1mm for position and 0.1 degrees for orientation for linkage digitization and better than +/-0.2mm and +/-0.2 degrees for CT digitization. Surface models of the radius and ulna were constructed from CT data, as an example application. Kinematics of the bones were measured for simulated forearm rotation. Screw-displacement axis analysis showed 0.1mm (proximal) translation of the radius (with respect to the ulna) from supination to neutral (85.2 degrees rotation) and 1.4mm (proximal) translation from neutral to pronation (65.3 degrees rotation). The motion of the radius with respect to the ulna was displayed using the surface models. This methodology is a useful tool for the measurement and application of rigid-body kinematics to computer models.

In order to perform cadaveric biomechanical studies of the human forearm and distal radio-ulnar joint, a dynamic simulator has been constructed. The device is based upon a Plexiglas frame, to which the ulna is secured in a vertical orientation and the humerus in a horizontal orientation. The hand is secured in a sliding bar linkage to a stepper-motor that is used to rotate the forearm. The tendons to be loaded are connected to pneumatic actuators that provide agonist and antagonist muscle loading resulting in torque along the forearm axis. The muscle loading profiles and magnitudes are programmable as a function of the pronation-supination position and direction. A magnetic tracking system is used to collect three-dimensional kinematics data of up to four segments, in conjunction with the muscle tendon loads, forearm torque and other prescribed experimental measures. All functions are under PC control using custom software written with LabVIEW (National Instruments, Austin, TX). For the DRUJ testing, the validity of the tendon loading protocol to produce physiologic torque/rotation patterns was verified using in vivo data. The relationship of individual muscle forces to forearm torque was determined by a cadaveric study.

The Knoop indenter has been used to characterise fully the Knoop microhardness (H(K)) anisotropy of compact bone. 2120 indentations were performed on mature ovine radii and a linear relationship was found between H(K) and the angle between the major diagonal of the indenter and the lamella boundaries (p<

Bearing surfaces of total condylar knees which are designed with a high degree of conformity to produce low stresses in the polyethylene tibial insert may be overconstrained. This study determines femoral and tibial bearing surface geometries which will induce the least destructive fatigue mechanisms in the polyethylene whilst conserving the laxity of the natural knee. Sixteen knee designs were generated by varying four parameters systematically to cover the range of contemporary knee designs. The parameters were the femoral frontal radius (30 or 70 mm), the difference between the femoral and tibial frontal radii (2 or 10 mm), the tibial sagittal radius (56 or 80 mm) and the posterior-distal transition angle (-8 or -20 degrees), which is the angle at which the small posterior arc of the sagittal profile transfers to the larger distal arc. Rigid body analyses determined the anterior-posterior and rotational motions as well as the contact points during the stance phase of gait for the different designs. In addition, a damage function which accumulated the fluctuating maximum shear stresses was used to predict the susceptibility to delamination wear of the polyethylene (damage score). This study predicted that of the 16 designs, the knee with a frontal radius of 70 mm, a difference in femoral and tibial frontal radii of 2 mm, a tibial sagittal radius of 80 mm and a posterior distal transition angle of -20 degrees would satisfy the conflicting needs of both resistance to delamination wear and natural kinematics.

Prevention of osteoporotic bone fractures requires accurate diagnostic methods to detect the increase in bone fragility at an early stage of osteoporosis. However, today's bone fracture risk prediction, primarily based on bone density measurement, is not sufficiently precise. There is increasing evidence that, in addition to bone density, also the bone microarchitecture and its mechanical loading conditions are important factors determining the fracture risk. Recently, it has been shown that new high-resolution imaging techniques in combination with new computer modeling techniques based on the finite-element (FE) method can account for these additional factors. These techniques might provide information that is more relevant for the prediction of bone fracture risk. So far, however, these new imaged-based FE techniques have not been feasible in-vivo. The objectives of this study were to quantify the load transfer through the trabecular network in a distal radius using a computer model based on in-vivo high-resolution images and to determine if common regions of fractures can be explained as a result of high tissue loading in these regions. The left distal radius and the two adjacent carpal bones of a healthy volunteer were imaged using a high-resolution three-dimensional CT system providing an isotropic resolution of 165 μm. The bone representation was converted into a FE-model that was used to calculate stresses and strains in the trabecular network. The two carpal bones were loaded using different load ratios (for each load case 1000 N in total) representing impact forces on the hand either in near-neutral position or ulnar/radial deviation. The load transfer through the trabecular network of the radius was characterized by the tissue strain energy density (SED) distribution for all load cases. It was found that the distribution of the tissue loading depends on the ratio of the forces acting on the carpal bones. For all load cases the higher SED values (on average: 0.02±0.08 (S.D.) N mm −2 ) are found in a 10 mm region adjacent to the articular surface which corresponds well with the region where Colles- or Chauffeur-fractures occur. We expect that, eventually, this new approach can lead to a better prediction of the fracture risk than methods based on bone density alone since it accounts for the bone microstructure as well as its loading conditions.