Mesenchymal stem cells-derived cartilage micropellets: A relevant in vitro model for biomechanical and mechanobiological studies of cartilage growth.

The prevalence of diseases that affect the articular cartilage is increasing due to population ageing, but the current treatments are only palliative. One innovative approach to repair cartilage defects is tissue engineering and the use of mesenchymal stem/stromal cells (MSCs). Although the combination of MSCs with biocompatible scaffolds has been extensively investigated, no product is commercially available yet. This could be explained by the lack of mechanical stimulation during in vitro culture and the absence of proper and stable cartilage matrix formation, leading to poor integration after implantation. The objective of the present study was to investigate the biomechanical behaviour of MSC differentiation in micropellets, a well-defined 3D in vitro model of cartilage differentiation and growth, in view of tissue engineering applications. MSC micropellet chondrogenic differentiation was induced by exposure to TGFß3. At different time points during differentiation (35 days of culture), their global mechanical properties were assessed using a very sensitive compression device coupled to an identification procedure based on a finite element parametric model. Micropellets displayed both a non-linear strain-induced stiffening behaviour and a dissipative behaviour that increased from day 14 to day 29, with a maximum instantaneous Young's modulus of 179.9 ± 18.8 kPa. Moreover, chondrocyte gene expression levels were strongly correlated with the observed mechanical properties. This study indicates that cartilage micropellets display the biochemical and biomechanical characteristics required for investigating and recapitulating the different stages of cartilage development.

Heterogeneous mechanical hyperelastic behavior in the porcine annulus fibrosus explained by fiber orientation: An experimental and numerical approach.

Our aim is to estimate regional mechanical properties of the annulus fibrosus (AF) using a multi-relaxation tensile test and to examine the relevance of using the transverse dilatations in the identification procedure. We collected twenty traction specimens from both outer (n = 10) and inner (n = 10) sites of the anterior quadrant of the annulus fibrosus of one pig spine. A 1-h multi-relaxation tensile test in the circumferential direction allowed us to measure the force in the direction of traction and the dilatations in all three directions. We performed a specific-sample finite element inverse analysis to identify variations, along the radial position, of material and structural parameters of a hyperelastic compressible and anisotropic constitutive law. Our experimental results reveal that the outer sites are subjected to a significantly greater stress than the inner sites and that both sites exhibit an auxetic behavior. Our numerical results suggest that the inhomogeneous behavior arises from significant variations of the fiber angle taken into account within the hyperelastic constitutive law. In addition, we found that the use of the measured transverse dilatations in the identification procedure had a strong impact on the identified mechanical parameters. This pilot study suggests that, in quasi-static conditions, the annulus fibrosus may be modeled by a hyperelastic compressible and anisotropic law with a fiber angle gradient from inner to outer periphery.

Rupture limit evaluation of human cerebral aneurysms wall: Experimental study.

BACKGROUND AND PURPOSE: Rupture risk of intracranial aneurysms is a major issue for public healthcare. A way to obtain an individual rupture risk assessment is a main objective of many research teams in the world. For many years, we have investigated the relationship between the mechanical properties of aneurysm wall tissues and the rupture risk. In this work, we try to go further and investigate rupture limit values. METHODS: Following surgical clipping, a specific conservation protocol was applied to aneurysmal tissues in order to preserve their mechanical properties. Thirty-nine intracranial aneurysms (27 females, 12 males) were tested using a uniaxial tensile test machine under physiological conditions, temperature, and saline isotonic solution. These represented 24 unruptured and 15 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a Yeoh hyperelastic model with 2 parameters. Moreover, uniaxial tensile tests were conducted until rupture of samples to obtain values of stress and strain rupture limit. RESULTS: The significant parameter a C2 of the hyperelastic Yeoh model, allowed us to classify samples' rigidity following the terminology we adopted in previous papers (Costalat et al., 2011; Sanchez et al., 2013): Soft, Stiff and Intermediate. Moreover, strain/stress rupture limit values were gathered and analyzed thanks to the tissue rigidity, the status of the aneurysm (initially ruptured or unruptured) and the gender of the patient. CONCLUSION: Strain rupture limit was found quite stable around 20% and seems not to be correlated with the status of the aneurysm (initially ruptured or unruptured), neither with the gender of the patient. However, stretch and stress rupture limit seems not to be independent on the rigidity. The study confirms that ruptured aneurysms mainly present a soft tissue and unruptured aneurysms present a stiff material.

