Analysis of Nonlinear Coupled Diffusion of Oxygen and Lactic Acid in Intervertebral Discs

Abstract

The transport of oxygen and lactate (i.e., lactic acid) in the human intervertebral disc was investigated accounting for the measured coupling between species via the pH level in the tissue. Uncoupled cases were also analyzed to identify the extent of the effect of such coupling on the solute gradients across the disc. Moreover, nonlinear lactic production rate versus lactic concentration and oxygen consumption rate versus oxygen concentration were considered. The nonlinear coupled diffusion equations were solved using an in-house finite element program and an axisymmetric model of the disc with distinct nucleus and anulus regions. A pseudotransient approach with a backward integration scheme was employed to improve convergence. Coupled simulations influenced the oxygen concentration and lactic acid concentration throughout the disc, in particular the gradient of concentrations along the disc mid-height to the nucleus-anulus boundary where the solutes reached their most critical values; minimum for the oxygen tension and maximum for the lactate. Results suggest that for realistic estimates of nutrient and metabolite gradients across the disc, it could be important to take into account the coupling between the rates of synthesis and overall local metabolite/nutrient concentration.

Notochordal intervertebral disc cells: Sensitivity to nutrient deprivation

“…We measured rates of energy metabolism per cell, since these are important in regulating local concentrations of nutrients and metabolites around the cells (35). We found that NCs are more active metabolically than MNPCs; rates of oxygen and glucose consumption and of lactate production in NCs were considerably higher than those in MNPCs under all conditions tested (Figure 2 and Table 1).…”

“…NCs, but not MNPCs, exhibited a positive Pasteur effect (i.e., an increase in glycolysis rate and hence in the rate of lactic acid production under low oxygen tension) ( Figure 2C). Although a positive Pasteur effect provides a pathway for maintaining ATP production under low oxygen tension, its effects in the disc could be harmful rather than beneficial, since in the center of the avascular disc both oxygen and glucose concentrations are low (35,46). Hence, a positive Pasteur effect will increase glucose demand and could push glucose levels below those necessary for survival, while, in addition, increased lactic acid production could lead to a fall in pH, also dangerous for NC survival ( Figure 3A).…”

Effects of mechanical compression on metabolism and distribution of oxygen and lactate in intervertebral disc

“…The metabolic rates of sodium and chloride ions were assumed to be zero (i.e., Q + =Q − =0). Based on the experimental data reported in the literature (Soukane et al, 2005;Bibby et al, 2005), an approximate linear relationship between pH and lactate was used to calculate pH within the IVD in this study and given as: (4) where A = −0.1 mM −1 and B = 7.5.…”

“…It is still unclear as to how the nutrition level in IVD is regulated by mechanical and biological factors, such as applied stress or strain, tissue degeneration, and endplate calcification. Recently, numerical analyses have been used to investigate the transport of nutrients and metabolites (e.g., oxygen, glucose, and lactate) within the human IVD (Selard et al, 2003;Soukane et al, 2005). In these previous theoretical studies, the complex geometry and nonhomogeneous properties of the human IVD were considered and the distribution of oxygen, glucose, and lactate within the IVD were shown to depend on solute diffusivity, cellular metabolic rates, the coupling effects between solute concentrations and consumptions/ productions, and boundary conditions (Selard et al, 2003;Soukane et al, 2005).…”

“…Recently, numerical analyses have been used to investigate the transport of nutrients and metabolites (e.g., oxygen, glucose, and lactate) within the human IVD (Selard et al, 2003;Soukane et al, 2005). In these previous theoretical studies, the complex geometry and nonhomogeneous properties of the human IVD were considered and the distribution of oxygen, glucose, and lactate within the IVD were shown to depend on solute diffusivity, cellular metabolic rates, the coupling effects between solute concentrations and consumptions/ productions, and boundary conditions (Selard et al, 2003;Soukane et al, 2005). Most recently, Soukane et al suggested that fluid loss and change in disc geometry which were assumed to be caused by static compression could affect the transport of nutrients and metabolites (Soukane et al, 2007).…”