Accuracy of determining the point of force application with piezoelectric force plates

The accuracy of determining the point of force application with piezoelectric force plates, as specified by the manufacturer, is lower than needed for certain applications. The purpose of this study was to evaluate the accuracy of a commonly used plate (KISTLER type 9287) and to improve it by proposing a correction algorithm. Forces were applied to a wooden board, supported in one corner by a stylus that rested on the force plate. To determine the influence of position and magnitude of the force vector, the stylus was placed on 117 different locations, and calibrated masses were used to exert vertical forces between 0 and 2000 N. To determine the influence of loading rate, dynamic tests were performed in which a subject ran across the board. In static tests at a given stylus position with actual coordinates x (short axis) and y (long axis), it was found that the calculated coordinates x and y of the point of force application had virtually constant values at forces above 1000 N. In dynamic tests, oscillations could occur in x and y with an amplitude of more than 20 mm. When these were avoided or removed by filtering, static and dynamic tests at a given stylus position showed the same values for x and y at forces above 1000 N. Across stylus positions, the errors x-x and y-y (measured at 1600 N) ranged from -20 to +20 mm. The average over 117 points of the absolute errors magnitude of x-x and magnitude of y-y amounted to 3.5 and 6.3 mm, respectively (mean values of three plates).(ABSTRACT TRUNCATED AT 250 WORDS)     

Enhancements in the accuracy of the center of pressure (COP) determined with piezoelectric force plates are dependent on the load distribution

Errors up to +/- 30 mm in determining the COP with piezoelectric force plates have been reported in the literature. To compensate for these errors, correction formulas were proposed, based on measurements with single point loads. In this paper, it will be shown that the errors in the COP depend on the load distribution. Two examples are presented: (1) simulated balance study, and (2) different pressure patterns during walking. Accurate corrections can only be made for forces distributed over a small area. Errors are expected to be overcompensated if there are only a few pressure peaks separated by large distances. These errors can be as large as the statistical errors (5.8 +/- 3.7 mm) after compensation. For certain situations, it is probably better not to use correction formulas.     

Compensation for inertial and gravity effects in a moving force platform

Force plates for human movement analysis provide accurate measurements when mounted rigidly on an inertial reference frame. Large measurement errors occur, however, when the force plate is accelerated, or tilted relative to gravity. This prohibits the use of force plates in human perturbation studies with controlled surface movements, or in conditions where the foundation is moving or not sufficiently rigid. Here we present a linear model to predict the inertial and gravitational artifacts using accelerometer signals. The model is first calibrated with data collected from random movements of the unloaded system and then used to compensate for the errors in another trial. The method was tested experimentally on an instrumented force treadmill capable of dynamic mediolateral translation and sagittal pitch. The compensation was evaluated in five experimental conditions, including platform motions induced by actuators, by motor vibration, and by human ground reaction forces. In the test that included all sources of platform motion, the root-mean-square (RMS) errors were 39.0 N and 15.3 N m in force and moment, before compensation, and 1.6 N and 1.1 N m, after compensation. A sensitivity analysis was performed to determine the effect on estimating joint moments during human gait. Joint moment errors in hip, knee, and ankle were initially 53.80 N m, 32.69 N m, and 19.10 N m, and reduced to 1.67 N m, 1.37 N m, and 1.13 N m with our method. It was concluded that the compensation method can reduce the inertial and gravitational artifacts to an acceptable level for human gait analysis.     

Atomic force pulling: probing the local elasticity of the cell membrane

We present a novel approach, based on atomic force microscopy, for exploring the local elastic properties of the membrane-skeleton complex in living cells. Three major elements constitute the basis for the proposed method: (1) pulling the cell membrane by increasing the adhesion of the tip to the cell surface provided via appropriate tip modification; (2) measuring force-distance curves with emphasis on selecting the appropriate withdrawal regions for analysis; (3) fitting of the theoretical model for axisymmetric bending of an annular thick plate to the experimental curve in the withdrawal region, prior to the detachment point of the tip from the cell membrane. This approach, applied to human erythrocytes, suggests a complimentary technique to the commonly used methods. The local use of this methodology for determining the bending modulus of the cell membrane of the human erythrocyte yields a value of (2.07+/-0.32) x 10(-19) J.     

Influence of sensor size on the accuracy of in-vivo ligament and tendon force measurements.

