Patient‐specific apparent diffusion maps used to model nutrient availability in degenerated intervertebral discs

Abstract

Abstract Introduction In this study, magnetic resonance imaging data was used to (1) model IVD‐specific gradients of glucose, oxygen, lactate, and pH; and (2) investigate possible effects of covariate factors (i.e., disc geometry, and mean apparent diffusion coefficient values) on the IVD’s microenvironment. Mathematical modeling of the patient’s specific IVD microenvironment could be important when selecting patients for stem cell therapy due to the increased nutrient demand created by that treatment. Materials and Methods Disc geometry and water diffusion coefficients were extracted from MRIs of 37 patients using sagittal T1‐weighted images, T2‐weighted images, and ADC Maps. A 2‐D steady state finite element mathematical model was developed in COMSOL Multiphysics® 5.4 to compute concentration maps of glucose, oxygen, lactate and pH. Results Concentration of nutrients (i.e., glucose, and oxygen) dropped with increasing distance from the cartilaginous endplates (CEP), whereas acidity levels increased. Most discs experienced poor nutrient levels along with high acidity values in the inner annulus fibrosus (AF). The disc’s physiological microenvironment became more deficient as degeneration progressed. For example, minimum glucose concentration in grade 4 dropped by 31.1% compared to grade 3 (p < 0.0001). The model further suggested a strong effect of the following parameters: disc size, AF and CEP diffusivities, metabolic reactions, and cell density on solute concentrations in the disc (p < 0.05). Conclusion The significance of this work implies that the individual morphology and physiological conditions of each disc, even among discs of the same Pfirrmann grade, should be evaluated when modeling IVD solute concentrations.

Keywords

• finite element modeling
• intervertebral disc
• mass transport
• mathematical model
• metabolism
• nutrient