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.     

Three-dimensional geometrical and mechanical modelling of the lumbar spine.

The main objective of this study is to design a three-dimensional geometrical and mechanical finite element model of the lumbar spine. The model's geometry is constructed using six parameters per vertebra. These parameters are digitized from two X-rays (anterio-posterior and lateral), thus yielding an individualized model which can be arrived at from the radiographs of a tested specimen. This procedure makes the model validation easier, as geometry is generally a factor of dispersion in experimental results. The geometrical reconstruction, in the form of a finite elements mesh, was effected for the whole lumbar spine. The global coherence of the model was verified.     

Functional implications of variation in lumbar vertebral count among hominins

As early as the 1970s, Robinson defined lumbar vertebrae according to their zygapophyseal orientation. He identified six lumbar elements in fossil Sts 14 Australopithecus africanus, one more than is commonly present in modern humans. It is now generally inferred that the modal number of lumbar vertebrae for australopiths and early Homo was six, from which the mode of five in later Homo is derived. The two central questions this study investigates are (1) to what extent do differences in human lumbar vertebral count affect lordotic shape and lumbar function, and (2) what does lumbar number variation imply about lumbar spine function in early hominins? To address these questions, I first outline a biomechanical model of lumbar number effect on lordotic function. I then identify relevant morphological differences in the human modal and extra-modal variants, which I use to test the model. These tests permit evaluation of the human L6 variant as a model for reconstructing early hominin modal number and spine function. Application of the biomechanical model in reconstructing australopith/early Homo lumbar spines highlights shared principles of Euler column strength and sagittal spine flexibility among early and modern hominins. Within modern humans, the extra-modal L6 variant has an extended series of three cranially positioned kyphotic vertebrae and strongly oblique zygapophyseal facets at the last lumbar level. Although they share the same radius and length of lumbar curvature, the L6 variant differs functionally from the L5 mode in its expanded range of sagittal flexion/extension and enhanced resistance to shear. Given the modal number of six lumbar vertebrae in australopiths and early Homo, lumbar spine mobility and strength would have been key properties of vertebral function in early bipeds whose upper and lower body segments were coupled by close approximation of the thorax and iliac crests.     

Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting.

A combined approach involving optimization and the finite element technique was used to predict biomechanical parameters in the lumbar spine during static lifting in the sagittal plane. Forces in muscle fascicles of the lumbar region were first predicted using an optimization-based force model including the entire lumbar spine. These muscle forces as well as the distributed upper body weight and the lifted load were then applied to a three-dimensional finite element model of the thoracolumbar spine and rib cage to predict deformation, the intradiskal pressure, strains, stresses, and load transfer paths in the spine. The predicted intradiskal pressures in the L3-4 disk at the most deviated from the in vivo measurements by 8.2 percent for the four lifting cases analyzed. The lumbosacral joint flexed, while the other lumbar joints extended for all of the four lifting cases studied (rotation of a joint is the relative rotation between its two vertebral bodies). High stresses were predicted in the posterolateral regions of the endplates and at the junctions of the pedicles and vertebral bodies. High interlaminar shear stresses were found in the posterolateral regions of the lumbar disks. While the facet joints of the upper two lumbar segments did not transmit any load, the facet joints of the lower two lumbar segments experienced significant loads. The ligaments of all lumbar motion segments except the lumbosacral junction provided only marginal moments. The limitations of the current model and possible improvements are discussed.     

Structural behavior of human lumbar spinal motion segments

The objectives of this study were to obtain linearized stiffness matrices, and assess the linearity and hysteresis of the motion segments of the human lumbar spine under physiological conditions of axial preload and fluid environment. Also, the stiffness matrices were expressed in the form of an 'equivalent' structure that would give insights into the structural behavior of the spine. Mechanical properties of human cadaveric lumbar L2-3 and L4-5 spinal motion segments were measured in six degrees of freedom by recording forces when each of six principal displacements was applied. Each specimen was tested with axial compressive preloads of 0, 250 and 500 N. The displacements were four slow cycles of +/-0.5mm in anterior-posterior and lateral displacements, +/-0.35 mm axial displacement, +/-1.5 degrees lateral rotation and +/-1 degrees flexion-extension and torsional rotations. There were significant increases with magnitude of preload in the stiffness, hysteresis area (but not loss coefficient) and the linearity of the load-displacement relationship. The mean values of the diagonal and primary off-diagonal stiffness terms for intact motion segments increased significantly relative to values with no preload by an average factor of 1.71 and 2.11 with 250 and 500 N preload, respectively (all eight tests p<0.01). Half of the stiffness terms were greater at L4-5 than L2-3 at higher preloads. The linearized stiffness matrices at each preload magnitude were expressed as an equivalent structure consisting of a truss and a beam with a rigid posterior offset, whose geometrical properties varied with preload. These stiffness properties can be used in structural analyses of the lumbar spine.     

