In-situ calibration of the implantable force transducer

Recently, an implantable force transducer (IFT) has been introduced [Xu et al. (1992, J. Biomech. Engng 114, 170–177)] which can be used in tight spaces where force recordings with established transducers, such as the buckle-type transducers, are not possible because of impingement artifacts. The IFT is easily implanted in chronic animal preparations; however, calibration of the IFT in terminal experiments has produced unreliable results. The problems of IFT calibration are that minute movements of the transducer within the tendon, slight misalignments of the tendon, or slight errors in the line of pull cause dramatic changes in the IFT voltage output for a given applied calibration load. Here, we propose a method that eliminates the above calibration problems primarily because the target tendon is left in situ, the calibration loads are applied by the muscles which insert into the target tendon, and the transducer is implanted into the target tendon about two weeks prior to calibration. The theoretical and experimental approaches are demonstrated for the cat patellar tendon, but in principle can be performed with any tendon. The results are repeatable, lie within expected values, and reproduce some of the basic properties which have been observed in prior IFT testing.     

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.     

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.     

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.     

Rate-independent characteristics of an arthroscopically implantable force probe in the human achilles tendon

The effect of loading rate on specimen calibration was investigated for an implantable force sensor of the two-point loading variety. This variety of sensor incorporates a strain gage to measure the compressive load applied to the sensor due to tensile loading in a soft tissue specimen. The Achilles tendon in each of four human cadaveric lower extremities was instrumented with a force sensor and then loaded in tension using a materials testing machine. Each specimen was tensile tested at three different displacement rates, 0.25, 2.5 and 12.7 cm s(-1), corresponding with mean loading rates of 33.8, 513.2, and 2838.6 N s(-1), respectively. A calibration curve relating the force sensor signal and applied tendon tension was generated for each specimen/ displacement rate combination. For each specimen, calibration curves were compared by calculating an RMS error for the entire data set (eRMS = 1.6% of the full load value) and a coefficient of determination, R2, of a curve fit through all of the data (R2 = 99.6%). Over the range of rates tested, no measurable change in sensor sensitivity due to loading rate was observed. Hysteresis for all displacement rates was on the order of 2.4%.     

Measuring ligament elasticity of the knee joint--elasticity measuring strip and its alternatives]

Those techniques for measuring ligament tension at the knee joint that are most commonly cited and easiest to carry out are discussed. These include four techniques based on the use of strain gauges. Apart from the Omega transducer and the buckle transducer, there is also the tendon force transducer, and the application of strain gauges to the bony ligament insertion sites. Other indirect measuring methods considered are the mercury strain transducer and the Hall effect transducer. The parameter measured with all of these methods is fluctuating current or voltage, which is then correlated with ligament tension. Three direct measurements are also discussed: the separation distances of marked fibres of the ligaments, replacement of fibres by threads, and a load cell/bone plug construction. The measured value is equated with the effective change in ligament length.     

Factors influencing the output of an implantable force transducer

The objective of this study was to evaluate the performance of the Arthroscopically Implantable Force Probe (AIFP; MicroStrain, Burlington VT) for measuring force in a patellar tendon graft. Transducer drift, reproducibility of output due to the number of loading cycles and device location, and sensitivity to the tendon cross-sectional area were investigated. The AIFP was initialized, and then implanted into five human patellar tendon grafts three times; twice within the same location and once in a different location. The tendons were cyclically loaded in uniaxial tension for 500 cycles in each insertion site. The AIFP was then removed from the tendon and the baseline output was remeasured. It was determined that transducer drift was negligible. The relationship between the tensile load applied to the graft and AIFP output was quadratic and specimen dependent. The cyclic load response of the tendon-AIFP interface demonstrated a 24.9% decrease over the first 20 loading cycles, and subsequent cycling yielded relatively reproducible output. The output of the transducer varied when it was removed from the tendon and then reimplanted in the same location (range 3.7-109. 4% error), as well as in the second location (range 1.5-202.8% error). No correlation was observed between the cross-sectional area of the tendon and transducer output. This study concludes that implantable force probes should be used with caution and calibrated without removing the transducer from the graft.     

Theoretical analysis of an implantable force transducer for tendon and ligament structures.

A mathematical model was developed for an implantable force transducer to be inserted within the midsubstance of a ligament or tendon. The model was generated by performing both equilibrium and strain-displacement analyses on a metallic, curved beam structure placed within a parallel-fibered tissue. The analysis permitted the transverse pressure acting between the device and fibers to be calculated along with peak device strain and sensitivity (ratio of strain output to axial tissue force). Transducer pressure and transducer strain were expressed in terms of nondimensionalized design factors. A parametric analysis of the key design factors was then performed. The transverse pressure was shown to vary little for large changes in these factors whereas device strain changed markedly. The analysis was verified by a bench test on an example device. Such a model permits a proposed design to be evaluated without having to conduct costly experiments.     

