Animal Modelling of Lumbar Corpectomy and Fusion and in vivo Growth of Spine Supporting Bone by Titanium Cage Implants: An Experimental Study

##正## In this study a lumbar spinal fusion animal model is established to assess the effect of spinal fusion cage,and explore theminimum area ratio of titanium cage section to vertebral section that ensures bone healing and biomechanical property.Lumbarcorpectomy was conducted by posterolateral approach with titanium cage implantation combined with plate fixation.Titaniumcages with the same length but different diameters were used.After implantation of titanium cages,the progress of bone healingwas observed and the bone biomechanical properties were measured,including deformation and displacement in axial compression,flexion,extension,and lateral bending motion.The factors affecting the in vivo growth of spine supporting body wereanalyzed.The results show that the area ratio of titanium cage section to vertebral section should reach 1/2 to ensure the bonehealing,sufficient bone intensity and biomechanical properties.Some bone healing indicators,such as BMP,suggest that there isa relationship between the peak time and the peak value of bone formation and metabolism markers and the bone healing strength.     

Finite element simulation of interactions between pelvic organs: Predictive model of the prostate motion in the context of radiotherapy

The setting up of predictive models of the pelvic organ motion and deformation may prove an efficient tool in the framework of prostate cancer radiotherapy, in order to deliver doses more accurately and efficiently to the clinical target volume (CTV). A finite element (FE) model of the prostate, rectum and bladder motion has been developed, investigating more specifically the influence of the rectum and bladder repletions on the gland motion. The required organ geometries are obtained after processing the computed tomography (CT) images, using specific softwares. Due to their structural characteristics, a 3D shell discretization is adopted for the rectum and the bladder, whereas a volume discretization is adopted for the prostate. As for the mechanical behavior modelling, first order Ogden hyperelastic constitutive laws for both the rectum and bladder are identified. The prostate is comparatively considered as more rigid and is accordingly modelled as an elastic tissue undergoing small strains. A FE model is then created, accounting for boundary and contact conditions, internal and applied loadings being selected as close as possible to available anatomic data.The order of magnitude of the prostate motion predicted by the FE simulations is similar to the measurements done on a deceased person, accounting for the delineation errors, with a relative error around 8%. Differences are essentially due to uncertainties in the constitutive parameters, pointing towards the need for the setting up of direct measurement of the organs mechanical behavior.     

Postfailure modulus strongly affects microcracking and mechanical property change in human iliac cancellous bone: a study using a 2D nonlinear finite element method

A two-dimensional (2D) finite element (FE) method was used to estimate the ability of bone tissue to sustain damage as a function of postfailure modulus. Briefly, 2D nonlinear compact-tension FE models were created from quantitative back-scattered electron images taken of human iliac crest bone specimens. The effects of different postfailure moduli on predicted microcrack propagation were examined. The 2D FE models were used as surrogates for real bone tissues. The crack number was larger in models with higher postfailure modulus, while mean crack length and area were smaller in these models. The rate of stiffness reduction was greater in the models with lower postfailure modulus. Hence, the current results supported the hypothesis that hard tissue postfailure properties have strong effects on bone microdamage morphology and the rate of change in apparent mechanical properties.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

Investigation of different cage designs and mechano-regulation algorithms in the lumbar interbody fusion process – A finite element analysis

Lumbar interbody fusion cages are commonly used to treat painful spinal degeneration and instability by achieving bony fusion. Many different cage designs exist, however the effect of cage morphology and material properties on the fusion process remains largely unknown. This finite element model study aims to investigate the influence of different cage designs on bone fusion using two mechano-regulation algorithms of tissue formation. It could be observed that different cages play a distinct key role in the mechanical conditions within the fusion region and therefore regulate the time course of the fusion process.     

Prediction of femoral strength using 3D finite element models reconstructed from DXA images: validation against experiments

Computed tomography (CT)-based finite element (FE) models may improve the current osteoporosis diagnostics and prediction of fracture risk by providing an estimate for femoral strength. However, the need for a CT scan, as opposed to the conventional use of dual-energy X-ray absorptiometry (DXA) for osteoporosis diagnostics, is considered a major obstacle. The 3D shape and bone mineral density (BMD) distribution of a femur can be reconstructed using a statistical shape and appearance model (SSAM) and the DXA image of the femur. Then, the reconstructed shape and BMD could be used to build FE models to predict bone strength. Since high accuracy is needed in all steps of the analysis, this study aimed at evaluating the ability of a 3D FE model built from one 2D DXA image to predict the strains and fracture load of human femora. Three cadaver femora were retrieved, for which experimental measurements from ex vivo mechanical tests were available. FE models were built using the SSAM-based reconstructions: using only the SSAM-reconstructed shape, only the SSAM-reconstructed BMD distribution, and the full SSAM-based reconstruction (including both shape and BMD distribution). When compared with experimental data, the SSAM-based models predicted accurately principal strains (coefficient of determination >0.83, normalized root-mean-square error <16%) and femoral strength (standard error of the estimate 1215 N). These results were only slightly inferior to those obtained with CT-based FE models, but with the considerable advantage of the models being built from DXA images. In summary, the results support the feasibility of SSAM-based models as a practical tool to introduce FE-based bone strength estimation in the current fracture risk diagnostics.     

