Using inverse finite element analysis to identify spinal tissue behaviour in situ.

In computational modelling of musculoskeletal applications, one of the critical aspects is ensuring that a model can capture intrinsic population variability and not only representative of a "mean" individual. Developing and calibrating models with this aspect in mind is key for the credibility of a modelling methodology. This often requires calibration of complex models with respect to 3D experiments and measurements on a range of specimens or patients. Most Finite Element (FE) software's do not have such a capacity embedded in their core tools. This paper presents a versatile interface between Finite Element (FE) software and optimisation tools, enabling calibration of a group of FE models on a range of experimental data. It is provided as a Python toolbox which has been fully tested and verified on Windows platforms. The toolbox is tested in three case studies involving in vitro testing of spinal tissues.

Morphological variation of the hemophilic talus.

Flattening of the trochlear tali is clinically observed as structural and functional changes advance in patients with hemarthropathy of the ankle. However, the degree of this flattening has not yet been quantified, and distribution of the morphological changes across the talus not yet defined. Chronologically sequential MR images of both a hemophilic patient group (N = 5) and a single scan from a nondiseased, sex-matched, control group (N = 11) were used to take four measurements of the trochlear talus morphology at three locations (medial, central and lateral) along the sagittal plane. Three ratios of interest were defined from these to assess whether the talar dome flattens with disease. The control group MRI measurements were validated against literature data obtained from CT scans or planar X-Rays. The influence of disease on talar morphology was assessed by direct comparison of the hemophilic cases with the control group. The values for all three ratios, in all locations, differed between the control and the hemophilic group. Flattening was indicated in the hemophilic group in the medial and lateral talus, but differences in the central talus were not statistically significant. This work demonstrates that morphological assessment of the talus from MR images is similar to that from CT scans or planar X-Rays. Talar flattening does occur with hemarthropathy, especially at the medial and lateral edges of the joint surface. General flattening of the trochlear talus was confirmed in this small patient sample, however the degree and rate of change is unique to each ankle.

Changes in subchondral bone morphology with osteoarthritis in the ankle.

Significant alterations to subchondral trabecular bone microarchitecture are observed in late-stage osteoarthritis (OA). However, detailed investigation of these changes to bone in the ankle are under-reported. This study aimed to fully characterise the trabecular morphology in OA ankle bone specimens compared to non-diseased (ND) controls using both standard and individual-trabecular segmentation-based (ITS) analyses. Ten ND tibial bone specimens were extracted from three cadaveric ankles, as well as five OA bone specimens from patients undergoing total ankle arthroplasty surgery. Each specimen was scanned using microcomputed tomography from which a 4 mm cuboidal volume was extracted for analysis. Morphological parameters for the subchondral trabecular bone were measured using BoneJ (NIH ImageJ) and 3D ITS for whole volumes and at each depth level in 1 mm increments. The results show an overall increase in bone volume fraction (p<0.01) and trabecular thickness (p<0.001) with OA, with a decrease in anisotropy (p<0.05). ITS analysis showed OA bone was composed of more rod-like trabeculae and plate-like trabeculae compared to ND bone. Numerous properties were depth dependent, but the results demonstrated that towards the subchondral bone plate, both rod- and plate-like trabeculae were thicker, rods were longer and plates had increased surface area. Overall, this study has verified key microstructural alterations to ankle subchondral bone that are found in other OA lower-limb joints. Depth-based analysis has highlighted differences of interest for further evaluation into the remodelling mechanisms that occur with OA, which is critical to understanding the role of subchondral bone microarchitecture in the progression of the disease.

Incorporating pathological gait into patient-specific finite element models of the haemophilic ankle.

