A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads

Due to the inherent limitations of DXA, assessment of the biomechanical properties of vertebral bodies relies increasingly on CT-based finite element (FE) models, but these often use simplistic material behaviour and/or single loading cases. In this study, we applied a novel constitutive law for bone elasticity, plasticity and damage to FE models created from coarsened pQCT images of human vertebrae, and compared vertebral stiffness, strength and damage accumulation for axial compression, anterior flexion and a combination of these two cases. FE axial stiffness and strength correlated with experiments and were linearly related to flexion properties. In all loading modes, damage localised preferentially in the trabecular compartment. Damage for the combined loading was higher than cumulated damage produced by individual compression and flexion. In conclusion, this FE method predicts stiffness and strength of vertebral bodies from CT images with clinical resolution and provides insight into damage accumulation in various loading modes.     

HR-pQCT-based homogenised finite element models provide quantitative predictions of experimental vertebral body stiffness and strength with the same accuracy as μFE models

This study validated two different high-resolution peripheral quantitative computer tomography (HR-pQCT)-based finite element (FE) approaches, enhanced homogenised continuum-level (hFE) and micro-finite element (μFE) models, by comparing them with compression test results of vertebral body sections. Thirty-five vertebral body sections were prepared by removing endplates and posterior elements, scanned with HR-pQCT and tested in compression up to failure. Linear hFE and μFE models were created from segmented and grey-level CT images, and apparent model stiffness values were compared with experimental stiffness as well as strength results. Experimental and numerical apparent elastic properties based on grey-level/segmented CT images (N=35) correlated well for μFE (r2=0.748/0.842) and hFE models (r2=0.741/0.864). Vertebral section stiffness values from the linear μFE/hFE models estimated experimental ultimate apparent strength very well (r2=0.920/0.927). Calibrated hFE models were able to predict quantitatively apparent stiffness with the same accuracy as μFE models. However, hFE models needed no back-calculation of a tissue modulus or any kind of fitting and were computationally much cheaper.     

Can micro-imaging based analysis methods quantify structural integrity of rat vertebrae with and without metastatic involvement?

This study compares the ability of μCT image-based registration, 2D structural rigidity analyses and multimodal continuum-level finite element (FE) modeling in evaluating the mechanical stability of healthy, osteolytic, and mixed osteolytic/osteoblastic metastatically involved rat vertebrae. μMR and μCT images (loaded and unloaded) were acquired of lumbar spinal motion segments from 15rnu/rnu rats (five per group). Strains were calculated based on image registration of the loaded and unloaded μCT images and via analysis of FE models created from the μCT and μMR data. Predicted yield load was also calculated through 2D structural rigidity analysis of the axial unloaded μCT slices. Measures from the three techniques were compared to experimental yield loads. The ability of these methods to predict experimental yield loads were evaluated and image registration and FE calculated strains were directly compared. Quantitatively for all samples, only limited weak correlations were found between the image-based measures and experimental yield load. In comparison to the experimental yield load, we observed a trend toward a weak negative correlation with median strain calculated using the image-based strain measurement algorithm (r=-0.405, p=0.067), weak significant correlations (p<0.05) with FE based median and 10th percentile strain values (r=-0.454, -0.637, respectively), and a trend toward a weak significant correlation with FE based mean strain (r=-0.366, p=0.09). Individual group analyses, however, yielded more and stronger correlations with experimental results. Considering the image-based strain measurement algorithm we observed moderate significant correlations with experimental yield load (p<0.05) in the osteolytic group for mean and median strain values (r=-0.840, -0.832, respectively), and in the healthy group for median strain values (r=-0.809). Considering the rigidity-based predicted yield load, we observed a strong significant correlation with the experimental yield load in the mixed osteolytic/osteoblastic group (r=0.946) and trend toward a moderate correlation with the experimental yield load in the osteolytic group (r=0.788). Qualitatively, strain patterns in the vertebral bodies generated using image registration and FEA were well matched, yet quantitatively a significant correlation was found only between mean strains in the healthy group (r=0.934). Large structural differences in metastatic vertebrae and the complexity of motion segment loading may have led to varied modes of failure. Improvements in load characterization, material properties assignments and resolution are necessary to yield a more generalized ability for image-based registration, structural rigidity and FE methods to accurately represent stability in healthy and pathologic scenarios.     

