Modelling the Influence of Heterogeneous Annulus Material Property Distribution on Intervertebral Disk Mechanics

A Novel Fiber-Reinforced Poroviscoelastic Bovine Intervertebral Disc Finite Element Model for Organ Culture Experiment Simulations

Intervertebral disc (IVD) degeneration and methods for repair and regeneration have commonly been studied in organ cultures with animal IVDs under compressive loading. With the recent establishment of a novel multi-axial organ culture system, accurate predictions of the global and local mechanical response of the IVD are needed for control system development and to aid in experiment planning. This study aimed to establish a finite element model of bovine IVD capable of predicting IVD behavior at physiological and detrimental load levels. A finite element model was created based on the dimensions and shape of a typical bovine IVD used in the organ culture. The nucleus pulposus (NP) was modeled as a neo-Hookean poroelastic material and the annulus fibrosus (AF) as a fiber-reinforced poroviscoelastic material. The AF consisted of 10 lamella layers and the material properties were distributed in the radial direction. The model outcome was compared to a bovine IVD in a compressive stress-relaxation experiment. A parametric study was conducted to investigate the effect of different material parameters on the overall IVD response. The model was able to capture the equilibrium response and the relaxation response at physiological and higher strain levels. Permeability and elastic stiffness of the AF fiber network affected the overall response most prominently. The established model can be used to evaluate the response of the bovine IVD at strain levels typical for organ culture experiments, to define relevant boundaries for such studies, and to aid in the development and use of new multi-axial organ culture systems.

Physiological and degenerative loading of bovine intervertebral disc in a bioreactor: A finite element study of complex motions

Intervertebral disc (IVD) degeneration and regenerative therapies are commonly studied in organ-culture experiments with uniaxial compressive loading. Recently, in our laboratory, we established a bioreactor system capable of applying loads in six degrees-of-freedom (DOF) to bovine IVDs, which replicates more closely the complex multi-axial loading of the IVD in vivo. However, the magnitudes of loading that are physiological (able to maintain cell viability) or mechanically degenerative are unknown for load cases combining several DOFs. This study aimed to establish physiological and degenerative levels of maximum principal strains and stresses in the bovine IVD tissue and to investigate how they are achieved under complex load cases related to common daily activities. The physiological and degenerative levels of maximum principal strains and stresses were determined via finite element (FE) analysis of bovine IVD subjected to experimentally established physiological and degenerative compressive loading protocols. Then, complex load cases, such as a combination of compression + flexion + torsion, were applied on the FE-model with increasing magnitudes of loading to discover when physiological and degenerative tissue strains and stresses were reached. When applying 0.1 MPa of compression and ±2-3° of flexion and ±1-2° of torsion the investigated mechanical parameters remained at physiological levels, but with ±6-8° of flexion in combination with ±2-4° of torsion, the stresses in the outer annulus fibrosus (OAF) exceeded degenerative levels. In the case of compression + flexion + torsion, the mechanical degeneration likely initiates at the OAF when loading magnitudes are high enough. The physiological and degenerative magnitudes can be used as guidelines for bioreactor experiments with bovine IVDs.

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.

Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter-lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

Investigation of Alterations in the Lumbar Disc Biomechanics at the Adjacent Segments After Spinal Fusion Using a Combined In Vivo and In Silico Approach

The development of adjacent segment degeneration (ASD) is a major concern after lumbar spinal fusion surgery, but the causative mechanisms remain unclear. This study used a combined in vivo and in silico method to investigate the changes of anatomical dimensions and biomechanical responses of the adjacent segment (L3-4) after spinal fusion (L4-S1) in five patients under weight-bearing upright standing conditions. The in vivo adjacent disc height changes before and after fusion were measured using a dual fluoroscopic imaging system (DFIS), and the measured in vivo intervertebral positions and orientations were used as displacement boundary conditions of the patient-specific three-dimensional (3D) finite element (FE) disc models to simulate the biomechanical responses of adjacent discs to fusion of the diseased segments. Our data (represented by medians and 95% confidence intervals) showed that a significant decrease by - 0.8 (- 1.2, - 0.4) mm (p < 0.05) in the adjacent disc heights occurred at the posterior region after fusion. The significant increases in disc tissue strains and stresses, 0.32 (0.21, 0.43) mm/mm (p < 0.05) and 1.70 (1.07, 3.60) MPa (p < 0.05), respectively, after fusion were found in the posterolateral portions of the outermost annular lamella. The intradiscal pressure of the adjacent disc was significantly increased by 0.29 (0.13, 0.47) MPa after fusion (p < 0.05). This study demonstrated that fusion could cause alterations in adjacent disc biomechanics, and the combined in vivo and in silico method could be a valuable tool for the quantitative assessment of ASD after fusion.