Haemarthrosis is an inherent clinical feature of haemophilia, a disease characterised by an absence or reduction in clotting proteins. Patients with severe haemophilia experience joint bleeding leading to blood-induced ankle arthropathy (haemarthropathy). Altered biomechanics of the ankle have been reported in people with haemophilia; however, the consequence of this on joint health is little understood. The aim of this study was to assess the changes in joint contact due to haemophilia disease-specific gait features using patient-specific modelling, to better understand the link between biomechanics and joint outcomes. Four, image-based, finite element models of haemophilic ankles were simulated through consecutive events in the stance phase of gait, using both patient-specific and healthy control group (n = 36) biomechanical inputs. One healthy control FE model was simulated through the healthy control stance phase of the gait cycle for a point of comparison. The method developed allowed cartilage contact mechanics to be assessed throughout the loading phase of the gait cycle. This showed areas of increased contact pressure in the medial and lateral regions of the talar dome, which may be linked to collapse in these regions. This method may allow the relationship between structure and function in the tibiotalar joint to be better understood.

A Finite Element Model to Investigate the Stability of Osteochondral Grafts Within a Human Tibiofemoral Joint.

Osteochondral grafting has demonstrated positive outcomes for treating articular cartilage defects by replacing the damaged region with a cylindrical graft consisting of bone with a layer of cartilage. However, factors that cause graft subsidence are not well understood. The aim of this study was to develop finite element (FE) models of osteochondral grafts within a tibiofemoral joint, suitable for an investigation of parameters affecting graft stability. Cadaveric femurs were used to experimentally calibrate the bone properties and graft-bone frictional forces for use in corresponding image-based FE models, generated from µCT scan data. Effects of cartilage defects and osteochondral graft repair were measured by examining contact pressure changes using further in vitro tests. Here, six defects were created in the femoral condyles, which were subsequently treated with osteochondral autografts or metal pins. Matching image-based FE models were created, and the contact patches were compared. The bone material properties and graft-bone frictional forces were successfully calibrated from the initial tests with good resulting levels of agreement (CCC = 0.87). The tibiofemoral joint experiment provided a range of cases that were accurately described in the resultant pressure maps and were well represented in the FE models. Cartilage defects and repair quality were experimentally measurable with good agreement in the FE model pressure maps. Model confidence was built through extensive validation and sensitivity testing. It was found that specimen-specific properties were required to accurately represent graft behaviour. The final models produced are suitable for a range of parametric testing to investigate immediate graft stability.

Injectable peptide-glycosaminoglycan hydrogels for soft tissue repair: in vitro assessment for nucleus augmentation.

We report the development of peptide-glycosaminoglycan hydrogels as injectable biomaterials for load-bearing soft tissue repair. The hydrogels are injectable as a liquid for clinical delivery, rapidly form a gel in situ, and mimic the osmotic swelling behaviour of natural tissue. We used a new in vitro model to demonstrate their application as a nucleus augmentation material for the treatment of intervertebral disc degeneration. Our study compared a complex lab gel preparation method to a simple clinical benchtop process. We showed pH differences did not significantly affect gel formation, and temperature variations had no impact on gel performance. Rheological results demonstrated consistency after benchtop mixing or needle injection. In our in vitro disc degeneration model, we established that peptide augmentation could restore the native biomechanical properties. This suggests the feasibility of minimally invasive peptide-GAG gel delivery, maintaining consistent properties across temperature and needle sizes while restoring disc height and stiffness in vitro.

Effect of meniscus modelling assumptions in a static tibiofemoral finite element model: importance of geometry over material.

Finite element studies of the tibiofemoral joint have increased use in research, with attention often placed on the material models. Few studies assess the effect of meniscus modelling assumptions in image-based models on contact mechanics outcomes. This work aimed to assess the effect of modelling assumptions of the meniscus on knee contact mechanics and meniscus kinematics. A sensitivity analysis was performed using three specimen-specific tibiofemoral models and one generic knee model. The assumptions in representing the meniscus attachment on the tibia (shape of the roots and position of the attachment), the material properties of the meniscus, the shape of the meniscus and the alignment of the joint were evaluated, creating 40 model instances. The values of material parameters for the meniscus and the position of the root attachment had a small influence on the total contact area but not on the meniscus displacement or the force balance between condyles. Using 3D shapes to represent the roots instead of springs had a large influence in meniscus displacement but not in knee contact area. Changes in meniscus shape and in knee alignment had a significantly larger influence on all outcomes of interest, with differences two to six times larger than those due to material properties. The sensitivity study demonstrated the importance of meniscus shape and knee alignment on meniscus kinematics and knee contact mechanics, both being more important than the material properties or the position of the roots. It also showed that differences between knees were large, suggesting that clinical interpretations of modelling studies using single geometries should be avoided.