Finite element analyses of human vertebral bodies embedded in polymethylmethalcrylate or loaded via the hyperelastic intervertebral disc models provide equivalent predictions of experimental strength

Quantitative computer tomography (QCT)-based finite element (FE) models of vertebral body provide better prediction of vertebral strength than dual energy X-ray absorptiometry. However, most models were validated against compression of vertebral bodies with endplates embedded in polymethylmethalcrylate (PMMA). Yet, loading being as important as bone density, the absence of intervertebral disc (IVD) affects the strength. Accordingly, the aim was to assess the strength predictions of the classic FE models (vertebral body embedded) against the in vitro and in silico strengths of vertebral bodies loaded via IVDs. High resolution peripheral QCT (HR-pQCT) were performed on 13 segments (T11/T12/L1). T11 and L1 were augmented with PMMA and the samples were tested under a 4° wedge compression until failure of T12. Specimen-specific model was generated for each T12 from the HR-pQCT data. Two FE sets were created: FE-PMMA refers to the classical vertebral body embedded model under axial compression; FE-IVD to their loading via hyperelastic IVD model under the wedge compression as conducted experimentally. Results showed that FE-PMMA models overestimated the experimental strength and their strength prediction was satisfactory considering the different experimental set-up. On the other hand, the FE-IVD models did not prove significantly better (Exp/FE-PMMA: R²=0.68; Exp/FE-IVD: R²=0.71, p=0.84). In conclusion, FE-PMMA correlates well with in vitro strength of human vertebral bodies loaded via real IVDs and FE-IVD with hyperelastic IVDs do not significantly improve this correlation. Therefore, it seems not worth adding the IVDs to vertebral body models until fully validated patient-specific IVD models become available.     

Localized damage in vertebral bone is most detrimental in regions of high strain energy density

It was hypothesized that damage to bone tissue would be most detrimental to the structural integrity of the vertebral body if it occurred in regions with high strain energy density, and not necessarily in regions of high or low trabecular bone apparent density, or in a particular anatomic location. The reduction in stiffness due to localized damage was computed in 16 finite element models of 10-mm-thick human vertebral sections. Statistical analyses were performed to determine which characteristic at the damage location--strain energy density, apparent density, or anatomic location--best predicted the corresponding stiffness reduction. There was a strong positive correlation between regional strain energy density and structural stiffness reduction in all 16 vertebral sections for damage in the trabecular centrum (p < 0.05, r2 = 0.43-0.93). By contrast, regional apparent density showed a significant negative correlation to stiffness reduction in only four of the sixteen bones (p < 0.05, r2 = 0.47-0.58). While damage in different anatomic locations did lead to different reductions in stiffness (p < 0.0001, ANOVA), no single location was consistently the most critical location for damage. Thus, knowledge of the characteristics of bone that determine strain energy density distributions can provide an understanding of how damage reduces whole bone mechanical properties. A patient-specific finite element model displaying a map of strain energy density can help optimize surgical planning and reinforcement of bone in individuals with high fracture risk.     

Micro-CT and micro-FE analysis of pedicle screw fixation under different loading conditions

Anchorage of pedicle screw instrumentation in the elderly spine with poor bone quality remains challenging. In this study, micro finite element (µFE) models were used to assess the specific influence of screw design and the relative contribution of local bone density to fixation mechanics. These were created from micro computer tomography (µCT) scans of vertebras implanted with two types of pedicle screws, including a full region-or-interest of 10 mm radius around each screw, as well as submodels for the pedicle and inner trabecular bone of the vertebral body. The local bone volume fraction (BV/TV) calculated from the µCT scans around different regions of the screw (pedicle, inner trabecular region of the vertebral body) were then related to the predicted stiffness in simulated pull-out tests as well as to the experimental pull-out and torsional fixation properties mechanically measured on the corresponding specimens. Results show that predicted stiffness correlated excellently with experimental pull-out strength (R² > 0.92, p < .043), better than regional BV/TV alone (R2 = 0.79, p = .003). They also show that correlations between fixation properties and BV/TV were increased when accounting only for the pedicle zone (R² = 0.66–0.94, p ≤ .032), but with weaker correlations for torsional loads (R² < 0.10). Our analyses highlight the role of local density in the pedicle zone on the fixation stiffness and strength of pedicle screws when pull-out loads are involved, but that local apparent bone density alone may not be sufficient to explain resistance in torsion.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