Intracranial aneurysmal pulsatility as a new individual criterion for rupture risk evaluation: biomechanical and numeric approach (IRRAs Project).

BACKGROUND AND PURPOSE: The present study follows an experimental work based on the characterization of the biomechanical behavior of the aneurysmal wall and a numerical study where a significant difference in term of volume variation between ruptured and unruptured aneurysm was observed in a specific case. Our study was designed to highlight by means of numeric simulations the correlation between aneurysm sac pulsatility and the risk of rupture through the mechanical properties of the wall. MATERIALS AND METHODS: In accordance with previous work suggesting a correlation between the risk of rupture and the material properties of cerebral aneurysms, 12 fluid-structure interaction computations were performed on 12 "patient-specific" cases, corresponding to typical shapes and locations of cerebral aneurysms. The variations of the aneurysmal volume during the cardiac cycle (ΔV) are compared by using wall material characteristics of either degraded or nondegraded tissues. RESULTS: Aneurysms were located on 6 different arteries: middle cerebral artery (4), anterior cerebral artery (3), internal carotid artery (1), vertebral artery (1), ophthalmic artery (1), and basilar artery (1). Aneurysms presented different shapes (uniform or multilobulated) and diastolic volumes (from 18 to 392 mm3). The pulsatility (ΔV/V) was significantly larger for a soft aneurysmal material (average of 26%) than for a stiff material (average of 4%). The difference between ΔV, for each condition, was statistically significant: P=.005. CONCLUSIONS: The difference in aneurysmal pulsatility as highlighted in this work might be a relevant patient-specific predictor of aneurysm risk of rupture.

Experimental analysis of the transverse mechanical behaviour of annulus fibrosus tissue.

Uniaxial tensile and relaxation tests were carried out on annulus fibrosus samples carved out in the circumferential direction. Images were shot perpendicularly to the loading direction. Digital image correlation techniques accurately measured the evolution of full displacement fields in both transverse directions: plane of fibres and plane of lamellae. In the fibre plane, strains were governed by the reorientation of fibres along the loading direction. This implies strong transverse shrinkage with quasi-linear behaviour. Conversely, a wide range of behaviour was observed in the lamella plane: from shrinkage to swelling. Strong nonlinear evolutions were generally obtained. The strain field in the lamella plane generally presented a central strip section with more pronounced swelling. Our physical interpretation relies on the porous nature of annulus tissue and its anisotropic stiffness. Indeed, the liquid over-pressure generated inside the sample by the strong shrinkage in the fibre plane discharges in the perpendicular direction since rigidity is lower in the lamella plane. Regarding the strain field measured in the lamella plane, this interpretation agrees with (a) symmetric strain distribution with respect to the longitudinal axis of samples, (b) the reversal in behaviour from shrinkage to swelling and (c) the decrease in strain during relaxation tests associated with outward flows. The variety of transverse behaviours observed experimentally could result from uncertainties regarding the initial reference state of tissue samples. Since the mechanical behaviour is highly nonlinear, experimental results underline that a slight uncertainty concerning the pre-stress applied to samples can lead to wide variability in the mechanical properties identified.

Biomechanical assessment of the individual risk of rupture of cerebral aneurysms: a proof of concept.

This study is a step towards a new biomechanical-based measurement of the patient specific risk of rupture of cerebral aneurysms. Following a previous experimental investigation suggesting a correlation between the risk of rupture and the material properties of cerebral aneurysms, fluid-structure interaction simulations are performed to compare the deformations of a patient-specific aneurysm when using degraded or undegraded materials. Results show that material properties have a major impact on the magnitude of systolic/diastolic aneurysmal volume variations along the cardiac cycle. Changes in terms of aneurysmal volume variations depending on the tissue characteristics are shown to be measurable by medical imaging. A one-at-a-time data uncertainty analysis is also presented and shows the robustness of this result to input data uncertainties. The study thus suggests that aneurysmal volume variations may be used as the basis of a biomechanical index of rupture risk.

