Effects of inserting a pressensor film into articular joints on the actual contact mechanics.

Fuji film has been widely used in studies aimed at obtaining the contact mechanics of articular joints. Once sealed for practical use in biological joints, Fuji Pressensor film has a total effective thickness of 0.30 mm, which is comparable to the cartilage thickness in the joints of many small animals. The average effective elastic modulus of Fuji film is approximately 100 MPa in compression, which is larger by a factor of 100-300 compared to that of normal articular cartilage. Therefore, inserting a Pressensor film into an articular joint will change the contact mechanics of the joint. The measurement precision of the Pressensor film has been determined systematically; however, the changes in contact mechanics associated with inserting the film into joints have not been investigated. This study was aimed at quantifying the changes in the contact mechanics associated with inserting sealed Fuji Pressensor film into joints. Spherical and cylindrical articular joint contact mechanics with and without Pressensor film and for varying degrees of surface congruency were analyzed and compared by using finite element models. The Pressensor film was taken as linearly elastic and the cartilage was assumed to be biphasic, composed of a linear elastic solid phase and an inviscid fluid phase. The present analyses showed that measurements of the joint contact pressures with Fuji Pressensor film will change the maximum true contact pressures by 10-26 percent depending on the loading, geometry of the joints, and the mechanical properties of cartilage. Considering this effect plus the measurement precision of the film (approximately 10 percent), the measured joint contact pressures in a joint may contain errors as large as 14-28 percent.     

In-vivo mitral annuloplasty ring transducer: Implications for implantation and annular downsizing

Mitral annuloplasty has been a keystone to the success of mitral valve repair in functional mitral regurgitation. Understanding the complex interplay between annular-ring stresses and left ventricular function has significant implications for patient-ring selection, repair failure, and patient safety. A step towards assessing these challenges is developing a transducer that can be implanted in the exact method as commercially available rings and can quantify multidirectional ring loading. An annuloplasty ring transducer was developed to measure stresses at eight locations on both the in-plane and out-of-plane surfaces of an annuloplasty ring's titanium core. The transducer was implanted in an ovine subject using 10 sutures at near symmetric locations. At implantation, the ring was observed to undersize the mitral annulus. The flaccid annulus exerted both compressive (−) and tensile stresses (+) on the ring ranging from −3.17 to 5.34 MPa. At baseline hemodynamics, stresses cyclically changed and peaked near mid-systole. Mean changes in cyclic stress from ventricular diastole to mid-systole ranged from −0.61 to 0.46 MPa (in-plane direction) and from −0.49 to 1.13 MPa (out-of-plane direction). Results demonstrate the variability in ring stresses that can be introduced during implantation and the cyclic contraction of the mitral annulus. Ring stresses at implantation were approximately 4 magnitudes larger than the cyclic changes in stress throughout the cardiac cycle. These methods will be extended to ring transducers of differing size and geometry. Upon additional investigation, these data will contribute to improved knowledge of annulus-ring stresses, LV function, and the safer development of mitral repair techniques.     

A detailed and validated three dimensional dynamic model of the patellofemoral joint

A detailed 3D anatomical model of the patellofemoral joint was developed to study the tracking, force, contact and stability characteristics of the joint. The quadriceps was considered to include six components represented by 15 force vectors. The patellar tendon was modeled using four bundles of viscoelastic tensile elements. Each of the lateral and medial retinaculum was modeled by a three-bundle nonlinear spring. The femur and patella were considered as rigid bodies with their articular cartilage layers represented by an isotropic viscoelastic material. The geometrical and tracking data needed for model simulation, as well as validation of its results, were obtained from an in vivo experiment, involving MR imaging of a normal knee while performing isometric leg press against a constant 140 N force. The model was formulated within the framework of a rigid body spring model and solved using forth-order Runge-Kutta, for knee flexion angles between zero and 50 degrees. Results indicated a good agreement between the model predictions for patellar tracking and the experimental results with RMS deviations of about 2 mm for translations (less than 0.7 mm for patellar mediolateral shift), and 4 degrees for rotations (less than 3 degrees for patellar tilt). The contact pattern predicted by the model was also consistent with the results of the experiment and the literature. The joint contact force increased linearly with progressive knee flexion from 80 N to 210 N. The medial retinaculum experienced a peak force of 18 N at full extension that decreased with knee flexion and disappeared entirely at 20 degrees flexion. Analysis of the patellar time response to the quadriceps contraction suggested that the muscle activation most affected the patellar shift and tilt. These results are consistent with the recent observations in the literature concerning the significance of retinaculum and quadriceps in the patellar stability.     