Alterations in the Geometry, Fiber Orientation, and Mechanical Behavior of the Lumbar Intervertebral Disc by Nucleus Swelling

Soft tissues observed in clinical medical images are often prestrained in tension by internal pressure or tissue hydration. For a native disc, nucleus swelling occurs in equilibrium with osmotic pressure induced by the high concentration of proteoglycan in the nucleus. The objective of this computational study was to investigate the effects of nucleus swelling on disc geometry, fiber orientation, and mechanical behavior by comparing those of prestrained and zero-pressure (unswelled) discs. Thermoelastic analysis techniques were repurposed in order to determine the zero-pressure disc geometry which, when pressurized, matches the prestrained disc geometry observed in clinical images. The zero-pressure geometry was then used in simulations to approximately represent a degenerated disc, which loses the ability of nucleus swelling but has not undergone distinct soft tissue remodeling/disruption. Our simulation results demonstrated that the loss of nucleus swelling caused a slight change in the disc geometry and fiber orientation, but a distinct deterioration in the resistance to intervertebral rotations including sagittal bending, lateral bending, and axial torsion. Different from rotational loading, in compression (with a displacement of 0.45 mm applied), a much larger stiffness (3.02 KN/mm) and a greater intradiscal pressure (IDP) (0.61 MPa) were measured in the zero-pressure disc, compared to the prestrained disc (1.41 KN/mm and 0.52 MPa). This computational study could be useful to understand mechanisms of disc degeneration, and guide the future design of disc tissue engineering material and biomimic disc implants.

Poroelastic Modeling of Highly Hydrated Collagen Hydrogels: Experimental Results vs. Numerical Simulation With Custom and Commercial Finite Element Solvers

This study presents a comparison between the performances of two Finite Element (FE) solvers for the modeling of the poroelastic behavior of highly hydrated collagen hydrogels. Characterization of collagen hydrogels has been a widespread challenge since this is one of the most used natural biomaterials for Tissue Engineering (TE) applications. V-Biomech® is a free custom FE solver oriented to soft tissue modeling, while Abaqus® is a general-purpose commercial FE package which is widely used for biomechanics computational modeling. Poroelastic simulations with both solvers were compared to two experimental protocols performed by Busby et al. (2013) and Chandran and Barocas (2004), also using different implementations of the frequently used Neo-Hookean hyperelastic model. The average differences between solvers outputs were under 5% throughout the different tests and hydrogel properties. Thus, differences were small enough to be considered negligible and within the variability found experimentally from one sample to another. This work demonstrates that constitutive modeling of soft tissues, such as collagen hydrogels can be achieved with either V-Biomech or Abaqus standard options (without user-subroutine), which is important for the biomechanics and biomaterials research community. V-Biomech has shown its potential for the validation of biomechanical characterization of soft tissues, while Abaqus' versatility is useful for the modeling and analysis of TE applications where other complex phenomena may also need to be captured.

Polyurethane as a strategy for annulus fibrosus repair and regeneration: a systematic review

Aim: Disc herniation is a spine disease that leads to suffering and disability. Discectomy is a Janus-faced approach that relieves pain symptoms but leave the intervertebral discs predisposed to herniation. This systematic review discussed the mechanical and biological requirements for a polyurethane-based biomaterial to be used in annular repair. Methods: Search strategy was performed in PubMed, Web of Science and Scopus databases to define the main mechanical properties, biological findings and follow-up aspects of these biomaterials. The range was limited to articles published from January 2000 to December 2017 in English language. Results: The search identified 82 articles. From these, a total of 18 articles underwent a full-text analysis, and 16 studies were included in the review. Conclusion: The polyurethane presents suitable properties to be used as an engineered solution to re-establish the microenvironment and biomechanical features of the intervertebral disc.

