Fiber reinforced hydrated networks recapitulate the poroelastic mechanics of articular cartilage.

The role of poroelasticity on the functional performance of articular cartilage has been established in the scientific literature since the 1960s. Despite the extensive knowledge on this topic there remain few attempts to design for poroelasticity and to our knowledge no demonstration of an engineered poroelastic material that approaches the physiological performance. In this paper, we report on the development of an engineered material that begins to approach physiological poroelasticity. We quantify poroelasticity using the fluid load fraction, apply mixture theory to model the material system, and determine cytocompatibility using primary human mesenchymal stem cells. The design approach is based on a fiber reinforced hydrated network and uses routine fabrication methods (electrohydrodynamic deposition) and materials (poly[ɛ-caprolactone] and gelatin) to develop the engineered poroelastic material. This composite material achieved a mean peak fluid load fraction of 68%, displayed consistency with mixture theory, and demonstrated cytocompatibility. This work creates a foundation for designing poroelastic cartilage implants and developing scaffold systems to study chondrocyte mechanobiology and tissue engineering. STATEMENT OF SIGNIFICANCE: Poroelasticity drives the functional mechanics of articular cartilage (load bearing and lubrication). In this work we develop the design rationale and approach to produce a poroelastic material, known as a fiber reinforced hydrated network (FiHy™), that begins to approach the native performance of articular cartilage. This is the first engineered material system capable of exceeding isotropic linear poroelastic theory. The framework developed here enables fundamental studies of poroelasticity and the development of translational materials for cartilage repair.

Axisymmetric ridges and circumferential buckling of indented shells of revolution.

When poking a thin shell-like structure, like a plastic water bottle, experience shows that an initial axisymmetric dimple forms around the indentation point. The ridge of this dimple, with increasing indentation, eventually buckles into a polygonal shape. The polygon order generally continues to increase with further indentation. In the case of spherical shells, both the underlying axisymmetric deformation and the buckling evolution have been studied in detail. However, little is known about the behavior of general geometries. In this work we describe the geometrical and mechanical features of the axisymmetric ridge that forms in indented general shells of revolution with non-negative Gaussian curvature and the conditions for circumferential buckling of this ridge. We show that under the assumption of "mirror buckling," a single unified description of this ridge can be written if the problem is nondimensionalized using the local slope of the undeformed shell midprofile at the ridge radial location. However, in dimensional form the ridge properties evolve in quite different ways for different midprofiles. Focusing on the indentation of shallow shells of revolution with constant Gaussian curvature, we use our theoretical framework to study the properties of the ridge at the circumferential buckling threshold and evaluate the validity of the mirror buckling assumption against a linear stability analysis on the shallow shell equations, showing very good agreement. Our results highlight that circumferential buckling in indented thin shells is controlled by a complex interplay between the geometry and the stress state in the ridge. The results of our study will provide greater insight into the mechanics of thin shells. This could enable indentation to be used as a means to measure the mechanical properties of a wide range of shell geometries or used to design shells with specific mechanical behaviors.

Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage.

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.

Elastocapillarity can control the formation and the morphology of beads-on-string structures in solid fibers.

Beads-on-string patterns have been experimentally observed in solid cylinders for a wide range of material properties and structural lengths, from millimetric soft gels to nanometric hard fibers. In this work, we combine theoretical analysis and numerical tools to investigate the formation and nonlinear dynamics of such beaded structures. We show that this morphological transition is driven by elastocapillarity, i.e., a complex interplay between the effects of surface tension and bulk elasticity. Unlike buckling or wrinkling, the presence of an axial elongation is found here to favor the onset of fiber beading, in agreement with existing experimental results on electrospun fibers, hydrogels, and nerves. Our results also prove that the applied stretch can be used in fabrication techniques to control the morphology of the emerging beads-on-string patterns. Such quantitative predictions open the way for several applications, from tissue engineering to the design of stretchable electronics and the microfabrication of functionalized surfaces.

Poroelastic response of articular cartilage by nanoindentation creep tests at different characteristic lengths.

Nanoindentation is an experimental technique which is attracting increasing interests for the mechanical characterization of articular cartilage. In particular, time dependent mechanical responses due to fluid flow through the porous matrix can be quantitatively investigated by nanoindentation experiments at different penetration depths and/or by using different probe sizes. The aim of this paper is to provide a framework for the quantitative interpretation of the poroelastic response of articular cartilage subjected to creep nanoindentation tests. To this purpose, multiload creep tests using spherical indenters have been carried out on saturated samples of mature bovine articular cartilage achieving two main quantitative results. First, the dependence of indentation modulus in the drained state (at equilibrium) on the tip radius: a value of 500 kPa has been found using the large tip (400 µm radius) and of 1.7 MPa using the smaller one (25 µm). Secon, the permeability at microscopic scale was estimated at values ranging from 4.5×10(-16) m(4)/N s to 0.1×10(-16) m(4)/N s, from low to high equivalent deformation. Consistently with a poroelastic behavior, the size-dependent response of the indenter displacement disappears when characteristic size and permeability are accounted for. For comparison purposes, the same protocol was applied to intrinsically viscoelastic homogeneous samples of polydimethylsiloxane (PDMS): both indentation modulus and time response have been found size-independent.

Poroviscoelastic finite element model including continuous fiber distribution for the simulation of nanoindentation tests on articular cartilage.

Articular cartilage is a soft hydrated tissue that facilitates proper load transfer in diarthroidal joints. The mechanical properties of articular cartilage derive from its structural and hierarchical organization that, at the micrometric length scale, encompasses three main components: a network of insoluble collagen fibrils, negatively charged macromolecules and a porous extracellular matrix. In this work, a constituent-based constitutive model for the simulation of nanoindentation tests on articular cartilage is presented: it accounts for the multi-constituent, non-linear, porous, and viscous aspects of articular cartilage mechanics. In order to reproduce the articular cartilage response under different loading conditions, the model considers a continuous distribution of collagen fibril orientation, swelling, and depth-dependent mechanical properties. The model's parameters are obtained by fitting published experimental data for the time-dependent response in a stress relaxation unconfined compression test on adult bovine articular cartilage. Then, model validation is obtained by simulating three independent experimental tests: (i) the time-dependent response in a stress relaxation confined compression test, (ii) the drained response of a flat punch indentation test and (iii) the depth-dependence of effective Poisson's ratio in a unconfined compression test. Finally, the validated constitutive model has been used to simulate multiload spherical nanoindentation creep tests. Upon accounting for strain-dependent tissue permeability and intrinsic viscoelastic properties of the collagen network, the model accurately fits the drained and undrained curves and time-dependent creep response. The results show that depth-dependent tissue properties and glycosaminoglycan-induced tissue swelling should be accounted for when simulating indentation experiments.