Development and validation of subject-specific finite element models for blunt trauma study

This study developed and validated finite element (FE) models of swine and human thoraxes and abdomens that had subject-specific anatomies and could accurately and efficiently predict body responses to blunt impacts. Anatomies of the rib cage, torso walls, thoracic, and abdominal organs were reconstructed from X-ray computed tomography (CT) images and extracted into geometries to build FE meshes. The rib cage was modeled as an inhomogeneous beam structure with geometry and bone material parameters determined directly from CT images. Meshes of soft components were generated by mapping structured mesh templates representative of organ topologies onto the geometries. The swine models were developed from and validated by 30 animal tests in which blunt insults were applied to swine subjects and CT images, chest wall motions, lung pressures, and pathological data were acquired. A comparison of the FE calculations of animal responses and experimental measurements showed a good agreement. The errors in calculated response time traces were within 10% for most tests. Calculated peak responses showed strong correlations with the experimental values. The stress concentration inside the ribs, lungs, and livers produced by FE simulations also compared favorably to the injury locations. A human FE model was developed from CT images from the Visible Human project and was scaled to simulate historical frontal and side post mortem human subject (PMHS) impact tests. The calculated chest deformation also showed a good agreement with the measurements. The models developed in this study can be of great value for studying blunt thoracic and abdominal trauma and for designing injury prevention techniques, equipments, and devices.     

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.     

Effects of the rib cage on thoracic spine flexibility.

Besides protecting the internal organs of the thorax, the rib cage is the site of numerous muscle attachments. It also decreases the overall flexibility of the thoracic spine. This study developed finite element (FE) models of the thoracic spine with and without the rib cage, and the effects of the rib cage on thoracic spine flexibility were determined. The numerical models were validated by comparing the maximum rotation of the models for several loading cases with experimental data in the literature. After adapting the material properties for the discs and ligaments, the calculated maximum rotations differed from the measured median values by less than 1 degrees without the rib cage and by less than 2.5 degrees with it. The rib cage decreased the mean flexibility of the thoracic spine by 23% to 47%, depending on the loading plane. Assuming the ribs to be rigid beams required a corresponding reduction of ligament stiffnesses in order to achieve the same agreement of the maximum rotations with the measured median values. Interconnecting the FE thoracic spine model plus rib cage with the existing detailed FE lumbar spine model improves the simulation of force directions of muscles attached to the rib cage or thoracolumbar spine. In addition, such a model is suitable for determining the effects of lumbar spine implants on spinal balance.     

Low pressure condition of a lipid core in an eccentrically developed carotid atheromatous plaque: a static finite element analysis

Plaque ruptures in atherosclerotic carotid arteries cause cerebral strokes. Accumulation of lipoproteins in the deep intimal layer forms a lipid core (LC), whose progression may be enhanced by mechanical conditions on the arterial wall. In this study, we investigated the pressure conditions of a liquid LC through numerical simulations of a sliced segment finite element (FE) model and a three-dimensional (3D) symmetric FE model. A model of an LC filled with nearly incompressible fluid was compared with incompressible and soft neo-Hookean LC models in a static FE analysis. Material constants for a nonlinear hyperelastic model of the arterial wall were identified based on an inflation test using a tube specimen. The results from the FE analysis of a sliced segment model show an LC fluid pressure as low as 1.9 kPa at a blood pressure of 16 kPa. A neo-Hookean LC model with a Young’s modulus of 0.06 kPa produced an almost uniform pressure in the LC within an error of 1.3 %. The 3D model predicted a similar level of LC pressure. Such low fluid pressure in the LC region may enhance the infiltration of lipoproteins and other substances from the lumen and facilitate transport through microvessels from the adventitia to the LC.     

Finite Element Analysis of a New Pedicle Screw-Plate System for Minimally Invasive Transforaminal Lumbar Interbody Fusion

Purpose

Minimally invasive transforaminal lumbar interbody fusion (MI-TLIF) is increasingly popular for the surgical treatment of degenerative lumbar disc diseases. The constructs intended for segmental stability are varied in MI-TLIF. We adopted finite element (FE) analysis to compare the stability after different construct fixations using interbody cage with posterior pedicle screw-rod or pedicle screw-plate instrumentation system.

