Assessment of tibial stiffness by vibration testing in situ--II. Influence of soft tissues, joints and fibula

The influence of soft tissues and joints on the vibration of the human tibia was examined by modal analysis on amputated lower limbs, where the soft tissues and the fibula were dissected gradually. Measurements were made in two different set ups, IFR and BRA, which were both designed to monitor fracture healing. In IFR, vibrations are generated by hammer impact on a relaxed hanging lower leg, with the knee flexed. Resonant frequencies are determined by a computer Fourier transform procedure. In BRA, a steady state vibration is induced in a lower leg, supported near the ankle and the tibial tuberosity, using an electromagnetic shaker. Resonant frequencies are determined from the maxima in vibration amplitudes. In both set ups the soft tissues have a similar influence on the vibration of the tibia: the skin hardly influences the determined modal parameter. The mass of the muscles influences both the resonant frequency and the damping. The fibula has a stiffening effect on the tibia. The influence of the joints is small in the IFR-set up: the tibia vibrates in conditions close to those for the free-free vibration. In the BRA-set up, the supports determine the boundary conditions.     

Identification of in-vivo vibration modes of human tibiae by modal analysis

When attempting to evaluate the mechanical properties of human bones in vivo by mechanical vibration analysis, some essential requirements must be met. A quantitative relation between measured vibration parameters (e.g., natural frequency) and mechanical bone properties must be available, in-vivo vibration modes should correctly be identified and the associated natural frequencies reproducibly and accurately measured, the influence of joints and soft tissues must be known. These problems were addressed by modal analysis (i.e., experimental determination of natural frequencies, mode shapes and damping ratios) of human tibiae in the following situations: 1) dry excised tibiae, 2) fresh excised tibiae, 3) in-vivo tibiae, 4) tibiae in an amputated leg, in different steps of dissection. In the in-vivo measuring conditions used by the authors, the tibia vibration is practically free-free. Two single bending modes (at +/- 270 Hz and +/- 340 Hz, respectively), each of them corresponding with one principal direction for bending, were identified. The difference between the natural frequencies observed in vivo and those of fresh excised tibiae is almost completely caused by the effect of muscles (added mass and damping), whereas joints and skin play only a minor role. Frequency differences between fresh and dry excised tibiae are largely accounted for by the absence of bone marrow in the latter.     

Assessment of tibial stiffness by vibration testing in situ--I. Identification of mode shapes in different supporting conditions

Vibrational methods to monitor fracture healing, the BRA and the IFR, are compared under different supporting conditions, excitation technique and signal processing. Mode shapes are identified by modal analysis. A wet excised human tibia and an amputation specimen are investigated. Excitation technique and signal processing caused only minor differences in the resonance frequencies. The supporting conditions had an important influence on the single bending modes changing both mode-shapes and frequencies. Thus the BRA-splint imposed a node at the malleolus. Modal analysis revealed the following modes in the two supporting conditions: BRA-splint: A 'rigid body' mode of 165 Hz in the sagittal plane. A single bending mode of 315 Hz close to the sagittal plane. IFR-hanging leg: A 'rigid-body' mode of 167 Hz close to the sagittal plane. Two single bending modes ('free-free'), a mode of 303 Hz close to the frontal plane and a mode of 470 Hz in the sagittal plane.     

Excessive compression of the human tibio-femoral joint causes ACL rupture

The knee is one of the most frequently injured joints in the human body. A recent study suggests that axial compressive loads on the knee may play a role in injury to the anterior cruciate ligament (ACL) for the flexed knee, because of an approximate 10 degrees posterior tilt in the tibial plateau (J. Orthop. Res. 16 (1998) 122-127). The hypothesis of the current study was that excessive axial compressive loads in the human tibio-femoral (TF) joint would cause relative displacement and rotation of the tibia with respect to the femur, and result in isolated injury to the ACL when the knee is flexed to 60 degrees , 90 degrees or 120 degrees . Sixteen isolated knees from eleven fresh cadaver donors (74.3+/-10.5 yr) were exposed to repetitive TF compressive loads increasing in intensity until catastrophic injury. ACL rupture was documented in 14/16 cases. The maximum TF joint compressive force for ACL failure was 5.1+/-2.1 kN for all flexion angles combined. For the 90 degrees flexed knee, the injury occurred with a relative anterior displacement of 5.4+/-3.8mm, a lateral displacement of 4.1+/-1.4mm, and a 7.8+/-7.0 degrees internal rotation of the tibia with respect to the femur.     

