Determination of trunk muscle forces for flexion and extension by using a validated finite element model of the lumbar spine and measured in vivo data

Muscle forces stabilize the spine and have a great influence on spinal loads. But little is known about their magnitude. In a former in vitro experiment, a good agreement with intradiscal pressure and fixator loads measured in vivo could be achieved for standing and extension of the lumbar spine. However, for flexion the agreement between in vitro and in vivo measurements was insufficient. In order to improve the determination of trunk muscle forces, a three-dimensional nonlinear finite element model of the lumbar spine with an internal fixation device was created and the same loads were applied as in a previous in vitro experiment. An extensive adaptation process of the model was performed for flexion and extension angles up to 20 degrees and -15 degrees, respectively. With this validated computer model intra-abdominal pressure, preload in the fixators, and a combination of hip- and lumbar flexion angle were varied until a good agreement between analytical and in vivo results was reached for both, intradiscal pressure and bending moments in the fixators. Finally, the fixators were removed and the muscle forces for the intact lumbar spine calculated. A good agreement with the in vivo results could only be achieved at a combination of hip- and lumbar flexion. For the intact spine, forces of 170, 100 and 600 N are predicted in the m. erector spinae for standing, 5 degrees extension and 30 degrees flexion, respectively. The force in the m. rectus abdominus for these body positions is less than 25 N. For more than 10 degrees extension the m. erector spinae is unloaded. The finite element method together with in vivo data allows the estimation of trunk muscle forces for different upper body positions in the sagittal plane. In our patients, flexion of the upper body was most likely a combination of hip- and lumbar spine bending.     

Estimation of trunk muscle forces using the finite element method and in vivo loads measured by telemeterized internal spinal fixation devices.

Direct quantitative measurement of muscle forces is not possible. Forces in the trunk muscles were estimated for standing and flexion of the upper body using three-dimensional, nonlinear finite element models of the lumbar spine with and without an internal spinal fixation device. Muscle forces assumed were two pairs dorsally and one ventrally, each representing several muscles. Muscle forces in the model with internal fixators were varied in discrete steps until the implant loads calculated closely corresponded to those measured in a patient with an instrumented implant. The calculated angles between adjacent lumbar vertebrae were compared with corresponding values measured on X-ray films of a patient as well as with literature values and served as a second criterion for predicting muscle forces. For the model without an implant, the muscle forces of the first model were slightly varied until the lumbar spine shape and the intradiscal pressure were physiological. The abdomen was shown to have a considerable supporting function for flexion.     

Activities of Everyday Life with High Spinal Loads

Activities with high spinal loads should be avoided by patients with back problems. Awareness about these activities and knowledge of the associated loads are important for the proper design and pre-clinical testing of spinal implants. The loads on an instrumented vertebral body replacement have been telemetrically measured for approximately 1000 combinations of activities and parameters in 5 patients over a period up to 65 months postoperatively. A database containing, among others, extreme values for load components in more than 13,500 datasets was searched for 10 activities that cause the highest resultant force, bending moment, torsional moment, or shear force in an anatomical direction. The following activities caused high resultant forces: lifting a weight from the ground, forward elevation of straight arms with a weight in hands, moving a weight laterally in front of the body with hanging arms, changing the body position, staircase walking, tying shoes, and upper body flexion. All activities have in common that the center of mass of the upper body was moved anteriorly. Forces up to 1650 N were measured for these activities of daily life. However, there was a large intra- and inter-individual variation in the implant loads for the various activities depending on how exercises were performed. Measured shear forces were usually higher in the posterior direction than in the anterior direction. Activities with high resultant forces usually caused high values of other load components.     

The rib cage reduces intervertebral disc pressures in cadaveric thoracic spines by sharing loading under applied dynamic moments

The effects of the rib cage on thoracic spine loading are not well studied, but the rib cage may provide stability or share loads with the spine. Intervertebral disc pressure provides insight into spinal loading, but such measurements are lacking in the thoracic spine. Thus, our objective was to examine thoracic intradiscal pressures under applied pure moments, and to determine the effect of the rib cage on these pressures. Human cadaveric thoracic spine specimens were positioned upright in a testing machine, and Dynamic pure moments (0 to ±5 N·m) with a compressive follower load of 400 N were applied in axial rotation, flexion - extension, and lateral bending. Disc pressures were measured at T4-T5 and T8-T9 using needle-mounted pressure transducers, first with the rib cage intact, and again after the rib cage was removed. Changes in pressure vs. moment slopes with rib cage removal were examined. Pressure generally increased with applied moments, and pressure-moment slope increased with rib cage removal at T4-T5 for axial rotation, extension, and lateral bending, and at T8-T9 for axial rotation. The results suggest the intact rib cage carried about 62% and 56% of axial rotation moments about T4-T5 and T8-T9, respectively, as well as 42% of extension moment and 36–43% of lateral bending moment about T4-T5 only. The rib cage likely plays a larger role in supporting moments than compressive loads, and may also play a larger role in the upper thorax than the lower thorax.     