Effect of an interspinous implant on loads in the lumbar spine.

Interspinous process implants are increasingly used to treat canal stenoses. Little information exists about the effects of implant height and stiffness on the biomechanical behavior of the lumbar spine. Therefore, a three-dimensional nonlinear finite element model of the osseoligamentous lumbar spine (L1 to L5) was created with a slightly degenerated disc at L3/L4. An interspinous implant was inserted at that segment. Implants with different heights and stiffnesses were studied. The model was loaded with the upper body weight and muscle forces to simulate walking and 25 degrees extension. Implant forces are influenced strongly by the height and negligibly by the elastic modulus of the implant. Intersegmental rotation at implant level is markedly reduced, while intradiscal pressure is slightly increased. Implant size and stiffness have only a minor effect on intradiscal pressure. The maximum von Mises stress in the vertebral arch is strongly increased by the implant.     

Morphometric variations of the lumbar vertebrae between Chinese and Indian adults.

A morphometric study of the lumbar vertebrae of 126 adult skeletons, 90 Chinese and 36 Indian, of both sexes without marginal osteophytes were performed. In each lumbar vertebra, the cephalad and caudad midsagittal diameters, the interpedicular diameter of the spinal canal as well as the midsagittal and transverse diameters and the height of the vertebral body were measured. The results showed that the midsagittal and transverse diameters, the heights of the lumbar vertebral bodies and the interpedicular diameters of the lumbar spinal canals increased progressively from L1 to L5, while the midsagittal diameters of the lumbar spinal canals decreased progressively from L1 to L5 in both Chinese and Indian adult skeletons. The lowest mean values of the cephalad and caudad midsagittal and the interpedicular diameters of the spinal canals in Chinese were found to be 5.04 +/- 0.15 mm at L5, 4.67 +/- 0.09 mm at L5 and 25.92 +/- 0.20 mm at L2, respectively, while in Indians they were found to be 4.54 +/- 0.18 mm at L5, 4.25 +/- 0.10 mm at L5 and 25.42 +/- 0.22 mm at L1, respectively. In addition, the mean diameters of the spinal canal and the vertebral body (except the height of the vertebral body) were significantly greater in the Chinese than in the Indian skeletons. The above findings indicate that the mean diameters of both the lumbar spinal canal and the vertebral body vary greatly between Chinese and Indian adults, i.e. there are no mean values of the vertebral dimensions that are valid for all populations.(ABSTRACT TRUNCATED AT 250 WORDS)     

Lumbar ontogenetic allometry and dimorphism in humans. A case for comparison between interspecific and intraspecific scaling

The ontogenetic allometry of the lumbar region of 1913 humans (1228 females and 685 males), ranging from newborn to 21-year-old individuals, was studied by means of length, width, projected surface area and bone mineral density of the segment L2 - L4, obtained by dual X-ray absorptiometry (DXA). All these parameters were regressed to body mass and height of the individuals, considered alternatively as the independent variable. Firstly, we addressed the comparison between the results obtained on both sexes in order to elucidate whether ontogenetic differences existed. Length of the segments increased significantly faster in females than in males, independently whether the regression was made against body mass or height, while in both types of regression width scaled in males faster than in females. Regarding bone mineral density, although males increased bone mineral density faster than females, slope differences were not significant. However, y-interception was significantly higher in females than in males when bone mineral density was regressed to body mass. Results on length and width are compared with others from previous research on allometry. Finally, global results are discussed as regards the slope predictions for interspecific scaling.     