Development of robust finite element models to investigate the stability of osteochondral grafts within porcine femoral condyles.

Osteoarthritis (OA) is the most prevalent chronic rheumatic disease worldwide with knee OA having an estimated lifetime risk of approximately 14%. Autologous osteochondral grafting has demonstrated positive outcomes in some patients, however, understanding of the biomechanical function and how treatments can be optimised remains limited. Increased short-term stability of the grafts allows cartilage surfaces to remain congruent prior to graft integration. In this study methods for generating specimen specific finite element (FE) models of osteochondral grafts were developed, using parallel experimental data for calibration and validation. Experimental testing of the force required to displace osteochondral grafts by 2 mm was conducted on three porcine knees, each with four grafts. Specimen specific FE models of the hosts and grafts were created from registered µCT scans captured from each knee (pre- and post-test). Material properties were based on the µCT background with a conversion between µCT voxel brightness and Young's modulus. This conversion was based on the results of the separate testing of eight porcine condyles and optimization of specimen specific FE models. The comparison between the experimental and computational push-in forces gave a strong agreement with a concordance correlation coefficient (CCC) = 0.75, validating the modelling approach. The modelling process showed that homogenous material properties based on whole bone BV/TV calculations are insufficient for accurate modelling and that an intricate description of the density distribution is required. The robust methodology can provide a method of testing different treatment options and can be used to investigate graft stability in full tibiofemoral joints.

The relationship between subchondral bone cysts and cartilage health in the Tibiotalar joint: A finite element analysis.

BACKGROUND: Subchondral bone cysts are a common presentation in ankle haemarthropathy. The relationship with ankle joint health has however not previously been investigated. The aim of this study was to assess the influence of subchondral bone cysts of differing shapes, volumes and depths on joint health. METHODS: Chronologically sequential Magnetic Resonance imaging scans of four hemophilic ankles with subchondral bone cysts present (N = 18) were used to build patient specific finite element models under two cystic conditions to assess their influence on cartilage contact pressures. Variables such as location, volume and depth were considered individually, to investigate whether certain cystic conditions may be more detrimental to cartilage health. FINDINGS: Significant quantifiable contact redistribution was seen in the presence of subchondral bone cysts and this redistribution reflected the shape and size of the cysts, however, with the presence of cysts in both bones in 10 of the 18 cases a direct relationship to volume could not be correlated. INTERPRETATION: This work demonstrated a redistribution of contact pressures in the presence of subchondral bone cysts. This alteration to loading history could be linked to cartilage degeneration due to the biological response to abnormal loading.

Biomechanical modelling of the facet joints: a review of methods and validation processes in finite element analysis.

There is an increased interest in studying the biomechanics of the facet joints. For in silico studies, it is therefore important to understand the level of reliability of models for outputs of interest related to the facet joints. In this work, a systematic review of finite element models of multi-level spinal section with facet joints output of interest was performed. The review focused on the methodology used to model the facet joints and its associated validation. From the 110 papers analysed, 18 presented some validation of the facet joints outputs. Validation was done by comparing outputs to literature data, either computational or experimental values; with the major drawback that, when comparing to computational values, the baseline data was rarely validated. Analysis of the modelling methodology showed that there seems to be a compromise made between accuracy of the geometry and nonlinearity of the cartilage behaviour in compression. Most models either used a soft contact representation of the cartilage layer at the joint or included a cartilage layer which was linear elastic. Most concerning, soft contact models usually did not contain much information on the pressure-overclosure law. This review shows that to increase the reliability of in silico model of the spine for facet joints outputs, more needs to be done regarding the description of the methods used to model the facet joints, and the validation for specific outputs of interest needs to be more thorough, with recommendation to systematically share input and output data of validation studies.