Hemiarthroplasty of hip joint: An experimental validation using porcine acetabulum

Biphasic properties of articular cartilage allow it to be an excellent bearing material and have been studied through several simplified experiments as well as finite element modelling. However, three-dimensional biphasic finite element (FE) models of the whole joint are rare. The current study was carried out to experimentally validate FE methodology for modelling hemiarthroplasty. Material properties such as equilibrium elastic modulus and permeability of porcine acetabular cartilage were initially derived by curve-fitting an experimental deformation curve with that obtained using FE. These properties were then used in the hemiarthroplasty hip joint modelling. Each porcine acetabular cup was loaded with 400N using a 34mm diameter CoCr femoral head. A specimen-specific FE model of each acetabular cup was created using μCT and a series of software processes. Each model was analysed under conditions similar to those tested experimentally. Contact stresses and contact areas predicted by the model, immediately after loading, were then compared with the corresponding experimentally measured values. Very high peak contact stresses (maximum experimental: 14.09MPa) were recorded. A maximum difference of 12.42% was found in peak contact stresses. The corresponding error for contact area was 20.69%. Due to a fairly good agreement in predicted and measured values of contact stresses and contact areas, the integrated methodology developed in this study can be used as a basis for future work. In addition, FE predicted total fluid load support was around 80% immediately after loading. This was lower than that observed in conforming contact problems involving biphasic cartilage and was due to a smaller local contact area and variable clearance making fluid exudation easier.     

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.     

A new transducer for facet force measurement in the lumbar spine: benchmark and in vitro test results.

A new transducer capable of direct measurement of time-dependent loads in human lumbar facet joints was developed and tested. The transducer was comprised of a force-sensitive resistor (FSR) in series with a pressure-sensitive film. A wide range of experiments revealed the performance attributes and limitations of the FSR. The output signal of the FSR is actually sensitive to both force and area of contact independently. Therefore, a pressure-sensitive film was used to quantify the contact area. At least two transformation equations were calculated for each FSR corresponding to known contact areas. Each equation was a linearization of the log of the FSR output vs the log of the applied ramp loads. Coefficients of determination (CD) were calculated for small (21 mm2) and large (32 mm2) contact areas, and were found to exceed 0.900 for all data. The average of nine cycles was nearly linear for some FSRs (CD of 0.999). FSR output signal and contact area were recorded in cadaveric lumbar facets under ramp load. The appropriate transformation equation was determined by a linear interpolation between benchmark equations based on the contact area measured in vitro. Facet force measurements compared well with those of other researchers. The transducer was found to be quite easy to use.     

Measurement of discrete vertical in-shoe stress with piezoelectric transducers

The purpose of this investigation was to design and validate a system suitable for non-invasive measurement of discrete in-shoe vertical plantar stress during dynamic activities. Eight transducers were constructed, with small piezoelectric ceramic squares (4.83 × 4.83 × 1.3 mm) used to generate a charge output proportional to vertical plantar stress. The mechanical properties of the transducers included 2.3% linearity and 3.7% hysteresis for stresses up to 2000 kPa and loading times up to 200 ms. System design efficacy was analysed by means of a multiple day, multiple trial data collection. With the transducers placed beneath plantar landmarks, the footstrike of one subject was recorded ten times on each of five days while running at 3.58 m/s on a treadmill. Within-day and between-day proportional error (PE) was used to estimate the error contained in the mean peak stress during foot contact. Within-day PE focused on trial to trial variability associated with the subject and equipment, and averaged 3.1% (range 2.5–4.0%) across transducer location. Between-day PE provided a cumulative estimate of subject, transducer placement, and random equipment variability, but excluded trial to trial variability. It ranged from 4.9 to 15.8%, with a mean of 9.9%. Peak stress, impulse, and sequence of loading data were examined to identify discrete foot function patterns and highlight the value of discrete stress analysis.     

