Contact analysis of a posterior cervical spine plate using a three-dimensional canine finite element model

Development of a finite element model of the ligamentous cervical vertebral column of a Great Dane

Cervical spondylomyelopathy (CSM), also known as wobbler syndrome, affects mainly large and giant-breed dogs, causing compression of the cervical spinal cord and/or nerve roots. Structural and dynamic components seem to play a role in the development of CSM; however, pathogenesis is not yet fully understood. Finite element models have been used for years in human medicine to study the dynamic behavior of structures, but it has been mostly overlooked in veterinary studies. To our knowledge, no specific ligamentous spine models have been developed to investigate naturally occurring canine myelopathies and possible surgical treatments. The goal of this study was to develop a finite element model (FEM) of the C₂-C₇ segment of the ligamentous cervical vertebral column of a neurologically normal Great Dane without imaging changes. The FEM of the intact C₂-C₇ cervical vertebral column had a total of 188,906 elements (175,715 tetra elements and 12,740 hexa elements). The range of motion (in degrees) for the FEM subjected to a moment of 2Nm was approximately 27.94 in flexion, 25.86 in extension, 24.14 in left lateral bending, 25.27 in right lateral bending, 17.44 in left axial rotation, and 16.72 in right axial rotation. We constructed a ligamentous FEM of the C₂-C₇ vertebral column of a Great Dane dog, which can serve as a platform to be modified and adapted for studies related to biomechanics of the cervical vertebral column and to further improve studies on osseous-associated cervical spondylomyelopathy.

Mechanical testing of bones: the positive synergy of finite-element models and in vitro experiments

Bone biomechanics have been extensively investigated in the past both with in vitro experiments and numerical models. In most cases either approach is chosen, without exploiting synergies. Both experiments and numerical models suffer from limitations relative to their accuracy and their respective fields of application. In vitro experiments can improve numerical models by: (i) preliminarily identifying the most relevant failure scenarios; (ii) improving the model identification with experimentally measured material properties; (iii) improving the model identification with accurately measured actual boundary conditions; and (iv) providing quantitative validation based on mechanical properties (strain, displacements) directly measured from physical specimens being tested in parallel with the modelling activity. Likewise, numerical models can improve in vitro experiments by: (i) identifying the most relevant loading configurations among a number of motor tasks that cannot be replicated in vitro; (ii) identifying acceptable simplifications for the in vitro simulation; (iii) optimizing the use of transducers to minimize errors and provide measurements at the most relevant locations; and (iv) exploring a variety of different conditions (material properties, interface, etc.) that would require enormous experimental effort. By reporting an example of successful investigation of the femur, we show how a combination of numerical modelling and controlled experiments within the same research team can be designed to create a virtuous circle where models are used to improve experiments, experiments are used to improve models and their combination synergistically provides more detailed and more reliable results than can be achieved with either approach singularly.

Verification, validation and sensitivity studies in computational biomechanics

Computational techniques and software for the analysis of problems in mechanics have naturally moved from their origins in the traditional engineering disciplines to the study of cell, tissue and organ biomechanics. Increasingly complex models have been developed to describe and predict the mechanical behavior of such biological systems. While the availability of advanced computational tools has led to exciting research advances in the field, the utility of these models is often the subject of criticism due to inadequate model verification and validation (V&V). The objective of this review is to present the concepts of verification, validation and sensitivity studies with regard to the construction, analysis and interpretation of models in computational biomechanics. Specific examples from the field are discussed. It is hoped that this review will serve as a guide to the use of V&V principles in the field of computational biomechanics, thereby improving the peer acceptance of studies that use computational modeling techniques.