Multichannel detrended fluctuation analysis reveals synchronized patterns of spontaneous spinal activity in anesthetized cats

The analysis of the interaction and synchronization of relatively large ensembles of neurons is fundamental for the understanding of complex functions of the nervous system. It is known that the temporal synchronization of neural ensembles is involved in the generation of specific motor, sensory or cognitive processes. Also, the intersegmental coherence of spinal spontaneous activity may indicate the existence of synaptic neural pathways between different pairs of lumbar segments. In this study we present a multichannel version of the detrended fluctuation analysis method (mDFA) to analyze the correlation dynamics of spontaneous spinal activity (SSA) from time series analysis. This method together with the classical detrended fluctuation analysis (DFA) were used to find out whether the SSA recorded in one or several segments in the spinal cord of the anesthetized cat occurs either in a random or in an organized manner. Our results are consistent with a non-random organization of the sets of neurons involved in the generation of spontaneous cord dorsum potentials (CDPs) recorded either from one lumbar segment (DFA-α mean = 1.04[Formula: see text]0.09) or simultaneously from several lumbar segments (mDFA-α mean = 1.01[Formula: see text]0.06), where α = 0.5 indicates randomness while α = 0.5 indicates long-term correlations. To test the sensitivity of the mDFA method we also examined the effects of small spinal lesions aimed to partially interrupt connectivity between neighboring lumbosacral segments. We found that the synchronization and correlation between the CDPs recorded from the L5 and L6 segments in both sides of the spinal cord were reduced when a lesion comprising the left dorsal quadrant was performed between the segments L5 and L6 (mDFA-[Formula: see text] = 0.992 as compared to initial conditions mDFA-α = 1.186). The synchronization and correlation were reduced even further after a similar additional right spinal lesion (mDFA-α = 0.924). In contrast to the classical methods, such as correlation and coherence quantification that define a relation between two sets of data, the mDFA method properly reveals the synchronization of multiple groups of neurons in several segments of the spinal cord. This method is envisaged as a useful tool to characterize the structure of higher order ensembles of cord dorsum spontaneous potentials after spinal cord or peripheral nerve lesions.     

The Distribution of Primary Nitric Oxide Synthase- and Parvalbumin- Immunoreactive Afferents in the Dorsal Funiculus of the Lumbosacral Spinal Cord in a Dog

1. The aim of the present study was to examine the distribution of unmyelinated, small-diameter myelinated neuronal nitric oxide synthase immunoreactive (nNOS-IR) axons and large-diameter myelinated neuronal nitric oxide synthase and parvalbumin-immunoreactive (PV-IR) axons in the dorsal funiculus (DF) of sacral (S1–S3) and lumbar (L1–L7) segments of the dog. 2. nNOS and PV immunohistochemical methods were used to demonstrate the presence of nNOS-IR and PV-IR in the large-diameter myelinated, presumed to be proprioceptive, axons in the DF along the lumbosacral segments. 3. Fiber size and density of nNOS-IR and PV-IR axons were used to compartmentalize the DF into five compartments (CI–CV). The first compartment (CI) localized in the lateralmost part of the DF, containing both unmyelinated and small-diameter myelinated nNOS-IR axons, is homologous with the dorsolateral fasciculus, or Lissauer tract. The second compartment (CII) having similar fiber organization as CI is situated more medially in sacral segments. Rostrally, in lower lumbar segments, CII moves more medially, and at upper lumbar level, CII reaches the dorsomedial angle of the DF and fuses with axons of CIV. CIII is the largest in the DF and the only one containing large-diameter myelinated nNOS-IR and PV-IR axons. The largest nNOS-IR and PV-IR axons of CIII (8.0–9.2 μm in diameter), presumed to be stem Ia proprioceptive afferents, are located in the deep portion of the DF close to the dorsal and dorsomedial border of the dorsal horn. The CIV compartment varies in shape, appearing first as a small triangular area in S3 and S2 segments, homologous with the Philippe–Gombault triangle. Beginning at S1 level, CIV acquires a more elongated shape and is seen throughout the lumbar segments as a narrow band of fibers extending just below the dorsal median septum in approximately upper two-thirds of the DF. The CV is located in the basal part of the DF. In general, CV is poor in nNOS-IR fibers; among them solitary PV-IR fibers are seen. 4. The analysis of the control material and the degeneration of the large- and medium-caliber nNOS-IR fibers after unilateral L7 and S1 dorsal rhizotomy confirmed that large-caliber nNOS-IR and and PV-IR axons, presumed to be proprioceptive Ia axons, and their ascending and descending collaterals are present in large number in the DF of the lumbosacral intumescence. However, in the DF of the upper lumbar segments, the decrease in the number of nNOS-IR and PV-IR fibers is quite evident.     

