Geometric and mechanical properties of human cervical spine ligaments

This study characterized the geometry and mechanical properties of the cervical ligaments from C2-T1 levels. The lengths and cross-sectional areas of the anterior longitudinal ligament, posterior longitudinal ligament, joint capsules, ligamentum flavum, and interspinous ligament were determined from eight human cadavers using cryomicrotomy images. The geometry was defined based on spinal anatomy and its potential use in complex mathematical models. The biomechanical force-deflection, stiffness, energy, stress, and strain data were obtained from 25 cadavers using in situ axial tensile tests. Data were grouped into middle (C2-C5) and lower (C5-T1) cervical levels. Both the geometric length and area of cross section, and the biomechanical properties including the stiffness, stress, strain, energy, and Young's modulus, were presented for each of the five ligaments. In both groups, joint capsules and ligamentum flavum exhibited the highest cross-sectional area (p < 0.005), while the longitudinal ligaments had the highest length measurements. Although not reaching statistical significance, for all ligaments, cross-sectional areas were higher in the C5-T1 than in the C2-C5 group; and lengths were higher in the C2-C5 than in the C5-T1 group with the exception of the flavum (Table 1 in the main text). Force-deflection characteristics (plots) are provided for all ligaments in both groups. Failure strains were higher for the ligaments of the posterior (interspinous ligament, joint capsules, and ligamentum flavum) than the anterior complex (anterior and posterior longitudinal ligaments) in both groups. In contrast, the failure stress and Young's modulus were higher for the anterior and posterior longitudinal ligaments compared to the ligaments of the posterior complex in the two groups. However, similar tendencies in the structural responses (stiffness, energy) were not found in both groups. Researchers attempting to incorporate these data into stress-analysis models can choose the specific parameter(s) based on the complexity of the model used to study the biomechanical behavior of the human cervical spine.     

Validation of vibration testing for the assessment of the mechanical properties of human lumbar motion segments

Experimental modal analysis is a non-destructive measurement technique, which applies low forces and small deformations to assess the integrity of a structure. It is therefore a promising method to study the mechanical properties of the spine in vivo. Previously, modal parameters successfully revealed artificially induced spinal injuries. The question remains however, whether experimental modal analysis can be applied successfully in human spinal segments with mechanical changes due to physiological processes. Since quasi-static mechanical testing is considered the "gold standard" for assessing intervertebral stiffness, the purpose of our study was to examine if the mechanical properties derived from vibration testing and quasi-static testing correlate. Six cadaver human spines (L1-L5) were loaded quasi-statically in bending and torsion, while an optical system measured the angular rotations of the individual motion segments. Subsequently, the polysegmental spines were divided into L2-L3 and L4-L5 segments and a shaker was used to vibrate the upper vertebra, while its response was obtained from accelerometers in anteroposterior and mediolateral directions. From the resulting frequency response function the eigenfrequencies (ratio between stiffness and mass) and vibration modes (pattern of motion) were determined. The vibration results showed clear eigenfrequencies for flexion-extension (mean 121.83Hz, SD 40.05Hz), lateroflexion (mean 132.17, SD 34.80Hz) and axial rotation (mean 236.17Hz, SD 81.45Hz). Furthermore, the correlation between static and dynamic tests was significant (r=0.73, p=0.01). In conclusion, the findings from this study show that experimental modal analysis is a valid method to assess the mechanical properties of human lumbar motion segments.     

Reaction of a human head/neck/torso system to shock

The purpose of this study is to predict human response to, and potential damage from, impact loading by using numerical and physical models to monitor the head and thoracic reactions, intervertebral disk pressures, muscle elongations, and some internal organ pressures. The numerical model consists of a three-dimensional lumped-parameter system of ten rigid bodies connected by nine intervertebral joints and 28 muscle pairs. The masses represent the head; cervical vertebrae C1-C2, C3-C4, C5-C6, C7-T1 (the first thoracic vertebra); the entire thorax; lumbar vertebrae L1-L2, L3, L4-L5; and the pelvis. The physical model consists of: a water-filled cadaver skull, held in position by attached ligaments; plastic skeletal components involving vertebrae, sternum, ribs and pelvis; silicon rubber intervertebral disks; fabric muscles and ligaments; and water-filled containers replicating the liver, spleen and kidneys. The pelvis of the model is affixed to a plate mounted on a sled that runs on a track. Loading is applied by deceleration from a given velocity that occurs due to the impact of the sled with a fixed aluminum block. Results from the numerical model are compared with corresponding experimental information from the physical structure. Good correlation was obtained in these comparisons up to about 200-250 ms after impact. The results indicate that the head, cervical muscles and disks in the lumbar region are subjected to the greatest force changes and thus are most likely to be injured.     

