Comparison of computed tomography based parametric and patient-specific finite element models of the healthy and metastatic spine using a mesh-morphing algorithm

Computational lumbar spine models: A literature review

BACKGROUND

Computational spine models of various types have been employed to understand spine function, assess the risk that different activities pose to the spine, and evaluate techniques to prevent injury. The areas in which these models are applied has expanded greatly, potentially beyond the appropriate scope of each, given their capabilities. A comprehensive understanding of the components of these models provides insight into their current capabilities and limitations.

METHODS

The objective of this review was to provide a critical assessment of the different characteristics of model elements employed across the spectrum of lumbar spine modeling and in newer combined methodologies to help better evaluate existing studies and delineate areas for future research and refinement.

FINDINGS

A total of 155 studies met selection criteria and were included in this review. Most current studies use either highly detailed Finite Element models or simpler Musculoskeletal models driven with in vivo data. Many models feature significant geometric or loading simplifications that limit their realism and validity. Frequently, studies only create a single model and thus can't account for the impact of subject variability. The lack of model representation for certain subject cohorts leaves significant gaps in spine knowledge. Combining features from both types of modeling could result in more accurate and predictive models.

INTERPRETATION

Development of integrated models combining elements from different model types in a framework that enables the evaluation of larger populations of subjects could address existing voids and enable more realistic representation of the biomechanics of the lumbar spine.

Computational Challenges in Tissue Engineering for the Spine

This paper deals with a brief review of the recent developments in computational modelling applied to innovative treatments of spine diseases. Additionally, it provides a perspective on the research directions expected for the forthcoming years. The spine is composed of distinct and complex tissues that require specific modelling approaches. With the advent of additive manufacturing and increasing computational power, patient-specific treatments have moved from being a research trend to a reality in clinical practice, but there are many issues to be addressed before such approaches become universal. Here, it is identified that the major setback resides in validation of these computational techniques prior to approval by regulatory agencies. Nevertheless, there are very promising indicators in terms of optimised scaffold modelling for both disc arthroplasty and vertebroplasty, powered by a decisive contribution from imaging methods.

Automated Pipeline to Generate Anatomically Accurate Patient-Specific Biomechanical Models of Healthy and Pathological FSUs

State-of-the-art preoperative biomechanical analysis for the planning of spinal surgery not only requires the generation of three-dimensional patient-specific models but also the accurate biomechanical representation of vertebral joints. The benefits offered by computational models suitable for such purposes are still outweighed by the time and effort required for their generation, thus compromising their applicability in a clinical environment. In this work, we aim to ease the integration of computerized methods into patient-specific planning of spinal surgery. We present the first pipeline combining deep learning and finite element methods that allows a completely automated model generation of functional spine units (FSUs) of the lumbar spine for patient-specific FE simulations (FEBio). The pipeline consists of three steps: (a) multiclass segmentation of cropped 3D CT images containing lumbar vertebrae using the DenseVNet network, (b) automatic landmark-based mesh fitting of statistical shape models onto 3D semantic segmented meshes of the vertebral models, and (c) automatic generation of patient-specific FE models of lumbar segments for the simulation of flexion-extension, lateral bending, and axial rotation movements. The automatic segmentation of FSUs was evaluated against the gold standard (manual segmentation) using 10-fold cross-validation. The obtained Dice coefficient was 93.7% on average, with a mean surface distance of 0.88 mm and a mean Hausdorff distance of 11.16 mm (N = 150). Automatic generation of finite element models to simulate the range of motion (ROM) was successfully performed for five healthy and five pathological FSUs. The results of the simulations were evaluated against the literature and showed comparable ROMs in both healthy and pathological cases, including the alteration of ROM typically observed in severely degenerated FSUs. The major intent of this work is to automate the creation of anatomically accurate patient-specific models by a single pipeline allowing functional modeling of spinal motion in healthy and pathological FSUs. Our approach reduces manual efforts to a minimum and the execution of the entire pipeline including simulations takes approximately 2 h. The automation, time-efficiency and robustness level of the pipeline represents a first step toward its clinical integration.