Whole-body vibration induced adaptation in knee extensors; consequences of initial strength, vibration frequency, and joint angle

It was hypothesized that both vibration frequency and muscle length modulate the strengthening of muscles that is assumed to result from whole-body vibration (WBV). Length of knee extensor muscles during vibration is affected by the knee joint angle; the lengths of the knee extensors increase with more flexed knee joint angles. In an intervention study 28 volunteers were randomly assigned to 1 of 4 groups. Each group received 4 weeks of WBV at 1 of 3 different frequencies (20, 27, or 34 Hz) or 1 of 2 different lengths of knee extensors. Voluntary, isometric knee extension moment-angle relationship was determined. Initially, stronger subjects reacted differently to WBV than weaker participants. In stronger subjects knee extension moment did not improve; in the weaker subjects considerable improvements were observed ranging from 10 to 50%. Neither vibration frequency nor muscle length during the intervention affected the improvements. In addition to strength, the knee joint angle at which the maximal joint moment was generated (optimal joint angle) was affected. When trained at short muscle lengths, optimal angle shifted to more extend joint position. WBV training at long muscle lengths tended to induce an opposite shift. The amount of this shift tended to be influenced by vibration frequency; the lower the vibration frequency the larger the shift. Shifts of optimal lengths occurred in both weaker and stronger subjects. This study shows that muscle length during training affects the angle of knee joint at which the maximal extension moment was generated. Moreover, in weaker subjects WBV resulted in higher maximal knee joint extension moments. Vibration frequency and muscle length during vibration did not affect this joint moment gain.     

In vivo measurement of translational stiffness of rabbit knees

This paper describes the design, evaluation, and preliminary results of a specialized testing device and surgical protocol to determine translational stiffness of a rabbit knee, replicating the clinical anterior drawer test. Coronal-plane transverse pins are inserted through the rabbit leg, two in the tibia and one in the distal femur, to hold and reproducibly position the leg in the device for tests at multiple time points. A linear stepper motor draws the tibia upward then returns to the home position, and a load cell measures the resisting force; force-displacement knee stiffness is then calculated. Initial evaluation of this testing device determined the effects of preconditioning, intra-operator repeatability, rabbit-to-rabbit variability, knee flexion angle (90 degrees vs. 135 degrees ), and anterior cruciate ligament (ACL) sectioning (0%, 25%, 50%, 75%, 100%). Knee stiffness generally decreased as ACL sectioning increased. This testing device and surgical protocol provide an objective and efficient method of determining translational rabbit knee stiffness in vivo, and are being used in an ongoing study to evaluate the effect of knee instability (via partial to complete ACL sectioning) on the development of post-traumatic osteoarthritis.     

Development of a three-dimensional finite element model of a human tibia using experimental modal analysis.

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.     

Directionality in the mechanical response to substrate vibration in a treehopper (Hemiptera: Membracidae: Umbonia crassicornis)

The use of substrate vibrations in communication and predator-prey interactions is widespread in arthropods. In many contexts, localization of the vibration source plays an important role. For small species on solid substrates, time and amplitude differences between receptors in different legs may be extremely small, and the mechanisms of vibration localization are unclear. Here we ask whether directional information is contained in the mechanical response of an insect's body to substrate vibration. Our study species was a membracid treehopper (Umbonia crassicornis) that communicates using bending waves in plant stems. We used a bending-wave simulator that allows precise control of the frequency, intensity and direction of the vibrational stimulus. With laser-Doppler vibrometry, we measured points on the substrate and on the insect's thorax and middle leg. Transfer functions showing the response of the body relative to the substrate revealed resonance at lower frequencies and attenuation at higher frequencies. There were two modes of vibration along the body's long axis, a translational and a rotational mode. Furthermore, the transfer functions measured on the body differed substantially depending on whether the stimulus originated in front of or behind the insect. Directional information is thus available in the mechanical response of the body of these insects to substrate vibration. These results suggest a vibration localization mechanism that could function at very small spatial scales.     