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.     

Biomechanical properties of human lumbar spine ligaments.

Biomechanical properties of the six major lumbar spine ligaments were determined from 38 fresh human cadaveric subjects for direct incorporation into mathematical and finite element models. Anterior and posterior longitudinal ligaments, joint capsules, ligamentum flavum, interspinous, and supraspinous ligaments were evaluated. Using the results from in situ isolation tests, individual force-deflection responses from 132 samples were transformed with a normalization procedure into mean force-deflection properties to describe the nonlinear characteristics. Ligament responses based on the mechanical characteristics as well as anatomical considerations, were grouped into T12-L2, L2-L4, and L4-S1 levels maintaining individuality and nonlinearity. A total of 18 data curves are presented. Geometrical measurements of original length and cross-sectional area for these six major ligaments were determined using cryomicrotomy techniques. Derived parameters including failure stress and strain were computed using the strength and geometry information. These properties for the lumbar spinal ligaments which are based on identical definitions used in mechanical testing and geometrical assay will permit more realistic and consistent inputs for analytical models.     

The Effect of Cauda Equina Constriction on Nitric Oxide Synthase Activity

Nitric oxide synthase (NOS) activity was studied in the gray and white matter regions of the spinal cord 2 and 5 days after multiple cauda equina constrictions of the central processes of L7-Co5 dorsal root ganglia neurons. The results show considerable differences in enzyme activity in the thoracic, upper lumbar, lower lumbar, and sacral segments. Increased NOS activity was observed at 2 days after multiple cauda equina constrictions in the dorsal, lateral, and ventral columns of the lower lumbar segments and in the ventral column of the upper lumbar segments. The values returned to control levels within 5 postconstriction days. In the lateral columns of thoracic segments taken 2 and 5 days after surgery, NOS activity was enhanced by 54% and 55% and in the upper lumbar segments by 130% and 163%, respectively. Multiple cauda equina constrictions performed surgically for 2 and 5 days caused a significant increase in NOS activity predominantly in the gray matter regions of thoracic segments. A quite different response was found 5 days postconstriction in the upper lumbar segments, where the enzyme activity was significantly decreased in the dorsal horn, intermediate zone, and ventral horn. No such extreme differences could be seen in the lower lumbar segments, where NOS activity was significantly enhanced only in the ventral horn. The data correspond with a higher number of NOS immunoreactive somata, quantitatively evaluated in the ventral horn of the lower lumbar segments at 5 days after multiple cauda equina constrictions. While the great region-dependent heterogeneity in NOS activity seen 2 and 5 days after multiple cauda equina constrictions is quite apparent and suggestive of an active role played by nitric oxide in neuroprotective or neurotoxic processes occurring in the gray and white matter of the spinal cord, the extent of damage or the degree of neuroprotection caused by nitric oxide in compartmentalized gray and white matter in this experimental paradigm would be possible only using longer postconstriction periods.     

Identifying critical regions for spike propagation in axon segments

Morphological reconstructions of axon segments reveal the abundance of geometrical ultrastructures that can dramatically affect the propagation of Action Potentials (AP). Moreover, deformations and swellings in axons resulting from brain traumas are associated to many neural dysfunctions and disorders. Our aim is to develop a computational framework to distinguish between geometrical enlargements that lead to minor changes in propagation from those that result in critical phenomenon such as reflection or blockage of the original traveling spike. We use a few geometrical parameters to model a prototypical shaft enlargement and explore the parameter space characterizing all possible propagation regimes and dynamics in an unmylienated AP model. Contrary to earlier notions that large diameter increases mostly lead to blocking, we demonstrate transmission is stable provided the geometrical changes occur in a slow manner. Our method also identifies a narrow range of parameters leading to a reflection regime. The distinction between these three regimes can be evaluated by a simple function of the geometrical parameters inferred through numerical simulations. We suggest that evaluating this function along axon segments can detect regions most susceptible to (i) transmission failure due to perturbations, (ii) structural plasticity, (iii) critical swellings caused by brain traumas and/or (iv) neurological disorders associated with the break down of spike train propagation.     