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.     

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.     

Characterization of in vivo Achilles tendon forces in rabbits during treadmill locomotion at varying speeds and inclinations

The objective of this study was to test the hypothesis that increasing the speed and inclination of the treadmill increases the peak Achilles tendon forces and their rates of rise and fall in force. Implantable force transducers (IFT) were inserted in the confluence of the medial and lateral heads of the left gastrocnemius tendon in 11 rabbits. IFT voltages were successfully recorded in 8 animals as the animals hopped on a treadmill at each of two speeds (0.1 and 0.3 mph) and inclinations (0 degrees and 12 degrees). Instrumented tendons were isolated shortly after sacrifice and calibrated. Contralateral unoperated tendons were failed in uniaxial tension to determine maximum or failure force, from which safety factor (ratio of maximum force to peak in vivo force) was calculated for each activity. Peak force and the rates of rise and fall in force significantly increased with increasing treadmill inclination (p<0.001). Safety factors averaged 30.8+/-7.5 for quiet standing, 7.0+/-2.9 for level hopping, and 5.2+/-0.7 for inclined hopping (mean+/-SEM). These in vivo force parameters will help tissue engineers better design functional tissue engineered constructs for rabbit Achilles tendon and other tendon repairs. Force patterns can also serve as input data for mechanical stimulation of tissue-engineered constructs in culture. Such approaches are expected to help accelerate tendon repair after injury.     

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.     

Description and error evaluation of an in vitro knee joint testing system

An experimental system for the analysis of knee joint biomechanics is presented. The system provides for the simultaneous recording of ligament forces using buckle transducers and three-dimensional joint motion using an instrumented spatial linkage, as in vitro specimens are subjected to a variety of external loads by a pneumatic loading apparatus with associated force transducers. The system components are described, and results of an evaluation of system errors and accuracy are presented. The experimental setup has been successfully used in the analysis of normal knee ligament mechanics, as well as surgical reconstructions of the anterior cruciate ligament. The system can also be adapted to test other human or animal in vitro joints.     

Intramuscular fluid pressure during isometric contraction of human skeletal muscle

Intramuscular fluid pressures were recorded in the vastus medialis of seven healthy male volunteers. Pressures were measured simultaneously at three different sites in the muscle by a catheter-tip transducer with extremely low volume-displacement characteristics and by two extracorporeal transducers connected to slit catheters. All three recording systems gave qualitatively similar results provided the catheters had inner diameters exceeding 0.53 mm and allowed measurement of pressures lasting as short as 1 s. Wick catheters yielded slower responses than slit catheters. At any position intramuscular fluid pressure increased linearly with force up to maximal voluntary contraction (MVC). However, slopes of these curves varied greatly mainly because the pressure was also a linear function of the distance from the fascia. The highest recorded pressure was 570 Torr. At prolonged submaximal contractions intramuscular fluid pressure oscillated independent of contraction force. The linearity of both the pressure-force relationship and the pressure-depth relationship is compatible with a simple model based on the law of Laplace because the muscle fibers are curved during contraction in this muscle. It is hypothesized that blood flow is first compromised deep in the muscle where pressure is highest and in general at lower stress or tension in short bulging muscles with great curvature of the fibers compared with long slender ones.     

In vivo forces generated by finger flexor muscles do not depend on the rate of fingertip loading during an isometric task

Risk factors for activity-related tendon disorders of the hand include applied force, duration, and rate of loading. Understanding the relationship between external loading conditions and internal tendon forces can elucidate their role in injury and rehabilitation. The goal of this investigation is to determine whether the rate of force applied at the fingertip affects in vivo forces in the flexor digitorum profundus (FDP) tendon and the flexor digitorum superficialis (FDS) tendon during an isometric task. Tendon forces, recorded with buckle force transducers, and fingertip forces were simultaneously measured during open carpal tunnel surgery as subjects (N=15) increased their fingertip force from 0 to 15N in 1, 3, and 10s. The rates of 1.5, 5, and 15N/s did not significantly affect FDP or FDS tendon to fingertip force ratios. For the same applied fingertip force, the FDP tendon generated more force than the FDS. The mean FDP to fingertip ratio was 2.4+/-0.7 while the FDS to tip ratio averaged 1.5+/-1.0 (p<0.01). The fine motor control needed to generate isometric force ramps at these specific loading rates probably required similar high activation levels of multiple finger muscles in order to stabilize the finger and control joint torques at the force rates studied. Therefore, for this task, no additional increase in muscle force was observed at higher rates. These findings suggest that for high precision, isometric pinch maneuvers under static finger conditions, tendon forces are independent of loading rate.     