Experimental and Computational Comparison of Intervertebral Disc Bulge for Specimen-Specific Model Evaluation Based on Imaging.

Finite element modelling of the spinal unit is a promising preclinical tool to assess the biomechanical outcome of emerging interventions. Currently, most models are calibrated and validated against range of motion and rarely directly against soft-tissue deformation. The aim of this contribution was to develop an in vitro methodology to measure disc bulge and assess the ability of different specimen-specific modelling approaches to predict disc bulge. Bovine bone-disc-bone sections (N = 6) were prepared with 40 glass markers on the intervertebral disc surface. These were initially magnetic resonance (MR)-imaged and then sequentially imaged using peripheral-qCT under axial compression of 1 mm increments. Specimen-specific finite-element models were developed from the CT data, using three different methods to represent the nucleus pulposus geometry with and without complementary use of the MR images. Both calibrated specimen-specific and averaged compressive material properties for the disc tissues were investigated. A successful methodology was developed to quantify the disc bulge in vitro, enabling observation of surface displacement on qCT. From the finite element model results, no clear advantage was found in using geometrical information from the MR images in terms of the models' ability to predict stiffness or disc bulge for bovine intervertebral disc.

Estimating tissue-level properties of porcine talar subchondral bone.

Tissue-level properties of bone play an important role when characterising apparent-level bone biomechanical behaviour and yet little is known about its effect at this hierarchical level. In combination with trabecular morphological data these properties can be used to predict bone strength, which becomes an invaluable tool for clinicians in patient treatment planning. This study developed specimen-specific micro-finite element (µFE) models using validated continuum-level models, containing grayscale-derived material properties, to indirectly establish tissue-level properties of porcine talar subchondral bone. Specimen-specific continuum finite element (hFE) models of subchondral trabecular bone were setup using µCT data of ten cylindrical specimens extracted from juvenile porcine tali. The models were validated using quasi-static uniaxial compression testing. Validated hFE models were used to calibrate the tissue modulus of corresponding µFE models by minimising the difference between the µFE and hFE stiffness values. Key trabecular morphological indices (BV/TV, DA, Conn.D, Tb.Th, EF) were evaluated. Good agreement was observed between hFE models and experiment (CCC = 0.66). Calibrated Etiss was 504 ± 37.65 MPa. Average BV/TV and DA for µFE specimens were 0.37 ± 0.05 and 0.68 ± 0.11, respectively. BV/TV (r2 = 0.667) correlated highly with µFE stiffness. The small intra-specimen variation to tissue-level properties suggests that variations to apparent-level stiffness originate from variations to microarchitecture rather than tissue mechanical properties.

Patient-specific parameterised cam geometry in finite element models of femoroacetabular impingement of the hip.

BACKGROUND: Impingement resulting in soft tissue damage has been observed in hips with abnormal morphologies. Geometric parameterisation can be used to automatically generate a range of bone geometries for use in computational models, including femurs with cam deformity on the femoral neck. METHODS: This study verified patient-specific parametric finite element models of 20 patients with cam deformity (10 female, 10 male) through comparison to their patient-specific segmentation-based equivalents. The parameterisation system was then used to generate further models with parametrically defined geometry to investigate morphological changes in both the femur and acetabulum and their effects on impingement. FINDINGS: Similar findings were observed between segmentation-based and parametric models when assessing soft tissue strains under impingement conditions, resulting from high flexion and internal rotations. Parametric models with cam morphology demonstrated that clinically used alpha angles should not be relied on for estimating impingement severity since planar views do not capture the full three-dimensional geometry of the joint. Furthermore, the parametric approach allowed study of labral shape changes, indicating higher strains can result from bony overcoverage. INTERPRETATION: The position of cams, as well as their size, can affect the level of soft tissue strain occurring in the hip. This highlights the importance of reporting the full details of three-dimensional geometry used when developing computational models of the hip joint and suggests that it could be beneficial to stratify the patient population when considering treatment options, since certain morphologies may be at greater risk of elevated soft tissue strain.