A continuous pure moment loading apparatus for biomechanical testing of multi-segment spine specimens

An apparatus is described that enables the application of continuous pure moment loads to multi-segment spine specimens. This loading apparatus allows continuous cycling of the spine between specified flexion and extension (or right and left lateral bending) maximum load endpoints. Using a six-degree-of-freedom load cell and three-dimensional optoelectronic stereophotogrammetry, characteristic displacement versus load hysteresis curves can be generated and analyzed for different spinal constructs of interest. Unlike quasi-static loading, the use of continuous loading permits the analysis of the spine's behaviour within the neutral zone. This information is of particular clinical significance given that the instability of a spinal segment is related to its flexibility within the neutral zone. Representative curves for the porcine lumbar spine in flexion-extension and lateral bending are presented to illustrate the capabilities of this system.     

Flexion and extension structural properties and strengths for male cervical spine segments

New vehicle safety standards are designed to limit the amount of neck tension and extension seen by out-of-position motor vehicle occupants during airbag deployments. The criteria used to assess airbag injury risk are currently based on volunteer data and animal studies due to a lack of bending tolerance data for the adult cervical spine. This study provides quantitative data on the flexion-extension bending properties and strength on the male cervical spine, and tests the hypothesis that the male is stronger than the female in pure bending. An additional objective is to determine if there are significant differences in stiffness and strength between the male upper and lower cervical spine. Pure-moment flexibility and failure testing was conducted on 41 male spinal segments (O-C2, C4-C5, C6-C7) in a pure-moment test frame and the results were compared with a previous study of females. Failures were conducted at approximately 90 N-m/s. In extension, the male upper cervical spine (O-C2) fails at a moment of 49.5 (s.d. 17.6)N-m and at an angle of 42.4 degrees (s.d. 8.0 degrees). In flexion, the mean moment at failure is 39.0 (s.d. 6.3 degrees) N-m and an angle of 58.7 degrees (s.d. 5.1 degrees). The difference in strength between flexion and extension is not statistically significant. The difference in the angles is statistically significant. The upper cervical spine was significantly stronger than the lower cervical spine in both flexion and extension. The male upper cervical spine was significantly stiffer than the female and significantly stronger than the female in flexion. Odontoid fractures were the most common injury produced in extension, suggesting a tensile mechanism due to tensile loads in the odontoid ligamentous complex.     

Ultimate strength of the lumbar spine in flexion--an in vitro study

The ultimate strength in flexion of 16 lumbar functional spinal units (FSU) was determined. The specimens were exposed to a combined static load of bending and shearing in the sagittal plane until overt rupture occurred (simulated flexion-distraction injuries). The biomechanical response of the FSU was measured with a force and moment platform. Mechanical displacement gauges were used to measure vertical displacements (flexion angulation) of the specimens. Photographs were taken after each loading step for determination of horizontal displacements and the centre of rotation. The lumbar FSU could resist a combination of bending moment and shear force of 156 Nm and 620 N respectively, before complete disruption occurred. The tension force acting on the posterior structures was 2.8 kN. The flexion angulation just before failure was 20 degrees and the anterior horizontal displacement between the upper and lower vertebrae was 9 mm. The centre of rotation was located in the posterior part of the lower vertebral body. The bone mineral content in the vertebrae appeared to be a good predictor of ultimate strength of the lumbar FSU. Knowledge of the biomechanical response of the lumbar spine under different static traumatic loads is a first step to better understand the injury mechanisms of the spine in traffic accidents.     

