A theoretical analysis of water transport through chondrocytes

Abstract

Because of the avascular nature of adult cartilage, nutrients and waste products are transported to and from the chondrocytes by diffusion and convection through the extracellular matrix. The convective interstitial fluid flow within and around chondrocytes is poorly understood. This theoretical study demonstrates that the incorporation of a semi-permeable membrane when modeling the chondrocyte leads to the following findings: under mechanical loading of an isolated chondrocyte the intracellular fluid pressure is on the order of tens of Pascals and the transmembrane fluid outflow, on the order of picometers per second, takes several days to subside; consequently, the chondrocyte behaves practically as an incompressible solid whenever the loading duration is on the order of minutes or hours. When embedded in its extracellular matrix (ECM), the chondrocyte response is substantially different. Mechanical loading of the tissue leads to a fluid pressure difference between intracellular and extracellular compartments on the order of tens of kilopascals and the transmembrane outflow, on the order of a nanometer per second, subsides in about 1 h. The volume of the chondrocyte decreases concomitantly with that of the ECM. The interstitial fluid flow in the extracellular matrix is directed around the cell, with peak values on the order of tens of nanometers per second. The viscous fluid shear stress acting on the cell surface is several orders of magnitude smaller than the solid matrix shear stresses resulting from the ECM deformation. These results provide new insight toward our understanding of water transport in chondrocytes.

Figure 1

Unconfined compression of isolated chondrocyte with rigid impermeable frictionless loading platens. Under a sufficiently large tare strain the cell is assumed to take a nearly cylindrical shape. The protoplasm and membrane have different water transport properties.

Figure 2

(a) Cell dilatation (relative change in volume) in the unconfined compression stress-relaxation response of a chondrocyte. E_Y = 1 kPa, ν = 0 or 0.33, L_P = 3×10⁻¹⁴ m³/N.s, r₀ = 10 µm, ε₀ = −0.10. (b) Intracellular fluid pressure and transmembrane fluid flux for the same conditions. The fluid flux is proportional to the pressure according to equation (5).

Figure 2

(a) Cell dilatation (relative change in volume) in the unconfined compression stress-relaxation response of a chondrocyte. E_Y = 1 kPa, ν = 0 or 0.33, L_P = 3×10⁻¹⁴ m³/N.s, r₀ = 10 µm, ε₀ = −0.10. (b) Intracellular fluid pressure and transmembrane fluid flux for the same conditions. The fluid flux is proportional to the pressure according to equation (5).

Figure 3

Confined compression of a cylindrical disk of cartilage. The finite element analysis considers a chondrocyte located halfway through the thickness of the disk.

Figure 4

(a) Intracellular and pericellular average fluid pressure from the finite element analysis of a chondrocyte embedded within its ECM. (b) Average fluid pressure difference (cell – ECM) and average transmembrane fluid flux (proportional to the pressure difference according to equation (5)).

Figure 4

(a) Intracellular and pericellular average fluid pressure from the finite element analysis of a chondrocyte embedded within its ECM. (b) Average fluid pressure difference (cell – ECM) and average transmembrane fluid flux (proportional to the pressure difference according to equation (5)).

Figure 5

Intracellular and pericellular average dilatation from the finite element analysis of a chondrocyte embedded within its ECM.

Figure 6

Fluid flux in the finite element analysis of a chondrocyte embedded within its ECM, evaluated at t=300 s: (a) Flux vectors, showing magnitude and direction. (b) Streamlines.

Figure 7

(a) Intracellular and pericellular average fluid pressure from the finite element analysis of a chondrocyte embedded within an agarose gel. (b) Average fluid pressure difference (cell – agarose) and average transmembrane fluid flux (proportional to the pressure difference according to equation (5)).

Figure 7

(a) Intracellular and pericellular average fluid pressure from the finite element analysis of a chondrocyte embedded within an agarose gel. (b) Average fluid pressure difference (cell – agarose) and average transmembrane fluid flux (proportional to the pressure difference according to equation (5)).

Figure 8

Intracellular and pericellular average dilatation from the finite element analysis of a chondrocyte embedded within agarose.