Examination of an in vitro methodology to evaluate the biomechanical performance of nucleus augmentation in axial compression.

Intervertebral disc degeneration is one of the leading causes of back pain, but treatment options remain limited. Recently, there have been advances in the development of biomaterials for nucleus augmentation; however, the testing of such materials preclinically has proved challenging. The aim of this study was to develop methods for fabricating and testing bone-disc-bone specimens in vitro for examining the performance of nucleus augmentation procedures. Control, nucleotomy and treated intervertebral disc specimens were fabricated and tested under static load. The nucleus was removed from nucleotomy specimens using a trans-endplate approach with a bone plug used to restore bony integrity. Specimen-specific finite element models were developed to elucidate the reasons for the variations observed between control specimens. Although the computational models predicted a statistically significant difference between the healthy and nucleotomy groups, the differences found experimentally were not significantly different. This is likely due to variations in the material properties, hydration and level of annular collapse. The deformation of the bone was also found to be non-negligible. The study provides a framework for the development of testing protocols for nucleus augmentation materials and highlights the need to control disc hydration and the length of bone retained to reduce inter-specimen variability.

Three-dimensional assessment of impingement risk in geometrically parameterised hips compared with clinical measures.

Abnormal bony morphology is a factor implicated in hip joint soft tissue damage and an increased lifetime risk of osteoarthritis. Standard 2-dimensional radiographic measurements for diagnosis of hip deformities, such as cam deformities on the femoral neck, do not capture the full joint geometry and are not indicative of symptomatic damage. In this study, a 3-dimensional geometric parameterisation system was developed to capture key variations in the femur and acetabulum of subjects with clinically diagnosed cam deformity. The parameterisation was performed for computed tomography scans of 20 patients (10 female and 10 male). Novel quantitative measures of cam deformity were taken and used to assess differences in morphological deformities between males and females. The parametric surfaces matched the more detailed, segmented hip bone geometry with low fitting error. The quantitative severity measures captured both the size and the position of cams and distinguished between cam and control femurs. The precision of the measures was sufficient to identify differences between subjects that could not be seen with the sole use of 2-dimensional imaging. In particular, cams were found to be more superiorly located in males than in females. As well as providing a means to distinguish between subjects more clearly, the new geometric hip parameterisation facilitates the flexible and rapid generation of a range of realistic hip geometries including cams. When combined with material property models, these stratified cam shapes can be used for further assessment of the effect of the geometric variation under impingement conditions.

Annulus fibrosus functional extrafibrillar and fibrous mechanical behaviour: experimental and computational characterisation.

The development of current surgical treatments for intervertebral disc damage could benefit from virtual environment accounting for population variations. For such models to be reliable, a relevant description of the mechanical properties of the different tissues and their role in the functional mechanics of the disc is of major importance. The aims of this work were first to assess the physiological hoop strain in the annulus fibrosus in fresh conditions (n = 5) in order to extract a functional behaviour of the extrafibrillar matrix; then to reverse-engineer the annulus fibrosus fibrillar behaviour (n = 6). This was achieved by performing both direct and global controlled calibration of material parameters, accounting for the whole process of experimental design and in silico model methodology. Direct-controlled models are specimen-specific models representing controlled experimental conditions that can be replicated and directly comparing measurements. Validation was performed on another six specimens and a sensitivity study was performed. Hoop strains were measured as 17 ± 3% after 10 min relaxation and 21 ± 4% after 20-25 min relaxation, with no significant difference between the two measurements. The extrafibrillar matrix functional moduli were measured as 1.5 ± 0.7 MPa. Fibre-related material parameters showed large variability, with a variance above 0.28. Direct-controlled calibration and validation provides confidence that the model development methodology can capture the measurable variation within the population of tested specimens.

Methodology to Produce Specimen-Specific Models of Vertebrae: Application to Different Species.

