Measurement of joint capsule tissue loading in the cat knee using calibrated mechanoreceptors

The vertical loading in the posterior capsule of the cat knee has been measured while the knee is rotated into hyperextension. Tissue loading was determined using a previously verified model of the capsule that represents its upper edge as a catenary suspension cable. Tensile loads in the cable were measured using the discharge of mechanoreceptive sensory neurons that had been calibrated as load sensors. The results revealed that the capsule is very lightly loaded in extension rotations. Less than 4% of the applied moment is sustained by the capsule.     

A biomechanical model of the posterior knee capsule of the cat

A biomechanical model is presented which represents the upper edge of the posterior knee capsule in the cat as a two-segment, vertically loaded catenary suspension cable from which the capsule sheet is suspended. Data are presented which show that the upper edge of the capsule is organized as a cable, which spans the notch between the femoral condyles. When a point load is applied to the cable, measurement of the cable shape allows for calculation of the cable tension and the downward distributed loads acting on the cable. This method was used to measure the in-vivo cable tension and the distributed downward loading acting on the capsule cable. The results show that the lateral side of the posterior joint capsule sustains a higher loading than the medial side.     

An implantable transducer for measuring tension in an anterior cruciate ligament graft.

The goal of this study was to develop a new implantable transducer for measuring anterior cruciate ligament (ACL) graft tension postoperatively in patients who have undergone ACL reconstructive surgery. A unique approach was taken of integrating the transducer into a femoral fixation device. To devise a practical in vivo calibration protocol for the fixation device transducer (FDT), several hypotheses were investigated: (1) The use of a cable versus the actual graft as the means for applying load to the FDT during calibration has no significant effect on the accuracy of the FDT tension measurements; (2) the number of flexion angles at which the device is calibrated has no significant effect on the accuracy of the FDT measurements; (3) the friction between the graft and femoral tunnel has no significant effect on measurement accuracy. To provide data for testing these hypotheses, the FDT was first calibrated with both a cable and a graft over the full range of flexion. Then graft tension was measured simultaneously with both the FDT on the femoral side and load cells, which were connected to the graft on the tibial side, as five cadaver knees were loaded externally. Measurements were made with both standard and overdrilled tunnels. The error in the FDT tension measurements was the difference between the graft tension measured by the FDT and the load cells. Results of the statistical analyses showed that neither the means of applying the calibration load, the number of flexion angles used for calibration, nor the tunnel size had a significant effect on the accuracy of the FDT. Thus a cable may be used instead of the graft to transmit loads to the FDT during calibration, thus simplifying the procedure. Accurate calibration requires data from just three flexion angles of 0, 45, and 90 deg and a curve fit to obtain a calibration curve over a continuous range of flexion within the limits of this angle group. Since friction did not adversely affect the measurement accuracy of the FDT, the femoral tunnel can be drilled to match the diameter of the graft and does not need to be overdrilled. Following these procedures, the error in measuring graft tension with the FDT averages less than 10 percent relative to a full-scale load of 257 N.     

Use of distraction loading to estimate subject-specific knee ligament slack lengths

Knee ligaments guide and restrain joint motion, and their properties influence joint mechanics. Inverse modeling schemes have been used to estimate specimen-specific ligament properties, where external joint forces are assumed to balance with internal ligament and contact forces. This study simplifies this assumption by adjusting experimental loads to remove internal contact forces. The purpose of this study was to use novel experimental loading in an inverse modeling scheme to estimate ligament slack lengths, perform validation using additional loading scenarios, and evaluate sensitivity to the applied loading. Joint kinematics and kinetics were experimentally measured for a set of load cases. An optimization scheme used a specimen-specific forward kinematics model to estimate ligament slack lengths by minimizing the residual between model and experimentally measured kinetics. The calibrated model was used for a form of validation by evaluating non-optimized load cases. Additionally, uncertainty analysis related kinetic errors to previously reported kinematic errors. The six DOF tibial reactions realized RMS errors less than 23 N and 0.75 Nm for optimized load cases, and 33 N and 2.25 Nm for the non-optimized load cases. The uncertainty analysis, which was performed using the optimized load cases, showed average kinetic RMS errors less than 26 N and 0.45 Nm. The model’s recruitment patterns were similar to those found in clinical and cadaveric studies. This study demonstrated that experimental distraction loading can be used in an inverse modeling scheme to estimate ligament slack lengths with a forward kinematics model.     

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.     

Reconstructed bone end loads on the canine forelimb during gait

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.     

Calibration and application of an intra-articular force transducer for the measurement of patellar tendon graft forces: an in situ evaluation.

