Geometrical aspects of patient-specific modelling of the intervertebral disc: collagen fibre orientation and residual stress distribution

Biomechanics of annulus fibrosus: Elastic fiber simplification and degenerative impact on damage initiation and propagation

This study addresses three primary objectives related to lumbar intervertebral disc (IVD) biomechanics under ramping quasi-static loading conditions. First, we explore the conditions justifying the simplification of axisymmetric elastic fiber families into single fiber bundles through discretized strain energy functions. Simulations reveal that a concentration factor exceeding 10 allows for a consistent deviation below 10% between simplified and non-simplified responses. Second, we investigate the impact of elastic fibers on the physiological stiffness in IVDs, revealing minimal influence on biological motions but significant effects on degeneration. Lastly, we examine the initiation and progression of annulus fibrosus (AF) damage. Our findings confirm the validity of simplifying elastic fiber families and underscore the necessity of considering elastic fiber damage in biomechanical studies of AF tissues. Elastic fibers contribute to increased biaxial stretch stiffness, and their damage significantly affects the loading capacity of the inner AF. Additionally, degeneration significantly alters the susceptibility to damage in the AF, with specific regions exhibiting higher vulnerability. Damage tends to extend circumferentially and radially, emphasizing the regional variations in collagen and elastic fiber properties. This study offers useful insights for refining biomechanical models, paving the way for a more comprehensive understanding of IVD responses and potential clinical implications.

Comprehensive modeling of annulus fibrosus: From biphasic refined characterization to damage accumulation under viscous loading

The annulus fibrosus (AF), a permeable, hydrated, and fiber-reinforced soft tissue, exhibits complex responses influenced by fluid pressure, osmotic pressure, and structural mechanics. Existing models struggle to comprehensively represent these intricate interactions and the heterogeneous solid responses within the AF. Additionally, the mechanisms driving differential damage accumulation between non-degenerative and degenerative intervertebral discs remain poorly understood. In this study, we introduce a biphasic-swelling damage model for the AF. We conceptually develop and rigorously validate this model through tissue-level tests employing various loading modes, consistently aligning model predictions with experimental data. Leveraging parametric geometric algorithms and custom Python scripts, we construct models simulating both non-degenerative and degenerative discs. Following calibration, we subject these models to viscous loading protocols. Our findings reveal the posterior AF's susceptibility to damage, contingent upon loading rate and water content. We elucidate the underlying mechanisms by examining the temporal evolution of fluid pressure, osmotic pressure, and the regionally dependent fiber network. This research presents a highly accurate model of the AF, providing valuable insights into disc damage. Future research endeavors should expand this model to incorporate ionic transport and diffusion, enabling a more profound exploration of intervertebral disc mechanobiology. This comprehensive model contributes to a better understanding of AF behavior and may inform therapeutic strategies for disc-related pathologies. STATEMENT OF SIGNIFICANCE: This research presents a comprehensive model of the annulus fibrosus (AF), a crucial component of the intervertebral disc that provides structural support and resists deformation. The study introduces a biphasic-swelling damage model for the AF and validates it through tissue-level tests. The model accounts for fluid pressure, osmotic pressure, and matrix mechanics, providing a more accurate representation of the AF's behavior. The study also investigates the differential damage accumulation between non-degenerative and degenerative discs, shedding light on the mechanisms driving disc degeneration. The findings have significant implications for medical treatments and interventions, as they highlight the posterior AF's susceptibility to damage. This research is of great interest to readers interested in biomechanics, tissue engineering, and medical treatments for disc degeneration.

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.

On the identification of the ultra-structural organization of elastic fibers and their effects on the integrity of annulus fibrosus

Due to the complicated structure of the elastic fiber network in annulus fibrosus, existing in-silico studies either simplified or just overlooked its distribution pattern. Nonetheless, experimental and simulation results have proven that elastic fibers are of great importance to maintaining the structural integrity of annulus fibrosus and therefore to ensuring the load-bearing ability of intervertebral discs. Such needs call for a fine model. This work aims at developing a biphasic annulus fibrosus model by incorporating the accurate distribution pattern of collagen and elastic fibers. Both the structural parameters and intrinsic mechanical parameters were successfully identified using single lamella and inter-lamella microscopy anatomy and micromechanical testing data. The proposed model was then used to implement finite element simulations on various anterior and posterolateral multi-lamellae annulus fibrosus specimens. In general, simulation results agree well with available experimental and simulation data. On this basis, the effects of elastic fibers on the integrity of annulus fibrosus were further investigated. It was found that elastic fibers significantly influence the free swelling, radial stretching and circumferential shear performances of annulus fibrosus. Nonetheless, no significant effects were found for the circumferential stretching capability. The proposed biphasic model considers for the first time the distribution characteristics of elastic fibers at two scales, including both the principal orientations of all fiber families and the detailed distribution pattern within each family. Better understandings on the functions of collagen and elastic fibers can therefore be realized. To further enhance its prediction capability, the current model can be extended in the future by taking the fiber-matrix interaction as well as progressive damages into consideration.