Load-Relaxation Properties of the Human Trunk in Response to Prolonged Flexion: Measuring and Modeling the Effect of Flexion Angle

Experimental studies suggest that prolonged trunk flexion reduces passive support of the spine. To understand alterations of the synergy between active and passive tissues following such loadings, several studies have assessed the time-dependent behavior of passive tissues including those within spinal motion segments and muscles. Yet, there remain limitations regarding load-relaxation of the lumbar spine in response to flexion exposures and the influence of different flexion angles. Ten healthy participants were exposed for 16 min to each of five magnitudes of lumbar flexion specified relative to individual flexion-relaxation angles (i.e., 30, 40, 60, 80, and 100%), during which lumbar flexion angle and trunk moment were recorded. Outcome measures were initial trunk moment, moment drop, parameters of four viscoelastic models (i.e., Standard Linear Solid model, the Prony Series, Schapery''s Theory, and the Modified Superposition Method), and changes in neutral zone and viscoelastic state following exposure. There were significant effects of flexion angle on initial moment, moment drop, changes in normalized neutral zone, and some parameters of the Standard Linear Solid model. Initial moment, moment drop, and changes in normalized neutral zone increased exponentially with flexion angle. Kelvin-solid models produced better predictions of temporal behaviors. Observed responses to trunk flexion suggest nonlinearity in viscoelastic properties, and which likely reflected viscoelastic behaviors of spinal (lumbar) motion segments. Flexion-induced changes in viscous properties and neutral zone imply an increase in internal loads and perhaps increased risk of low back disorders. Kelvin-solid models, especially the Prony Series model appeared to be more effective at modeling load-relaxation of the trunk.     

Spinal stability and role of passive stiffness in dynamic squat and stoop lifts

The spinal stability and passive-active load partitioning under dynamic squat and stoop lifts were investigated as the ligamentous stiffness in flexion was altered. Measured in vivo kinematics of subjects lifting 180 N at either squat or stoop technique was prescribed in a nonlinear transient finite element model of the spine. The Kinematics-driven approach was utilized for temporal estimation of muscle forces, internal spinal loads and system stability. The finite element model accounted for nonlinear properties of the ligamentous spine, wrapping of thoracic extensor muscles and trunk dynamic characteristics while subject to measured kinematics and gravity/external loads. Alterations in passive properties of spine substantially influenced muscle forces, spinal loads and system stability in both lifting techniques, though more so in stoop than in squat. The squat technique is advocated for resulting in smaller spinal loads. Stability of spine in the sagittal plane substantially improved with greater passive properties, trunk flexion and load. Simulation of global extensor muscles with curved rather than straight courses considerably diminished loads on spine and increased stability throughout the task.     

Comparative strengths and structural properties of the upper and lower cervical spine in flexion and extension

The purpose of this study is to test the hypothesis that the upper cervical spine is weaker than the lower cervical spine in pure flexion and extension bending, which may explain the propensity for upper cervical spine injuries in airbag deployments. An additional objective is to evaluate the relative strength and flexibility of the upper and lower cervical spine in an effort to better understand injury mechanisms, and to provide quantitative data on bending responses and failure modes. Pure moment flexibility and failure testing was conducted on 52 female spinal segments in a pure-moment test frame. The average moment at failure for the O-C2 segments was 23.7+/-3.4Nm for flexion and 43.3+/-9.3Nm for extension. The ligamentous upper cervical spine was significantly stronger in extension than in flexion (p=0.001). The upper cervical spine was significantly stronger than the lower cervical spine in extension. The relatively high strength of the upper cervical spine in tension and in extension is paradoxical given the large number of upper cervical spine injuries in out-of-position airbag deployments. This discrepancy is most likely due to load sharing by the active musculature.     

Contact pressure in the facet joint during sagittal bending of the cadaveric cervical spine