Assessment of Factors Influencing Finite Element Vertebral Model Predictions

This study aimed to establish model construction and configuration procedures for future vertebral finite element analysis by studying convergence, sensitivity, and accuracy behaviors of semiautomatically generated models and comparing the results with manually generated models. During a previous study, six porcine vertebral bodies were imaged using a microcomputed tomography scanner and tested in axial compression to establish their stiffness and failure strength. Finite element models were built using a manual meshing method. In this study, the experimental agreement of those models was compared with that of semiautomatically generated models of the same six vertebrae. Both manually and semiautomatically generated models were assigned gray-scale-based, element-specific material properties. The convergence of the semiautomatically generated models was analyzed for the complete models along with material property and architecture control cases. A sensitivity study was also undertaken to test the reaction of the models to changes in material property values, architecture, and boundary conditions. In control cases, the element-specific material properties reduce the convergence of the models in comparison to homogeneous models. However, the full vertebral models showed strong convergence characteristics. The sensitivity study revealed a significant reaction to changes in architecture, boundary conditions, and load position, while the sensitivity to changes in material property values was proportional. The semiautomatically generated models produced stiffness and strength predictions of similar accuracy to the manually generated models with much shorter image segmentation and meshing times. Semiautomatic methods can provide a more rapid alternative to manual mesh generation techniques and produce vertebral models of similar accuracy. The representation of the boundary conditions, load position, and surrounding environment is crucial to the accurate prediction of the vertebral response. At present, an element size of 2×2×2mm3 appears sufficient since the error at this size is dominated by factors, such as the load position, which will not be improved by increasing the mesh resolution. Higher resolution meshes may be appropriate in the future as models are made more sophisticated and computational processing time is reduced.

Subject-specific finite element models of long bones: An in vitro evaluation of the overall accuracy

The determination of the mechanical stresses induced in human bones is of great importance in both research and clinical practice. Since the stresses in bones cannot be measured non-invasively in vivo, the only way to estimate them is through subject-specific finite element modelling. Several methods exist for the automatic generation of these models from CT data, but before bringing them in the clinical practice it is necessary to assess their accuracy in the predictions of the bone stresses. Particular attention should be paid to those regions, like the epiphyseal and metaphyseal parts of long bones, where the automatic methods are typically less accurate. Aim of the present study was to implement a general procedure to automatically generate subject-specific finite element models of bones from CT data and estimate the accuracy of this general procedure by applying it to one real femur. This femur was tested in vitro under five different loading scenarios and the results of these tests were used to verify how the adoption of a simplified two-material homogeneous model would change the accuracy with respect to the density-based inhomogeneous one, with special attention paid to the epiphyseal and metaphyseal proximal regions of the bone. The results showed that the density-based inhomogeneous model predicts with a very good accuracy the measured stresses (R(2)=0.91, RMSE=8.6%, peak error=27%), while the two-material model was less accurate (R(2)=0.89, RMSE=9.6%, peak error=35%). The results showed that it is possible to automatically generate accurate finite element models of bones from CT data and that the strategy of material properties mapping has a significant influence on its accuracy.

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.

Structural and functional anatomy of the neck musculature of the dog (Canis familiaris)

The morphometric properties and the anatomical relationships of the entire musculature of the canine cervical spine are reported herein. These data were obtained from the dissection of cadavers of six dogs. Total muscle length, muscle weight, fascicle length and angles of pennation were recorded for each muscle comprising the canine cervical spine. Based upon these properties, physiological cross-section area (PCSA) and architectural index were estimated. When scaled by whole body mass, the values of each of these parameters were found to be similar between all dogs. Muscles that course from the cranial neck to the shoulder girdle or the rib cage (e.g. brachiocephalicus and rhomboideus capitis) were found to have relatively long fascicles and low PCSA values and thus appear to be designed for rapid excursions. By contrast, muscles that primarily support the neck and shoulder against gravitational forces (e.g. serratus ventralis and trapezius) were found to have relatively high PCSA values and short fascicle lengths, and thus have the capacity to generate large forces. Differences of morphometry as well as nomenclature were found between the canine and human neck musculature. Nevertheless, many similarities exist; in particular, both species have similar muscles adapted to force generation or large excursions. We thus conclude that the canine neck may be used as a modelling tool for biomechanical investigations of the human cervical region as long as the differences listed are borne in mind.

Automatic generation of accurate subject-specific bone finite element models to be used in clinical studies

Most of the finite element models of bones used in orthopaedic biomechanics research are based on generic anatomies. However, in many cases it would be useful to generate from CT data a separate finite element model for each subject of a study group. In a recent study a hexahedral mesh generator based on a grid projection algorithm was found very effective in terms of accuracy and automation. However, so far the use of this method has been documented only on data collected in vitro and only for long bones. The present study was aimed at verifying if this method represents a procedure for the generation of finite element models of human bones from data collected in vivo, robust, accurate, automatic and general enough to be used in clinical studies. Robustness, automation and numerical accuracy of the proposed method were assessed on five femoral CT data sets of patients affected by various pathologies. The generality of the method was verified by processing a femur, an ileum, a phalanx, a proximal femur reconstruction, and the micro-CT of a small sample of spongy bone. The method was found robust enough to cope with the variability of the five femurs, producing meshes with a numerical accuracy and a computational weight comparable to those found in vitro. Even when the method was used to process the other bones the levels of mesh conditioning remained within acceptable limits. Thus, it may be concluded that the method presents a generality sufficient to cope with almost any orthopaedic application.