Subject-specific models of the hindfoot reveal a relationship between morphology and passive mechanical properties

The morphology of the bones, articular surfaces and ligaments and the passive mechanical characteristics of the ankle complex were reported to vary greatly among individuals. The goal of this study was to test the hypothesis that the variations observed in the passive mechanical properties of the healthy ankle complex are strongly influenced by morphological variations. To evaluate this hypothesis six numerical models of the ankle joint complex were developed from morphological data obtained from MRI of six cadaveric lower limbs, and from average reported data on the mechanical properties of ligaments and articular cartilage. The passive mechanical behavior of each model, under a variety of loading conditions, was found to closely match the experimental data obtained from each corresponding specimen. Since all models used identical material properties and were subjected to identical loads and boundary conditions, it was concluded that the observed variations in passive mechanical characteristics were due to variations in morphology, thus confirming the hypothesis. In addition, the average and large variations in passive mechanical behavior observed between the models were similar to those observed experimentally between cadaveric specimens. The results suggest that individualized subject-specific treatment procedures for ankle complex disorders are potentially superior to a one-size-fits-all approach.     

Search for critical loading condition of the spine--a meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2-L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Ex vivo measurement of lumbar intervertebral disc pressure using fibre-Bragg gratings

Methods were developed to measure intervertebral disc pressure using optical fibre-Bragg gratings (FBGs). The FBG sensor was calibrated for hydrostatic pressure in a purpose-built apparatus and the average sensitivity was determined to be -5.7 +/- 0.085 pm/MPa (mean +/- SD). The average coefficient of determination (r(2)) for the calibration data was 0.99, and the average hysteresis of the sensor was 2.13% of full scale. The FBG was used to measure intradiscal pressure response to compressive load in five lumbar functional spine units. The pressure measured by the FBG sensor varied linearly with applied compressive load with coefficients of determination ranging from 0.84 to 0.97. The FBG sensor's sensitivity to compressive load ranged from 0.702 +/- 0.043 kPa/N (mean +/- SD) in a L1-L2 specimen, to 1.07 +/- 0.069 kPa/N in a L4-L5 specimen. These measurements agree with those of previous studies in lumbar spines. Two strain gauge pressure sensors were also used to measure intradiscal pressure response to compressive load. The measured pressure sensitivity to load ranged from 0.251 kPa/N (L4-L5) to 0.850 kPa/N (L2-L3). The average difference in pressure sensitivity to load between Sensors 1 and 2 was 12.9% of the value for Sensor 1, with a range from 1.1% to 20.4%, which suggests that disc pressure was not purely hydrostatic. This may have contributed to the difference between the responses of the FBG and strain gauge sensors.     

Localization of the lamellated corpuscle neurons of the cat large intestine mesentery

Electrical activity and ultrastructure of lamellated corpuscles (Pacinian corpuscles) of the cat large intestine mesentery were studied 10 days after uni- and bilateral extirpation of the lumbar spinal ganglia. Terminal degenerated in all the receptors, and there were no electrical reactions at bilateral extripation of ganglia L3-L4, they were preserved in some receptors at bilateral extirpation of ganglia L2-L3 and L4-L5 and at unilateral extirpation of ganglia L3-L4. Structure of the receptors and electrical reactions were preserved in all the lamellated corpuscles at bilateral extirpation at the level of L1-L2 and L5-L6. After enucleation of the corpuscles from the large intestine mesentery, in some neurons of ganglia L3-L4, chromatolysis was observed. After the caudal mesenteric nerve was sectioned, there were no electrical reactions in the lamellated corpuscles of the large intestine mesentery. Hence, the sensitive neurons-theri peripheral processes participate in the formation of the lamellated corpuscles of the cat large intestine mesentery-are situated in the lumbar ganglia L3 and L4.     

