Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disk

Analytical and finite element models (FEMs) were used to quantify poroelastic material properties for a human intervertebral disk. An axisymmetric FEM based on a poroelastic view of disk constituents was developed for a representative human spinal motion segment (SMS). Creep and steady-state response predicted by FEMs agreed with experimental observations, i.e., long-time creep occurs with flow in the SMS, whereas for rapid steady-state loading an "undrained," nearly incompressible response is evident. A relatively low value was determined for discal permeability. Transient and long-term creep FE analyses included the study of deformation, pore fluid flow, stress, and pore fluid pressure. Relative fluid motion associated with transient creep is related to nuclear nutrition and the overall mechanical response in the normal disk. Degeneration of the disk may be associated with an increase in permeability.     

Mechanical properties of lumbar spine motion segments under large loads

The mechanical behavior of fourteen fresh human lumbar motion segments taken at autopsy from males with an average age of 29 yr was studied. Forces up to 1029 N were applied in anterior, posterior and lateral shear; and moments up to 95 Nm were applied in flexion, extension, lateral bending and torsion. In response to these loads endplate displacements up to 9 mm and rotations up to 18 degrees were measured. Stiffness values ranged from 53 to 140 N mm-1 in response to the shear forces and 6-11 Nm degree-1 in response to the moments. Lumbar motion segments can develop significant passive resistances to loads in situations where they are allowed to undergo substantial deformations.     

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.     

Age-sensitivity of time-related in vivo deformability of human lumbar motion segments and discs in pure centric tension

The goal of this study was to document the effect of aging, sex and disc level on time-dependent in vivo tensile deformability of human lumbar-lumbosacral motion segments and discs in pure centric tension, when the contracting effect of muscles can be neglected. Elongations of segments L3-L4, L4-L5 and L5-S1 were measured during the usual suspension hydrotraction therapy of patients, by using a subaqual ultrasound measuring method reported in (Kurutz et al., 2002a, 2003). Patients were suspended cervically in lukewarm water for 20 min, loaded by 20-20 N lead weights on ankles. The mean initial elastic elongations (strains) of segments or discs were about 0.8 mm (10%) for patients under 40 years; 0.5 mm (6%) between 40-60 years; and 0.2 mm (3%) over 60 years. The mean final viscoelastic elongations were 1.5 mm (18%) under 40 years; 1.2 mm (15%) between 40-60 years; and 0.6 mm (7%) over 60 years. In the beginning/end of the treatment, patients of extended segments were on average 6/8 years younger than those with unextended ones. Based on the in vivo measured elongations, initial tensile stiffness was obtained in terms of aging, sex and disc level. For the above age-classes, the approximate mean tensile stiffness of less/more degenerated lumbar FSUs or discs were about 600/800, 800/1000 and 1800/2800 N/mm, respectively. A new terminology, the so-called age-sensitivity has been introduced as a value of 0.01-0.04 mm/year elongation capacity decrease per a year of aging, after the age of 35. No significant difference was found between sexes regarding age-dependence in tension.     

In vivo age- and sex-related creep of human lumbar motion segments and discs in pure centric tension

In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presented, in terms of aging, sex and disc level. Time-related elongations of segments L3-4, L4-5 and L5-S1 were measured during the usual 20 min long traction hydrotherapy of patients, by using a computerized subaqual ultrasound measuring method [Kurutz et al., 2002a. Orvosi Hetilap 143 (13), 673-684; Kurutz et al., 2003. Journal of Bioengineering and Biomechanics 5 (1), 67-92]. Elongation of segments was considered as a change of the distance between two adjacent spinous processes. Based on these experiments, in vivo creep of human lumbar FSUs was investigated in centric tension, in terms of sex, age and disc level. Three-parameter rheological models were used to determine viscoelastic tensile moduli of human lumbar FSUs and discs. From three time-related measured elongation values, in vivo damping constants with creep functions were calculated for each segment, in terms of sex, aging and disc level. It has been demonstrated that initial elastic elongations decrease, concerning stiffness increase with aging. Similarly, tensile creep elongations decrease, damping properties increase with aging. Former observations concerning the difference in deformation propagation of men and women in time, have been verified by means of creep analysis: although males have higher initial elastic deformability, due to a smaller damping of females, the deformation propagation of women overtakes men in creep process. This tendency is more significant with aging. Increasing damping was observed in distal direction, both for males and females.     