In-vivo tendon forces are commonly measured using transducers, which detect tension in the tendon fibers. A poorly understood source of measurement errors is the difference in stress distribution within the tendon between experimental and transducer calibration conditions. The objective of this study was to investigate this source of error, and to determine whether these errors could be minimized by proper selection of transducer size. The study was conducted using the infrapatellar ligament (patellar tendon) of New Zealand White rabbits. Tendon force was measured with two different size implantable force transducers (IFTs), one Wide and one Narrow, and by a strain gaged load cell in series with the tendon. Tests were conducted at five different loading conditions selected to produce five different stress distributions within the tendon. One loading condition corresponded to a typical post-experiment calibration, and the data from that condition were used to develop a calibration equation for the transducer. The errors that resulted from using this calibration were determined by comparing the tendon force measured by the in-series load cell with the force predicted from the IFT output using the calibration equation. Changes in stress distribution produced measurement errors up to 64 N with the Narrow IFT but only 24 N with the Wide IFT. We found the measurement error was dependent on sensor width. Our results support the hypothesis that measurement errors can be caused by differences in tendon stress distribution between calibration and experimental conditions. We further showed that these errors can be minimized by using an IFT, which samples the tension in a large percentage of the tendon fibers. Information from this study can be used for selection of an appropriately sized implantable force transducer for measuring tendon and ligament force.     

Calibration of measured center of pressure of a new stairway design for kinetic analysis of stair climbing

A stairway that allows the collection of kinetic data is essential for biomechanical studies on stair climbing. There is a need to validate the measured center of pressure (COP) on the surface of a stair in order to verify the accuracy of the calculation of joint kinetics. The purpose of this study was to validate a new stairway design for kinetic analysis of stair climbing through a calibration and error analysis of the COP obtained from this system. The new stairway design allows the collection of kinetic data for multiple steps without any constraint to foot placement. Known vertical forces were applied to known locations on the surface of each stair and each force plate. Multiple regression analyses were conduced to determine the distribution pattern of the error in the measured COP. It was found that the error in the COP was a function of location on the stair or force plate. The magnitude of the vertical force had no significant effect on the error in the measured COP. The distribution pattern of the error in the measured COP on the force plates used in this study matched the results in the literature. A healthy female subject was used as the subject in a stair climbing test. The error in the measured COP had a significant effect on the calculated joint resultant moments, especially the abduction-adduction and internal-external rotation moments. The correction of these errors should make the kinetic calculation in stair climbing more accurate.     

The validation of a portable force plate for measuring force-time data during jumping and landing tasks

The purpose of this study was to determine the reliability and validity of a portable force plate when analyzing jumping and landing tasks. Subjects performed 3 drop vertical jumps and 3 drop landings on both a standard strain gauge laboratory force plate and a portable force plate. In contrast to typical laboratory installed force plates, the portable 6-component force plate can be easily transported and used onsite at various training or data collection sites and incorporates Hall effect technology. The measured parameters included maximum force and time to maximum force for initial stance of the both tests, maximum takeoff force, and time to maximum takeoff force for the drop vertical jump. The Pearson correlation coefficients for the drop landing and the drop vertical jump for maximum force (r = 0.942, r = 0.940), time to maximum force (r = 0.891, r = 0.920) and for drop jump maximum jumping force (r = 0.971), and time to maximum takeoff force (r = 0.917) were all high and indicate that the force data collected by a resistor-type portable force plate provide similar measures to a standard strain-gauge laboratory force plate. Additionally, the within session reliability of the drop landing and the drop vertical jump measured by the portable force plate showed high interclass correlation coefficients for examined variables of 0.979 and 9.67 for maximum landing force and 0.917 and 0.920 for time to maximum landing force, respectively. The interclass correlation coefficients for the maximum takeoff force and time to maximum takeoff force during the drop vertical jump were 0.991 and 0.86. The results indicate the force and timing measurements from the portable force plate were both valid and reliable. Use of the portable force plate may facilitate methods of force measurement that can be applied out into the field and therefore a valuable tool for on site landing and jump force measurements in a variety of settings for large numbers of subjects.     

Validation of the Boussinesq equation for use in traction field determination

Cell traction force plays an important role in many biological processes. Several traction force microscopy methods have been developed to determine cell traction forces based on the Boussinesq solution. This approach, however, is rooted in a half-space assumption. The purpose of this study was to determine the error induced in the half-space assumption using a finite element method (FEM). It demonstrates that displacement error between the FEM and the Boussinesq equation can be used to measure the accuracy of the Boussinesq equation, although singularity exists in the loading point. For one concentrated force, significant difference between the FEM and the Boussinesq equation occurs in the whole field; this difference decreases with an increase in the plate thickness. However, in the case of the balanced forces, the offset of the balanced forces decreases the errors in the middle area. Overall, this study demonstrates that increasing the thickness of the polyacrylamide gel is important for reducing the error of the Boussinesq equation when determining the displacement field of the gel under loads.     

