Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion

We propose to model planar movements between two human segments by means of rolling-without-slipping kinematic pairs. We compute the path traced by the instantaneous center of rotation (ICR) as seen from the proximal and distal segments, thus obtaining the fixed and moving centrodes, respectively. The joint motion is then represented by the rolling-without-slipping of one centrode on the other. The resulting joint kinematic model is based on the real movement and accounts for nonfixed axes of rotation; therefore it could improve current models based on revolute pairs in those cases where joint movement implies displacement of the ICR. Previous authors have used the ICR to characterize human joint motion, but they only considered the fixed centrode. Such an approach is not adequate for reproducing motion because the fixed centrode by itself does not convey information about body position. The combination of the fixed and moving centrodes gathers the kinematic information needed to reproduce the position and velocities of moving bodies. To illustrate our method, we applied it to the flexion-extension movement of the head relative to the thorax. The model provides a good estimation of motion both for position variables (mean R(pos)=0.995) and for velocities (mean R(vel)=0.958). This approach is more realistic than other models of neck motion based on revolute pairs, such as the dual-pivot model. The geometry of the centrodes can provide some information about the nature of the movement. For instance, the ascending and descending curves of the fixed centrode suggest a sequential movement of the cervical vertebrae.     

Quantifying the centre of rotation pattern in a multi-body model of the lumbar spine

Understanding the kinematics of the spine provides paramount knowledge for many aspects of the clinical analysis of back pain. More specifically, visualisation of the instantaneous centre of rotation (ICR) enables clinicians to quantify joint laxity in the segments, avoiding a dependence on more inconclusive measurements based on the range of motion and excessive translations, which vary in every individual. Alternatively, it provides motion preserving designers with an insight into where a physiological ICR of a motion preserving prosthesis can be situated in order to restore proper load distribution across the passive and active elements of the lumbar region. Prior to the use of an unconstrained dynamic musculoskeletal model system, based on multi-body models capable of transient analysis, to estimate segmental loads, the model must be kinematically evaluated for all possible sensitivity due to ligament properties and the initial locus of intervertebral disc (IVD). A previously calibrated osseoligamentous model of lumbar spine was used to evaluate the changes in ICR under variation of the ligament stiffness and initial locus of IVD, when subjected to pure moments from 0 to 15 Nm. The ICR was quantified based on the closed solution of unit quaternion that improves accuracy and prevents coordinate singularities, which is often observed in Euler-based methods and least squares principles. The calculation of the ICR during flexion/extension revealed complexity and intrinsic nonlinearity between flexion and extension. This study revealed that, to accommodate a good agreement between in vitro data and the multi-body model predictions, in flexion more laxity is required than in extension. The results showed that the ICR location is concentrated in the posterior region of the disc, in agreement with previous experimental studies. However, the current multi-body model demonstrates a sensitivity to the initial definition of the ICR, which should be recognised as a limitation of the method. Nevertheless, the current simulations suggest that, due to the constantly evolving path of the ICR across the IVD during flexion–extension, a movable ICR is a necessary condition in multi-body modelling of the spine, in the context of whole body simulation, to accurately capture segmental kinematics and kinetics.     

Application of a stand-alone interbody fusion cage based on a novel porous TiO2/glass ceramic--2: Biomechanical evaluation after implantation in the sheep cervical spine]