The objective of this study was to evaluate two calibration methods for the "Arthroscopically Implantable Force Probe" (AIFP) that are potentially suitable for in vivo use: (1) a direct, experimentally based method performed by applying a tensile load directly to the graft after it is harvested but prior to implantation (the "pre-implantation" technique), and (2) an indirect method that utilizes cadaver-based analytical expressions to transform the AIFP output versus anterior shear load relationship, which may be established in vivo, to resultant graft load (the "post-implantation" technique). The AIFP outputs during anterior shear loading of the knee joint using these two calibration methods were compared directly to graft force measurements using a ligament cutting protocol and a 6 DOF load cell. The mean percent error (actual-measured)/(actual)* 100) associated with the pre-implantation calibration ranged between 85 and 175 percent, and was dependent on the knee flexion angle tested. The percent error associated with the post-implantation technique was evaluated in two load ranges: loads less than 40 N, and loads greater than 40 N. For graft force values greater than 40 N, the mean percent errors inherent to the post-implantation calibration method ranged between 20 and 29 percent, depending on the knee flexion angle tested. Below 40 N, these errors were substantially greater. Of the two calibration methods evaluated, the post-implantation approach provided a better estimate of the ACL graft force than the pre-implantation technique. However, the errors for the post-implantation approach were still high and suggested that caution should be employed when using implantable force probes for in vivo measurement of ACL graft forces.     

In vivo calibration of a femoral fixation device transducer for measuring anterior cruciate ligament graft tension: a study in an ovine model

Toward developing a transducer for measuring in vivo tension in anterior cruciate ligament grafts in humans, the objectives of this study were to determine the following: (1) whether the calibration of a previously reported femoral fixation device transducer (FDT) (Ventura et al., 1998) is affected by the presence of the graft when implanted in the tibial metaphysis of an ovine model, (2) whether the FDT remains calibrated at 4 weeks postoperatively, and (3) whether the biological incorporation of the graft occurs prior to a change in the FDT calibration. The FDT was implanted in the hind limb of five sheep using an extra-articular procedure. Both the proximal common digital extensor tendon (i.e., graft) and a Teflon-coated wire were looped around the FDT inside a tunnel in the tibial metaphysis. The FDT was calibrated on three occasions using the loop of wire: once intraoperatively before graft insertion, once intraoperatively after graft insertion, and once postoperatively after the animals had been sacrificed at 4 weeks. Following sacrifice, the load transmitted to the FDT by the graft was also determined. The FDT exhibited linear calibration intraoperatively both before and after graft insertion with an average error relative to the calibration before insertion of the graft of -4.6 percent of full-scale load (150 N) and this average relative error was not significantly different from zero (p = 0.183). After 4 weeks of implantation, the average relative percent error was -5.0 percent and was not significantly different from zero (p = 0.434) indicating that the FDT remained calibrated in the in vivo environment. Because only 15 percent of the graft tension was transmitted to the FDT after 4 weeks, biological incorporation of the graft preceded the loss of calibration. In light of these findings, the FDT offers the capability of measuring the intra-articular ACL graft tension in vivo in animal models and possibly humans before the biological bond develops and also of monitoring the formation and maturation of the biological bond between a graft and bone tunnel.     

Design and calibration of load sensing orthopaedic implants

Contact forces and moments act on orthopaedic implants such as joint replacements. The three forces and three moment components can be measured by six internal strain gauges and wireless telemetric data transmission. The accuracy of instrumented implants is restricted by their small size, varying modes of load transfer, and the accuracy of calibration. Aims of this study were to test with finite element studies design features to improve the accuracy, to develop simple but accurate calibration arrangements, and to select the best mathematical method for calculating the calibration constants. Several instrumented implants, and commercial and test transducers were calibrated using different loading setups and mathematical methods. It was found that the arrangement of flexible elements such as bellows or notches between the areas of load transfer and the central sensor locations is most effective to improve the accuracy. Increasing the rigidity of the implant areas, which are fixed in bones or articulate against joint surfaces, is less effective. Simple but accurate calibration of the six force and moment components can be achieved by applying eccentric forces instead of central forces and pure moments. Three different methods for calculating the measuring constants proved to be equally well suited. Employing these improvements makes it possible to keep the average measuring errors of many instrumented implants below 1-2% of the calibration ranges, including cross talk. Additional errors caused by noise of the transmitted signals can be reduced by filtering if this is permitted by the sampling rate and the required frequency content of the loads.     

