A cycle ergometer mounted on a standard force platform for three-dimensional pedal forces measurement during cycling

This report describes a new method allowing to measure the three-dimensional forces applied on right and left pedals during cycling. This method is based on a cycle ergometer mounted on a force platform. By recording the forces applied on the force platform and applying the fundamental mechanical equations, it was possible to calculate the instantaneous three-dimensional forces applied on pedals. It was validated by static and dynamic tests. The accuracy of the present system was -7.61 N, -3.37 N and -2.81 N, respectively, for the vertical, the horizontal and the lateral direction when applying a mono-directional force and -4.52 N when applying combined forces. In pedaling condition, the orientation and magnitude of the pedal forces were comparable to the literature. Moreover, this method did not modify the mechanical properties of the pedals and offered the possibility for pedal force measurement with materials often accessible in laboratories. Measurements obtained showed that this method has an interesting potential for biomechanical analyses in cycling.     

Sensitivity of temporomandibular joint force calculations to errors in muscle force measurements

A two-dimensional, five-muscle model was used to determine the degree of precision required for accurate calculation of temporomandibular joint force magnitude and direction. The sensitivity of the calculations to each variable were assessed by incrementing each variable through its presumed biological range and were expressed as rate of change in the joint force per unit change in each variable. Sensitivity of the calculations to variables depends upon both bite force direction and bite position. The bite force direction with maximum precision for joint force magnitude produced minimal precision for joint force direction. The accuracy needed for each muscle force varied greatly. The effect of error for each muscle parameter depended upon the magnitude, direction, and moment arm length of the muscle force relative to those of the resultant muscle force. If each of the five muscle forces was known to the nearest 1% of total muscle force magnitude, 1 degree of muscle force direction, and 1 mm of moment arm length, temporomandibular joint force magnitude could be calculated to the nearest 4 kg and joint force direction to the nearest 7 degrees. It is not known whether this precision for the muscle forces is possible.     

A novel force transducer for the measurement of grip force.

A new strain gauge transducer has been developed to measure functional grip forces. The gripping area is a cylinder of diameter 30 mm and length 150 mm and simulates the handle of a number of devices, allowing a range of activities to be studied. The device measures radial forces divided into six components and forces of up to 250 N per segment can be measured with an accuracy of +/- 1%. The device therefore gives information about the magnitude and distribution of force around the cylinder during gripping, and has been shown to be a valuable research tool in a study of four different types of grip, providing valuable input data for biomechanical models.     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

An instrumented shoe—A portable force measuring device

Effective protection from fracture for diseased or partially healed bones can be quantitatively developed only with a knowledge of the external forces applied to the bone. While force studies using force plates have documented the forces for certain activities, a more portable force measuring device is required to determine forces during most daily activities. The authors have developed an instrumented shoe with load cells attached directly to the shoe which measured orthogonal components of foot-to-ground forces and moments. Goniometers simultaneously monitor the position of the lower leg. The signals are transported to a system of loads acting at the lower leg. Typical load curves are presented.     

Theory of electrostatic effects in soft biological interfaces using atomic force microscopy.

We calculated the electrostatic force between a planar interface, such as a planar-supported lipid bilayer membrane, and the tip of a stylus on which another lipid bilayer or some other biomacromolecular system might be deposited. We considered styli with rounded tips as well as conical tips. To take into account the effect of dynamical hydrogen-bonded structures in the aqueous phase, we used a theory of nonlocal electrostatics. We used the Derjaguin approximation and identified the systems for which its use is valid. We pointed out where our approach differs from previous calculations and to what extent the latter are inadequate. We found that 1) the nonlocal interactions have significant effects over distances of 10-15 A from the polar zone and that, at the surface of this zone, the effect on the calculated force can be some orders of magnitude; 2) the lipid dipoles and charges are located a distance L from the hydrophobic layer in the aqueous medium and this can have consequences that may not be appreciated if it is ignored; 3) dipoles, located in the aqueous region, can give rise to forces even though the polar layer is unchanged, and if this is ignored the interpretation of force data can be erroneous if an attempt is made to rationalize an observed force with a knowledge of an uncharged surface; 4) the shape of the stylus tip can be very important, and a failure to take this into account can result in incorrect conclusions, a point made by other workers; and 5) when L is nonzero, the presence of charges and dipoles can yield a force that can be nonmonotonic as a function of ionic concentration.     