Calibration and validation of a novel hybrid model of the lumbosacral spine in ArtiSynth-The passive structures

In computational biomechanics, two separate types of models have been used predominantly to enhance the understanding of the mechanisms of action of the lumbosacral spine (LSS): Finite element (FE) and musculoskeletal multibody (MB) models. To combine advantages of both models, hybrid FE-MB models are an increasingly used alternative. The aim of this paper is to develop, calibrate, and validate a novel passive hybrid FE-MB open-access simulation model of a ligamentous LSS using ArtiSynth. Based on anatomical data from the Male Visible Human Project, the LSS model is constructed from the L1-S1 rigid vertebrae interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, and facet joints. A mesh convergence study, sensitivity analyses, and systematic calibration were conducted with the hybrid functional spinal unit (FSU) L4/5. The predicted mechanical responses of the FSU L4/5, the lumbar spine (L1-L5), and the LSS were validated against literature data from in vivo and in vitro measurements and in silico models. Spinal mechanical responses considered when loaded with pure moments and combined loading modes were total and intervertebral range of motions, instantaneous axes and centers of rotation, facet joint contact forces, intradiscal pressures, disc bulges, and stiffnesses. Undesirable correlations with the FE mesh were minimized, the number of crisscrossed collagen fiber rings was reduced to five, and the individual influences of specific anatomical structures were adjusted to in vitro range of motions. Including intervertebral motion couplings for axial rotation and nonlinear stiffening under increasing axial compression, the predicted kinematic and structural mechanics responses were consistent with the comparative data. The results demonstrate that the hybrid simulation model is robust and efficient in reproducing valid mechanical responses to provide a starting point for upcoming optimizations and extensions, such as with active skeletal muscles.

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).

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.

Numerical implementation of an osmo-poro-visco-hyperelastic finite element solver: application to the intervertebral disc

This work deals with the finite element (FE) implementation of a biphasic poroelastic formulation specifically developed to address the intricate behaviour of the Intervertebral Disc (IVD) and other highly hydrated soft tissues. This formulation is implemented in custom FE solver V-Biomech, being the validation performed with a lumbar IVD model, which was compared against the analogous FE model of Williams et al. and the experiments of Tyrrell et al. Good agreement with these benchmarks was achieved, meaning that V-Biomech and its novel poroelastic formulation are a viable alternative for simulation of biphasic soft tissues.

Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand

Quantification of lumbar spine load transfer is important for understanding low back pain, especially among persons with a lower limb amputation. Computational modeling provides a helpful solution for obtaining estimates of in vivo loads. A multiscale model was constructed by combining musculoskeletal and finite element (FE) models of the lumbar spine to determine tissue loading during daily activities. Three-dimensional kinematic and ground reaction force data were collected from participants with ([Formula: see text]) and without ([Formula: see text]) a unilateral transtibial amputation (TTA) during 5 sit-to-stand trials. We estimated tissue-level load transfer from the multiscale model by controlling the FE model with intervertebral kinematics and muscle forces predicted by the musculoskeletal model. Annulus fibrosis stress, intradiscal pressure (IDP), and facet contact forces were calculated using the FE model. Differences in whole-body kinematics, muscle forces, and tissue-level loads were found between participant groups. Notably, participants with TTA had greater axial rotation toward their intact limb ([Formula: see text]), greater abdominal muscle activity ([Formula: see text]), and greater overall tissue loading throughout sit-to-stand ([Formula: see text]) compared to able-bodied participants. Both normalized (to upright standing) and absolute estimates of L4-L5 IDP were close to in vivo values reported in the literature. The multiscale model can be used to estimate the distribution of loads within different lumbar spine tissue structures and can be adapted for use with different activities, populations, and spinal geometries.

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.

Integrated Design Approaches for 3D Printed Tissue Scaffolds: Review and Outlook

Emerging 3D printing technologies are enabling the fabrication of complex scaffold structures for diverse medical applications. 3D printing allows controlled material placement for configuring porous tissue scaffolds with tailored properties for desired mechanical stiffness, nutrient transport, and biological growth. However, tuning tissue scaffold functionality requires navigation of a complex design space with numerous trade-offs that require multidisciplinary assessment. Integrated design approaches that encourage iteration and consideration of diverse processes including design configuration, material selection, and simulation models provide a basis for improving design performance. In this review, recent advances in design, fabrication, and assessment of 3D printed tissue scaffolds are investigated with a focus on bone tissue engineering. Bone healing and fusion are examples that demonstrate the needs of integrated design approaches in leveraging new materials and 3D printing processes for specified clinical applications. Current challenges for integrated design are outlined and emphasize directions where new research may lead to significant improvements in personalized medicine and emerging areas in healthcare.

Numerical Prediction of the Mechanical Failure of the Intervertebral Disc under Complex Loading Conditions

Finite element modeling has been widely used to simulate the mechanical behavior of the intervertebral disc. Previous models have been generally limited to the prediction of the disc behavior under simple loading conditions, thus neglecting its response to complex loads, which may induce its failure. The aim of this study was to generate a finite element model of the ovine lumbar intervertebral disc, in which the annulus was characterized by an anisotropic hyperelastic formulation, and to use it to define which mechanical condition was unsafe for the disc. Based on published in vitro results, numerical analyses under combined flexion, lateral bending, and axial rotation with a magnitude double that of the physiological ones were performed. The simulations showed that flexion was the most unsafe load and an axial tensile stress greater than 10 MPa can cause disc failure. The numerical model here presented can be used to predict the failure of the disc under all loading conditions, which may support indications about the degree of safety of specific motions and daily activities, such as weight lifting.