Determining Tension–Compression Nonlinear Mechanical Properties of Articular Cartilage from Indentation Testing

Abstract

The indentation test is widely used to determine the in situ biomechanical properties of articular cartilage. The mechanical parameters estimated from the test depend on the constitutive model adopted to analyze the data. Similar to most connective tissues, the solid matrix of cartilage displays different mechanical properties under tension and compression, termed tension-compression nonlinearity (TCN). In this study, cartilage was modeled as a porous elastic material with either a conewise linear elastic matrix with cubic symmetry or a solid matrix reinforced by a continuous fiber distribution. Both models are commonly used to describe the TCN of cartilage. The roles of each mechanical property in determining the indentation response of cartilage were identified by finite element simulation. Under constant loading, the equilibrium deformation of cartilage is mainly dependent on the compressive modulus, while the initial transient creep behavior is largely regulated by the tensile stiffness. More importantly, altering the permeability does not change the shape of the indentation creep curves, but introduces a parallel shift along the horizontal direction on a logarithmic time scale. Based on these findings, a highly efficient curve-fitting algorithm was designed, which can uniquely determine the three major mechanical properties of cartilage (compressive modulus, tensile modulus, and permeability) from a single indentation test. The new technique was tested on adult bovine knee cartilage and compared with results from the classic biphasic linear elastic curve-fitting program.

Calcium signaling of in situ chondrocytes in articular cartilage under compressive loading: Roles of calcium sources and cell membrane ion channels

“…ER calcium store: Cartilage explants were incubated in 1 μM thapsigargin to deplete the calcium stored in the ER, which is the major intracellular calcium store in chondrocytes . As the vehicle control for thapsigargin treated samples, cartilage samples were incubated in DMEM supplemented with 0.25% v/v DMSO . PLC‐IP 3 pathway: Cartilage sample was incubated in 11 mM neomycin to inhibit the phospholipase C (PLC) from hydrolyzing phospholipids into inositol triphosphate (IP 3 ) and diacylglycerol (DAG).…”

“…29 As the vehicle control for thapsigargin treated samples, cartilage samples were incubated in DMEM supplemented with 0.25% v/v DMSO. 3 PLC-IP 3 pathway: Cartilage sample was incubated in 11 mM neomycin to inhibit the phospholipase C (PLC) from hydrolyzing phospholipids into CALCIUM SIGNALING OF IN SITU CHONDROCYTES inositol triphosphate (IP 3 ) and diacylglycerol (DAG). IP 3 can induce the calcium release from ER.…”

“…Metabolic activities of chondrocytes can be regulated by the physical stimuli induced by the daily mechanical loading on cartilage . Due to the multi‐phasic nature of cartilage, compressive loading on cartilage can generate changes in mechanical, hydrostatic, chemical, and electrical signals across the tissue . Oscillation of intracellular calcium ([Ca 2+ ] i ) concentration is among the earliest and most fundamental molecular responses of chondrocytes to most physical stimuli, including compression, fluid flow, hydrostatic pressure, osmotic stres, and electric current, as shown by previous studies using monolayer chondrocytes or chondrocytes seeded in hydrogels.…”

“…Physical stimuli and Ca 2þ influx can also trigger the release of adenosine triphosphate (ATP) from membrane vesicles into the extracellular space and activate the purinergic receptors (e.g., P2Y family) and ligand gated ion channels (e.g., P2X family) on plasma membrane. 19 Activation of P2Y receptors can subsequently stimulate the activation of intracellular phospholipase C (PLC) and the generation of inositol 1,4,5-trisphosphate (IP 3 ), which can bind to the IP 3 receptors on ER and induce rapid Ca 2þ release into cytosol. The PLC-IP 3 pathway can also be activated by many other G protein-couple receptors or even mechanical stress on the cell membrane.…”

Maximum shear strain-based algorithm can predict proteoglycan loss in damaged articular cartilage

“…The solid compartment is composed of a viscoelastic fibrillar part, i.e., the collagen network, and a swelling non-fibrillar part comprising primarily of PGs. Depth-dependent mechanical behavior (Szarko and Xia 2012) and tension-compression nonlinearity (Chen et al 2016) of cartilage are encompassed by the FRPVES model. For the non-fibrillar part, the strain energy density function W nf was defined based on a hyperelastic compressible neo-Hookean solid material where = T is the right Cauchy-Green deformation tensor and is the deformation gradient tensor.…”