Circumferential vibration of microtubules with long axial wavelength

This paper uses an orthotropic shell model to investigate in detail the long axial wavelength circumferential vibration of microtubules (MTs). The deformation patterns in the vibrations were explored and their phonon dispersion relations were presented for MTs with increasing radius. It was shown that with the growth of the axial wavelength, the associated frequency of MTs would finally approach a nonzero asymptotic value, rising considerably with the increase of circumferential wave number but dropping linearly with the growing radius. This study corrects the previous misunderstanding drawn by an oversimplified model, and points out that a parabolic dispersion law does not apply to the circumferential modes when the MT bending stiffness is properly considered.     

Motion of the knee after condylar resurfacing--an in vivo study.

The purpose of this study was determine the amounts of rotation and displacement occurring in a relatively unconstrained condylar replacement knee, and to compare the motion with a matched group of normal knees. The motion was measured using an electromagnetic device, the 3-Space Tracker, for various common activities, for 25 normal volunteers and 25 total knee patients. The main variables studied were internal-external rotation of the tibia about its long axis and anterior-posterior displacement of the femoral origin with respect to the tibia, as a function of flexion angle or per cent of gait cycle. The motion of the total knees was very similar to that of the normals. For sitting, standing and free-swing, the knee rotated internally by 5-10 degrees and the femur displaced posteriorly by 9-14 mm, as the knee was flexed from 0 to 90 degrees. For walking and going upstairs and downstairs the absolute values of the rotations and displacements were similar to the above. However, the mean values of rotation were less due to greater variation in the rotation patterns, due probably to the increased laxity of the knee during the swing phases. From these data, taking the mean motions and one standard deviation (S.D.), it is suggested that a knee prosthesis should allow a rotation from minus to plus 12 degrees (a total range of 24 degrees) and an anterior-posterior displacement of 13 mm. It is suggested that these motions be subject to progressive restraint from the neutral position in the manner of the natural knee.     

In vivo tracking of the human patella.

The purpose of this study was to describe the dynamic, in vivo, three-dimensional tracking pattern of the patella for one normal male subject. Intracortical pins were inserted into the patella, tibia, and femur. The subject performed seated and squatting knee flexion/extension, and maximum voluntary quadriceps contractions. In addition, the vastus medialis oblique was subjected to maximal electrical stimulation. Motions of the markers attached to the intracortical pins were analyzed using an automated video system. Patellar and tibial motions were determined relative to a femoral reference system. While the tibia flexed 50 degrees from full extension (seated condition), the patella flexed 30.3 degrees, tilted laterally 10.3 degrees, and shifted laterally 8.6 mm. In general, these results show qualitative agreement with the data collected from cadaveric specimens [van Kampen and Huiskes, J. orthop. Res. 8, 372-382 (1990)]. The differences present may reflect different passive constraints to patellar motions, and different relative loading of the individual quadriceps components, in our study compared to the cadaveric study. Only small differences were found between patellar motions in the seated and squatting conditions. Differences in patellar displacements produced by (1) maximal electrical stimulation of the vastus medialis oblique, and (2) maximum voluntary quadriceps contraction, at 30 degrees knee flexion and full extension, may reflect the dominant influence of passive constraints, and the vastus lateralis, on normal patellar motions. Further in vivo study of patellar tracking seems warranted to evaluate surgical and conservative interventions for patellofemoral disorders.     

The effect of wire plane tilt and olive wires on proximal tibia fracture fragment stability and fracture site motion

To analyze the effect of the tilt angle relationship between the crossed wire plane and the bone axis on the stiffness of fine wire external fixation, load-deformation behavior was compared across different tilt angles (0 degree, 10 degrees, and 20 degrees) of the plane containing crossed smooth or olive wires under identical conditions of central axial compression, medial compression-bending, posterior compression-bending, posteromedial compression-bending, and torsion. Stiffness values were calculated from the load-deformation and torque-angle curves. A tilt angle of 20 degrees with olive wires provided significantly greater stiffness compared to smooth wires at any angle in any loading condition (p < 0.05). A tilt angle of 20 degrees with olive wires was also significantly more stiff than a tilt angle of 0 degree with olive wires in any loading condition. In torsion, olive wires with 10 degrees and 20 degrees tilt were not significantly different, while in posterior bending olive wires with 10 degrees tilt were significantly stiffer than olive wires with 0 degree or 20 degrees tilt. With smooth wires, tilting the wire plane caused a decrease in stiffness in posterior bending, posteromedial bending, and torsion. Overall, the use of olive wires in conjunction with tilting the wire plane enhances the fixation stiffness for proximal tibia fractures while allowing more options for wire configurations that avoid neurovascular and musculotendinous structures, and wounds.     