Hypersensitivity of trunk biomechanical model predictions to errors in image-based kinematics when using fully displacement-control techniques

Recent advances in medical imaging techniques have allowed pure displacement-control trunk models to estimate spinal loads with no need to calculate muscle forces. Sensitivity of these models to the errors in post-imaging evaluation of displacements (reported to be ∼0.4–0.9° and 0.2–0.3 mm in vertebral displacements) has not yet been investigated. A Monte Carlo analysis was therefore used to assess the sensitivity of results in both musculoskeletal (MS) and passive finite element (FE) spine models to errors in measured displacements. Six static activities in upright standing, flexed, and extended postures were initially simulated using a force-control hybrid MS-FE model. Computed vertebral displacements were subsequently used to drive two distinct fully displacement-control MS and FE models. Effects of alterations in the reference vertebral displacements (at 3 error levels with SD (standard deviation) = 0.1, 0.2, and 0.3 mm in input translations together with, respectively, 0.2, 0.4, and 0.6° in input rotations) were investigated on the model predictions. Results indicated that outputs of both models had substantial task-dependent sensitivities to errors in the measured vertebral translations. For instance, L5-S1 intradiscal pressures (IDPs) were considerably affected (SD values reaching 1.05 MPa) and axial compression and shear forces even reversed directions as translation errors increased to 0.3 mm. Outputs were however generally much less sensitive to errors in measured vertebral rotations. Accounting for the accuracies in image-based kinematics measurements, therefore, it is concluded that the current measured vertebral translation errors at and beyond 0.1 mm are too large to drive biomechanical models of the spine.     

The biomechanics of human femurs in axial and torsional loading: comparison of finite element analysis, human cadaveric femurs, and synthetic femurs

To assess the performance of femoral orthopedic implants, they are often attached to cadaveric femurs, and biomechanical testing is performed. To identify areas of high stress, stress shielding, and to facilitate implant redesign, these tests are often accompanied by finite element (FE) models of the bone/implant system. However, cadaveric bone suffers from wide specimen to specimen variability both in terms of bone geometry and mechanical properties, making it virtually impossible for experimental results to be reproduced. An alternative approach is to utilize synthetic femurs of standardized geometry, having material behavior approximating that of human bone, but with very small specimen to specimen variability. This approach allows for repeatable experimental results and a standard geometry for use in accompanying FE models. While the synthetic bones appear to be of appropriate geometry to simulate bone mechanical behavior, it has not, however, been established what bone quality they most resemble, i.e., osteoporotic or osteopenic versus healthy bone. Furthermore, it is also of interest to determine whether FE models of synthetic bones, with appropriate adjustments in input material properties or geometric size, could be used to simulate the mechanical behavior of a wider range of bone quality and size. To shed light on these questions, the axial and torsional stiffness of cadaveric femurs were compared to those measured on synthetic femurs. A FE model, previously validated by the authors to represent the geometry of a synthetic femur, was then used with a range of input material properties and change in geometric size, to establish whether cadaveric results could be simulated. Axial and torsional stiffnesses and rigidities were measured for 25 human cadaveric femurs (simulating poor bone stock) and three synthetic "third generation composite" femurs (3GCF) (simulating normal healthy bone stock) in the midstance orientation. The measured results were compared, under identical loading conditions, to those predicted by a previously validated three-dimensional finite element model of the 3GCF at a variety of Young's modulus values. A smaller FE model of the 3GCF was also created to examine the effects of a simple change in bone size. The 3GCF was found to be significantly stiffer (2.3 times in torsional loading, 1.7 times in axial loading) than the presently utilized cadaveric samples. Nevertheless, the FE model was able to successfully simulate both the behavior of the 3GCF, and a wide range of cadaveric bone data scatter by an appropriate adjustment of Young's modulus or geometric size. The synthetic femur had a significantly higher stiffness than the cadaveric bone samples. The finite element model provided a good estimate of upper and lower bounds for the axial and torsional stiffness of human femurs because it was effective at reproducing the geometric properties of a femur. Cadaveric bone experiments can be used to calibrate FE models' input material properties so that bones of varying quality can be simulated.     

