An experimental and finite element poroelastic creep response analysis of an intervertebral hydrogel disc model in axial compression

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.

Differences in time-dependent mechanical properties between extruded and molded hydrogels

The mechanical properties of hydrogels used in biomaterials and tissue engineering applications are critical determinants of their functionality. Despite the recent rise of additive manufacturing, and specifically extrusion-based bioprinting, as a prominent biofabrication method, comprehensive studies investigating the mechanical behavior of extruded constructs remain lacking. To address this gap in knowledge, we compared the mechanical properties and swelling properties of crosslinked gelatin-based hydrogels prepared by conventional molding techniques or by 3D bioprinting using a BioBots Beta pneumatic extruder. A preliminary characterization of the impact of bioprinting parameters on construct properties revealed that both Young's modulus and optimal extruding pressure increased with polymer content, and that printing resolution increased with both printing speed and nozzle gauge. High viability (>95%) of encapsulated NIH 3T3 fibroblasts confirmed the cytocompatibility of the construct preparation process. Interestingly, the Young's moduli of extruded and molded constructs were not different, but extruded constructs did show increases in both the rate and extent of time-dependent mechanical behavior observed in creep. Despite similar polymer densities, extruded hydrogels showed greater swelling over time compared to molded hydrogels, suggesting that differences in creep behavior derived from differences in microstructure and fluid flow. Because of the crucial roles of time-dependent mechanical properties, fluid flow, and swelling properties on tissue and cell behavior, these findings highlight the need for greater consideration of the effects of the extrusion process on hydrogel properties.

A novel method for the accurate evaluation of Poisson's ratio of soft polymer materials

A new method with a simple algorithm was developed to accurately measure Poisson's ratio of soft materials such as polyvinyl alcohol hydrogel (PVA-H) with a custom experimental apparatus consisting of a tension device, a micro X-Y stage, an optical microscope, and a charge-coupled device camera. In the proposed method, the initial positions of the four vertices of an arbitrarily selected quadrilateral from the sample surface were first measured to generate a 2D 1st-order 4-node quadrilateral element for finite element numerical analysis. Next, minimum and maximum principal strains were calculated from differences between the initial and deformed shapes of the quadrilateral under tension. Finally, Poisson's ratio of PVA-H was determined by the ratio of minimum principal strain to maximum principal strain. This novel method has an advantage in the accurate evaluation of Poisson's ratio despite misalignment between specimens and experimental devices. In this study, Poisson's ratio of PVA-H was 0.44 ± 0.025 (n = 6) for 2.6–47.0% elongations with a tendency to decrease with increasing elongation. The current evaluation method of Poisson's ratio with a simple measurement system can be employed to a real-time automated vision-tracking system which is used to accurately evaluate the material properties of various soft materials.

Experimental and numerical tribological studies of a boundary lubricant functionalized poro-viscoelastic PVA hydrogel in normal contact and sliding

Hydrogels are a cross-linked network of polymers swollen with liquid and have the potential to be used as a synthetic replacement for local defects in load bearing tissues such as articular cartilage. Hydrogels display viscoelastic time dependent behavior, therefore experimental analysis of stresses at the surface and within the gel is difficult to perform. A three-dimensional model of a hydrogel was developed in the commercial finite element software ABAQUS™, implementing a poro-viscoelastic constitutive model along with a contact-dependent flow state and friction conditions. Water content measurements, sliding, and indentation experiments were performed on neat polyvinyl alcohol (PVA), and on low friction boundary lubricant functionalized (BLF-PVA) hydrogels, both manufactured by freeze-thaw processes. Modulus results from the indentation experiments and coefficient of friction values from the sliding experiments were used as material property inputs to the model, while water content was used to calculate initial flow conditions. Tangential force and normal displacement data from a three-dimensional simulation of sliding were compared with the experiments. The tangential force patterns indicated important similarities with the fabricated hydrogels that included an initially high force value due to time dependent deformation followed by a decrease in a stabile value. A similar trend was observed with the normal displacement. These comparisons rendered the model suitable as a representation and were used to analyze the development and propagation of stresses in the immediate surface region. The results showed that in a three-dimensional stress field during sliding, the maximum stress shifted to the surface and rotated closer to the leading edge of contact. This occurred because the stress field becomes dominated by an amplified compressive stress at the leading edge due to the biphasic viscoelastic response of the material during sliding. Also, the complex multi-axial contact stress field was reduced to focus predominately on stress in the contact surface region in the direction of sliding. The results showed that during biphasic viscoelastic frictional sliding, the maximum tensile stress develops at the trailing edge of contact and a compressive stress develops at the leading edge in the direction of motion. The BLF-PVA hydrogels displayed a decrease in this tensile and compressive stress as compared to the standard PVA. The diminishment of these stresses would be expected to give the BLF-PVA hydrogels lower material wear with greater life expectancy as a synthetic articular cartilage implant.