Morphometric properties and innervation of muscle compartments in rat medial gastrocnemius

The rat medial gastrocnemius (MG) muscle is composed of the proximal and distal compartments. In this study, morphometric properties of the compartments and their muscle fibres at five levels of the muscle length and the innervation pattern of these compartments from lumbar segments were investigated. The size and number of muscle fibres in the compartments were different. The proximal compartment at the largest cross section (25% of the muscle length) had 34% smaller cross-sectional area but contained a slightly higher number of muscle fibres (max. 5521 vs. 5360) in comparison to data for the distal compartment which had the largest cross-sectional area at 40% of the muscle length. The muscle fibre diameters revealed a clear tendency within both compartments to increase along the muscle (from the knee to the Achilles tendon) up to 46.9?μm in the proximal compartment and 58.4?μm in the distal one. The maximal tetanic and single twitch force evoked by stimulation of L4, L5, and L6 ventral roots in whole muscle and compartments were measured. The MG was innervated from L4 and L5, only L5, or L5 and L6 segments. The proximal compartment was innervated by axons from L5 or L5 and L4, and the distal one from L5, L5 and L6, or L5 and L4 segments. The forces produced by the compartments summed non-linearly. The tetanic forces of the proximal and distal compartments amounted to 2.24 and 4.86?N, respectively, and their algebraic sums were 11% higher than the whole muscle force (6.37?N).     

Nucleus implant parameters significantly change the compressive stiffness of the human lumbar intervertebral disc

Nucleus replacement by a synthetic material is a recent trend for treatment of lower back pain. Hydrogel nucleus implants were prepared with variations in implant modulus, height, and diameter Human lumbar intervertebral discs (IVDs) were tested in compression for intact, denucleated, and implanted condition. Implantation of nucleus implants with different material and geometric parameters into a denucleated IVD significantly altered the IVD compressive stiffness. Variations in the nucleus implant parameters significantly change the compressive stiffness of the human lumbar IVD. Implant geometrical variations were more effective than those of implant modulus variations in the range examined.     

Vertebrae numbers of the early hominid lumbar spine

General doctrine holds that early hominids possessed a long lumbar spine with six segments. This is mainly based on Robinson's (1972) interpretation of a single partial Australopithecus africanus skeleton, Sts 14, from Sterkfontein, South Africa. As its sixth last presacral vertebra exhibits both thoracic and lumbar characteristics, current definitions of lumbar vertebrae and lumbar ribs are discussed in the present study. A re-analysis of its entire preserved vertebral column and comparison with Stw 431, another partial A. africanus skeleton from Sterkfontein, and the Homo erectus skeleton KNM-WT 15000 from Nariokotome, Kenya, did not provide strong evidence for the presence of six lumbar vertebrae in either of these early hominids. Thus, in Sts 14 the sixth last presacral vertebra has on one side a movable rib. In Stw 431, the corresponding vertebra shows indications for a rib facet. In KNM-WT, 15000 the same element is very fragmentary, but the neighbouring vertebrae do not support the view that it is L1. Although in all three fossils the transitional vertebra at which the articular facets change orientation seems to be at Th11, this is equal to a large percentage of modern humans. Indeed, a modal number of five lumbar vertebrae, as in modern humans, is more compatible with evolutionary principles. For example, six lumbar vertebrae would require repetitive shortening and lengthening not only of the lumbar, but also of the entire precaudal spine. Furthermore, six lumbar vertebrae are claimed to be biomechanically advantageous for early hominid bipedalism, yet an explanation is lacking as to why the lumbar region should have shortened in later humans. All this raises doubts about previous conclusions for the presence of six lumbar vertebrae in early hominids. The most parsimonious explanation is that they did not differ from modern humans in the segmentation of the vertebral column.