A simple force platform.

The force platform consists of a sandwhich of steel, Rockwool and concrete plates about 900 X 700 mm in surface. Four steel rings were bolted to the under side of the steel plate in each corner. Each steel ring was furnished with only one strain gauge, two of which were placed on the outer- respectively on the inner side of each ring. The four strain gauges were connected to a measuring bridge. Before mounting the rings on the steel plate, the sensitivity to pressure of each ring was adjusted in such a way that they were all similar. Because of this the platform responded with a signal which was independent of where a pressure was applied within the surface of the platform. The platform showed a rectilinear response for static forces up to 500 kp with a stable zero value. In response to dynamic forces the platform showed a resononance frequency of about 50 Hz, with a damping factor of 0.15. Calibration of dynamic forces was carried out by calculation of the forces during a vertical jump compared with what would be expected from the time of flight also registered by the platform-measuring-bridge-ink-writer-set-up. The time of flight was significantly higher (11%) than exected from the time-force relations beforetake-off. This was esplained partly by the relatively low damping factor in the system, partly by the subjects not extending their knees at landing on the platform.     

Immuno-atomic force microscopy of purple membrane.

The atomic force microscope is a useful tool for imaging native biological structures at high resolution. In analogy to conventional immunolabeling techniques, we have used antibodies directed against the C-terminus of bacteriorhodopsin to distinguish the cytoplasmic and extracellular surface of purple membrane while imaging in buffer solution. At forces > or = 0.8 nN the antibodies were removed by the scanning stylus and the molecular topography of the cytoplasmic purple membrane surface was revealed. When the stylus was retracted, the scanned membrane area was relabeled with antibodies within 10 min. The extracellular surface of purple membrane was imaged at 0.7 nm resolution, exhibiting a major and a minor protrusion per bacteriorhodopsin monomer. As confirmed by immuno-dot blot analysis and sodium dodecyl sulfate-gel electrophoresis, labeling of the purple membrane was not observed if the C-terminus of bacteriorhodopsin was cleaved off by papain.     

The effect of muscular pre-tensing on the sprint start

Pre-tensed and conventional starts that exert, respectively, large and small forces against the starting blocks in the "set" position (0.186 vs. 0.113 N per newton of body weight) were analyzed. The starts were videotaped, and the horizontal forces exerted on feet and hands were obtained from separate force plates. In the pre-tensed start, the legs received larger forward impulses early in the acceleration (0.18 vs. 0.15 N x s per kilogram of mass in the first 0.05 s), but the hands received larger backward impulses (-0.08 vs. -0.04 N x s x kg(-1)). At the end of the acceleration phase, there was no significant difference in horizontal velocity between the two types of start and only trivial differences in the center of mass positions. The results did not show a clear performance change when the feet were pressed hard against the blocks while waiting for the gun.     

Mechanical properties of shock-absorbing pylons used in transtibial prostheses

Prosthetic manufacturers have developed shock-absorbing pylons to attenuate the transient forces of foot-ground contact in order to supplement the residual capacity of lower limb amputees. The purpose of this study was to measure the elastic and damping properties of two frequently prescribed pylons (the ICON Shock Pylon and the Mercury TT Pyramid Pylon) at frequencies enveloping those observed during gait using pseudo-static compressive and dynamic cyclic testing methods. Results showed that the spring constants were linear functions of deformation (ranging from 74 to 110 N/mm and 91 to 157 N/mm for the ICON and the TT Pylons, respectively) while the damping force was a function of the square root of velocity combined with a coulomb element (1.6x0.5 + 21 and 7.4x0.5 + 102 N for the ICON and the TT Pylon, respectively).     