Calibration of the shear wave speed-stress relationship in ex vivo tendons

It has recently been shown that shear wave speed in tendons is directly dependent on axial stress. Hence, wave speed could be used to infer tendon load provided that the wave speed-stress relationship can be calibrated and remains robust across loading conditions. The purpose of this study was to investigate the effects of loading rate and fluid immersion on the wave speed-stress relationship in ex vivo tendons, and to assess potential calibration techniques. Tendon wave speed and axial stress were measured in 20 porcine digital flexor tendons during cyclic (0.5, 1.0 and 2.0 Hz) or static axial loading. Squared wave speed was highly correlated to stress (r²_avg = 0.98) and was insensitive to loading rate (p = 0.57). The constant of proportionality is the effective density, which reflects the density of the tendon tissue and additional effective mass added by the adjacent fluid. Effective densities of tendons vibrating in a saline bath averaged 1680 kg/m³ and added mass effects caused wave speeds to be 22% lower on average in a saline bath than in air. The root-mean-square error between predicted and measured stress was 0.67 MPa (6.7% of maximum stress) when using tendon-specific calibration parameters. These errors increased to 1.31 MPa (13.1% of maximum stress) when calibrating based on group-compiled data from ten tendons. These results support the feasibility of calculating absolute tendon stresses from wave speed squared based on linear calibration relationships.     

A contact algorithm for density-based load estimation

An algorithm, which includes contact interactions within a joint, has been developed to estimate the dominant loading patterns in joints based on the density distribution of bone. The algorithm is applied to the proximal femur of a chimpanzee, gorilla and grizzly bear and is compared to the results obtained in a companion paper that uses a non-contact (linear) version of the density-based load estimation method. Results from the contact algorithm are consistent with those from the linear method. While the contact algorithm is substantially more complex than the linear method, it has some added benefits. First, since contact between the two interacting surfaces is incorporated into the load estimation method, the pressure distributions selected by the method are more likely indicative of those found in vivo. Thus, the pressure distributions predicted by the algorithm are more consistent with the in vivo loads that were responsible for producing the given distribution of bone density. Additionally, the relative positions of the interacting bones are known for each pressure distribution selected by the algorithm. This should allow the pressure distributions to be related to specific types of activities. The ultimate goal is to develop a technique that can predict dominant joint loading patterns and relate these loading patterns to specific types of locomotion and/or activities.     

In vivo tendon force measurement of 2-week duration in sheep

Tendon tension in vivo may be determined indirectly by measuring intratendinous pressure, by using a buckle transducer or by measuring the tendon strain. All of these methods require appropriate calibration, which is highly dependent on various variables. To measure the tendon load in vivo during a period of 2 weeks in sheep, a measurement technique has been developed using a force sensor interposed serially between the humeral head and the tendon end. Within a supporting frame, a flexion-sensitive force transducer is subjected to three-point bending stress. The load is transmitted by sutures from the tendon end through a hole in the sensor frame, orthogonal to the force transducer. In this configuration, the sensor measures the tensile force acting on the tendon, largely independent of the loading direction. The sensor was screwed to the humeral head and connected to the tendon end which was previously released from its insertion site along with a bone chip, using sutures. Connecting wires passed subcutaneously to a skin outlet about 30 cm away from the transducer. The sensor output was linear to the measured load up to 300 N, with maximum hysteresis of 18% full scale. All sensors worked in vivo without drift over a period of up to 14 days with no change in the calibration data. Forces up to 310 N have been recorded in vivo with daily tension measurements. This study shows that serial tendon tension measurement is feasible and allows for reliable, repeatable recording of the absolute tendon tension at the expense of tendon integrity.     

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.     

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Relationships between femoral fracture loads for two load configurations

Studies of proximal femoral strength usually involve one of two types of loading conditions, loading similar to joint loading during single-limb stance or loading simulating impact from a fall. When interpreting the results of studies involving only one of these load configurations, the question arises as to their applicability to the other configuration. In addition, it is desirable to know whether, for an individual bone, fracture load for one load configuration is indicative of fracture load for the other configuration. In this study, the relationship between proximal femoral fracture loads for single-limb stance loading and loading simulating impact from a type of fall was determined from mechanical testing of 17 matched pairs of human proximal femora. Fracture loads for these two configurations were found to be linearly related (r = 0.901, p < 0.001). However, the correlation between fracture loads is not notably stronger than correlations currently available between fracture load and measures of bone density and geometry. In addition, the regression results indicate that 81% of the variance in fracture load for one loading condition is accounted for by fracture load for the other loading condition. Thus, 19% of the variance remains unexplained, indicating that the results of studies involving only one load configuration are not necessarily indicative of those that would be found for another configuration.     