A global verification study of a quasi-static knee model with multi-bundle ligaments

The ligaments of the knee consist of fiber bundles with variable orientations, lengths and mechanical properties. In concept, however, these structures were too often seen as homogeneous structures, which are either stretched or slack during knee motions. In previous studies, we proposed a new structural concept of the ligaments of the knee. In this concept, the ligaments were considered as multi-bundle structures, with nonuniform mechanical properties and zero force lengths. The purpose of the present study was to verify this new concept.

For this purpose, laxity characteristics of a human knee joint were compared as measured in an experiment and predicted in a model simulation study. In the experiment, the varus-valgus and anterior-posterior laxities of a knee-joint specimen containing the ligaments and the articular surfaces only, were determined. From this knee-joint, geometric and mechanical parameters were derived to supply the parameters for a three-dimensional quasi-static knee-joint model. These parameters included (i) the three-dimensional insertion points of bundles, defined in the four major knee ligaments, (ii) the mechanical properties of these ligament, as functions of their relative insertion orientations and (iii) three-dimensional representations of the articular surfaces. With this model the experiments were simulated. If knee-model predictions and experimental results agree, then the multi-bundle ligament models are validated, at least with respect to their functional role in anterior-posterior and varus-valgus loading of the joint.

The model described the laxity characteristics in AP-translation and VV-rotation of the cadaveric knee-joint specimen reasonably well. Both display the same patterns of laxity changes during knee flexion. Only if a varus moment of 8 N m was applied and if the tibia was posteriorly loaded, did the model predict a slightly higher laxity than that measured experimentally.

From the model-experiment comparisons it was concluded that the proposed structural representations of the ligaments and their mechanical property distributions seem to be valid for studying the anterior-posterior and varus-valgus laxity characteristics of the human knee-joint.     

How does the geometry affect the internal biomechanics of a lumbar spine bi-segment finite element model? Consequences on the validation process

Numerical modelling can provide a thorough understanding of the mechanical influence on the spinal tissues and may offer explanations to mechanically linked pathologies. Such objective might be achieved only if the models are carefully validated. Sensitivity study must be performed in order to evaluate the influence of the approximations inherent to modelling. In this study, a new geometrically accurate L3-L5 lumbar spine bi-segmental finite-element model was acquired by modifying a previously existing model. The effect of changes in bone geometry, ligament fibres distribution, nucleus position and disc height was investigated in flexion and extension by comparison of the results obtained from the model before and after the geometrical update. Additional calculations were performed in axial rotation and lateral bending in order to compare the computed ranges of motion (ROM) with experimental results. It was found that the geometrical parameters affected the stress distribution and strain energy in the zygapophysial joints, the ligaments, and the intervertebral disc, changing qualitatively and quantitatively their relative role in resisting the imposed loads. The predicted ROM were generally in good agreement with the experimental results, independently of the geometrical changes. Hence, although the model update affected its internal biomechanics, no conclusions could be drawn from the experimental data about the validation of a particular geometry. Hence the validation of the lumbar spine model should be based on the relative role of its structural components and not only on its global mobility.     

Lumbar spine finite element model for healthy subjects: development and validation

Finite element (FE) method is a proven powerful and efficient tool to study the biomechanics of the human lumbar spine. However, due to the large inter-subject variability of geometries and material properties in human lumbar spines, concerns existed on the accuracy and predictive power of one single deterministic FE model with one set of spinal geometry and material properties. It was confirmed that the combined predictions (median or mean value) of several distinct FE models can be used as an improved prediction of behavior of human lumbar spine under identical loading and boundary conditions. In light of this improved prediction, five FE models (L1-L5 spinal levels) of the human lumbar spine were developed based on five healthy living subjects with identical modeling method. The five models were extensively validated through experimental and computational results in the literature. Mesh convergence and material sensitivity analysis were also conducted. We have shown that the results from the five FE models developed in this paper were consistent with the experimental data and simulation results from the existing literature. The validated modeling method introduced in this study can be used in modeling dysfunctional lumber spines such as disc degeneration and scoliosis in future work.     