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.     

A phenomenological model and validation of shortening-induced force depression during muscle contractions

History-dependent effects on muscle force development following active changes in length have been measured in a number of experimental studies. However, few muscle models have included these properties or examined their impact on force and power output in dynamic cyclic movements. The goal of this study was to develop and validate a modified Hill-type muscle model that includes shortening-induced force depression and assess its influence on locomotor performance. The magnitude of force depression was defined by empirical relationships based on muscle mechanical work. To validate the model, simulations incorporating force depression were developed to emulate single muscle in situ and whole muscle group leg extension experiments. There was excellent agreement between simulation and experimental values, with in situ force patterns closely matching the experimental data (average RMS error <1.5 N) and force depression in the simulated leg extension exercise being similar in magnitude to experimental values (6.0% vs. 6.5%, respectively). To examine the influence of force depression on locomotor performance, simulations of maximum power pedaling with and without force depression were generated. Force depression decreased maximum crank power by 20–40%, depending on the relationship between force depression and muscle work used. These results indicate that force depression has the potential to substantially influence muscle power output in dynamic cyclic movements. However, to fully understand the impact of this phenomenon on human movement, more research is needed to characterize the relationship between force depression and mechanical work in large muscles with different morphologies.     

Peak dynamic force in human gait

Studies were made of the forces generated at heel stroke in human gait using both force plates having a high resonant frequencies (capable of picking up high frequency components in the contact force) as well as a force transducer inserted into the heel of the shoe of the subjects. The output traces were analyzed for the existence of high frequency impulsive loads during a normal walking cycle. The effect of the complicance of the foot and floor was studied with the force transducers. The results showed that during normal human gait the lower limb is subjected to a high frequency impulsive load at heel strike. The severity of this impulse varied with the individual, the velocity and angle with which the limb aproached the ground and the compliance of the two materials coming in contact at heel strike. The magnitude of this peak force varied from 0.5 to 1.25 times body weight and its frequency components from 10 to 75 Hz.     

Investigation of optimal follower load path generated by trunk muscle coordination

It has been reported that the center of rotation of each vertebral body is located posterior to the vertebral body center. Moreover, it has been suggested that an optimized follower load (FL) acts posterior to the vertebral body center. However, the optimal position of the FL with respect to typical biomechanical characteristics regarding spinal stabilization, such as joint compressive force, shear force, joint moment, and muscle stress, has not been studied. A variation in the center of rotation of each vertebra was formulated in a three-dimensional finite element model of the lumbar spine with 117 pairs of trunk muscles. Then, the optimal translation of the FL path connecting the centers of rotations was estimated by solving the optimization problem that was to simultaneously minimize the compressive forces, the shear forces, and the joint moments or to minimize the cubic muscle stresses. An upright neutral standing position and a standing position with 200N in both hands were considered. The FL path moved posterior, regardless of the optimization criteria and loading conditions. The FL path moved 5.0 and 7.8mm posterior in upright standing and 4.1mm and 7.0mm posterior in standing with 200N in hands for each optimization scheme. In addition, it was presented that the optimal FL path may have advantages in comparison to the body center FL path. The present techniques may be important in understanding the spine stabilization function of the trunk muscles.     

The effects of muscle stretching and shortening on isometric forces on the descending limb of the force-length relationship

The purpose of this study was to examine the effects of stretching and shortening on the isometric forces at different lengths on the descending limb of the force-length relationship. Cat soleus (N = 10) was stretched and shortened by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these dynamic contractions were compared to the isometric forces at the corresponding muscle lengths. We found a shift of the force-length relationship to greater force values following muscle stretching, and to smaller force values following muscle shortening. Shifts in both directions critically depended on the magnitude of stretching/shortening and the final muscle length. We confirm recent findings that the steady-state isometric force following some stretch conditions clearly exceeded the maximal isometric forces at optimum muscle length, and that force enhancement was associated with an increase in the passive force, i.e., a passive force enhancement. When the passive force enhancement was subtracted from the total force enhancement, forces following stretch were always equal to or smaller than the isometric force at optimum muscle length. Together, these findings led to the conclusions: (a). that force enhancement is composed of an "active and a "passive" component; (b). that the "passive" component of force enhancement allows for forces greater than the maximal isometric forces at the muscle's optimum length; and (c). that force enhancement and force depression are critically affected by muscle length and stretch/shortening amplitude.     