Structural repertoire of the human VH segments.

The VH gene segments produce the part of the VH domains of antibodies that contains the first two hypervariable regions. The sequences of 83 human VH segments with open reading frames, from several individuals, are currently known. It has been shown that these sequences are likely to form a high proportion of the total human repertoire and that an individual's gene repertoire produces about 50 VH segments with different protein sequences. In this paper we present a structural analysis of the amino acid sequences produced by the 83 segments. Particular residue patterns in the sequences of V domains imply particular main-chain conformations, canonical structures, for the hypervariable regions. We show that, in almost all cases, the residue patterns in the VH segments imply that the first hypervariable regions have one of three different canonical structures and that the second hypervariable regions have one of five different canonical structures. The different observed combinations of the canonical structures in the first and second regions means that almost all sequences have one of seven main-chain folds. We describe, in outline, structures of the antigen binding site loops produced by nearly all the VH segments. The exact specificity of the loops is produced by (1) sequence differences in their surface residues, particularly at sites near the centre of the combining site, and (2) sequence differences in the hypervariable and framework regions that modulate the relative positions of the loops.     

Distribution of reticulospinal fibers and theri endings in the lumbar segments of the rat spinal cord]

After stereotaxis lexions in the nucleus reticularis gigantocellularis of the modulla oblongata and nucleus reticularis pontis caudalis, the distribution of degenerating nerve fibers in the lumbar segments of the spinal cord has been studied by silver impregnation methods of Nauta and Fink-Heimer. Degenerating reticulo-spinal fibers and fragments of axonal terminations were found in the area of n. motorius ventro-medialis and n. motorius ventro-lateralis, as well as partly in n. motorius dorso-lateralis close to motoneurons and their dendrites. Mainly they pass into layers VII and VIII. This fact indicates the existence of direct-reticulo-motoneuronal synaptic connections in rats, which coincides with electrophysiological data.     

Uncertainty analysis of material properties and morphology parameters in numerical models regarding the motion of lumbar vertebral segments

Abstract

The kinematics of a spinal motion segment is determined by the material properties of the soft-tissue and the morphology. The material properties can vary within subjects and between vertebral levels, leading to a wide possible range of motion of a spinal segment independently on its morphology. The goal of this numerical study was to identify the most influential material parameters concerning the kinematics of a spinal motion segment and their plausible ranges. Then, a method was tested to deduce the material properties automatically, based on a given ROM and morphology. A fully parametric finite element model of the morphology and material properties of a lumbar spinal motion segment was developed. The impact of uncertainty of twelve spinal material parameters, as well as the size of the gap between the articular surfaces of the facet joints was examined. The simulation results were compared to our own in vitro data. The flexibility of a lumbar segment was especially influenced by the properties of the anterior annulus region, the facet gap size and the interspinous ligament. The high degree of uncertainty in the material properties and facet gap size published in the literature can lead to a wide scatter in the motion of a spinal segment, with a range of 6°-17° in the intact condition in flexion/extension, from 5°-22° in lateral bending and from 3°-14° in axial rotation. Statistical analysis of the variability might help to estimate the sensitivity and total uncertainty propagated through biomechanical simulations, affecting the reliability of the predictions.     

Load-displacement properties of lower cervical spine motion segments

The load-displacement behavior of 35 fresh adult cervical spine motion segments was measured in compression, shear, flexion, extension, lateral bending and axial torsion tests. Motion segments were tested both intact and with posterior elements removed. Applied forces ranged to 73.6 N in compression and to 39 N in shear, while applied moments ranged to 2.16 Nm. For each mode of loading, principal and coupled motions were measured and stiffnesses were calculated. The effect of disc degeneration on motion segment stiffnesses and the moments required for motion segment failure were also measured. In compression, the stiffnesses of the cervical motion segments were similar to those of thoracic and lumbar motion segments. In other modes of loading, cervical stiffnesses were considerably smaller than thoracic or lumbar stiffnesses. Removal of the posterior elements decreased cervical motion segment stiffnesses by as much as 50%. Degenerated cervical discs were less stiff in compression and stiffer in shear than less degenerated discs, but in bending or axial torsion, no statistically significant differences were evident. Bending moments causing failure were an order of magnitude lower than those for lumbar segments.     