Biomechanical wall properties of human intracranial aneurysms resected following surgical clipping (IRRAs Project).

BACKGROUND AND PURPOSE: Individual rupture risk assessment of intracranial aneurysms is a major issue in the clinical management of asymptomatic aneurysms. Aneurysm rupture occurs when wall tension exceeds the strength limit of the wall tissue. At present, aneurysmal wall mechanics are poorly understood and thus, risk assessment involving mechanical properties is inexistent. Aneurysm computational hemodynamics studies make the assumption of rigid walls, an arguable simplification. We therefore aim to assess mechanical properties of ruptured and unruptured intracranial aneurysms in order to provide the foundation for future patient-specific aneurysmal risk assessment. This work also challenges some of the currently held hypotheses in computational flow hemodynamics research. METHODS: A specific conservation protocol was applied to aneurysmal tissues following clipping and resection in order to preserve their mechanical properties. Sixteen intracranial aneurysms (11 female, 5 male) underwent mechanical uniaxial stress tests under physiological conditions, temperature, and saline isotonic solution. These represented 11 unruptured and 5 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a 3-parameter (C(10), C(01), C(11)) Mooney-Rivlin hyperelastic model. Each aneurysm was classified according to its biomechanical properties and (un)rupture status. RESULTS: Tissue testing demonstrated three main tissue classes: Soft, Rigid, and Intermediate. All unruptured aneurysms presented a more Rigid tissue than ruptured or pre-ruptured aneurysms within each gender subgroup. Wall thickness was not correlated to aneurysmal status (ruptured/unruptured). An Intermediate subgroup of unruptured aneurysms with softer tissue characteristic was identified and correlated with multiple documented risk factors of rupture. CONCLUSION: There is a significant modification in biomechanical properties between ruptured aneurysm, presenting a soft tissue and unruptured aneurysms, presenting a rigid material. This finding strongly supports the idea that a biomechanical risk factor based assessment should be utilized in the to improve the therapeutic decision making.

Sensitivity analysis of periprosthetic healing to cell migration, growth factor and post-operative gap using a mechanobiological model.

A theoretical rationale, which could help in the investigation of mechanobiological factors affecting periprosthetic tissue healing, is still an open problem. We used a parametric sensitivity analysis to extend a theoretical model based on reactive transport and computational cell biology. The numerical experimentation involved the drill hole, the haptotactic and chemotactic migrations, and the initial concentration of an anabolic growth factor. Output measure was the mineral fraction in tissue surrounding a polymethymethacrylate (PMMA) canine implant (stable loaded implant, non-critical gap). Increasing growth factor concentration increased structural matrix synthesis. A cell adhesion gradient resulted in heterogeneous bone distribution and a growth factor gradient resulted in homogeneous bone distribution in the gap. This could explain the radial variation of bone density from the implant surface to the drill hole, indicating less secure fixation. This study helps to understand the relative importance of various host and clinical factors influencing bone distribution and resulting implant fixation.

Substructuring and poroelastic modelling of the intervertebral disc.

We proposed a substructure technique to predict the time-dependant response of biological tissue within the framework of a finite element resolution. Theoretical considerations in poroelasticity preceded the calculation of the sub-structured poroelastic matrix. The transient response was obtained using an exponential fitting method. We computed the creep response of an MRI 3D reconstructed L(5)-S(1) intervertebral disc of a scoliotic spine. The FE model was reduced from 10,000 degrees of freedom for the full 3D disc to only 40 degrees of freedom for the sub-structured model defined by 10 nodes attached to junction nodes located on both lower and upper surfaces of the disc. Comparisons of displacement fields were made between the full poroelastic FE model and the sub-structured model in three different loading conditions: compression, offset compression and torsion. Discrepancies in displacement were lower than 10% for the first time steps when time-dependant events were significant. The substructuring technique provided an exact solution in quasi-static behavior after pressure relaxation. Couplings between vertical and transversal displacements predicted by the reference FE model were well stored by the sub-structured model despite the drastic reduction of degrees of freedom. Finally, we demonstrated that substructuring was very efficient to reduce the size of numerical models while respecting the time-dependant behavior of the structure. This result highlighted the potential interest of substructure techniques in large-scale models of musculoskeletal structures.