Animals are becoming more and more common as in vivo models for the human spine. Especially the sheep cervical spine is stated to be of good comparability and usefulness in the evaluation of in vivo radiological, biomechanical and histological behaviour of new bone replacement materials, implants and cages for cervical spine interbody fusion. In preceding biomechanical in vitro examinations human cervical spine specimens were tested after fusion with either a cubical stand-alone interbody fusion cage manufactured from a new porous TiO2/glass composite (Ecopore) or polymethylmethacrylate (PMMA) after discectomy. Following our first experience with the use of the new material and its influence on the primary stability after in vitro application we carried out fusions of 20 sheep cervical spines levels with either PMMA or an Ecopore-cage, and performed radiological examinations during the following 2-4 months. In this second part of the study we intended the biomechanical evaluation of the spine segments with reference to the previously determined morphological findings, like subsidence of the implants, significant increase of the kyphosis angle and degree of the bony fusion along with the interpretation of the results. 20 sheep cervical spines segments with either PMMA- or Ecopore-fusion in the levels C2/3 and C4/5 were tested, in comparison to 10 native corresponding sheep cervical spine segments. Non-destructive biomechanical testing was performed, including flexion/extension, lateral bending and axial rotation using a spine testing apparatus. Three-dimensional range of motion (ROM) was evaluated using an ultrasound measurement system. In the native spine segments C2/3 and C4/5 the ROM increased in cranio-caudal direction particulary in flexion/extension, less pronounced in lateral flexion and axial rotation (p < 0.05). The overall ROM of both tested segments was greatest in lateral flexion, reduced to 52% in flexion/extension and to 16% in axial rotation. After 2 months C2/3- and C4/5-segments with PMMA-fusion and C2/3-segments with Ecopore-interposition showed decrease of ROM in lateral flexion in comparison to the native segments, indicating increasing stiffening. However, after 4 months all operated segments, independent from level or implanted material, were stiffer than the comparable native segments. The decrease of the ROM correlated with the radiological-morphological degree of fusion. Our evaluation of the new porous TiO2/glass composite as interbody fusion cage has shown satisfactory radiological results as well as distinct biomechanical stability and fusion of the segments after 4 months in comparison to PMMA. After histological analysis of the bone-biomaterial-interface, further examinations of this biomaterial previous to an application as alternative to other customary cages in humans are necessary.     

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.     

Biomechanics of the C5-C6 Spinal Unit Before and After Placement of a disc prosthesis

The study consists of a biomechanical comparison between the intact C5–C6 spinal segment and the same segment implanted with the Bryan^TM artificial disc prosthesis (Medtronic Ltd., Memphis, TN, USA), by the use of the finite element (FE) method. Our target is the prediction of the influence of prosthesis placement on the resulting mechanics of the C5–C6 spine unit. A FE model of the intact C5–C6 segment was built, employing realistic models of the vertebrae, disc and ligaments. Simulations were conducted imposing a compression preload combined to a flexion/extension moment, a pure lateral bending moment and a pure torsion moment, and the calculated results were compared to data from literature. The model was then modified to include the Bryan^TM cervical disc prosthesis, and the simulations were repeated. The location of the instantaneous center of rotation (ICR) of C5 with respect to C6 throughout flexion/extension was calculated in both models. In general, the moment–rotation curves obtained from the disc prosthesis-implanted model were comparable to the curves obtained from the intact model, except for a slightly greater stiffness induced by the artificial disc. The position of the calculated ICRs was rather stable throughout flexion-extension and was generally confined to a small area, qualitatively matching the corresponding physiological region, in both models. These results imply that the Bryan^TM disc prosthesis allows to correctly reproduce a physiological flexion/extension at the implanted level. The results of this study have quantified aspects that may assist in optimizing cervical disc replacement primarily from a biomechanical point of view.     

A technique for quantifying the bending moment acting on the lumbar spine in vivo

The bending properties of cadaveric lumbar spines were measured and used to convert in vivo measurements of lumbar flexion into bending moments ('stresses'). Forty-two lumbar motion segments were subjected to complex physiological loading and graphs were obtained of bending moment vs flexion angle. Variability was reduced by expressing both variables as a percentage of their values at the elastic limit. Data were averaged for each lumbar level, and a composite bending curve was compiled for the lumbar spine, L1-S1. A linear relationship was established between lumbar flexion measured in vitro and in vivo. This enabled values of 'per cent lumbar flexion' measured in vivo to be converted into 'per cent maximum bending moment' with a maximum likely error of about +/- 8%, which is equivalent to about +/- 5 Nm at L5-S1 for an average person. The technique was applied to 28 subjects, using dynamic measurements of lumbar flexion obtained with the '3-Space Isotrack' system. The bending moment at L5-S1 was 12 Nm on average when picking a pen up off the floor. Highly significant increases in bending moment were observed when heavier and bulkier objects were lifted.     