A modular instrument for exploring the mechanics of cardiac myocytes

The cardiac ventricular myocyte is a key experimental system for exploring the mechanical properties of the diseased and healthy heart. Millions of primary myocytes, which remain viable for 4-6 h, can be readily isolated from animal models. However, currently available instrumentation allows the mechanical properties of only a few physically loaded myocytes to be explored within 4-6 h. Here we describe a modular and inexpensive prototype instrument that could form the basis of an array of devices for probing the mechanical properties of single mammalian myocytes in parallel. This device would greatly increase the throughput of scientific experimentation and could be applied as a high-content screening instrument in the pharmaceutical industry. The instrument module consists of two independently controlled Lorentz force actuators-force transducers in the form of 0.025 x 1 x 5 mm stainless steel cantilevers with 0.5 m/N compliance and 360-Hz resonant frequency. Optical position sensors focused on each cantilever provide position and force resolution of <1 nm/ radicalHz and <2 nN/ radicalHz, respectively. The motor structure can produce peak displacements and forces of +/-200 mum and +/-400 microN, respectively. Custom Visual Basic.Net software provides data acquisition, signal processing, and digital control of cantilever position. The functionality of the instrument was demonstrated by implementation of novel methodologies for loading and attaching healthy mammalian ventricular myocytes to the force sensor and actuator and use of stochastic system identification techniques to measure their passive dynamic stiffness at various sarcomere lengths.     

Parameters influencing the accuracy of the point of force application determined with piezoelectric force plates.

Errors up to +/- 30 mm in determining the point of force application with piezoelectric force plates have been reported in the literature (Kistler, 1984. Multicomponent Measuring Force Plate for Biomechanics and Industry. Kistler, Switzerland; Bobbert and Schamhardt, 1990. Journal of Biomechanics 23, 705-710; Sommer et al., 1997. Proceedings of the XVI th I.S.B. Congress). To explain the main factors influencing the systematic errors the force plate system is modeled as a two-dimensional beam structure. By this model it is strongly indicated that the cause for the errors in determining the point of force application are bending moments in the measurement posts. The main parameters influencing the shape and magnitude of the error function are the ratios between the bending stiffness of the plate and the bending and compressive stiffnesses of the measurement posts. In the current design it is therefore not possible to eliminate the cause for the errors by changing the constructive parameters. By comparing the error functions derived with the beam model to the correction formulas given in the literature an improved algorithm is proposed. This paper shall help biomechanists in understanding the basic concepts of determining the point of force application with force plates and in constructing custom-made force plates for specific applications.     

Seed-breaking forces exerted by orang-utans with their teeth in captivity and a new technique for estimating forces produced in the Wild

Orang-utans (Pongo pygmaeus) at the Singapore Zoological Gardens were presented with two thick-shelled edible seeds, Mezzettia parviflora (Annonaceae) and Macadamia ternifolia (Proteaceae) in order to estimate their maximum bite forces. The orang-utans could break the Macadamia seeds in one bite, while those of Mezzettia required repeated attempts. Examination of shell fragments showed that many had scratches and some had clear, but small (ca. 1–2 mm diameter), impressions on them. Building upon this information, semi-imitative tests were performed on the seeds in a universal testing machine by loading them in compression with either flat plates or metal casts of orang-utan cheek teeth. The maximum forces required to break the seeds were similar with both the flat plates and the metal teeth; the average for the Macadamia seeds being about 2,000 N (which forms a minimum estimate for the maximum bite forces in orang-utans) and for the Mezzettia seeds, 6,000 N. The work done with the metal teeth was much greater than with the plates. A mechanical analysis showed that this extra work went into producing permanent impressions (“bite marks”) in the shell with the tooth cusps. These impressions were larger than those found on the shells of seeds bitten by the orang-utans. Nevertheless, it is shown theoretically that the size of these indentations can give an estimate of the bite forces used. The maximum force developed in the machine tests with the metal teeth was correlated with the force calculated from analysis of the bite marks. The method is suitable for use in field studies where the marks left on remnants of hard foods eaten by primates may be used to estimate, very roughly, the forces used to produce them. © 1994 Wiley-Liss, Inc.     