Forcing a connection: impacts of single-molecule force spectroscopy on in vivo tension sensing

Mechanical tension plays a large role in cell development ranging from morphology to gene expression. On the molecular level, the effects of tension can be seen in the dynamic arrangement of membrane proteins as well as the recruitment and activation of intracellular proteins. Forces applied to biopolymers during in vitro force measurements offer greater understanding of the effects of tension on molecules in live cells, and experimental techniques involving test tubes and live cells can often overlap. Indeed, when forces exerted on cellular components can be calibrated ex vivo with force spectroscopy, a powerful tool is available for researchers in probing cellular mechanotransduction on the molecular scale. This review will discuss the techniques used in measuring both cellular traction forces and single-molecule force spectroscopy. Emphasis will be placed on the use of fluorescence reporter systems for the development of in vivo tension sensors that can be used for calibration with single molecule force methods.     

Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique

A technique to study the three-dimensional (3D) mechanical characteristics of the ankle and of the subtalar joints in vivo and in vitro is described. The technique uses an MR scanner compatible 3D positioning and loading linkage to load the hindfoot with precise loads while the foot is being scanned. 3D image processing algorithms are used to derive from the acquired MR images bone morphology, hindfoot architecture, and joint kinematics. The technique was employed to study these properties both in vitro and in vivo. The ankle and subtler joint motion and the changes in architecture produced in response to an inversion load and an anterior drawer load were evaluated. The technique was shown to provide reliable measures of bone morphology. The left-to-right variations in bone morphology were less than 5%. The left-to-right variations in unloaded hindfoot architecture parameters were less than 10%, and these properties were only slightly affected by inversion and anterior drawer loads. Inversion and anterior drawer loads produced motion both at the ankle and at the subtalar joint. In addition, high degree of coupling, primarily of internal rotation with inversion, was observed both at the ankle and at the subtalar joint. The in vitro motion produced in response to inversion and anterior drawer load was greater than the in vivo motion. Finally, external motion, measured directly across the ankle complex, produced in response to load was much greater than the bone movements measured through the 3D stress MRI technique indicating the significant effect of soft tissue and skin interference.     

Effects of elastic loading on porcine trachealis muscle mechanics

To shorten in vivo, airway smooth muscle must overcome an elastic load provided by cartilage and lung parenchyma. We examined the effects of linear elastic loads (0.2-80 g/cm) on the active changes in porcine trachealis muscle length and tension in response to electrical field stimulation in vitro. Increasing elastic loads produced an exponential decrease in the shortening and velocity of shortening while causing an increase in tension generation of muscle strips stimulated by electrical field stimulation. Shortening was decreased by 50% at a load of 8 g/cm. At small elastic loads (less than or equal to 1 g/cm) contractile responses approximated isotonic responses (shortening approximately 60% of starting length), whereas at large loads (20 g/cm) responses approximated isometric responses with minimal shortening (20%). We conclude that elastic loading significantly alters the mechanical properties of airway smooth muscle in vitro, effects that are likely relevant to the loads against which the smooth muscle must contract in vivo.     

An experimental method for measuring force on the spinal facet joint: description and application of the method.

A technique is described for measuring load magnitude and resultant load contact location in the facet joint in response to applied loads and moments, and the technique applied to the canine lumbar spine motion segment. Due to the cantilever beam geometry of the cranial articular process, facet joint loads result in surface strains on the lateral aspect of the cranial articular process. Strains were quantified by four strain gages cemented to the bony surface of the process. Strain measured at any one gage depended on the loading site on the articular surface of the caudal facet and on the magnitude of the facet load. Determination of facet loads during in vitro motion segment testing required calibration of the strains to known loads of various magnitudes applied to multiple sites on the caudal facet. The technique is described in detail, including placement of the strain gages. There is good repeatability of strains to applied facet loads and the strains appear independent of load distribution area. Error in the technique depends on the location of the applied facet loads, but is only significant in nonphysiologic locations. The technique was validated by two independent methods in axial torsion. Application of the technique to five in vitro canine L2-3 motion segments testing resulted in facet loads (in newtons, N) of 74+ / -23 N (mean + / -STD) in 2 newton-meter, Nm, extension, to unloaded in flexion. Lateral bending resulted in loads in the right facet of 40+ / -32 N for 1 Nm right lateral bending and 54+ / -29 N for 1 Nm left lateral bending. 4 Nm Torsion with and without 100 N axial compression resulted in facet loads of 92+ / -27 N and 69+ / -19 N, respectively. The technique is applicable to dynamic and in vivo studies.