3-D anatomically based dynamic modeling of the human knee to include tibio-femoral and patello-femoral joints

An anatomical dynamic model consisting of three body segments, femur, tibia and patella, has been developed in order to determine the three-dimensional dynamic response of the human knee. Deformable contact was allowed at all articular surfaces, which were mathematically represented using Coons' bicubic surface patches. Nonlinear elastic springs were used to model all ligamentous structures. Two joint coordinate systems were employed to describe the six-degrees-of-freedom tibio-femoral (TF) and patello-femoral (PF) joint motions using twelve kinematic parameters. Two versions of the model were developed to account for wrapping and nonwrapping of the quadriceps tendon around the femur. Model equations consist of twelve nonlinear second-order ordinary differential equations coupled with nonlinear algebraic constraint equations resulting in a Differential-Algebraic Equations (DAE) system that was solved using the Differential/Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory. Model calculations were performed to simulate the knee extension exercise by applying non-linear forcing functions to the quadriceps tendon. Under the conditions tested, both "screw home mechanism" and patellar flexion lagging were predicted. Throughout the entire range of motion, the medial component of the TF contact force was found to be larger than the lateral one while the lateral component of the PF contact force was found to be larger than the medial one. The anterior and posterior fibers of both anterior and posterior cruciate ligaments, ACL and PCL, respectively, had opposite force patterns: the posterior fibers were most taut at full extension while the anterior fibers were most taut near 90 degrees of flexion. The ACL was found to carry a larger total force than the PCL at full extension, while the PCL carried a larger total force than the ACL in the range of 75 degrees to 90 degrees of flexion.     

A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints

This study describes a general set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean +/- stand. dev. error in translation: 0.63 +/- 1.19 mm, 0.10 +/- 0.71 mm, -0.29 +/- 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 +/- 1.71 degrees, 0.27 +/- 2.38 degrees, -1.13 +/- 1.83 degrees in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room.     

A comparison of a mechanical sector and a linear array transducer for ultrasound-guided transvaginal oocyte retrieval (OPU) in the cow

A comparison was made between a linear array and a mechanical multiple angle sector (MAP) transducer for ultrasound-guided transvaginal oocyte retrieval (ovum pick-up, OPU) in the cow. The ovaries of five dairy cows were punctured, in a twice-weekly OPU program lasting for 4 weeks, using two different 5.0-MHz transducers equipped with an identical disposable needle-guidance system. Both ovaries were visualized using each transducer before puncture and the number of follicles with a diameter of less than 5 mm (small) and with a diameter equal to or greater than 5 mm (large) was recorded. Subsequently, one ovary of the pair was punctured guided by the MAP, while the other was punctured using the linear array transducer. During the next puncture session on a given animal, the two systems were switched and used on the alternate ovary in a crossover design. Parameters assessed for each system were: the total number of follicles visualized in each diameter class, and the total number of retrieved oocytes per cow. A significant difference was found for the ability to visualize smaller follicles in favor of the MAP transducer, with an average visualization of 71.6 +/- 30.3 small follicles per cow during the 4-week trial period, compared to 59.8 +/- 25.7 for the linear array transducer (t-test for paired samples, P = 0.007). No differences were found in the visualization of large follicles. A numerically greater number of oocytes were retrieved using the MAP transducer, compared to the linear array, (averages of 14.2 +/- 7.2 versus 7.4 +/- 6.1, respectively), although these differences were not statistically significant. In conclusion, both systems can be effectively used for oocyte retrieval in the cow, however, the MAP transducer demonstrated superior visualization of small follicles.     

Analysis of the gliding pattern of the canine flexor digitorum profundus tendon through the A2 pulley

Friction between a tendon and its pulley was first quantified using the concept of the arc of contact. Studies of human tendons conformed closely to a theoretical nylon cable/nylon rod model. However, we observed differences in measured friction that depended on the direction of motion in the canine model. We hypothesized that fibrocartilaginous nodules in the tendon affected the measurements and attempted to develop a theoretical model to explain the observations we made. Two force transducers were connected to each end of the canine flexor digitorum profundus tendon and the forces were recorded when it was moved through the A2 pulley toward a direction of flexion by an actuator and then reversed a direction toward extension. The changes of a force as a function of tendon excursion were evaluated in 20 canine paws. A bead cable/rod model was developed to simulate the canine tendon-pulley complex. To interpret the results, a free-body diagram was developed. The two prominent fibrocartilaginous nodules in the tendon were found to be responsible for deviation from a theoretical nylon cable gliding around the rod model, in a fashion analogous to the effect of the patella on the quadriceps mechanism. A bead cable/rod model qualitatively reproduced the findings observed in the canine tendon-pulley complex. Frictional coefficient of the canine flexor tendon-pulley was 0.016+/-0.005. After accounting for the effect created by the geometry of two fibrocartilaginous nodules within the tendon, calculation of frictional force in the canine tendon was possible.     