3D Printing of Materials with Tunable Failure via Bioinspired Mechanical Gradients

Mechanical gradients are useful to reduce strain mismatches in heterogeneous materials and thus prevent premature failure of devices in a wide range of applications. While complex graded designs are a hallmark of biological materials, gradients in manmade materials are often limited to 1D profiles due to the lack of adequate fabrication tools. Here, a multimaterial 3D-printing platform is developed to fabricate elastomer gradients spanning three orders of magnitude in elastic modulus and used to investigate the role of various bioinspired gradient designs on the local and global mechanical behavior of synthetic materials. The digital image correlation data and finite element modeling indicate that gradients can be effectively used to manipulate the stress state and thus circumvent the weakening effect of defect-rich interfaces or program the failure behavior of heterogeneous materials. Implementing this concept in materials with bioinspired designs can potentially lead to defect-tolerant structures and to materials whose tunable failure facilitates repair of biomedical implants, stretchable electronics, or soft robotics.

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.

In silico investigation of vertebroplasty as a stand-alone treatment for vertebral burst fractures

BACKGROUND

The use of percutaneous vertebroplasty as a stand-alone treatment for stable vertebral burst fractures has been investigated in vitro and in clinical studies. These studies present inconsistent results on the mechanical response of vertebroplasty-treated burst fractures. In addition, observations of the loss of sagittal alignment after vertebroplasty raise questions on the applicability of vertebroplasty for burst fractures. Therefore, the aim of this study was to investigate the mechanical stability of burst fractures after stand-alone treatment by vertebroplasty.

METHODS

Finite element simulations were performed with models generated from two laboratory-induced burst fractures in human thoracolumbar specimens. The burst fracture models were virtually injected with various cement volumes using a unipedicular or bipedicular approach. The models were subjected to four individual loads (compression, lateral bending, extension and torsion) and a multi-axial load case in the physiological range.

FINDINGS

All treated burst fractures showed improvements in stiffness and a reduction in inter-fragmentary displacements, thus potentially providing a suitable mechanical environment for fracture healing. However, large volumes of the trabecular bone (<43%), cement (<53%) and bone-cement composite (<58%) were predicted to experience strain levels exceeding the yield point. While damage was not specifically modeled, this implies a potential collapse of the treated vertebra due to local failure.

INTERPRETATION

To improve the primary stability and to prevent the collapse of treated burst fractures, the use of posterior instrumentation is suggested as an adjunct to vertebroplasty.

Derivation of inter-lamellar behaviour of the intervertebral disc annulus

The inter-lamellar connectivity of the annulus fibrosus in the intervertebral disc has been shown to affect the prediction of the overall disc behaviour in computational models. Using a combined experimental and computational approach, the inter-lamellar mechanical behaviour of the disc annulus was investigated under conditions of radial loading.

Twenty-seven specimens of anterior annulus fibrosus were dissected from 12 discs taken from four frozen ovine thoracolumbar spines. Specimens were grouped depending on their radial provenance within the annulus fibrosus. Standard tensile tests were performed. In addition, micro-tensile tests under microscopy were used to observe the displacement of the lamellae and inter-lamellar connections. Finite elements models matching the experimental protocols were developed with specimen-specific geometries and boundary conditions assuming a known lamellar behaviour. An optimisation process was used to derive the interface stiffness values for each group. The assumption of a linear cohesive interface was used to model the behaviour of the inter-lamellar connectivity.

The interface stiffness values derived from the optimisation process were consistently higher than the corresponding lamellar values. The interface stiffness values of the outer annulus were from 43% to 75% higher than those of the inner annulus. Tangential stiffness values for the interface were from 6% to 39% higher than normal stiffness values within each group and similar to values reported by other investigators. These results reflect the intricate fibrous nature of the inter-lamellar connectivity and provide values for the representation of the inter-lamellar behaviour at a continuum level.