Spinal constraint modulates head instantaneous center of rotation and dictates head angular motion

The head is kinematically constrained to the torso through the spine and thus, the spine dictates the amount of output head angular motion expected from an input impact. Here, we investigate the spinal kinematic constraint by analyzing the head instantaneous center of rotation (HICOR) with respect to the torso in head/neck sagittal extension and coronal lateral flexion during mild loads applied to 10 subjects. We found the mean HICOR location was near the C5-C6 intervertebral joint in sagittal extension, and T2-T3 intervertebral joint in coronal lateral flexion. Using the impulse-momentum relationship normalized by subject mass and neck length, we developed a non-dimensional analytical ratio between output angular velocity and input linear impulse as a function of HICOR location. The ratio was 0.65 and 0.50 in sagittal extension and coronal lateral flexion respectively, implying 30% greater angular velocities in sagittal extension given an equivalent impulse. Scaling to subject physiology also predicts larger required impulses given greater subject mass and neck length to achieve equivalent angular velocities, which was observed experimentally. Furthermore, the HICOR has greater motion in sagittal extension than coronal lateral flexion, suggesting the head and spine can be represented with a single inverted pendulum in coronal lateral flexion, but requires a more complex representation in sagittal extension. The upper cervical spine has substantial compliance in sagittal extension, and may be responsible for the complex motion and greater extension angular velocities. In analyzing the HICOR, we can gain intuition regarding the neck’s role in dictating head motion during external loading.     

Intervertebral reaction force prediction using an enhanced assembly of OpenSim models

OpenSim offers a valuable approach to investigating otherwise difficult to assess yet important biomechanical parameters such as joint reaction forces. Although the range of available models in the public repository is continually increasing, there currently exists no OpenSim model for the computation of intervertebral joint reactions during flexion and lifting tasks. The current work combines and improves elements of existing models to develop an enhanced model of the upper body and lumbar spine. Models of the upper body with extremities, neck and head were combined with an improved version of a lumbar spine from the model repository. Translational motion was enabled for each lumbar vertebrae with six controllable degrees of freedom. Motion segment stiffness was implemented at lumbar levels and mass properties were assigned throughout the model. Moreover, body coordinate frames of the spine were modified to allow straightforward variation of sagittal alignment and to simplify interpretation of results. Evaluation of model predictions for level L1–L2, L3–L4 and L4–L5 in various postures of forward flexion and moderate lifting (8 kg) revealed an agreement within 10% to experimental studies and model-based computational analyses. However, in an extended posture or during lifting of heavier loads (20 kg), computed joint reactions differed substantially from reported in vivo measures using instrumented implants. We conclude that agreement between the model and available experimental data was good in view of limitations of both the model and the validation datasets. The presented model is useful in that it permits computation of realistic lumbar spine joint reaction forces during flexion and moderate lifting tasks. The model and corresponding documentation are now available in the online OpenSim repository.     

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.     

Biomechanicsl evaluation of a stand-alone interbody fusion cage based on porous TiO2/glass-ceramic on the human cervical spine]

Recently, there has been a rapid increase in the use of cervical spine interbody fusion cages, differing in design and biomaterial used, in competition to autologous iliac bone graft and bone cement (PMMA). Limited biomechanical differences in primary stability, as well as advantages and disadvantages of each cage or material have been investigated in studies, using an in vitro human cervical spine model. 20 human cervical spine specimens were tested after fusion with either a cubical stand-alone interbody fusion cage manufactured from a new porous TiO2/glass composite (Ecopore) or PMMA after discectomy. Non-destructive biomechanical testing was performed, including flexion/extension and lateral bending using a spine testing apparatus. Three-dimensional segmental range of motion (ROM) was evaluated using an ultrasound measurement system. ROM increased more in flexion/extension and lateral bending after PMMA fusion (26.5%/36.1%), then after implantation of the Ecopore-cage (8.1%/7.8%). In this first biomechanical in vitro examination of a new porous ceramic bone replacement material a) the feasibility and reproducibility of biomechanical cadaveric cervical examination and its applicability was demonstrated, b) the stability of the ceramic cage as a stand alone interbody cage was confirmed in vitro, and c) basic information and knowledge for our intended biomechanical and histological in vivo testing, after implantation of Ecopore in cervical sheep spines, were obtained.     