Methods

A L3–S1 FE model was modified to simulate decompression and fusion at L4–L5 segment. Fixation modes included unilateral plate (UP), unilateral rod (UR), bilateral plate (BP), bilateral rod (BR) and UP+UR fixation. The inferior surface of the S1 vertebra remained immobilized throughout the load simulation, and a bending moment of 7.5 Nm with 400N pre-load was applied on the L3 vertebra to recreate flexion, extension, lateral bending, and axial rotation. Range of motion (ROM) and Von Mises stress were evaluated for intact and instrumentation models in all loading planes.

Results

All reconstructive conditions displayed decreased motion at L4–L5. The pedicle screw-plate system offered equal ROM to pedicle screw-rod system in unilateral or bilateral fixation modes respectively. Pedicle screw stresses for plate system were 2.2 times greater than those for rod system in left lateral bending under unilateral fixation. Stresses for plate were 3.1 times greater than those for rod in right axial rotation under bilateral fixation. Stresses on intervertebral graft for plate system were similar to rod system in unilateral and bilateral fixation modes respectively. Increased ROM and posterior instrumentation stresses were observed in all loading modes with unilateral fixation compared with bilateral fixation in both systems.

Conclusions

Transforaminal lumbar interbody fusion augmentation with pedicle screw-plate system fixation increases fusion construct stability equally to the pedicle screw-rod system. Increased posterior instrumentation stresses are observed in all loading modes with plate fixation, and bilateral fixation could reduce stress concentration.     

Representation of passive spinal element contributions to in vitro flexion-extension using a polynomial model: illustration using the porcine lumbar spine

A polynomial modeling approach was developed to describe the contribution of individual passive spinal elements to the lumbar spinal motion segment flexion-extension motion. Flexion-extension moment-angle curves from porcine lumbar spines tested using a robotic testing system were described using sixth-order polynomials; the polynomials describing different dissection conditions were subtracted to describe the contribution of individual spinal elements to the motion segment flexion-extension properties. This modeling approach is a powerful and straightforward method for representing the mechanics of individual spinal tissues in biomechanical models and could easily be expanded to incorporate other features such as axial load.     

A phase-contrast microscopy-based method for modeling the mechanical behavior of mesenchymal stem cells

We present three-dimensional (3D) finite element (FE) models of single, mesenchymal stem cells (MSCs), generated from images obtained by optical phase-contrast microscopy and used to quantify the structural responses of the studied cells to externally applied mechanical loads. Mechanical loading has been shown to affect cell morphology and structure, phenotype, motility and other biological functions. Cells experience mechanical loads naturally, yet under prolonged or sizable loading, damage and cell death may occur, which motivates research regarding the structural behavior of loaded cells. For example, near the weight-bearing boney prominences of the buttocks of immobile persons, tissues may become highly loaded, eventually leading to massive cell death that manifests as pressure ulcers. Cell-specific computational models have previously been developed by our group, allowing simulations of cell deformations under compressive or stretching loads. These models were obtained by reconstructing specific cell structures from series of 2D fluorescence, confocal image-slices, requiring cell-specific fluorescent-staining protocols and costly (confocal) microscopy equipment. Alternative modeling approaches represent cells simply as half-spheres or half-ellipsoids (i.e. idealized geometries), which neglects the curvature details of the cell surfaces associated with changes in concentrations of strains and stresses. Thus, we introduce here for the first time an optical image-based FE modeling, where loads are simulated on reconstructed 3D geometrical cell models from a single 2D, phase-contrast image. Our novel modeling method eliminates the need for confocal imaging and fluorescent staining preparations (both expensive), and makes cell-specific FE modeling affordable and accessible to the biomechanics community. We demonstrate the utility of this cost-effective modeling method by performing simulations of compression of MSCs embedded in a gel.     

Estimation of in vivo inter-vertebral loading during motion using fluoroscopic and magnetic resonance image informed finite element models

Finite element (FE) models driven by medical image data can be used to estimate subject-specific spinal biomechanics. This study aimed to combine magnetic resonance (MR) imaging and quantitative fluoroscopy (QF) in subject-specific FE models of upright standing, flexion and extension. Supine MR images of the lumbar spine were acquired from healthy participants using a 0.5 T MR scanner. Nine 3D quasi-static linear FE models of L3 to L5 were created with an elastic nucleus and orthotropic annulus. QF data was acquired from the same participants who performed trunk flexion to 60° and trunk extension to 20°. The displacements and rotations of the vertebrae were calculated and applied to the FE model. Stresses were averaged across the nucleus region and transformed to the disc co-ordinate system (S1 = mediolateral, S2 = anteroposterior, S3 = axial). In upright standing S3 was predicted to be −0.7 ± 0.6 MPa (L3L4) and −0.6 ± 0.5 MPa (L4L5). S3 increased to −2.0 ± 1.3 MPa (L3L4) and −1.2 ± 0.6 MPa (L4L5) in full flexion and to −1.1 ± 0.8 MPa (L3L4) and −0.7 ± 0.5 MPa (L4L5) in full extension. S1 and S2 followed similar patterns; shear was small apart from S23. Disc stresses correlated to disc orientation and wedging. The results demonstrate that MR and QF data can be combined in a participant-specific FE model to investigate spinal biomechanics in vivo and that predicted stresses are within ranges reported in the literature.     