The measurement of the variation in the surface strains of Achilles tendon grafts using imaging techniques

Uniaxial tensile tests are commonly used to characterize the structural and material properties of tendons and ligaments. During these tests, the stress and strain distributions applied to the specimen are assumed to be uniform. However, few studies have investigated the strain distributions throughout the tissue. The purpose of this study was to use imaging techniques to measure the strains around the circumference of 11 mm wide Achilles tendon grafts during a uniaxial tensile test. Pairs of radiopaque beads with a diameter of 2mm were affixed around the mid-substance of the tendon in four different locations. The motion of the beads was recorded using a cine fluoroscope. This system was shown to measure the displacement of the beads with an accuracy of 0.02 mm. During the uniaxial tensile test, large variations in local tissue strains were observed. At 10 MPa of applied stress, the local tissue strain varied from an average of 2.5-8.7%, an increase in strain of more than three times. As a result of these large variations, the modulus calculated from the stress-strain data varied from an average of 217 to 897 MPa, an increase of approximately 4 times. Furthermore, these data suggest that underestimates of the elastic modulus may result if a uniform strain distribution is assumed. These results indicate that during uniaxial tensile tests, the assumption of uniform stress and strain distributions should be carefully considered and small, uniform specimens should be used when measuring the material properties of soft tissues.     

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.     

The effect of design variables of condylar total knees on the joint forces in step climbing based on a computer model.

The ability to climb a steep step or rise from a low chair after total knee replacement may be enhanced if the required force in the quadriceps muscle is reduced. This can potentially be achieved if the total knee produces a large lever arm measured from the femoral-tibial contact point to the patellar ligament. A reduced quadriceps force would also reduce the patello-femoral force and the femoral-tibial contact force. The contact point location is likely to be a function of the geometry of the femoral and tibial components in the sagittal plane, including the relative distal and posterior radii of the femoral profile, the location of the bottom-of-the-dish of the tibial surface, the radius of the tibial surface, and the presence or absence of the posterior cruciate ligament. A three-dimensional model of the knee was developed including the quadriceps and various ligaments. In the study, the motion was confined to flexion extension and displacement in the sagittal plane. The quadriceps was assumed to be the only muscle acting. A standard software package (Pro/Mechanica) was used for the analysis. For a femoral component with a smaller distal radius, there was 12% reduction in the quadriceps muscle force and up to 11% reduction in the patello-femoral force from about 100 up to 60 degrees flexion. However, apart from that, there were less than 10% differences in all the forces as a function of all of the design variables studied. This was attributed to the relatively small changes in the lever arm of the patella tendon, since the tendon moves in an anterior-posterior direction along with the femur. An additional factor explaining the results was the change in the anterior-posterior contact point as controlled by the forces in the patella tendon and in the soft tissues. The results imply that for a standard condylar replacement knee, the muscle and contact forces are not greatly affected by the geometrical design variables.     

Cadaveric study of the arterial anatomy of the upper lip

Arterial distribution of the upper lip was investigated in this study. The location, course, length, and diameter of the superior labial artery and its alar and septal branches were determined on 14 preserved cadaver heads. Another cadaver head was used to show the arterial tree by the colored silicone injection technique. The superior labial artery was the main artery of the upper lip and always originated from the facial artery. The superior labial artery was 45.4 mm in length, with a range from 29 to 85 mm. The mean distance of the origin of the superior labial artery from the labial commissura was 12.1 mm. The superior labial artery was 1.3 mm in external diameter at its origin. The mean distance of origin of the superior labial artery from the lower border of the mandible was 46.4 mm. The alar division of the superior labial artery was mostly found as a single branch (82 percent). Its mean length was 14.8 mm and the mean diameter at the origin was 0.5 mm. The distance between the origins of the superior labial artery and the septal branch was 33.3 mm. The septal branch was single in most of the cases (90 percent). The mean length of the septal branch was 18.0 mm and the diameter at its origin was 0.9 mm. After all dissections, it was concluded that the arterial distribution of the upper lip was not constant. The superior labial artery can occur in different locations unilaterally and bilaterally, with the branches showing variability.     