Simulated active control produces repeatable motion pathways of the elbow in an in vitro testing system.

The purpose of this study was to determine if the repeatability and pattern of elbow kinematics are affected by changing the relative magnitudes of loads applied to muscles around the elbow in vitro. In eight cadaveric upper extremities, passive and three methods of simulated active elbow flexion were tested with the forearm maintained in both pronation and supination. Passive flexion involved moving the elbow manually through a full arc of motion. Simulated active flexion used a custom designed loading system to generate elbow motion by applying loads to various tendons via pneumatic actuators. Three different simulated active loading protocols, with loading ratios based on muscle activity and physiologic cross-sectional area, were tested. Testing was performed initially on an intact elbow, and then an unstable elbow model created by transection of the lateral collateral ligament (i.e. the radial and lateral ulnar collateral ligaments). An electromagnetic tracking device was used to measure rotation of the ulna relative to the humerus. Varus-valgus angulation and internal-external rotation were less repeatable during passive flexion than simulated active flexion, regardless of the loading ratio used, in both the intact (p<0.05) and unstable (p<0.05) elbows. Throughout the arc of flexion, the motion pathways were similar for the three simulated active motion protocols employed in this study (p>0.05). The pathways followed during passive motion were different from those generated with simulated active motion, especially in the unstable elbow with the forearm supinated (p<0.001). These results suggest that using simulated active motion rather than manual passive motion can improve the repeatability of elbow kinematics generated in the laboratory, and that a wide range of muscle loading ratios may produce similar kinematic output.     

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.     

Clinical spinal instability and low back pain.

Clinical instability is an important cause of low back pain. Although there is some controversy concerning its definition, it is most widely believed that the loss of normal pattern of spinal motion causes pain and/or neurologic dysfunction. The stabilizing system of the spine may be divided into three subsystems: (1) the spinal column; (2) the spinal muscles; and (3) the neural control unit. A large number of biomechanical studies of the spinal column have provided insight into the role of the various components of the spinal column in providing spinal stability. The neutral zone was found to be a more sensitive parameter than the range of motion in documenting the effects of mechanical destabilization of the spine caused by injury and restabilization of the spine by osteophyle formation, fusion or muscle stabilization. Clinical studies indicate that the application of an external fixator to the painful segment of the spine can significantly reduce the pain. Results of an in vitro simulation of the study found that it was most probably the decrease in the neutral zone, which was responsible for pain reduction. A hypothesis relating the neutral zone to pain has been presented. The spinal muscles provide significant stability to the spine as shown by both in vitro experiments and mathematical models. Concerning the role of neuromuscular control system, increased body sway has been found in patients with low back pain, indicating a less efficient muscle control system with decreased ability to provide the needed spinal stability.     

Double-step registration of in vivo stereophotogrammetry with both in vitro 6-DOFs electrogoniometry and CT medical imaging

Standard registration techniques of bone morphology to motion analysis data often lead to unsatisfactory motion simulation because of discrepancies during the location of anatomical landmarks in the datasets. This paper describes an iterative registration method of a three-dimensional (3D) skeletal model with both 6 degrees-of-freedom joint kinematics and standard motion analysis data. The method is demonstrated in this paper on the lower limb. The method includes two steps. A primary registration allowed synchronization of in vitro kinematics of the knee and ankle joints using flexion/extension angles from in vivo gait analysis. Results from primary registration were then improved by a so-called advanced registration, which integrated external constraints obtained from experimental gait pre-knowledge. One cadaver specimen was analyzed to obtain both joint kinematics of knee and ankle joints using 3D electrogoniometry, and 3D bone morphology from medical imaging data. These data were registered with motion analysis data from a volunteer during the execution of locomotor tasks. Computer graphics output was implemented to visualize the results for a motion of sitting on a chair. Final registration results allowed the observation of both in vivo motion data and joint kinematics from the synchronized specimen data. The method improved interpretation of gait analysis data, thanks to the combination of realistic 3D bone models and joint mechanism. This method should be of interest both for research in gait analysis and medical education. Validation of the overall method was performed using RMS of the differences between bone poses estimated after registration and original data from motion analysis.     