The facet joint contributes to the normal biomechanical function of the spine by transmitting loads and limiting motions via articular contact. However, little is known about the contact pressure response for this joint. Such information can provide a quantitative measure of the facet joint's local environment. The objective of this study was to measure facet pressure during physiologic bending in the cervical spine, using a joint capsule-sparing technique. Flexion and extension bending moments were applied to six human cadaveric cervical spines. Global motions (C2-T1) were defined using infra-red cameras to track markers on each vertebra. Contact pressure in the C5-C6 facet was also measured using a tip-mounted pressure transducer inserted into the joint space through a hole in the postero-inferior region of the C5 lateral mass. Facet contact pressure increased by 67.6 ± 26.9 kPa under a 2.4 Nm extension moment and decreased by 10.3 ± 9.7 kPa under a 2.7 Nm flexion moment. The mean rotation of the overall cervical specimen motion segments was 9.6 ± 0.8° and was 1.6 ± 0.7° for the C5-C6 joint, respectively, for extension. The change in pressure during extension was linearly related to both the change in moment (51.4 ± 42.6 kPa/Nm) and the change in C5-C6 angle (18.0 ± 108.9 kPa/deg). Contact pressure in the inferior region of the cervical facet joint increases during extension as the articular surfaces come in contact, and decreases in flexion as the joint opens, similar to reports in the lumbar spine despite the difference in facet orientation in those spinal regions. Joint contact pressure is linearly related to both sagittal moment and spinal rotation. Cartilage degeneration and the presence of meniscoids may account for the variation in the pressure profiles measured during physiologic sagittal bending. This study shows that cervical facet contact pressure can be directly measured with minimal disruption to the joint and is the first to provide local pressure values for the cervical joint in a cadaveric model.     

Model and in vivo studies on human trunk load partitioning and stability in isometric forward flexions

To resolve the trunk redundancy to determine muscle forces, spinal loads, and stability margin in isometric forward flexion tasks, combined in vivo-numerical model studies was undertaken. It was hypothesized that the passive resistance of both the ligamentous spine and the trunk musculature plays a crucial role in equilibrium and stability of the system. Fifteen healthy males performed free isometric trunk flexions of approximately 40 degrees and approximately 65 degrees +/- loads in hands while kinematics by skin markers and EMG activity of trunk muscles by surface electrodes were measured. A novel kinematics-based approach along with a nonlinear finite element model were iteratively used to calculate muscle forces and internal loads under prescribed measured postures and loads considered in vivo. Stability margin was investigated using nonlinear, linear buckling, and perturbation analyses under various postures, loads and alterations in ligamentous stiffness. Flexion postures significantly increased activity in extensor muscles when compared with standing postures while no significant change was detected in between flexed postures. Compression at the L5-S1 substantially increased from 570 and 771 N in upright posture, respectively, for +/-180 N, to 1912 and 3308 N at approximately 40 degrees flexion, and furthermore to 2332 and 3850 N at approximately 65 degrees flexion. Passive ligamentous/muscle components resisted up to 77% of the net moment. In flexion postures, the spinal stability substantially improved due both to greater passive stiffness and extensor muscle activities so that, under 180 N, no muscle stiffness was required to maintain stability. The co-activity of abdominal muscles and the muscle stiffness were of lesser concern to maintain stability in forward flexion tasks as compared with upright tasks. An injury to the passive system, on one hand, required a substantial compensatory increase in active muscle forces which further increased passive loads and, hence, the risk of injury and fatigue. On the other hand, it deteriorated the system stability which in turn could require greater additional muscle activation. This chain of events would place the entire trunk active-passive system at higher risks of injury, fatigue and instability.     

Sensitivity of lumbar spine response to follower load and flexion moment: finite element study

The follower load (FL) combined with moments is commonly used to approximate flexed/extended posture of the lumbar spine in absence of muscles in biomechanical studies. There is a lack of consensus as to what magnitudes simulate better the physiological conditions. Considering the in-vivo measured values of the intradiscal pressure (IDP), intervertebral rotations (IVRs) and the disc loads, sensitivity of these spinal responses to different FL and flexion moment magnitudes was investigated using a 3D nonlinear finite element (FE) model of ligamentous lumbosacral spine. Optimal magnitudes of FL and moment that minimize deviation of the model predictions from in-vivo data were determined. Results revealed that the spinal parameters i.e. the IVRs, disc moment, and the increase in disc force and moment from neutral to flexed posture were more sensitive to moment magnitude than FL magnitude in case of flexion. The disc force and IDP were more sensitive to the FL magnitude than moment magnitude. The optimal ranges of FL and flexion moment magnitudes were 900–1100 N and 9.9–11.2 Nm, respectively. The FL magnitude had reverse effect on the IDP and disc force. Thus, magnitude for FL or flexion that minimizes the deviation of all the spinal parameters together from the in-vivo data can vary. To obtain reasonable compromise between the IDP and disc force, our findings recommend that FL of low magnitude must be combined with flexion moment of high intensity and vice versa.     