The influence of ligament modelling strategies on the predictive capability of finite element models of the human knee joint

In finite element (FE) models knee ligaments can represented either by a group of one-dimensional springs, or by three-dimensional continuum elements based on segmentations. Continuum models closer approximate the anatomy, and facilitate ligament wrapping, while spring models are computationally less expensive. The mechanical properties of ligaments can be based on literature, or adjusted specifically for the subject. In the current study we investigated the effect of ligament modelling strategy on the predictive capability of FE models of the human knee joint. The effect of literature-based versus specimen-specific optimized material parameters was evaluated. Experiments were performed on three human cadaver knees, which were modelled in FE models with ligaments represented either using springs, or using continuum representations. In spring representation collateral ligaments were each modelled with three and cruciate ligaments with two single-element bundles. Stiffness parameters and pre-strains were optimized based on laxity tests for both approaches. Validation experiments were conducted to evaluate the outcomes of the FE models.Models (both spring and continuum) with subject-specific properties improved the predicted kinematics and contact outcome parameters. Models incorporating literature-based parameters, and particularly the spring models (with the representations implemented in this study), led to relatively high errors in kinematics and contact pressures. Using a continuum modelling approach resulted in more accurate contact outcome variables than the spring representation with two (cruciate ligaments) and three (collateral ligaments) single-element-bundle representations. However, when the prediction of joint kinematics is of main interest, spring ligament models provide a faster option with acceptable outcome.     

Differences in 3D vs. 2D analysis in lumbar spinal fusion simulations

Lumbar interbody fusion is currently the gold standard in treating patients with disc degeneration or segmental instability. Despite it having been used for several decades, the non-union rate remains high. A failed fusion is frequently attributed to an inadequate mechanical environment after instrumentation. Finite element (FE) models can provide insights into the mechanics of the fusion process. Previous fusion simulations using FE models showed that the geometries and material of the cage can greatly influence the fusion outcome. However, these studies used axisymmetric models which lacked realistic spinal geometries. Therefore, different modeling approaches were evaluated to understand the bone-formation process.Three FE models of the lumbar motion segment (L4–L5) were developed: 2D, Sym-3D and Nonsym-3D. The fusion process based on existing mechano-regulation algorithms using the FE simulations to evaluate the mechanical environment was then integrated into these models. In addition, the influence of different lordotic angles (5, 10 and 15°) was investigated. The volume of newly formed bone, the axial stiffness of the whole segment and bone distribution inside and surrounding the cage were evaluated.In contrast to the Nonsym-3D, the 2D and Sym-3D models predicted excessive bone formation prior to bridging (peak values with 36 and 9% higher than in equilibrium, respectively). The 3D models predicted a more uniform bone distribution compared to the 2D model.The current results demonstrate the crucial role of the realistic 3D geometry of the lumbar motion segment in predicting bone formation after lumbar spinal fusion.     

Mechanical thresholds for initiation and persistence of pain following nerve root injury: mechanical and chemical contributions at injury

There is much evidence supporting the hypothesis that magnitude of nerve root mechanical injury affects the nature of the physiological responses which can contribute to pain in lumbar radiculopathy. Specifically, injury magnitude has been shown to modulate behavioral hypersensitivity responses in animal models of radiculopathy. However, no study has determined the mechanical deformation thresholds for initiation and maintenance of the behavioral sensitivity in these models. Therefore, it was the purpose of this study to quantify the effects of mechanical and chemical contributions at injury on behavioral outcomes and to determine mechanical thresholds for pain onset and persistence. Male Holtzman rats received either a silk or chromic gut ligation of the L5 nerve roots, a sham exposure of the nerve roots, or a chromic exposure in which no mechanical deformation was applied but chromic gut material was placed on the roots. Using image analysis, nerve root radial strains were estimated at the time of injury. Behavioral hypersensitivity was assessed by measuring mechanical allodynia continuously throughout the study. Chromic gut ligations produced allodynia responses for nerve root strains at two-thirds of the magnitudes of those strains which produced the corresponding behaviors for silk ligation. Thresholds for nerve root compression producing the onset (8.4%) and persistence of pain (17.4%-22.2%) were determined for silk ligation in this lumbar radiculopathy model. Such mechanical thresholds for behavioral sensitivity in a painful radiculopathy model begin to provide biomechanical data which may have utility in broader experimental and computational models for relating injury biomechanics and physiologic responses of pain.     