Influence of pelvic shape on strain patterns: A computational analysis using finite element mesh morphing techniques

The pelvis functions to transmit upper body loads to the lower limbs and is critical in human locomotion. Semi-automated, finite element (FE) morphing techniques eliminate the need for segmentation and have shown to accelerate the generation of multiple specimen-specific pelvic FE models to enable the study of pelvic mechanical behaviour. The purpose of this research was to produce simulated human pelvic FE models representing android, gynecoid, anthropoid and platypelloid morphologies and to isolate differences in strain patterns due to anatomic shape under physiologic loading. Using five initially generated specimen-specific FE models, each specimen-specific FE model was reconfigured into three different morphologies using FE mesh morphing techniques. Significantly different strains were found comparing the gynecoid (classical female pelvis') to the android ('true male pelvis') models (p = 0.040), with strains twice as high in the superior pubic rami. No significant differences were seen in comparing overall strains between the other pelvic shapes (p = 0.61-0.126). The highest strain regions in all models were found in the supra-acetabular regions, with high strains also found in the regions of the superior pubic rami, the greater sciatic notch and sacral regions about the L5 vertebrae. Quantifying the contributions of shape to strain in the pelvis may increase the understanding of sex and patient-specific differences in fracture risk and motivate the consideration of treatment strategies that account for anatomic pelvic differences.

Case-specific non-linear finite element models to predict failure behavior in two functional spinal units

Current finite element (FE) models predicting failure behavior comprise single vertebrae, thereby neglecting the role of the posterior elements and intervertebral discs. Therefore, this study aimed to develop a more clinically relevant, case-specific non-linear FE model of two functional spinal units able to predict failure behavior in terms of (i) the vertebra predicted to fail; (ii) deformation of the specimens; (iii) stiffness; and (iv) load to failure. For this purpose, we also studied the effect of different bone density-mechanical properties relationships (material models) on the prediction of failure behavior. Twelve two functional spinal units (T6-T8, T9-T11, T12-L2, and L3-L5) with and without artificial metastases were destructively tested in axial compression. These experiments were simulated using CT-based case-specific non-linear FE models. Bone mechanical properties were assigned using four commonly used material models. In 10 of the 11 specimens our FE model was able to correctly indicate which vertebrae failed during the experiments. However, predictions of the three-dimensional deformations of the specimens were less promising. Whereas stiffness of the whole construct could be strongly predicted (R²  = 0.637-0.688, p < 0.01), we obtained weak correlations between FE predicted and experimentally determined load to failure, as defined by the total reaction force exhibiting a drop in force (R²  = 0.219-0.247, p > 0.05). Additionally, we found that the correlation between predicted and experimental fracture loads did not strongly depend on the material model implemented, but the stiffness predictions did. In conclusion, this work showed that, in its current state, our FE models may be used to identify the weakest vertebra, but that substantial improvements are required in order to quantify in vivo failure loads. © 2018 The Authors. Journal of Orthopaedic Research® Published by Wiley Periodical, Inc. on behalf of Orthopaedic Research Society. J Orthop Res 36:3208-3218, 2018.

Morphing the feature-based multi-blocks of normative/healthy vertebral geometries to scoliosis vertebral geometries: development of personalized finite element models

Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.

A model-based approach for estimation of changes in lumbar segmental kinematics associated with alterations in trunk muscle forces

The kinematics information from imaging, if combined with optimization-based biomechanical models, may provide a unique platform for personalized assessment of trunk muscle forces (TMFs). Such a method, however, is feasible only if differences in lumbar spine kinematics due to differences in TMFs can be captured by the current imaging techniques. A finite element model of the spine within an optimization procedure was used to estimate segmental kinematics of lumbar spine associated with five different sets of TMFs. Each set of TMFs was associated with a hypothetical trunk neuromuscular strategy that optimized one aspect of lower back biomechanics. For each set of TMFs, the segmental kinematics of lumbar spine was estimated for a single static trunk flexed posture involving, respectively, 40° and 10° of thoracic and pelvic rotations. Minimum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 0° to 0.7° and 0 mm to 0.04 mm, respectively. Maximum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 2.4° to 7.6° and 0.11 mm to 0.39 mm, respectively. The differences in kinematics of lumbar segments between each combination of two sets of TMFs in 97% of cases for angular deformation and 55% of cases for translational deformation were within the reported accuracy of current imaging techniques. Therefore, it might be possible to use image-based kinematics of lumbar segments along with computational modeling for personalized assessment of TMFs.