Finite element analysis of the initial stability of ankle arthrodesis with internal fixation: flat cut versus intact joint contours

OBJECTIVE

Qualitative comparison of the initial stability provided by two joint preparation techniques and various screw configurations in ankle arthrodesis, using the finite element method.Design. A three-dimensional model of a healthy ankle was developed from computed tomography images. Two groups of models were built, one with the joint contours resected to produce flat surfaces, and the second with the joint contours preserved. In each case, a variety of screw orientations were examined.

BACKGROUND

Despite the improved results of ankle arthrodesis, failure rates due to non-union are still reported. The initial stability of the arthrodesis construct seems important in the final outcome of the fusion.

METHODS

Non-linear contact finite element analyses were performed in the arthrodesis constructs subjected to internal/external torsion and dorsiflexion. Micromotions at the bone-to-bone interface were calculated for frictionless and Coulomb friction contact, and compared for the two joint preparation techniques and screw configurations.

RESULTS

Overall lower peak micromotions were predicted when preserving the joint contours both in torsion and dorsiflexion. For both preparation techniques, the lowest micromotions tended to occur with the screws inserted at 30 degrees with respect to the long axis of the tibia, crossing above the fusion site. Inclusion of friction in the models caused a general decrease on the magnitude of the micromotions as compared to the frictionless case, but did not affect the ranking of the models.

CONCLUSIONS

The finite element method can be used as a qualitative tool to study the initial stability of ankle arthrodesis, overcoming the difficulties of measuring bone-to-bone interface micromotions experimentally. Better initial stability was predicted for ankle arthrodesis when the joint contours were preserved rather than resected. Crossing the screws above the fusion site at a steeper angle also tended to increase the stability at the fusion site.

RELEVANCE

Finite element analyses can help during the pre-operative planning of ankle arthrodesis. When bone density is not compromised, preserving the joint contour and inserting the screws at less than 45 degrees to the long axis of the tibia, crossing over the arthrodesis site, may offer better initial stability.

Virtual power based algorithm for decoupling large motions from infinitesimal strains: application to shoulder joint biomechanics

New trends of numerical models of human joints require more and more computation of both large amplitude joint motions and fine bone stress distribution. Together, these problems are difficult to solve and very CPU time consuming. The goal of this study is to develop a new method to diminish the calculation time for this kind of problems which include calculation of large amplitude motions and infinitesimal strains. Based on the Principle of Virtual Power, the present method decouples the problem into two parts. First, rigid body motion is calculated. The bone micro-deformations are then calculated in a second part by using the results of rigid body motions as boundary conditions. A finite element model of the shoulder was used to test this decoupling technique. The model was designed to determine the influence of humeral head shape on stress distribution in the scapula for different physiological motions of the joint. Two versions of the model were developed: a first version completely deformable and a second version based on the developed decoupling method. It was shown that biomechanical variables, as mean pressure and von Mises stress, calculated with the two versions were sensibly the same. On the other hand, CPU time needed for calculating with the new decoupled technique was more than 6 times less than with the completely deformable model.

Finite element analysis in spine research

Finite element analysis is a widely accepted tool used in many industries and research activities. It allows new designs to be thoroughly 'tested' before a prototype is even manufactured, components and systems which cannot readily be experimented upon to be examined, and 'diagnostic' investigations to be undertaken. Finite element models are already making an important contribution to our understanding of the spine and its components. Models are being used to reveal the biomechanical function of the spine and its behaviour when healthy, diseased or damaged. They are also providing support in the design and application of spinal instrumentation. The spine is a very complex structure, and many of the models are simplified and idealized because of the complexity and uncertainty in the geometry, material properties and boundary conditions of these problems. This type of modelling simplification is not peculiar to spinal modelling problems. Indeed, the idealization is often a strength when there is such uncertainty and variation between one individual and another, allowing cause-effect relationships to be isolated and fully explored, and the inherent variability of experimental tests to be eliminated. This paper reviews the development of finite element analysis in spinal modelling. It shows how modelling provides a wealth of information on our physiological performance, reduces our dependence on animal and cadaveric experiments and is an invaluable complement to clinical studies. It also leads to the conclusion that, as computing power and software capabilities increase, it is quite conceivable that in the future it will be possible to generate patient-specific models that could be used for patient assessment and even pre- and inter-operative planning.