Simulating intervertebral disc cell behaviour within 3D multifactorial environments

Abstract

Motivation: Low back pain is responsible for more global disability than any other condition. Its incidence is closely related to intervertebral disc (IVD) failure, which is likely caused by an accumulation of microtrauma within the IVD. Crucial factors in microtrauma development are not entirely known yet, probably because their exploration in vivo or in vitro remains tremendously challenging. In silico modelling is, therefore, definitively appealing, and shall include approaches to integrate influences of multiple cell stimuli at the microscale. Accordingly, this study introduces a hybrid Agent-based (AB) model in IVD research and exploits network modelling solutions in systems biology to mimic the cellular behaviour of Nucleus Pulposus cells exposed to a 3D multifactorial biochemical environment, based on mathematical integrations of existing experimental knowledge. Cellular activity reflected by mRNA expression of Aggrecan, Collagen type I, Collagen type II, MMP-3 and ADAMTS were calculated for inflamed and non-inflamed cells. mRNA expression over long periods of time is additionally determined including cell viability estimations. Model predictions were eventually validated with independent experimental data.

Results: As it combines experimental data to simulate cell behaviour exposed to a multifactorial environment, the present methodology was able to reproduce cell death within 3 days under glucose deprivation and a 50% decrease in cell viability after 7 days in an acidic environment. Cellular mRNA expression under non-inflamed conditions simulated a quantifiable catabolic shift under an adverse cell environment, and model predictions of mRNA expression of inflamed cells provide new explanation possibilities for unexpected results achieved in experimental research.

Availabilityand implementation: The AB model as well as used mathematical functions were built with open source software. Final functions implemented in the AB model and complete AB model parameters are provided as Supplementary Material. Experimental input and validation data were provided through referenced, published papers. The code corresponding to the model can be shared upon request and shall be reused after proper training.

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

Schematic illustration of included factors in AB model simulations. Glc, glucose; Lac, lactate; IL-1β, Interleukin 1β

Fig. 2.

Overview of the AB simulation workflow

Fig. 3.

Visualization of the methodology to approximate continuous functions. Example of cellular activity in terms of Agg mRNA expression based on glc concentrations (Rinkler et al., 2010)

Fig. 4.

Coupling of experimental results, by using the equation from Mendoza et al. (2006). Note that pH varies from 6.5 to 7.4, thus it is represented within the function as values from 0 to 0.9

Fig. 5.

Visualization of immunopositivity within the AB model world (left) and zoom (right). Red: NP-cells immunopositive for IL1-β. Triangle shaped: dead immunopositive cells. Yellow: proliferated cells

Fig. 6.

Schematic representation of the inflammation submodel. C, concentration; N, number; n, normalized

Fig. 7.

Instantaneous cellular activity in terms of mRNA expression of immunonegative (a) and immunopositive (b) NP cells under glc and pH BC imposed by Saggese et al. 2018 (pH 7.0)

Fig. 8.

Parameter variation on Agg, Col-II an MMP-3 mRNA expression of immunonegative (upper row) and immunopositive cells (lower row)

Fig. 9.

Simulation of cell viability over days in either glc-free medium or acidic environment, with and without the effect of IL-1βprotein