Developmental characteristics of the human lumbar spinal column at various periods of ontogeny

Regularities in development and differentiation of vertebrae have been investigated according to ageing. The data concerning the size of the vertebral canal at the level of the lumbar vertebral bodies and intervertebral discs, intensity of increase of these dimensions in various age periods, the character of spatial relations of sizes and form of the canal has been analysed. The transversal section area of the canal and the body in the corresponding segment varies between 1:3 and 1:5.5. By means of x-ray osteophotometry the mineralization degree of the lumbar vertebral bodies has been determined in men of various age. An important fact has been stated on a close connection between mineral saturation in juvenile and first mature ages with induces of general strength.     

End-cap for the biomechanical testing of spinal segments

Precise mechanical loading is essential in the in vitro evaluation of spinal fixation instrumentation, but the control of experimental variables is difficult because of variations in specimen morphology, size and end conditions, and gross specimen flexibility. This paper describes an end-cap which is simple in design, time efficient in its attachment to the spine and which provides precise positioning and rigid control of the end fixation points, resulting in excellent experimental control. It is easily adapted to human or animal specimens and provides a reliable load application unit, which permits specific physiological end conditions to be applied.     

Evoked activity in the ventral horn of the lumbar segments of the spinal cord during cortical inhibition of cortical motor responses

Electrical activity in the flexor nerve and focal potentials (FP) in the medial and lateral zones of the ventral horn (VH) of segments L₆ and L₇ of the spinal cord, evoked by excitation of the contralateral motor cortex, were recorded in delicate experiments on cats. These focal potentials were studied during inhibition of the flexor response that developed as a result of prior excitation of the ipsilateral cortex ("cortical inhibition"). During the inhibition the FP's of the medial zone (layer VIII, according to Rexed) were greatly increased, mainly in their negative components, their time-characteristics being altered. When the interval between excitations was 50 msec (in that case the inhibition was most pronounced) the medial FP's arose against a negative background, which was a late component of the previous activity evoked by conditioning excitation. The appearance of this late component was correlated with the development of inhibition of the cortical flexor response. At the same time a positive condition developed in the lateral zone, in the region of the nucleus biceps-semitendinosus, which indicated orientation in a lateral direction of the interneurons discharging in the medial zone at late periods after the conditioning excitation. Inhibition of the flexor response was accompanied by depression of the lateral FP's without change in their sign or in the time-structure of their components. It is suggested that cortical inhibition of the cortical flexor response arises at the interneuron level. The functional structure of that inhibitory pathway is discussed.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 3, No. 2, pp. 185–193, March–April, 1971.     

Contribution of vertebral [corrected] bodies, endplates, and intervertebral discs to the compression creep of spinal motion segments

Spinal segments show non-linear behavior under axial compression. It is unclear to what extent this behavior is attributable to the different components of the segment. In this study, we quantified the separate contributions of vertebral bodies and intervertebral discs to creep of a segment. Secondly, we investigated the contribution of bone and osteochondral endplate (endplates including cartilage) to the deformation of the vertebral body. From eight porcine spines a motion segment, a disc and a vertebral body were dissected and subjected to mechanical testing. In an additional test, cylindrical samples, machined from the lowest thoracic vertebrae of 11 porcine spines, were used to compare the deformation of vertebral bone and endplate. All specimens were subjected to three loading cycles, each comprising a loading phase (2.0 MPa, 15 min) and a recovery phase (0.001 MPa, 30 min). All specimens displayed substantial time-dependent height changes. Average creep was the largest in motion segments and smallest in vertebral bodies. Bone samples with endplates displayed substantially more creep than samples without. In the early phase, behavior of the vertebra was similar to that of the disc. Visco-elastic deformation of the endplate therefore appeared dominant. In the late creep phase, behavior of the segment was similar to that of isolated discs, suggesting that in this phase the disc dominated creep behavior, possibly by fluid flow from the nucleus. We conclude that creep deformation of vertebral bodies contributes substantially to creep of motion segments and that within a vertebral body endplates play a major role.