Biomechanical analysis of lumbar interbody fusion cages with various lordotic angles: a finite element study

Inappropriate lordotic angle of lumbar fusion cage could be associated with cage damage or subsidence. The biomechanical influence of cage lordotic angle on lumbar spine has not been fully investigated. Four surgical finite element models were constructed by inserting cages with various lordotic angles at L3-L4 disc space. The four motion modes were simulated. The range of motion (ROM) decreased with increased lordotic angle of cage in flexion, extension, and rotation, whereas it was not substantially changed in bending. The maximum stress in cage decreased with increased lordotic angle of cage in all motion modes. The maximum stress in endplate at surgical level increased with increased lordotic angle of cage in flexion and rotation, whereas it was not substantially changed in extension and bending. The facet joint force (FJF) was much smaller than that for the intact conditions in extension, bending, and rotation, while it was not substantially changed in flexion. In conclusion, the ROM, stresses in the cage and endplate at surgical level are sensitive to the lordotic angle of cage. The increased cage lordotic angle may provide better stability and reduce the risk of cage damage, whereas it may increase the risk of subsidence in flexion and rotation.     

Effect of lumbar fasciae on the stability of the lower lumbar spine

The biomechanical effect of tensioning the lumbar fasciae (LF) on the stability of the spine during sagittal plane motion was analysed using a validated finite element model of the normal lumbosacral spine (L4-S1). To apply the tension in the LF along the direction of the fibres, a local coordinate was allocated using dummy rigid beam elements that originated from the spinous process. Up to 10 Nm of flexion and 7.5 Nm of extension moment was applied with and without 20 N of lateral tension in the LF. A follower load of 400 N was additionally applied along the curvature of the spine. To identify how the magnitude of LF tension related to the stability of the spine, the tensioning on the fasciae was increased up to 40 N with an interval of 10 N under 7.5 Nm of flexion/extension moment. A fascial tension of 20 N produced a 59% decrease in angular motion at 2.5 Nm of flexion moment while there was a 12.3% decrease at 10 Nm in the L5-S1 segment. Its decrement was 53 and 9.6% at 2.5 Nm and 10 Nm, respectively, in the L4-L5 segment. Anterior translation was reduced by 12.1 and 39.0% at the L4-L5 and L5-S1 segments under 10 Nm of flexion moment, respectively. The flexion stiffness shows an almost linear increment with the increase in fascial tension. The results of this study showed that the effect of the LF on the stability of the spine is significant.     

Does prolonged seated deskwork alter the lumbar flexion relaxation phenomenon?

Sustained maximum lumbar spine flexion can increase the angle at which the low back flexion relaxation phenomenon (FRP) is observed. This adaptation has been hypothesized to have implications for the control of lumbar spine stability and increase the potential for low back injury. The objective of this study was to investigate if similar changes in the FRP would occur from sub-maximal spine flexion induced by an extended continuous duration of seated office deskwork. Twenty-three participants (12 male and 11 female) performed three bouts of full forward spine flexion interspersed with two 1-h periods of seated deskwork. Lumbar spine angular kinematics and electromyographic activity from the lumbar erector spinae were obtained throughout all trials. The angles at which myoelectric silence occurred (FRP onset) were documented. Lumbar flexion at FRP onset increased by 1.3 ± 1.5° after 1-h of sitting (p < 0.05) with no further increase after 2-h. However, when the angle at the FRP onset was normalized to the total range of flexion, there was no difference in the FRP onset. These results suggest that the seated posture may induce residual deformation in the viscoelastic passive tissues of the low back; this could increase the challenge of controlling spine motion and reduce the load-bearing capacity of the lumbar spine system during activities performed following extended bouts of sitting.