Trunk strength,muscle activity and spinal loads in maximum isometric flexion and extension exertions: A combined in vivo-computational study

Determination of the trunk maximum voluntary exertion moment capacity and associated internal spinal forces could serve in proper selection of workers for specific occupational task requirements, injury prevention and treatment outcome evaluations. Maximum isometric trunk exertion moments in flexion and extension along with surface EMG of select trunk muscles are measured in 12 asymptomatic subjects. Subsequently and under individualized measured harness-subject forces, kinematics and upper trunk gravity, an iterative kinematics-driven finite element model is used to compute muscle forces and spinal loads in 4 of these subjects. Different co-activity and intra-abdominal pressure levels are simulated. Results indicate significantly larger maximal resistant moments and spinal compression/shear forces in extension exertions than flexion exertions. The agonist trunk muscles reach their maximum force generation (saturation) to greater extent in extension exertions compared to flexion exertions. Local lumbar extensor muscles are highly active in extension exertions and generate most of the internal spinal forces. The maximum exertion attempts produce large spinal compression and shear loads that increase with the antagonist co-activity level but decrease with the intra-abdominal pressure. Intra-abdominal pressure decreases agonist muscle forces in extension exertions but generally increase them in flexion exertions.     

Analysis of large compression loads on lumbar spine in flexion and in torsion using a novel wrapping element

Axial compression on the spine could reach large values especially in lifting tasks which also involve large rotations. Experimental and numerical investigations on the spinal multi motion segments in presence of physiological compression loads cannot adequately be carried out due to the structural instability and artefact loads. To circumvent these problems, a novel wrapping cable element is used in a nonlinear finite element model of the lumbosacral spine (L1-S1) to investigate the role of moderate to large compression loads on the lumbar stiffness in flexion and axial moments/rotations. The compression loads up to 2,700 N was applied with no instability or artefact loads. The lumbar stiffness substantially increased under compression force, flexion moment, and axial torque when applied alone. The presence of compression preloads significantly stiffened the load-displacement response under flexion and axial moments/rotations. This stiffening effect was much more pronounced under larger preloads and smaller moments/rotations. Compression preloads also increased intradiscal pressure, facet contact forces, and maximum disc fibre strain at different levels. Forces in posterior ligaments were, however, diminished with compression preload. The significant increase in spinal stiffness, hence, should be considered in biomechanical studies for accurate investigation of the load partitioning, system stability, and fixation systems/disc prostheses.     

Effect of bone graft characteristics on the mechanical behavior of the lumbar spine

There is little information about the influence of bone graft size, position and elasticity on the mechanical behavior of the lumbar spine. Intersegmental motion, intradiscal pressure and stresses in the lumbar spine were calculated using a three-dimensional, nonlinear finite element model which included an internal spinal fixation device and a bone graft. Cross-sectional area, position, and elastic modulus of the graft were varied in this study. Bone grafts, especially very stiff ones, increase stresses on adjacent endplates. Though larger grafts lead to less contact pressure, it is difficult to judge the quality of different bone graft positions. In general, ventral flexion results in lower maximum contact pressure than lateral bending. There is always little intersegmental rotation in the bridged region compared with that of an intact spine.A larger graft with low stiffness should be favored from a mechanical point of view. Patients should avoid lateral bending of the upper body shortly after surgery.     

The effect of follower load on the intersegmental coupled motion characteristics of the human thoracic spine: An in vitro study using entire rib cage specimens

The mechanical coupling behaviour of the thoracic spine is still not fully understood. For the validation of numerical models of the thoracic spine, however, the coupled motions within the single spinal segments are of importance to achieve high model accuracy. In the present study, eight fresh frozen human thoracic spinal specimens (C7-L1, mean age 54 ± 6 years) including the intact rib cage were loaded with pure bending moments of 5 Nm in flexion/extension (FE), lateral bending (LB), and axial rotation (AR) with and without a follower load of 400 N. During loading, the relative motions of each vertebra were monitored. Follower load decreased the overall ROM (T1-T12) significantly (p < 0.01) in all primary motion directions (extension: −46%, left LB: −72%, right LB: −72%, left AR: −26%, right AR: −26%) except flexion (−36%). Substantial coupled motion was found in lateral bending with ipsilateral axial rotation, which increased after a follower load was applied, leading to a dominant axial rotation during primary lateral bending, while all other coupled motions in the different motion directions were reduced under follower load. On the monosegmental level, the follower load especially reduced the ROM of the upper thoracic spine from T1-T2 to T4-T5 in all motion directions and the ROM of the lower thoracic spine from T9-T10 to T11-T12 in primary lateral bending. The facet joints, intervertebral disc morphologies, and the sagittal curvature presumably affect the thoracic spinal coupled motions depending on axial compressive preloading. Using these results, the validation of numerical models can be performed more accurately.     