Image-based continuum-level finite element models have been used for bones to evaluate fracture risk and the biomechanical effects of diseases and therapies, capturing both the geometry and tissue mechanical properties. Although models of vertebrae of various species have been developed, an inter-species comparison has not yet been investigated. The purpose of this study was to derive species-specific modelling methods and compare the accuracy of image-based finite element models of vertebrae across species. Vertebral specimens were harvested from porcine (N = 12), ovine (N = 13) and bovine (N = 14) spines. The specimens were experimentally loaded to failure and apparent stiffness values were derived. Image-based finite element models were generated reproducing the experimental protocol. A linear relationship between the element grayscale and elastic modulus was calibrated for each species matching in vitro and in silico stiffness values, and validated on independent sets of models. The accuracy of these relationships were compared across species. Experimental stiffness values were significantly different across species and specimen-specific models required species-specific linear relationship between image grayscale and elastic modulus. A good agreement between in vitro and in silico values was achieved for all species, reinforcing the generality of the developed methodology.

Modelling the failure precursor mechanism of lamellar fibrous tissues, example of the annulus fibrosus.

The aims of this study were to assess the damage and failure strengths of lamellar fibrous tissues, such as the anterior annulus fibrosus (AF), and to develop a mathematical model of damage propagation of the lamellae and inter-lamellar connections. This level of modelling is needed to accurately predict the effect of damage and failure induced by trauma or clinical interventions. 26 ovine anterior AF cuboid specimens from 11 lumbar intervertebral discs were tested in radial tension and mechanical parameters defining damage and failure were extracted from the in-vitro data. Equivalent 1D analytical models were developed to represent the specimen strength and the damage propagation, accounting for the specimen dimensions and number of lamellae. Model parameters were calibrated on the in-vitro data. Similar to stiffness values reported for other orientations, the outer annulus was found stronger than the inner annulus in the radial direction, with failure at higher stress values. The inner annulus failed more progressively, showing macroscopic failure at a higher strain value. The 1D analytical model of damage showed that lamellar damage is predominant in the failure mechanism of the AF. The analytical model of the connections between lamellae allowed us to represent separately damage processes in the lamellae and the inter-lamellar connections, which cannot be experimentally tested individually.

Subject-specific multi-validation of a finite element model of ovine cervical functional spinal units.

The complex motion and geometry of the spine in the cervical region makes it difficult to determine how loads are distributed through adjacent vertebrae or between the zygapophysial (facet) joints and the intervertebral disc. Validated finite element modes can give insight on this distribution. The aim of this contribution was to produce direct validation of subject-specific finite element models of Functional Spinal Units (FSU׳s) of the cervical spine and to evaluate the importance of including fibre directionality in the mechanical description of the annulus fibrosus. Eight specimens of cervical FSU׳s were prepared from five ovine spines and mechanically tested in axial compression monitoring overall load and displacements as well as local facet joints pressure and displacement. Subject-specific finite element models were produced from microCT image data reproducing the experimental setup and measuring global axial force and displacement as well as local facet joints displacement and contact forces. Material models and parameters were taken from the literature, testing isotropic and anisotropic materials for the annulus fibrosus. The validated models showed that adding the direction of the fibres to their non-linear behaviour in the description of the annulus fibrosus improves the predictions at large strain values but not at low strain values. The load transferred through the facet joints was always accurate, irrespective of the annulus material model, while the predicted facet displacement was larger than the measured one but not significantly. This is, to the authors׳ knowledge, the first subject-specific direct validation study on a group of specimens, accounting for inter-subject variability.

Prediction of the mechanical response of canine humerus to three-point bending using subject-specific finite element modelling.

Subject-specific finite element models could improve decision making in canine long-bone fracture repair. However, it preliminary requires that finite element models predicting the mechanical response of canine long bone are proposed and validated. We present here a combined experimental-numerical approach to test the ability of subject-specific finite element models to predict the bending response of seven pairs of canine humeri directly from medical images. Our results show that bending stiffness and yield load are predicted with a mean absolute error of 10.1% (±5.2%) for the 14 samples. This study constitutes a basis for the forthcoming optimization of canine long-bone fracture repair.