Dual delivery for stem cell differentiation using dexamethasone and bFGF in/on polymeric microspheres as a cell carrier for nucleus pulposus regeneration

This study aimed to investigate the feasibility of the nanostructured 3D poly(lactide-co-glycolide) (PLGA) constructs, which are loaded with dexamethasone (DEX) and growth factor embedded heparin/poly(L-lysine) nanoparticles via a layer-by-layer system, to serve as an effective scaffold for nucleus pulposus (NP) tissue engineering. Our results demonstrated that the microsphere constructs were capable of simultaneously releasing basic fibroblast growth factor and DEX with approximately zero order kinetics. The dual bead microspheres showed no cytotoxicity, and promoted the proliferation of the rat mesenchymal stem cells (rMSCs) by lactate dehydrogenase assay and CCK-8 assay. After 4 weeks of cultivation in vitro, the rMSCs-scaffold hybrids contained significantly higher levels of sulfated GAG/DNA and collagen type II than the control samples. Moreover, quantitative real time PCR analysis revealed that the expression of disc-matrix proteins including collagen type II, aggrecan, and versican in the rMSCs-scaffold hybrids was significantly higher than that in the control group, whereas the expression of osteogenic differentiation marker (collagen type I) was decreased. Taken together, these data indicate that Dex/bFGF PLGA microspheres could be used as a scaffold to improve the rMSCs growth and differentiating into NP like cells, and reduce the inflammatory response for IVD tissue engineering.

Three-dimensional morphometry of strained bovine periodontal ligament using synchrotron radiation-based tomography

The periodontal ligament (PDL) is a highly vascularized soft connective tissue. Previous studies suggest that the viscous component of the mechanical response may be explained by the deformation-induced collapse and expansion of internal voids (i.e. chiefly blood vessels) interacting with liquids (i.e. blood and interstitial fluids) flowing through the pores. In the present work we propose a methodology by means of which the morphology of the PDL vascular plexus can be monitored at different levels of compressive and tensile strains. To this end, 4-mm-diameter cylindrical specimens, comprising layers of bone, PDL and dentin covered by cementum, were strained at stretch ratios ranging from lambda = 0.6 to lambda = 1.4 and scanned using synchrotron radiation-based computer tomography. It was concluded that: (1) the PDL vascular network is layered in two distinct planes of blood vessels (BVs): an inner layer (close to the tooth), in which the BVs run in apico-coronal direction, and an outer layer (close to the alveolar bone), in which the BVs distribution is more diffuse; (2) during tension and compression, the porosity tissue is kept fairly constant; (3) mechanical straining induces important changes in BV diameters, possibly modifying the permeability of the PDL and thus contributing to the viscous component of the viscoelastic response observed under compressive forces.

Parametric Finite Element Analysis of Physical Stimuli Resulting From Mechanical Stimulation of Tissue Engineered Cartilage

While mechanical stimulation of cells seeded within scaffolds is widely thought to be beneficial, the amount of benefit observed is highly variable between experimental systems. Although studies have investigated specific experimental loading protocols thought to be advantageous for cartilage growth, less is known about the physical stimuli (e.g., pressures, velocities, and local strains) cells experience during these experiments. This study used results of a literature survey, which looked for patterns in the efficacy of mechanical stimulation of chondrocyte seeded scaffolds, to inform the modeling of spatial patterns of physical stimuli present in mechanically stimulated constructs. The literature survey revealed a large variation in conditions used in mechanical loading studies, with a peak to peak strain of 10% (i.e., the maximum amount of deformation experienced by the scaffold) at 1 Hz on agarose scaffolds being the most frequently studied parameters and scaffold. This loading frequency was then used as the basis for simulation in the finite element analyses. 2D axisymmetric finite element models of 2×4 mm2 scaffolds with 360 modulus/permeability combinations were constructed using COMSOLMULTIPHYSICS software. A time dependent coupled pore pressure/effective stress analysis was used to model fluid/solid interactions in the scaffolds upon loading. Loading was simulated using an impermeable frictionless loader on the top boundary with fluid and solid displacement confined to the radial axis. As expected, all scaffold materials exhibited classic poro-elastic behavior having pressurized cores with low fluid flow and edges with high radial fluid velocities. Under the simulation parameters of this study, PEG scaffolds had the highest pressure and radial fluid velocity but also the lowest shear stress and radial strain. Chitosan and KLD-12 simulated scaffold materials had the lowest radial strains and fluid velocities, with collagen scaffolds having the lowest pressures. Parametric analysis showed maximum peak pressures within the scaffold to be more dependent on scaffold modulus than on permeability and velocities to depend on both scaffold properties similarly. The dependence of radial strain on permeability or modulus was more complex; maximum strains occurred at lower permeabilities and moduli, and the lowest strain occurred at the stiffest most permeable scaffold. Shear stresses within all scaffolds were negligible. These results give insight into the large variations in metabolic response seen in studies involving mechanical stimulation of cell-seeded constructs, where the same loading conditions produce very different results due to the differences in material properties.