An analysis of the measurement principle of smart brackets for 3D force and moment monitoring in orthodontics

Measuring the three-dimensional (3D) force-moment (F/M) systems applied for correcting tooth malposition is highly desirable for accurate spatial control of tooth movement and for reducing traumatic side effects such as irreversible root resorption. To date, suitable tools for monitoring the applied F/M system during therapy are lacking. We have previously introduced a true-scale orthodontic bracket with an integrated microelectronic stress sensor system for 3D F/M measurements on individual teeth with a perspective for clinical application. The underlying theoretical concept assumes a linear correlation between externally applied F/M systems and mechanical stresses induced within the smart bracket. However, in combined applications of F/M components the actual wire-bracket contacts may differ from those caused by separate applications of corresponding individual F/M components, thus violating the principle of linear superposition of mechanical stresses. This study systematically evaluates this aspect using finite element (FE) simulations and measurements with a real smart bracket. The FE analysis indicated that variability in the wire-bracket contacts is a major source for measurement errors. By taking the critical F/M combinations into account in the calibration of the real smart bracket, we were able to reduce the mean measurement error in five of the six F/M components to values <0.12 N and <0.04 N cm. Bucco-lingually directed forces still showed mean errors up to 0.21 N. Improving the force measurement accuracy and integrating components for telemetric energy and data transfer are the next steps towards clinical application of intelligent orthodontic appliances based on smart brackets.     

Theoretical Study on the Dynamic Behavior of a Plate-Like Micro-Cantilever with Multiple Particles Attached

In this study, the dynamic characteristics of a plate-like micro-cantilever beam attached with multiple concentrated masses are studied. The vibration modes of the cantilever plate are represented by combinations of beam functions. Using classical mechanics (the effect of size is not considered) and the corrected Cosserat’s theorem (the effect of size is considered), we employ the Lagrange equations to establish a dynamic model of the plate-like micro-cantilever beam attached with multiple concentrated masses. The accuracy of the model proposed in this paper is verified by comparing with the results of published literature. Then, the natural frequencies of the cantilever plates are calculated with self-compiled algorithms, and the results of the plates with 1–5 masses are displayed. The results are in high accordance with the exact solution, and all errors are within 0.5%. The analysis shows that the proposed model and analysis method converges quickly and is highly efficient. In addition, the effects of characteristic lengths, Poisson''s ratios and plate thickness on the micro-cantilever plate’s resonant frequency for the first five modes are analyzed.     

Expansion of surface epithelium provides the major extrinsic force for bending of the neural plate.

Neurulation, formation of the neural tube, requires both intrinsic forces (i.e., those generated within the neural plate) and extrinsic forces (i.e., those generated outside the neural plate in adjacent tissues), but the precise origin of these forces is unclear. In this study, we addressed the question of which tissue produces the major extrinsic force driving bending of the neural plate. We have previously shown that 1) extrinsic forces are required for bending and 2) such forces are generated lateral to the neural plate. Three tissues flank the neural plate prior to its bending: surface epithelium, mesoderm, and endoderm. In the present study, we removed two of these layers, namely, the endoderm and mesoderm, underlying and lateral to the neural plate; bending still occurred, often with complete formation of a neural tube, although the latter usually rotated toward the side of tissue depletion. These results suggest that the surface epithelium, the only tissue remaining after microsurgery, provides the major extrinsic force for bending of the neural plate and that the mesoderm (and perhaps endoderm) stabilizes the neuraxis, maintaining its proper orientation and position on the midline.     

Fiberoptic measurement of tendon forces is influenced by skin movement artifact

Fiberoptic cables have previously been used for tendon force measurements in vivo. To measure forces in the Achilles tendon, a cable is passed mediolaterally through the skin and tendon, transverse to the loading axis. As the tendon is loaded, its fibers compress the cable and modulate the intensity of transmitted light, which can be related to tendon force by an in situ calibration. The relative movement between skin and tendon at the cable entry and exit sites may cause error by bending the cable and thus altering transducer output. Cadaver simulations of walking were conducted to compare fiberoptic measurements of Achilles tendon forces to known loads applied to the tendon by actuators attached in series. Force measurement errors, which were high when the skin was intact (RMS errors 24-81% peak forces), decreased considerably after skin removal (RMS errors 10-33% peak forces). The fiberoptic transducer is a useful tool for measurement of tendon forces in situ under natural loading conditions when skin can be removed, but caution should be exercised during in vivo use of this technique or under circumstances where skin is in contact with the fiberoptic cable at the insertion and exit sites.     