Effects of external trunk loads on lumbar spine stability

Stability of the lumbar spine is an important factor in determining spinal response to sudden loading. Using two different methods, this study evaluated how various trunk load magnitudes and directions affect lumbar spine stability. The first method was a quick release procedure in which effective trunk stiffness and stability were calculated from trunk kinematic response to a resisted-force release. The second method combined trunk muscle EMG data with a biomechanical model to calculate lumbar spine stability. Twelve subjects were tested in trunk flexion, extension, and lateral bending under nine permutations of vertical and horizontal trunk loading. The vertical load values were set at 0, 20, and 40% of the subject's body weight (BW). The horizontal loads were 0, 10, and 20% of BW. Effective spine stability as obtained from quick release experimentation increased significantly (p<0.01) with increased vertical and horizontal loading. It ranged from 785 (S.D.=580) Nm/rad under no-load conditions to 2200 (S.D.=1015) Nm/rad when the maximum horizontal and vertical loads were applied to the trunk simultaneously. Stability of the lumbar spine achieved prior to force release and estimated from the biomechanical model explained approximately 50% of variance in the effective spine stability obtained from quick release trials in extension and lateral bending (0.53相似文献   

Dynamic Biomechanical Examination of the Lumbar Spine with Implanted Total Spinal Segment Replacement (TSSR) Utilizing a Pendulum Testing System

Background

Biomechanical investigations of spinal motion preserving implants help in the understanding of their in vivo behavior. In this study, we hypothesized that the lumbar spine with implanted total spinal segment replacement (TSSR) would exhibit decreased dynamic stiffness and more rapid energy absorption compared to native functional spinal units under simulated physiologic motion when tested with the pendulum system.

Methods

Five unembalmed, frozen human lumbar functional spinal units were tested on the pendulum system with axial compressive loads of 181 N, 282 N, 385 N, and 488 N before and after Flexuspine total spinal segment replacement implantation. Testing in flexion, extension, and lateral bending began by rotating the pendulum to 5°; resulting in unconstrained oscillatory motion. The number of rotations to equilibrium was recorded and bending stiffness (N-m/°) was calculated and compared for each testing mode.

Results

The total spinal segment replacement reached equilibrium with significantly fewer cycles to equilibrium compared to the intact functional spinal unit at all loads in flexion (p<0.011), and at loads of 385 N and 488 N in lateral bending (p<0.020). Mean bending stiffness in flexion, extension, and lateral bending increased with increasing load for both the intact functional spinal unit and total spinal segment replacement constructs (p<0.001), with no significant differences in stiffness between the intact functional spinal unit and total spinal segment replacement in any of the test modes (p>0.18).

Conclusions

Lumbar functional spinal units with implanted total spinal segment replacement were found to have similar dynamic bending stiffness, but absorbed energy at a more rapid rate than intact functional spinal units during cyclic loading with an unconstrained pendulum system. Although the effects on clinical performance of motion preserving devices is not fully known, these results provide further insight into the biomechanical behavior of this device under approximated physiologic loading conditions.     

On the estimate of the two dominant axes of the knee using an instrumented spatial linkage

This article presents the validation of a technique to assess the appropriateness of a 2 degree-of-freedom model for the human knee, and, in which case, the dominant axes of flexion/extension and internal/external longitudinal rotation are estimated. The technique relies on the use of an instrumented spatial linkage for the accurate detection of passive knee kinematics, and it is based on the assumption that points on the longitudinal rotation axis describe nearly circular and planar trajectories, whereas the flexion/extension axis is perpendicular to those trajectories through their centers of rotation. By manually enforcing a tibia rotation while bending the knee in flexion, a standard optimization algorithm is used to estimate the approximate axis of longitudinal rotation, and the axis of flexion is estimated consequently. The proposed technique is validated through simulated data and experimentally applied on a 2 degree-of-freedom mechanical joint. A procedure is proposed to verify the fixed axes assumption for the knee model. The suggested methodology could be possibly valuable in understanding knee kinematics, and in particular for the design and implant of customized hinged external fixators, which have shown to be effective in knee dislocation treatment and rehabilitation.