A validated computational framework to evaluate the stiffness of 3D printed ankle foot orthoses

The purpose of this study was to create and validate a standardized framework for the evaluation of the ankle stiffness of two designs of 3D printed ankle foot orthoses (AFOs). The creation of four finite element (FE) models allowed patient-specific quantification of the stiffness and stress distribution over their specific range of motion during the second rocker of the gait. Validation was performed by comparing the model outputs with the results obtained from a dedicated experimental setup, which showed an overall good agreement with a maximum relative error of 10.38% in plantarflexion and 10.66% in dorsiflexion. The combination of advanced computer modelling algorithms and 3D printing techniques clearly shows potential to further improve the manufacturing process of AFOs.     

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

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

The influence of material property and morphological parameters on specimen-specific finite element models of porcine vertebral bodies

The use of finite element (FE) methods in spinal research is increasing, but there is only limited information available on the influence of different input parameters on the model predictions. The aim of this study was to investigate the role of these parameters in FE models of the vertebral body. Experimental tests were undertaken on porcine lumbar vertebral bodies and scans of the specimens were used to create specimen-specific FE models. Three models were created for each specimen with combinations of generic and specimen-specific parameters. Stiffness and strength predictions were also made directly from the specimen trabecular bone volume fraction (BVF) and cross-sectional area (CSA). The agreement between the experimental results and the FE models with generic morphology was poorer (concordance coefficients = 0.058, 0.125 for stiffness, strength) than those made from the BVF and CSA (concordance coefficients = 0.638, 0.609). The greatest levels of agreement were found with the morphologically specific models including element-specific material properties (concordance coefficients = 0.881, 0.752). This indicates that highly specific models, both in terms of morphology and bone quality, are necessary if the FE tool is to be used effectively for spinal research and clinical practice.     

Statistical shape and appearance models for fast and automated estimation of proximal femur fracture load using 2D finite element models

Estimating the risk of osteoporotic fractures is an important diagnostic step that needs to be taken before medicinal treatment. Densitometry-based criteria are normally used in clinical practice for this purpose. However, densitometry-based techniques could not explain all low-energy fractures. As patient-specific finite element (FE) models allow for consideration of other parameters (e.g. load conditions) that are known to be associated with fracture, they are considered promising candidates for more accurate fracture risk estimation. Nevertheless, they are often time consuming, expensive, and complex to build and may need the type of expertise that is not normally available in clinical settings. In this study, we report the development of an automated platform for estimating proximal femur fracture loads using patient-specific 2D FE models generated using dual-energy x-ray absorptiometry (DXA) scans. First, a statistical shape and appearance model (SSAM) is built using DXA scans of patients screened for osteoporosis following a low energy fracture. SSAM is then used together with Active Appearance Models (AAM) for automated segmentation of the proximal femur from new unseen DXA scans. The mean point-to-curve error of the automated procedure, i.e. 1.2–1.4 mm, is shown to be only slightly larger than the intra-observer variability of manual segmentation, i.e. 1.0 mm. Moreover, the developed platform automatically meshes the segmented shape, assigns density-based mechanical properties, assigns loads and boundary conditions, submits the 2D FE model for solution, and performs post-processing of the 2D FE simulation data to determine fracture loads. The fracture loads predicted using the manually generated and automatically generated 2D FE models are shown to be very close with a mean difference of around 8.8%. Repeated measures ANOVA showed no significant differences between the fracture loads calculated using FE models manually generated by three independent observers and those calculated using the automatically generated FE models (p>0.05).     

