Penetrating annulus fibrosus injuries affect dynamic compressive behaviors of the intervertebral disc via altered fluid flow: an analytical interpretation

Abstract

Extensive experimental work on the effects of penetrating annular injuries indicated that large injuries impact axial compressive properties of small animal intervertebral discs, yet there is some disagreement regarding the sensitivity of mechanical tests to small injury sizes. In order to understand the mechanism of injury size sensitivity, this study proposed a simple one dimensional model coupling elastic deformations in the annulus with fluid flow into and out of the nucleus through both porous boundaries and through a penetrating annular injury. The model was evaluated numerically in dynamic compression with parameters obtained by fitting the solution to experimental stress-relaxation data. The model predicted low sensitivity of mechanical changes to injury diameter at both small and large sizes (as measured by low and high ratios of injury diameter to annulus thickness), with a narrow range of high sensitivity in between. The size at which axial mechanics were most sensitive to injury size (i.e., critical injury size) increased with loading frequency. This study provides a quantitative hypothetical model of how penetrating annulus fibrosus injuries in discs with a gelatinous nucleus pulposus may alter disc mechanics by changing nucleus pulposus fluid pressurization through introduction of a new fluid transport pathway though the annulus. This model also explains how puncture-induced biomechanical changes depend on both injury size and test protocol.

Fig. 1

A pilot study implicated puncture injury as mechanism of altered fluid transport. Schematic of test apparatus (a) and rat caudal IVD before (b) and after (c) puncture with a 30 gauge needle.

Fig. 2

Schematic representation of analytical model with penetrating AF injury. This simplified model of the IVD is represented as a pressure vessel constrained by axial, R_a, and radial, R_b, elasticity. This model is capable of three fluid transport mechanisms: injury flow, represented as a pipe of hydraulic diameter, d, which exhibits Poiseuille flow; porous flow, governed by Darcy's Law, with effective permeability, K_e; and storage, representing fluid redistribution upon radial bulging restrained by radial elasticity spring.

Fig. 3

Model validation showing fit to experimental stress-relaxation data (a) and sensitivity to variations in parameters R_a, R_b, and K_e (b)–(d)

Fig. 4

Dynamic compressive storage stiffness (a) and loss stiffness (b) relative to un-punctured as a function of d/L ratio

Fig. 5

Critical d/L ratio increases linearly as a function of loading frequency

Fig. 6

Calculation of surface strains (a) and resulting effect on the area of an elliptical hole (b) for bounding cases representing fast loading (constant volume) and slow loading (constant radius)