A statistical human rib cage geometry model accounting for variations by age, sex, stature and body mass index

In this study, we developed a statistical rib cage geometry model accounting for variations by age, sex, stature and body mass index (BMI). Thorax CT scans were obtained from 89 subjects approximately evenly distributed among 8 age groups and both sexes. Threshold-based CT image segmentation was performed to extract the rib geometries, and a total of 464 landmarks on the left side of each subject׳s ribcage were collected to describe the size and shape of the rib cage as well as the cross-sectional geometry of each rib. Principal component analysis and multivariate regression analysis were conducted to predict rib cage geometry as a function of age, sex, stature, and BMI, all of which showed strong effects on rib cage geometry. Except for BMI, all parameters also showed significant effects on rib cross-sectional area using a linear mixed model. This statistical rib cage geometry model can serve as a geometric basis for developing a parametric human thorax finite element model for quantifying effects from different human attributes on thoracic injury risks.

Total hip arthroplasty by using a cementless ultrashort stem: A subject-specific finite element analysis for a young patient clinical case

In this article, a subject-specific finite element analysis has been developed to study a clinical case of a surgically misaligned hip prosthesis with an ultrashort stem. It was set out to study the strain energy density pattern, comparing the results obtained with computed tomography images. The authors developed two other numerical models: the first one analyzes the stress and strain distributions in the healthy femur (without prosthesis) and the second one analyzes the same boneimplant biomechanical system of the clinical case but assuming the prosthesis in the proper position. The misaligned prosthesis produced an overload at the proximal posterior plane of the femur, as confirmed by computed tomography images, which detect the formation of new bone. The numerical model of the correctly positioned prosthesis demonstrated that the bone is not overloaded and that the position of neutral axis does not significantly shift from the physiological condition.

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.

Automated subject-specific, hexahedral mesh generation via image registration

Generating subject-specific, all-hexahedral meshes for finite element analysis continues to be of significant interest in biomechanical research communities. To date, most automated methods "morph" an existing atlas mesh to match with a subject anatomy, which usually result in degradation in mesh quality because of mesh distortion. We present an automated meshing technique that produces satisfactory mesh quality and accuracy without mesh repair. An atlas mesh is first developed using a script. A subject-specific mesh is generated with the same script after transforming the geometry into the atlas space following rigid image registration, and is transformed back into the subject space. By meshing the brain in 11 subjects, we demonstrate that the technique's performance is satisfactory in terms of both mesh quality (99.5% of elements had a scaled Jacobian >0.6 while <0.01% were between 0 and 0.2) and accuracy (average distance between mesh boundary and geometrical surface was 0.07 mm while <1% greater than 0.5mm). The combined computational cost for image registration and meshing was <4 min. Our results suggest that the technique is effective for generating subject-specific, all-hexahedral meshes and that it may be useful for meshing a variety of anatomical structures across different biomechanical research fields.

Evaluation of the generality and accuracy of a new mesh morphing procedure for the human femur

