Combining the probabilistic finite element model and artificial neural network to study nutrient levels in the human intervertebral discs

Abstract

BackgroundDiffusion distance and diffusivity are known to affect nutrient transport rates, but the probabilistic analysis of these two factors remains vacant. There is a lack of effective tools to evaluate disc nutrient levels. MethodsFive-hundred-disc samples with different combinations of morphological and water content parameters were generated, which were used to evaluate nutrient levels in unloaded and loaded states. Spearman correlation coefficients between inputs and responses were calculated. Artificial neural networks were trained to predict nutrient concentrations based on the dataset generated by the probabilistic finite element model. FindingsIn unloaded and loaded states, the minimum oxygen concentration of nucleus pulposus was negatively correlated with disc height (r = −0.83, p < 0.01 and r = −0.76, p < 0.01, respectively), and the minimum glucose concentration of annulus fibrosus was positively correlated with its water content (r = 0.68, p < 0.01 and r = 0.73, p < 0.01, respectively). The maximum lactate concentration of cartilage endplate was affected by endplate thickness (r = 0.94, p < 0.01 and r = 0.95, p < 0.01, respectively). For trained neural networks, nutrient concentrations could be well predicted, with coefficients of determination greater than 0.95 and mean absolute percentage errors less than 5 %. InterpretationThis study underscores the importance of disc height, annulus fibrosus water content, and endplate thickness in regulating nutrient levels, and precise control of these parameters should be prioritized in the design of tissue-engineered discs. Moreover, artificial neural networks might be a promising tool for evaluating nutrient levels.