Cells, growth factors and bioactive surface properties in a mechanobiological model of implant healing.

Interface conditions are of prime importance for implant fixation in the early post-operative period and modelling of specific biochemical interactions at implant surface is still missing. We hypothesized that updating osteoblast adhesion properties and growth factor source in an active zone located at the implant surface was relevant to model biochemical interactions of implant with its environment. We proposed an innovative set of diffusive-convective-reactive equations which relevant parameters were the cell decay factor, the cell motility and the growth factor balance. Initial comparison with histomorphometic results from a stable PMMA canine implant model provided an encouraging base to implement a numerical sensitivity analysis to evaluate the role of three types of bioactive surfaces: acid-etched titanium, coarse grit-blasted acid-etched titanium and coarse grit-blasted acid-etched titanium with RGDS peptide. We found that cell diffusion decrease (acid-etched+RGDS peptide vs. PMMA), and increase of local growth factor fraction (PMMA vs. acid-etched+RGDS peptide), significantly improved the amount of mineralized tissue on the implant surface. When the variation of structural fraction to cell motility and growth factor synthesis was investigated, an envelope pattern with an optimum was obtained but this could be exceeded for strong surface modifications and/or for high growth factor concentrations. The model also confirmed that implant bioactive properties should play a limited role to reduce heterogeneity of new-formed tissue. In conclusion, we suggested that our innovative theoretical approach was relevant to investigate implant fixation and could potentially help in reduction of implant revision.

Mechanical behavior of annulus fibrosus: a microstructural model of fibers reorientation.

Experimental uniaxial tensile tests have been carried out on annulus tissue samples harvested on pig and lamb lumbar intervertebral discs. When subjecting the samples to loading cycles, the stress-strain curves exhibit strong nonlinearities and hysteresis. This particular behavior results from the anisotropic microstructure of annulus tissue composed of woven oriented collagen fibers embedded in the extracellular matrix. During uniaxial tension, the collagen fibers reorient toward the loading direction increasing its global stiffness. To describe this behavior, we propose a heuristic two-dimensional rheological model based on three mechanical and one geometrical characteristics. The latter one is the fibers orientation angle becoming the key parameter that govern the macroscopic mechanical behavior. The experimental results are used to identify the physical properties associated with the rheological model, leading to an accurate representation of the stress-strain curve over a complete loading cycle. In this framework, the fibers reorientation can solely account for the rigidity increase while the hysteresis is associated with liquid viscous flows through the matrix. Based on this representation, unusual coupling effects between strains and fluid flows can be observed, that would significantly affect the cell nutrients transport mechanisms.

Intra-operative quantification of the surgical gesture in orbital surgery: application to the proptosis reduction.

BACKGROUND: Proptosis is characterized by a protrusion of the eyeball due to an increase of the orbital tissue volume. To recover a normal eyeball positioning, the most frequent surgical technique consists in the osteotomy of orbital walls combined with a loading on the eyeball to initiate tissue decompression. The first biomechanical models dealing with proptosis reduction, validated in one patient, have been previously proposed by the authors. METHODS: This paper proposed an experimental method to quantify the intra-operative clinical gesture in proptosis reduction, and the pilot study concerned one clinical case. The eyeball's backward displacement was measured by an optical 3D localizer and the load applied by the surgeon was simultaneously measured by a custom-made force gauge. Quasi-static stiffness of the intra-orbital content was evaluated. FINDINGS: The average values for the whole experiment was 16 N (SD: 3N) for the force exerted by the surgeon and 9 mm (SD: 4mm) for the eyeball backward displacement. The averaged quasi-static stiffness of the orbital content was evaluated to 2.4N/mm (SD: 1.2) and showed a global decrease of 45% post-operatively. INTERPRETATION: The protocol and the associated custom-designed devices allowed loads, induced displacements and macroscopic stiffness of the orbital content to be measured intra-operatively. The clinical relevance has been demonstrated in a pilot study. To our knowledge, no study has been published allowing the clinical gesture in proptosis reduction to be quantified intra-operatively. Associating an enlarged database and validated patient-related predictive models will reinforce the surgical efficiency and patient comfort contributing to diagnosis and intra-operative guidance.