Tibiofemoral joint contact force in deep knee flexion and its consideration in knee osteoarthritis and joint replacement

The aim of the study was to estimate the tibiofemoral joint force in deep flexion to consider how the mechanical load affects the knee. We hypothesize that the joint force should not become sufficiently large to damage the joint under normal contact area, but should become deleterious to the joint under the limited contact area. Sixteen healthy knees were analyzed using a motion capture system, a force plate, a surface electromyography, and a knee model, and then tibiofemoral joint contact forces were calculated. Also, a contact stress simulation using the contact areas from the literature was performed. The peak joint contact forces (M +/- SD) were 4566 +/- 1932 N at 140 degrees in rising from full squat and 4479 +/- 1478 N at 90 degrees in rising from kneeling. Under normal contact area, the tibiofemoral contact stresses in deep flexion were less than 5 MPa and did not exceed the stress to damage the cartilage. The contact stress simulation suggests that knee prosthesis having the contact area smaller than 200 mm2 may be problematic since the contact stress in deep flexion would become larger than 21 MPa, and it would lead damage or wear of the polyethylene.     

Pressure erosion of the femoral trochlea, patella baja, and altered patellar surfaces

As knee flexion increases, so do tendofemoral and patellofemoral compression forces. Three cases of long-standing uncorrected flexion contractures of the knees are presented that resulted in marked erosion of the femoral trochlea, patella baja, and remodeled patellar articular surfaces likely reflecting increased angles of flexion. It is probable that the deep femoral grooves are the result of adaptation under high-level persistent contact loads from the quadriceps tendon. These examples expand our knowledge of bone remodeling and offer information of potential use in studying ancient skeletal samples.     

Experimental determination of forces transmitted through the patello-femoral joint

Tensions in the quadriceps tendon and infrapatellar ligament were measured as a function of flexion angle in eight cadaver knees using a load cell of a materials tester to determine the quadriceps force and a spring balance to quantify the patellar tendon force. The ratio between the tensions in the quadriceps tendon and the patellar tendon (FQ/FP) ranged from 1.55 at 70 degrees of flexion to 0.86 at 10 degrees of flexion. The patello-femoral joint reaction (PFJR) force for extension against resistance was maximal at 60 degrees. No change in the quadriceps force required to extend the knee occurred with changes of the Q-angle of +/- 5 degrees. This study demonstrates that FQ does not equal FP as several authors have reported (Bandi, 1972; Barry, 1979; Ficat and Hungerford, 1977; Hungerford and Barry, 1979; Reilly and Martens, 1972; Smidt, 1973). Furthermore, the difference in FQ and FP influences both the magnitude and direction of PFJR. Studies that assess the influence of surgical procedures which alter the patello-femoral joint or the extensor mechanism must take these differences into account.     

A mechanical apparatus with microprocessor controlled stress profile for cyclic compression of cultured articular cartilage explants

An apparatus was designed for mechanical compression of cultured articular cartilage explants with acylindrical plain-ended loading head (diameter 2-5 mm) driven by a stepping motor. A load cell under the culture dish was applied for feedback regulation utilizing a microprocessor-based control unit. The operating programs allowed either continuous or cyclic loading, the latter with adjustable loading/resting ratio. The improvements in the present design compared with previously described apparatuses for similar purposes include: (1) the accurately controlled compression by a load cell and a rapid feedback circuit; (2) the wide range of selectable stresses (25 kPa-12.5 MPa) with both continuous and cyclic loading modes; (3) the ability to handle cycles as short as 1 s with 15 ms peak loading phase. Using a 4 s cycle and 0.5 MPa load for 1.5 h resulted in a significantly enhanced incorporation of radiosulphate in cultured bovine articular cartilage explants, suggesting a stimulation of proteoglycan synthesis. Light and scanning electron microscopic examinations revealed a slight depression and superficial alterations in cartilage structure at the impact site following high pressures. We expect that this apparatus will help in revealing how articular cartilage tissue and chondrocytes respond to external mechanical stimuli.