Radial forces within muscle fibers in rigor

Considering the widely accepted cross-bridge model of muscle contraction (Huxley. 1969. Science [Wash. D. C.]. 164:1356-1366), one would expect that attachment of angled cross-bridges would give rise to radial as well as longitudinal forces in the muscle fiber. These forces would tend, in most instances, to draw the myofilaments together and to cause the fiber to decrease in width. Using optical techniques, we have observed significant changes in the width of mechanically skinned frog muscle fibers when the fibers are put into rigor by deleting ATP from the bathing medium. Using a high molecular weight polymer polyvinylpyrrolidone (PVP-40; number average mol. wt. (Mn) = 40,000) in the bathing solution, we were able to estimate the magnitude of the radial forces by shrinking the relaxed fiber to the width observed with rigor induction. With rigor, fiber widths decreased up to approximately 10%, with shrinking being greater at shorter sarcomere spacing and at lower PVP concentrations. At higher PVP concentrations, some fibers actually swelled slightly. Radial pressures seen with rigor in 2 and 4% PVP ranged up to 8.9 x 10(3) N/m2. Upon rigor induction, fibers exerted a longitudinal force of approximately 1 x 10(5) N/m2 that was inhibited by high PVP concentrations (greater than or equal to 13%). In very high PVP concentrations (greater than or equal to 20%), fibers exerted an anomalous force, independent of ATP, which ranged up to 6 x 10(4) N/m2 at 60% PVP. Assuming that all the radial force is the result of cross- bridge attachment, we calculated that rigor cross-bridges exert a radial force of 0.2 x 1.2 x 10(-9) N per thick filament in sarcomeres near rest length. This force is of roughly the same order of magnitude as the longitudinal force per thick filament in rigor contraction or in maximal (calcium-activated) contraction of skinned fibers in ATP- containing solutions. Inasmuch as widths of fibers stretched well beyond overlap of thick and thin filaments decreased with rigor, other radially directed forces may be operating in parallel with cross-bridge forces.     

Evaluating amber force fields using computed NMR chemical shifts

NMR chemical shifts can be computed from molecular dynamics (MD) simulations using a template matching approach and a library of conformers containing chemical shifts generated from ab initio quantum calculations. This approach has potential utility for evaluating the force fields that underlie these simulations. Imperfections in force fields generate flawed atomic coordinates. Chemical shifts obtained from flawed coordinates have errors that can be traced back to these imperfections. We use this approach to evaluate a series of AMBER force fields that have been refined over the course of two decades (ff94, ff96, ff99SB, ff14SB, ff14ipq, and ff15ipq). For each force field a series of MD simulations are carried out for eight model proteins. The calculated chemical shifts for the ¹H, ¹⁵N, and ¹³C^a atoms are compared with experimental values. Initial evaluations are based on root mean squared (RMS) errors at the protein level. These results are further refined based on secondary structure and the types of atoms involved in nonbonded interactions. The best chemical shift for identifying force field differences is the shift associated with peptide protons. Examination of the model proteins on a residue by residue basis reveals that force field performance is highly dependent on residue position. Examination of the time course of nonbonded interactions at these sites provides explanations for chemical shift differences at the atomic coordinate level. Results show that the newer ff14ipq and ff15ipq force fields developed with the implicitly polarized charge method perform better than the older force fields.