An implantable telemetry device to measure intra-articular tibial forces

Tibial forces are important because they determine polyethylene wear, stress distribution in the implant, and stress transfer to underlying bone. Theoretic estimates of tibiofemoral forces have varied between three and six times the body weight depending on the mathematical models used and the type of activity analyzed. An implantable telemetry system was therefore developed to directly measure tibiofemoral compressive forces. This system was tested in a cadaver knee in a dynamic knee rig. A total knee tibial arthroplasty prosthesis was instrumented with four force transducers located at the four corners of the tibial tray. These transducers measured the total compressive forces on the tibial tray and the location of the center of pressure. A microprocessor performed analog-to-digital signal conversion and performed pulse code modulation of a surface acoustic wave radio frequency oscillator. This signal was then transmitted through a single pin hermetic feed-through tantalum wire antenna located at the tip of the stem. The radio frequency signal was received by an external antenna connected to a receiver and to a computer for data acquisition. The prosthesis was powered by external coil induction. The tibial transducer accurately measured both the magnitude and the location of precisely applied external loads. Successful transmission of the radio frequency signal up to a range of 3m was achieved through cadaveric bone, bone cement, and soft tissue. Reasonable accuracy was obtained in measuring loads applied through a polyethylene insert. The implant was also able to detect unicondylar loading with liftoff.     

Oblique scaling: an algorithm to correct for a non-perpendicular camera view in tendon strain measurements

Image distortion due to a non-perpendicular camera view introduces serious errors in tendon and ligament strain measurements when data are recorded using a single camera. These errors can be corrected with the oblique scaling algorithm using two pairs of scaling markers attached to the tendon surface. Computer simulations show that application of this algorithm reduces errors over 100 times to less than 0.06%. The method is relatively insensitive to measurement errors in the scaling marker distance but sensitive to the accuracy of alignment of the scaling markers. It can be concluded that the oblique scaling algorithm eliminates the influences of a non-perpendicular camera view in single-camera tendon and ligament strain measurements.     

A miniature piezoelectric polymer transducer for in vitro measurement of the dynamic contact stress distribution.

Previous studies of contact pressure measurement between articular surfaces have been mostly limited to static techniques. The purpose of our study was to develop a new dynamic technique for a direct measurement of the local contact stresses, and to apply the new method to an in vitro cadaver study of the patellofemoral joint pressures. The miniature transducer consists of a 2 mm diameter and 28 microns thick piece of piezoelectric polymer film sandwiched between two stainless steel electrodes of similar diameter. A water-resistant capsule consisting of Teflon film and Hysol epoxy was applied around the transducer. The transducer was 3 mm in diameter and 0.7 mm in thickness. A 3 mm well was made at six locations in the patella, corresponding to superior, middle, and inferior regions of both facets. Six transducers were cemented within each well, flush with the articular cartilage. The transducers were calibrated in situ before and after the experiment. The femur was rigidly fixed to the loading apparatus and the tibia was allowed to flex and extend through a 90 degrees range of motion using an Instron and a pulley system connected to the quadriceps tendon. Q angles of 0, 5, 10 and 15 degrees were established by adjusting the direction of the quadriceps tendon. Stresses ranging from 0.1-1.3 MPa were recorded at various locations. These values varied in flexion and extension. An overall decrease in these stresses was noted after tuberosity elevation up to 1.5 cm, following which increased values up to 1.8 MPa were recorded mostly in the superior section.(ABSTRACT TRUNCATED AT 250 WORDS)     

A mathematical model of force transmission from intrafascicularly terminating muscle fibers

Many long skeletal muscles are comprised of fibers that terminate intrafascicularly. Force from terminating fibers can be transmitted through shear within the endomysium that surrounds fibers or through tension within the endomysium that extends from fibers to the tendon; however, it is unclear which pathway dominates in force transmission from terminating fibers. The purpose of this work was to develop mathematical models to (i) compare the efficacy of lateral (through shear) and longitudinal (through tension) force transmission in intrafascicularly terminating fibers, and (ii) determine how force transmission is affected by variations in the structure and properties of fibers and the endomysium. The models demonstrated that even though the amount of force that can be transmitted from an intrafascicularly terminating fiber is dependent on fiber resting length (the unstretched length at which passive stress is zero), endomysium shear modulus, and fiber volume fraction (the fraction of the muscle cross-sectional area that is occupied by fibers), fibers that have values of resting length, shear modulus, and volume fraction within physiologic ranges can transmit nearly all of their peak isometric force laterally through shearing of the endomysium. By contrast, the models predicted only limited force transmission ability through tension within the endomysium that extends from the fiber to the tendon. Moreover, when fiber volume fraction decreases to unhealthy ranges (less than 50%), the force-transmitting potential of terminating fibers through shearing of the endomysium decreases significantly. The models presented here support the hypothesis that lateral force transmission through shearing of the endomysium is an effective mode of force transmission in terminating fibers.