Subpopulations of early thymocytes. A cross-correlation flow cytometric analysis of adult mouse Ly-2-L3T4-(CD8-CD4-) thymocytes using eight different surface markers

Putative early thymocytes, the Ly-2-L3T4-(CD8-CD4-) cells representing 3 to 4% of adult CBA mouse thymic lymphocytes, were isolated in high purity (99.5%). They were then stained by using mAb and analyzed by flow cytometry for the expression of six additional surface antigenic markers. Cross-correlation of the data obtained from a complete series of successive two-parameter analyses revealed the existence of about 11 discrete subsets, falling into four-main groups, within the Ly-2-L3T4- population. All subsets consisted of relatively large lymphoid cells. The most numerous group of Ly-2-L3T4- cells was Ly-1 low B2A2-M1/69 high Thy-1 high Pgp-1 low and by these markers resembled Ly-2+L3T4+ cortical blasts. Many of the cells in this group were positive for the IL-2R and/or for MEL-14. A second major group of Ly-2-L3T4- cells was Ly-1 high B2A2-M1/69 low Pgp-1 high, and resembled in some respects activated mature T cells. This group had previously been shown to be absent from the embryonic thymus. The group could be divided into Thy-1 high and Thy-1 low subsets. None of the cells in this group were positive for the IL-2R and very few expressed MEL-14. A third group, 13% of the Ly-2-L3T4- population, was Ly-1 low B2A2-M1/69 low Pgp-1 high, and could also be divided into Thy-1 high and Thy-1 low subsets. A final minor group, 9% of the Ly-2-L3T4- population, was Ly-1 high B2A2-M1/69 high Pgp-1 low Thy-1 high. The particular pattern of markers on these subsets, combined with subsequent information on their properties, makes it unlikely that they all represent sequential steps in one continuous developmental stream, and indicates that complex developmental steps have occurred, even at this supposedly early stage of T cell differentiation.     

Biomechanical comparison of the effects of anterior,posterior and transforaminal lumbar interbody fusion on vibration characteristics of the human lumbar spine

Previous studies have compared the effects of different interbody fusion approaches on biomechanical responses of the lumbar spine to static loadings. However, very few have dealt with the whole body vibration (WBV) condition that is typically present in vehicles. This study was designed to determine the biomechanical differences among anterior, posterior and transforaminal lumbar interbody fusion (ALIF, PLIF and TLIF) under vertical WBV. A previously developed and validated finite element (FE) model of the intact L1–sacrum human lumbar spine was modified to simulate ALIF, PLIF and TLIF with bilateral pedicle screw fixation at L4–L5. Comparative studies on dynamic responses to the axial cyclic loading in these developed models were conducted. The results showed that at the fused L4–L5 level, dynamic responses of the von-Mises stress in L4 inferior and L5 superior endplates for the ALIF, PLIF and TLIF models were increased compared with the intact model. The endplate stresses in the TLIF model were lower than in the ALIF and PLIF models, but the TLIF generated greater stresses in the screws and rods compared with the ALIF and PLIF. At other levels, a decrease in dynamic responses of the disc bulge, annulus stress and intradiscal pressure was observed in all the fusion models compared with the intact one, but there was no obvious difference in these dynamic responses among the ALIF, PLIF and TLIF models. These findings might be useful in understanding vibration characteristics of the whole lumbar spine after different types of fusion surgery.     