Measuring three-dimensional knee kinematics under torsional loading

Excessive knee joint laxity is often used as an indicator of joint disease or injury. Clinical assessment devices are currently limited to anterior–posterior drawer measurements, while tools used to measure movement in the remaining degrees of freedom are either invasive or prone to soft tissue artefact. The objective of this work was, therefore, to develop a methodology whereby in vivo knee joint kinematics could be measured in three dimensions under torsional loading while still maintaining a non-invasive procedure. A device designed to administer a subject-normalized torque in the transverse plane of the knee was securely fastened to the outer frame of an open magnetic resonance imaging (MRI) magnet. Low resolution 3D T1-weighted images (6.25 mm slice thickness) were generated by the 0.2 Tesla MRI scanner in less than 3 min while the joint was under load. The 3D image volume was then shape-matched to a high resolution image volume (1.56 mm slice thickness) scanned in a no-load position. Three-dimensional rotations and translations of the tibia with respect to the femur were calculated by comparing the transformation matrices before and after torque was applied. Results from six subjects showed that this technique was repeatable over five trials with the knee in extended and flexed positions. Differences in range of rotation were shown between subjects and between knee positions, suggesting that this methodology has sufficient utility for further application in clinical studies.     

Intralimb compensation strategy depends on the nature of joint perturbation in human hopping

Due to the well-described spring-mass dynamics of bouncing gaits, human hopping is a tractable model for elucidating basic neuromuscular compensation principles. We tested whether subjects would employ a multi-joint or single-joint response to stabilize leg stiffness while wearing a spring-loaded ankle-foot orthosis (AFO) that applied localized resistive and assistive torques to the ankle. We analyzed kinematics and kinetics data from nine subjects hopping in place on one leg, at three frequencies (2.2, 2.4, and 2.8Hz) and three orthosis conditions (freely articulating AFO, AFO with plantarflexion resistance, and AFO with plantarflexion assistance). Leg stiffness was invariant across AFO conditions, however, compensation strategy depended upon the nature of the applied load. Biological ankle stiffness increased in response to a resistive load at twice the rate that it decreased with an assitive load. Ankle adjustments alone fully compensated for an assistive load with no net change in combined (biological plus applied) total ankle stiffness (p > or =0.133). In contrast, a resistive load resulted in a 7.4-9.0% increase in total ankle stiffness across frequencies and a concomitant 10-15% increase in knee joint stiffness at each frequency (p< or =0.037). The increased knee joint stiffness in response to resistive ankle load allowed subjects to maintain a more flexed knee at mid-stance, which attenuated the effect of the increased total ankle joint stiffness to preserve leg stiffness and whole limb biomechanical performance. Our findings suggest humans maintain invariant leg stiffness in bouncing gaits through different intralimb compensation strategies that are specific to the nature of the joint loading.     

Apparent mass of the standing human body when using a whole-body vibration training machine: Effect of knee angle and input frequency

Several studies have investigated the transmission of vibration from the vibrating plate of a whole-body vibration training machine (WBVTM) to different locations on the human body. No known work has investigated the interface force between the vibrating plate of the machine and the human body. This paper investigates the effect of bending the knees and the vibration frequency on the interface force (presented as apparent mass (AM)) between the vibrating plate and the body. Twelve male subjects stood with four different knee angles (180, 165, 150 and 135°) and were exposed to sinusoidal vertical vibration at eight frequencies in the range of 17–42 Hz. The vertical acceleration and the interface force between the body and the vibrating plate were measured and used to calculate the AM. The acceleration and force depended on the frequency and were found to vary with both the adopted posture and subject. The AM generally decreased with increasing the frequency but showed a peak at 24 Hz which was clearer when the knees were bent. Bending the knees showed an effect similar to increasing the damping of a system with base excitation; increasing the damping reduced the AM in the resonance region but increased the AM at higher frequencies. Users of WBVTMs have to be careful when choosing the training posture: although, as shown in previous studies, bending the knees reduces the transmission of vibration to the spine, it increases the interface forces which might indicate increased stresses on the lower legs and joints.     