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.     

Finite element simulation of spinal deformities correction by in situ contouring technique

Biomechanical models have been proposed in order to simulate the surgical correction of spinal deformities. With these models, different surgical correction techniques have been examined: distraction and rod rotation. The purpose of this study was to simulate another surgical correction technique: the in situ contouring technique. In this way, a comprehensive three-dimensional Finite Element (FE) model with patient-specific geometry and patient-specific mechanical properties was used. The simulation of the surgery took into account elasto-plastic behavior of the rod and multiple moments loading and unloading representing the surgical maneuvers. The simulations of two clinical cases of hyperkyphosis and scoliosis were coherent with the surgeon's experience. Moreover, the results of simulation were compared to post-operative 3D measurements. The mean differences were under 5 degrees for vertebral rotations and 5 mm for spinal lines. These simulations open the way for future predictive tools for surgical planning.     

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.     

Finite Element Analysis of Minimal Invasive Transforaminal Lumbar Interbody Fusion

The purpose of our study is to develop and validate three-dimensional finite element models of transforaminal lumbar interbody fusion, and explore the most appropriate method of fixation and fusion by comparing biomechanical characteristics of different fixation method. We developed four fusion models: bilateral pedicle screws fixation with a single cage insertion model (A), bilateral pedicle screws fixation with two cages insertion model (B), unilateral pedicle screws fixation with a single cage insertion model (C), and unilateral pedicle screws fixation with two cages insertion model (D); the models were subjected to different forces including anterior bending, posterior extension, left bending, right bending, rotation, and axial compressive. The von Mises stress of the fusion segments on the pedicle screw and cages was recorded. Angular variation and stress of pedicle screw and cage were compared. There were differences of Von Mises peak stress among four models, but were within the range of maximum force. The angular variation in A, B, C, and D decreased significantly compared with normal. There was no significant difference of angular variation between A and B, and C and D. Bilateral pedicle screws fixation had more superior biomechanics than unilateral pedicle screws fixation. In conclusion, the lumbar interbody fusion models were established using varying fixation methods, and the results verified that unilateral pedicle screws fixation with a single cage could meet the stability demand in minimal invasive transforaminal interbody fusion.     

Study on effect of graded facetectomy on change in lumbar motion segment torsional flexibility using three-dimensional continuum contact representation for facet joints

Facet joints provide rigidity to the lumbar motion segment and thus protect the disk, particularly against torsional injury. A surgical procedure that fully or partially removes the facet joints (facetectomy) will decrease the mechanical stiffness of the motion segment, and potentially place the disk at risk of injury. Analytical models can be used to understand the effect of facet joints on motion segment stability. Using a facet joint model that represents the contact area as contact between two surfaces rather than as point contact, it was concluded that a substantial sudden change in rotational motion, due to applied torsion moment, was observed after 75 percent of any one of the facet joints was removed. Applied torsional moment loading produced coupled extension motion in the intact motion segment. This coupled motion also experienced a large change following complete unilateral facetectomy. Clinically, the present study showed that surgical intervention in the form of unilateral or bilateral total facetectomy might require fusion to reduce the primary torsion motion.     

Multilevel finite element modeling for the prediction of local cellular deformation in bone

The underlying mechanisms by which bone cells respond to mechanical stimuli or how mechanical loads act on osteocytes housed in lacunae in bone are not well understood. In this study, a multilevel finite element (FE) approach is applied to predict local cell deformations in bone tissue. The local structure of the matrix dictates the local mechanical environment of an osteocyte. Cell deformations are predicted from detailed linear FE analysis of the microstructure, consisting of an arrangement of cells embedded in bone matrix material. This work has related the loads applied to a whole femur during the stance phase of the gait cycle to the strain of a single lacuna and of canaliculi. The predicted bone matrix strains around osteocyte lacunae and canaliculi were nonuniform and differed significantly from the macroscopically measured strains. Peak stresses and strains in the walls of the lacuna were up to six times those in the bulk extracellular matrix. Significant strain concentrations were observed at sites where the process meets the cell body.