Finite element study of nutrient diffusion in the human intervertebral disc.
Sélard E., Shirazi-Adl A., Urban JP.
STUDY DESIGN: The diffusion of small nutrients in the intervertebral human disc was examined using a finite element model. OBJECTIVE: To investigate nutrient transport into the disc using a numerical approach. SUMMARY OF BACKGROUND DATA: The intervertebral disc is the largest avascular tissue in the body. Nutrients necessary for cellular survival diffuse from the blood supply around the disc margins to the cells. Limited analytical studies have been performed and compared with measurements. However, the studies have only considered supply through the center of the nucleus and have only examined single solutes. A more sophisticated model is required to investigate the solute supply. MATERIALS AND METHODS: An axisymmetric finite element model has been created to study the transport of three solutes, i.e., oxygen, glucose, and lactate, using nonlinear consumption-concentration and production-concentration rates. For each of them, data for the consumption/production rate, diffusivity, and concentration in the blood were taken from experimental measurements and used in the model. The effect of varying disc height, exchange area with the blood supply, solute consumption rates, and diffusivities was investigated. RESULTS: The model predicted that concentrations of oxygen and glucose, which are consumed by cells, fell towards the disc center. Concentration levels decreased with a decrease in fractional exchange area and diffusivity, or with an increase in disc height and consumption rate. In contrast, the concentration of lactate, produced by the cells, was highest in the center and fell towards the disc-blood vessel interface. The absolute values of concentrations were in agreement with available measurements in vivo and those computed by few available analytical models, indicating the reliability of the finite element simulations. CONCLUSIONS: Finite element methods can be used to predict concentration gradients of solutes throughout the disc in relation to changes in disc and endplate morphology, disc properties, and cellular activities. This study provides a foundation for investigating the effect of load-induced changes or effects of changes in cellular metabolism on disc nutritional supply.