Minimizing pulling geometry errors in atomic force microscope single molecule force spectroscopy

In atomic force microscopy-based single molecule force spectroscopy (AFM-SMFS), it is assumed that the pulling angle is negligible and that the force applied to the molecule is equivalent to the force measured by the instrument. Recent studies, however, have indicated that the pulling geometry errors can drastically alter the measured force-extension relationship of molecules. Here we describe a software-based alignment method that repositions the cantilever such that it is located directly above the molecule's substrate attachment site. By aligning the applied force with the measurement axis, the molecule is no longer undergoing combined loading, and the full force can be measured by the cantilever. Simulations and experimental results verify the ability of the alignment program to minimize pulling geometry errors in AFM-SMFS studies.     

Design and experimental evaluation of adjustable bone plates for mandibular fracture fixation

Conventional bone plates are commonly used for surgical mandibular fracture fixation. Improper alignment between bone segments, however, can result in malocclusion. Current methods of fixation require a surgeon to visually align segments of bone and affix a metal plate using bone screws, after which little can be done to adjust alignment. A method of adjusting fracture alignment after plate placement, without screw removal, presents an improvement over costly and risky revision surgery. A modified bone plate has been designed with a deformable section to give surgeons the ability to reduce misalignments at the fracture site. The mechanics of deformation for various adjustment mechanisms was explored analytically, numerically, and experimentally to ensure that the adjustable plate is comparable to conventional bone plates. A static force of 358.8 N is required to deform the adjustable bone plate, compared with predicted values of 351 N using numerical simulation and 362 N using a simple beam theory. Dynamic testing was performed to simulate in vivo loading conditions and evaluate load-capacity in both deformed and un-deformed bone plates. Results indicate that bending stiffness of a rectangular bone plate is 709 N/mm, compared with 174 N/mm for an octagonal plate and 176 N/mm for standard plates. Once deformed, the rectangular and octagonal plates had a stiffness of 323 N/mm and 228 N/mm, respectively. Un-deformed and deformed adjustable bone plates have efficacy in bone segment fixation and healing.     

Calibration of EMG to force for knee muscles is applicable with submaximal voluntary contractions.

PURPOSE: In this study, the influence of using submaximal isokinetic contractions about the knee compared to maximal voluntary contractions as input to obtain the calibration of an EMG-force model for knee muscles is investigated. METHODS: Isokinetic knee flexion and extension contractions were performed by healthy subjects at five different velocities and at three contraction levels (100%, 75% and 50% of MVC). Joint angle, angular velocity, joint moment and surface EMG of five knee muscles were recorded. Individual calibration values were calculated according to [C.A.M. Doorenbosch, J. Harlaar, A clinically applicable EMG-force model to quantify active stabilization of the knee after a lesion of the anterior cruciate ligament, Clinical Biomechanics 18 (2003) 142-149] for each contraction level. RESULTS: First, the output of the model, calibrated with the 100% MVC was compared to the actually exerted net knee moment at the dynamometer. Normalized root mean square errors were calculated [A.L. Hof, C.A.N. Pronk, J.A. van Best, Comparison between EMG to force processing and kinetic analysis for the calf muscle moment in walking and stepping, Journal of Biomechanics 20 (1987) 167-187] to compare the estimated moments with the actually exerted moments. Mean RMSD errors ranged from 0.06 to 0.21 for extension and from 0.12 to 0.29 for flexion at the 100% trials. Subsequently, the calibration results of the 50% and 75% MVC calibration procedures were used. A standard signal, representing a random EMG level was used as input in the EMG force model, to compare the three models. Paired samples t-tests between the 100% MVC and the 75% MVC and 50% MVC, respectively, showed no significant differences (p>0.05). CONCLUSION: The application of submaximal contractions of larger than 50% MVC is suitable to calibrate a simple EMG to force model for knee extension and flexion. This means that in clinical practice, the EMG to force model can be applied by patients who cannot exert maximal force.     

A simple method to estimate force plate inertial components in a moving surface

Support surface perturbations are a common paradigm for the study of balance and postural control. Forces and moments acquired from force plates mounted on, or within, the moving surface will contain components resulting from the inertia of the force plate itself. These force plate inertial components must be removed in order to accurately estimate forces resulting from contact with the force plate. This is particularly important when these contact forces are to be used in further calculations, such as an inverse dynamics analysis of joint kinetics. An estimate of the FPIC can be derived using the kinematics of the moving surface and the inertial properties of the force plate. This technique allowed for a reduction of up to 85% of the peak and integrated FPIC acquired from AMTI (OR6-7) force plates during translations of 0.1m, and surface rotations of 10 degrees, using a ramp stimulus of 150 ms duration.     