Neural adaptive control for vibration suppression in composite fin-tip of aircraft

In this paper, we present a neural adaptive control scheme for active vibration suppression of a composite aircraft fin tip. The mathematical model of a composite aircraft fin tip is derived using the finite element approach. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes very accurately. Piezo-electric actuators and sensors are placed at optimal locations such that the vibration suppression is a maximum. Model-reference direct adaptive neural network control scheme is proposed to force the vibration level within the minimum acceptable limit. In this scheme, Gaussian neural network with linear filters is used to approximate the inverse dynamics of the system and the parameters of the neural controller are estimated using Lyapunov based update law. In order to reduce the computational burden, which is critical for real-time applications, the number of hidden neurons is also estimated in the proposed scheme. The global asymptotic stability of the overall system is ensured using the principles of Lyapunov approach. Simulation studies are carried-out using sinusoidal force functions of varying frequency. Experimental results show that the proposed neural adaptive control scheme is capable of providing significant vibration suppression in the multiple bending modes of interest. The performance of the proposed scheme is better than the H(infinity) control scheme.     

Evaluation of the use of resonant frequencies to characterize physical properties of human long bones

Human tibiae were subjected to steady state vibration over a frequency range to evaluate the use of clinical measurements of resonant frequency to characterize osteoporosis. Displacement and force transmitted to the bone were monitored and used to obtain measures of dynamic mass, stiffness, damping and resonant frequency. Initial results indicate that resonant frequency F is a less sensitive indicator of change in state than either generalized mass M or generalized stiffness K due to the functional relationship of these three parameters.     

Effects of ankle position during static stretching for the hamstrings on the decrease in passive stiffness

Static stretching is frequently performed to improve flexibility of the hamstrings, although the ankle position during hamstring stretching has not been fully investigated. We investigated the effects of ankle position during hamstring stretching on the decrease in passive stiffness. Fourteen healthy men performed static stretching for the hamstrings with the ankle dorsiflexed and plantar-flexed in a randomized order on different days. The hip was passively flexed to the maximum angle which could be tolerated without stretch pain with the knee fully extended; this was maintained for 5 min, with 1-min stretching performed in 5 sessions. Final angles and passive stiffness were measured before and after stretching. The final angle was defined as that formed by the tibia and horizontal plane when the knee was passively extended from hip and knee angles at 90° flexion to the maximum extension angle which could be tolerated without stretch pain. Passive stiffness was determined by the slope of torque–angle curve during the measurement of the final angle. The final angle significantly increased after stretching with the ankle dorsiflexed and plantar-flexed, whereas passive stiffness significantly decreased only after stretching with the ankle planter-flexed. The results suggest that passive stiffness decreases after stretching with the ankle planter-flexed but not after stretching with the ankle dorsiflexed, although the range of joint motion increases regardless of the ankle position during 5-min stretching for the hamstrings. These results indicate that static stretching should be performed with the ankle plantar-flexed when aiming to decrease passive stiffness of the hamstrings.     

A comparison of electrical activity in the triceps surae at maximum isometric contraction with the knee and ankle at various angles

The purpose of this study was to test the endurance of the soleus muscle, and to examine the joint position at which it is most active, while simultaneously suppressing the activity of the gastrocnemius. Ten young males performed maximum isometric contraction of the triceps surae for 100 s, and the endurance and plantar flexion torque of this muscle were measured at various angles of the knee and ankle joints. The electromyogram was measured simultaneously and subsequently converted into integrated electromyogram (IEMG) values. With the knee flexed at 130 degrees, the rate of change in IEMG values for the soleus (0.454% x s(-1)) with the ankle in a neutral position was significantly higher than that for the medial and lateral gastrocnemius. Both with the ankle dorsiflexed at 10 degrees and in the neutral position, the rate of change in IEMG for the soleus was significantly higher with the knee flexed at 90 degrees and 130 degrees than with the knee fully extended. With the knee flexed at 90 degrees and 130 degrees, the IEMG activity of the soleus during the initial (5-10 s) and final 5 s tended to be higher than those for the medial and lateral gastrocnemius, regardless of the ankle joint position. We conclude that the position in which the soleus acts most selectively during a sustained maximum isometric contraction of the triceps surae is with the ankle in a neutral position and the knee flexed at 130 degrees.