Comparative cross-linking study on the 50S ribosomal subunit from Escherichia coli

We have carried out an extensive protein-protein cross-linking study on the 50S ribosomal subunit of Escherichia coli using four different cross-linking reagents of varying length and specificity. For the unambiguous identification of the members of the cross-linked protein complexes, immunoblotting techniques using antisera specific for each individual ribosomal protein have been used, and for each cross-link, the cross-linking yield has been determined. With the smallest cross-linking reagent diepoxybutane (4 A), four cross-links have been identified, namely, L3-L19, L10-L11, L13-L21, and L14-L19. With the sulfhydryl-specific cross-linking reagent o-phenylenedimaleimide (5.2 A) and p-phenylenedimaleimide (12 A), the cross-links L2-L9, L3-L13, L3-L19, L9-L28, L13-L20, L14-L19, L16-L27, L17-L32, and L20-L21 were formed; in addition, the cross-link L23-L29 was exclusively found with the shorter o-phenylenedimaleimide. The cross-links obtained with dithiobis(succinimidyl propionate) (12 A) were L1-L33, L2-L9, L2-L9-L28, L3-L19, L9-L28, L13-L21, L14-L19, L16-L27, L17-L32, L19-L25, L20-L21, and L23-L34. The good agreement of the cross-links obtained with the different cross-linking reagents used in this study demonstrates the reliability of our cross-linking approach. Incorporation of our cross-linking results into the three-dimensional model of the 50S ribosomal subunit derived from immunoelectron microscopy yields the locations for 29 of the 33 proteins within the larger ribosomal subunit.     

Non-linearities in apparent mass and transmissibility during exposure to whole-body vertical vibration

The causes of low back pain associated with prolonged exposure to whole-body vibration are not understood. An understanding of non-linearities in the biomechanical responses is required to identify the mechanisms responsible for the dynamic characteristics of the body, to allow for the non-linearities when predicting the influence of seating dynamics, and to predict the adverse effects caused by various magnitudes of vibration. Twelve subjects were exposed to six magnitudes, 0.25-2.5ms(-2) rms, of vertical random vibration in the frequency range 0.2-20Hz. The apparent masses of the subjects were determined together with transmissibilities measured from the seat to various locations on the body surface: the upper and lower abdominal wall, at L3, over the posterior superior iliac spine and the iliac crest. There were significant reductions in resonance frequencies for both the apparent mass and the transmissibilities to the lower abdomen with increases in vibration magnitude. The apparent mass resonance frequency reduced from 5.4-4. 2Hz as the magnitude of the vibration increased from 0.25-2.5ms(-2) rms. Vertical motion of the lumbar spine and pelvis showed resonances at about 4Hz and between 8 and 10Hz. When exposed to vertical vibration, the human body shows appreciable non-linearities in its biodynamic responses. Biodynamic models should be developed to reflect the non-linearity.     

Influences of Endplate Removal and Bone Mineral Density on the Biomechanical Properties of Lumbar Spine

Purpose

To investigate (1) effects of endplate removal and bone mineral density (BMD) on biomechanical properties of lumbar vertebrae (2) whether the distributions of mechanical strength and stiffness of endplate are affected by BMD.

Methods

A total of thirty-one lumbar spines (L1-L5) collected from fresh cadavers were used in this study. Bone density was measured using lateral DEXA scans and parts of samples were performed with partial or entire endplate removal. All the specimens were divided into three BMD groups. According to endplate integrity of the lumbar vertebrae, each BMD group was then divided into three subgroups: subgroup A: intact endplate; subgroup B: central region of endplate removal; subgroup C: entire endplate removal. The axial compression test was conducted with material testing system at a speed of 2mm/min. The experimental results were statistically analyzed using SPSS 17.0.

Results

(1) Significant differences of biomechanical properties occurred among normal BMD, osteoporotic and serious osteoporotic group (P<0.05). (2) Spearman analysis showed that BMD was positively correlated with the failure load and stiffness of lumbar vertebrae. (3) For each BMD group, significant differences of biomechanical properties were found between subgroup A and C, and between subgroup B and C (P<0.05). (4) For each BMD group, there was no statistical difference of biomechanical properties between subgroup A and B (P>0.05).

Conclusions

Entire endplate removal can significantly decrease the structural properties of lumbar vertebrae with little change in biomechanical properties by preservation of peripheral region of the endplate. BMD is positively correlated to the structural properties of the lumbar vertebrae.     

Impact of material and morphological parameters on the mechanical response of the lumbar spine – A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.