Various papers described mesh morphing techniques for computational biomechanics, but none of them provided a quantitative assessment of generality, robustness, automation, and accuracy in predicting strains. This study aims to quantitatively evaluate the performance of a novel mesh-morphing algorithm. A mesh-morphing algorithm based on radial-basis functions and on manual selection of corresponding landmarks on template and target was developed. The periosteal geometries of 100 femurs were derived from a computed tomography scan database and used to test the algorithm generality in producing finite element (FE) morphed meshes. A published benchmark, consisting of eight femurs for which in vitro strain measurements and standard FE model strain prediction accuracy were available, was used to assess the accuracy of morphed FE models in predicting strains. Relevant parameters were identified to test the algorithm robustness to operative conditions. Time and effort needed were evaluated to define the algorithm degree of automation. Morphing was successful for 95% of the specimens, with mesh quality indicators comparable to those of standard FE meshes. Accuracy of the morphed meshes in predicting strains was good (R(2)>0.9, RMSE%<10%) and not statistically different from the standard meshes (p-value=0.1083). The algorithm was robust to inter- and intra-operator variability, target geometry refinement (p-value>0.05) and partially to the number of landmark used. Producing a morphed mesh starting from the triangularized geometry of the specimen requires on average 10 min. The proposed method is general, robust, automated, and accurate enough to be used in bone FE modelling from diagnostic data, and prospectively in applications such as statistical shape modelling.

Validation of computational models in biomechanics

The topics of verification and validation have increasingly been discussed in the field of computational biomechanics, and many recent articles have applied these concepts in an attempt to build credibility for models of complex biological systems. Verification and validation are evolving techniques that, if used improperly, can lead to false conclusions about a system under study. In basic science, these erroneous conclusions may lead to failure of a subsequent hypothesis, but they can have more profound effects if the model is designed to predict patient outcomes. While several authors have reviewed verification and validation as they pertain to traditional solid and fluid mechanics, it is the intent of this paper to present them in the context of computational biomechanics. Specifically, the task of model validation will be discussed, with a focus on current techniques. It is hoped that this review will encourage investigators to engage and adopt the verification and validation process in an effort to increase peer acceptance of computational biomechanics models.

Current progress in patient-specific modeling

We present a survey of recent advancements in the emerging field of patient-specific modeling (PSM). Researchers in this field are currently simulating a wide variety of tissue and organ dynamics to address challenges in various clinical domains. The majority of this research employs three-dimensional, image-based modeling techniques. Recent PSM publications mostly represent feasibility or preliminary validation studies on modeling technologies, and these systems will require further clinical validation and usability testing before they can become a standard of care. We anticipate that with further testing and research, PSM-derived technologies will eventually become valuable, versatile clinical tools.

A new approach for assigning bone material properties from CT images into finite element models

Generation of subject-specific finite element (FE) models from computed tomography (CT) datasets is of significance for application of the FE analysis to bone structures. A great challenge that remains is the automatic assignment of bone material properties from CT Hounsfield Units into finite element models. This paper proposes a new assignment approach, in which material properties are directly assigned to each integration point. Instead of modifying the dataset of FE models, the proposed approach divides the assignment procedure into two steps: generating the data file of the image intensity of a bone in a MATLAB program and reading the file into ABAQUS via user subroutines. Its accuracy has been validated by assigning the density of a bone phantom into a FE model. The proposed approach has been applied to the FE model of a sheep tibia and its applicability tested on a variety of element types. The proposed assignment approach is simple and illustrative. It can be easily modified to fit users' situations.

Mesh morphing and response surface analysis: quantifying sensitivity of vertebral mechanical behavior

Vertebrae provide essential biomechanical stability to the skeleton. In this work novel morphing techniques were used to parameterize three aspects of the geometry of a specimen-specific finite element (FE) model of a rat caudal vertebra (process size, neck size, and end-plate offset). Material properties and loading were also parameterized using standard techniques. These parameterizations were then integrated within an RSM framework and used to produce a family of FE models. The mechanical behavior of each model was characterized by predictions of stress and strain. A metamodel was fit to each of the responses to yield the relative influences of the factors and their interactions. The direction of loading, offset, and neck size had the largest influences on the levels of vertebral stress and strain. Material type was influential on the strains, but not the stress. Process size was substantially less influential. A strong interaction was identified between dorsal-ventral offset and dorsal-ventral off-axis loading. The demonstrated approach has several advantages for spinal biomechanical analysis by enabling the examination of the sensitivity of a specimen to multiple variations in shape, and of the interactions between shape, material properties, and loading.