Disc size markedly influences concentration profiles of intravenously administered solutes in the intervertebral disc: a computational study on glucosamine as a model solute

Abstract

Purpose: Tests on animals of different species with large differences in intervertebral disc size are commonly used to investigate the therapeutic efficacy of intravenously injected solutes in the disc. We hypothesize that disc size markedly affects outcome.

Methods: Here, using a small non-metabolized molecule, glucosamine (GL) as a model solute, we calculate the influence of disc size on transport of GL into rat, rabbit, dog and human discs for 10 h post intravenous-injection. We used transient finite element models and considered an identical GL supply for all animals.

Results: Huge effects of disc size on GL concentration profiles were found. Post-injection GL concentration in the rat disc reached 70% blood concentration within 15 min but remained below 10% in the human disc nucleus throughout. The GL rapidly penetrated post-injection into smaller discs resulting in homogeneous concentrations. In contrast, GL concentration, albeit at much lower levels, increased with time in the human disc with a small outward flux at the annulus periphery at longer periods.

Conclusions: Changes in the disc size hugely influenced GL concentrations throughout the disc at all regions and times. Increases in administered dose can neither remedy the very low concentration levels in the disc center in larger human disc at early post-injection hours nor alter the substantial differences in concentration profiles estimated among various species. The size effect will only be exacerbated as molecular weight of the solute increases and as the endplate calcifies. Extrapolation of findings from animal to human discs on the efficacy of intravenously administered solutes must proceed with great caution.

Fig. 1

Axisymmetric finite element models of species intervertebral discs, from top to bottom, human, dog, rabbit and rat consisting of 4 distinct regions with different properties: nucleus (NP), inner annulus (IA), outer annulus (OA) and cartilaginous endplate (CEP). Temporal variation of source supplies via blood vessels is prescribed at the outer annulus periphery and CEP as depicted by arrows for the human disc. The symmetry about the disc mid-horizontal plane is considered. Dimensions are all in mm

Fig. 2

Changes in glucosamine concentration with time at the disc boundary in all 4 species. The inset figure shows the initial concentration in the first 60 s post-injection

Fig. 3

Mean Concentrations in human, dog, rabbit and rat disc regions for different CEP exchange areas; (left) 100 %, (right) 50 %

Fig. 4

Concentration profiles along the midplane of the disc radius (z = 0) at 15 min—10 h for rat, rabbit, dog and human discs assuming 50 % CEP

Fig. 5

Concentration profiles through the depth of the disc in the disc center (r = 0) at 15 min—10 h for rat, rabbit, dog and human discs, assuming 50 % CEP

Fig. 6

Total (integrated over time) glucosamine entered from each source supply (50 % CEP condition, top: normalized over its disc volume for each case)

Fig. 7

Changes in concentration with time at the disc center (r = z = 0) for rat, rabbit, dog and human discs with different endplate permeabilities (100 versus 50 % CEP)

Fig. 8

Percentage of total diffused GL via OA and CEP pathways to the total GL in the disc for the case with 50 % CEP