Measurement of geometric deformation of lumbar intervertebral discs under in-vivo weightbearing condition

Quantitative data of spinal intervertebral disc deformation is instrumental for investigation of spinal disc pathology. In this study, we employed a combined dual fluoroscopic imaging system and the MR imaging technique to determine the lumbar disc deformation in living human subjects. Discs at L2-3, L3-4 and L4-5 levels were investigated in 8 normal subjects. The geometric deformation of the discs under full body weight loading condition (upright standing) was determined using the supine, non-weightbearing condition as a reference. The average maximum tensile deformation was -21% in compression and 24% in tension, and maximum shear deformation on the disc surface reached 26%. The data indicated that different portions of the disc are under different tensile and shear deformation. Further, discs of L2-3, L3-4 and L4-5 have different deformation behavior under the physiological weightbearing condition. In general, the higher level discs have higher deformation values. The technique used in this study can be used to investigate the deformation behaviors of diseased discs as well as the efficacy of different surgical modalities at restoring normal disc deformation patterns.

Can compressive stress be measured experimentally within the annulus fibrosus of degenerated intervertebral discs?

The aims were to assess the ability of a pressure transducer to measure compressive stress within the annulus fibrosus of degenerated intervertebral discs. Measurements could help to explain the mechanisms of disc failure and low back pain.

The methods used were as follows. Thirteen full-depth cores of annulus, 7 mm in diameter, were removed from the middle and outer annuli of two severely degenerated human discs and constrained within a metal cylinder. Then static compressive forces were applied by a planeended metal indenter of diameter 6.8 mm, while a strain-gauged pressure transducer, side mounted in a needle of diameter 0.9 mm and calibrated in saline, was pulled through the issue. The transducer output was converted into stress, and the average measured stress was compared with the nominal applied stress. Measurements were repeated at up to 21 load levels, with the transducer oriented vertically and horizontally.

The results showed that the measured and applied stress were linearly related (average r2=0.98) with a mean gradient (calibration factor) of 0.98 (vertical stress) and 0.92 (horizontal stress). Gradients ranged between 1.28 and 0.73. Damaged transducers grossly under-recorded ‘stress’ even though their output remained proportional to applied load.

It was concluded that pressure transducers can measure compressive stress inside a degenerated human annulus. The tissue is sufficiently deformable to allow efficient coupling of stress between the matrix and transducer membrane. Damage to the transducer can give misleading results.

Nondegradable hydrogels for the treatment of focal cartilage defects

Nondegradable materials have long been suggested for the treatment of articular cartilage defects; however, the mechanics of the implant/tissue system necessary to ensure long-term function are unknown. The objective of this study was to explore the performance of nondegradable hydrogel implants in cartilage defects. Our hypothesis was that the structural integrity of the implant and surrounding tissue would be influenced by the compressive modulus of the material used, and that superior results would be obtained with the implantation of a more compliant material. Poly(vinyl alcohol)-poly(vinyl pyrrolidone) hydrogel implants of two different moduli were implanted into osteochondral defects in a rabbit model. Six-month postoperative histological and mechanical data were used to assess the wear and fixation of the implants. The compliant implants remained well fixed and a thin layer of soft tissue grew over the surface of the implants. However, gross deformation of the compliant implants occurred and debris was evident in surrounding bone. The stiffer implants were dislocated from their implantation site, but with no accompanying evidence of debris or implant deformation. Our hypothesis that superior results would be obtained with implantation of a more compliant material was rejected; a compromise between the wear and fixation properties dependent on modulus was found.