Influence of the moment exerted by the athlete on the pole in pole-vaulting performance

Current studies on pole-vaulting focus mostly on energy transfer data [Ekevad, M., Lundberg, B., 1995. Simulation of "smart" pole vaulting. Journal of Biomechanics 28, 1079-1090; Ekevad, M., Lundberg, B., 1997. Influence of pole length and stiffness on the energy conversion in pole-vaulting. Journal of Biomechanics, 30, 259-264; Linthorne, N.P., 2000. Energy loss in the pole vault take-off and the advantage of the flexible pole. Sports Engineering 3, 205-218; Schade, F., Arampatzis, A., Bruggemann, G.P., 2006. Reproducibility of energy parameters in the pole vault. Journal of Biomechanics 39, 146-147.] and often fail to take into account the actions exerted on the pole [Arampatzis, Schade, Bruggemann, 2004. Effect of the pole-human body interaction on pole-vaulting performance. Journal of Biomechanics 37, 1353-1360]. The present study integrates the 3D kinematics data of the athlete but also the actions measured at the end of the pole in the planting box and on the track during the last stride before take-off. It proposes a mechanical model allowing determination of the pole-vaulter's actions on the pole. The model is based on a global mechanical approach. The pole-vaulter's action on his upper and lower hand is concentrated on one middle point to solve the dynamics problem. The model was applied to seven experienced pole-vaulters. The force and the moment exerted on the pole by the pole-vaulter during the last stride before take off and during jump stage, were calculated. This analysis of the compressive force and bending moment for seven pole-vaulters helps to highlight the impact of the moment in the performance. The conclusion is confirmed by an additional comparative study carried out on two pole-vaulters, with comparable morphologies and performing with the same pole.     

Influence of loading rate and cable migration on fiberoptic measurement of tendon force

Several investigators have recently used fiberoptic cables to measure tendon forces in situ. The technique may be subject to significant error due to cable migration and differences in the loading rates used for calibration and those experienced during measurement. This in vitro study examined the impact of these potential sources of error on transducer accuracy. A fiberoptic cable was passed perpendicular to the fibers of four Achilles tendons in the mediolateral direction and each specimen was cyclically loaded to 1000 N. The influence of loading rate on transducer output was investigated by comparing results from tests conducted at 20, 200 and 1000 N/s. The effect of cable migration was examined by comparing the outputs obtained after displacing the cable one tendon width medially and laterally along its path in the tendon and then repeating the 200 N/s testing protocol. It was possible to obtain nonlinear specimen-specific relationships between the fiberoptic output and tendon force. Differences in loading rate resulted in root-mean-square (RMS) errors not larger than 17% maximum load. Hysteresis effects caused RMS errors smaller than 5% maximum load. Cable migration errors were less than 27%. The total RMS error due to the combined effects of loading rate difference and cable movement was less than 32%. Fiberoptic measurement of tendon force is attractive due to its low cost, easy implementation and comparable accuracy relative to other implantable force transducers. Although additional factors such as cable placement, edge artifacts due where the transducer exits the skin and non-uniform loading may also influence fiberoptic output, careful control of loading rate and transducer movement during calibration is imperative if maximum accuracy is to be achieved.     

Evaluation and validation of Biolog OmniLog® system for antibacterial activity assays

Minimal inhibitory concentration of antimicrobials, determined by the broth microdilution method, requires visual assessment or absorbance measurement using a spectrophotometer. Both procedures are usually performed manually, requiring the presence of an operator to assess the plates at specific time point. To increase the throughput of antimicrobial susceptibility testing, and concurrently convert into an automatic assay, the Biolog OmniLog^® system was validated for a new, label-free application using standard 96-well microplates. OmniLog was evaluated for its signal strength to ensure that the signal intensity, detected and measured by the system's camera, was satisfactory. Variability due to the plate location inside the OmniLog incubator, as well as variation between wells, was investigated. Then the system was validated by determining the minimal inhibitory concentration of ciprofloxacin, piperacillin and linezolid against a selected Gram-negative and Gram-positive strains. No significant difference was observed in relation to position of the plates within the system. Plate edge effects were noticeable, thus the edge wells were not included in further experiments. Minimal inhibitory concentration results were comparable to those obtained by conventional protocol as well as to values defined by the Clinical Laboratory Standards Institute or published in the literature.