Personalised mechanical properties of scoliotic vertebrae determined in vivo using tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

Finite element analysis of moment-rotation relationships for human cervical spine

A comprehensive, geometrically accurate, nonlinear C0-C7 FE model of head and cervical spine based on the actual geometry of a human cadaver specimen was developed. The motions of each cervical vertebral level under pure moment loading of 1.0 Nm applied incrementally on the skull to simulate the movements of the head and cervical spine under flexion, tension, axial rotation and lateral bending with the inferior surface of the C7 vertebral body fully constrained were analysed. The predicted range of motion (ROM) for each motion segment were computed and compared with published experimental data. The model predicted the nonlinear moment-rotation relationship of human cervical spine. Under the same loading magnitude, the model predicted the largest rotation in extension, followed by flexion and axial rotation, and least ROM in lateral bending. The upper cervical spines are more flexible than the lower cervical levels. The motions of the two uppermost motion segments account for half (or even higher) of the whole cervical spine motion under rotational loadings. The differences in the ROMs among the lower cervical spines (C3-C7) were relatively small. The FE predicted segmental motions effectively reflect the behavior of human cervical spine and were in agreement with the experimental data. The C0-C7 FE model offers potentials for biomedical and injury studies.     

Personalised Mechanical Properties of Scoliotic Vertebrae Determined In Vivo Using Tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Mechanical variables affecting balloon kyphoplasty outcome--a finite element study

It is still unclear how a vertebral fracture should be stabilised and strengthened without endangering the remaining intact bone of the augmented vertebra or the adjacent vertebrae. Numerical modelling may provide insight. To date, however, few finite element (FE) spine models have been developed which are both multi-segmental and capture a more complete anatomy of the vertebrae. A 3-D, two-functional unit, CT-based, lumbar spine, FE model was developed and used to predict load transfer and likelihood of fracture following balloon kyphoplasty. The fractured anterior wall and injected cement were modelled in a two-functional spinal unit model with osteoporotic bone properties. Parameters investigated included: cement stiffness, cement volume and height restoration. Models were assessed based on stresses and a user-defined fracture-predicting field. Augmentation altered the stress distribution; shielding was dependent on positioning of the cement; and fracture algorithm found incomplete height restoration to increase the likelihood of fracture, particularly in adjacent vertebrae.     

A one-dimensional model of the spinal cerebrospinal-fluid compartment

Modeling of the cerebrospinal fluid (CSF) system in the spine is strongly motivated by the need to understand the origins of pathological conditions such as the emergence and growth of fluid-filled cysts in the spinal cord. In this study, a one-dimensional (1D) approximation for the flow in elastic conduits was used to formulate a model of the spinal CSF compartment. The modeling was based around a coaxial geometry in which the inner elastic cylinder represented the spinal cord, middle elastic tube represented the dura, and the outermost tube represented the vertebral column. The fluid-filled annuli between the cord and dura, and the dura and vertebral column, represented the subarachnoid and epidural spaces, respectively. The system of governing equations was constructed by applying a 1D form of mass and momentum conservation to all segments of the model. The developed 1D model was used to simulate CSF pulse excited by pressure disturbances in the subarachnoid and epidural spaces. The results were compared to those obtained from an equivalent two-dimensional finite element (FE) model which was implemented using a commercial software package. The analysis of linearized governing equations revealed the existence of three types of waves, of which the two slower waves can be clearly related to the wave modes identified in previous similar studies. The third, much faster, wave emanates directly from the vertebral column and has little effect on the deformation of the spinal cord. The results obtained from the 1D model and its FE counterpart were found to be in good general agreement even when sharp spatial gradients of the spinal cord stiffness were included; both models predicted large radial displacements of the cord at the location of an initial cyst. This study suggests that 1D modeling, which is computationally inexpensive and amenable to coupling with the models of the cranial CSF system, should be a useful approach for the analysis of some aspects of the CSF dynamics in the spine. The simulation of the CSF pulse excited by a pressure disturbance in the epidural space, points to the possibility that regions of the spinal cord with abnormally low stiffness may be prone to experiencing large strains due to coughing and sneezing.