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.

MOTIVATION: Biological mechanisms contributing to atherogenesis are multiple and complex. The early stage of atherosclerosis (AS) is characterized by the accumulation of low-density lipoprotein (LDL) droplets, leading to the creation of foam cells (FC). To address the difficulty to explore the dynamics of interactions that controls this process, this study aimed to develop a model of agents and infer on the most influential cell- and molecule-related parameters. RESULTS: FC started to accumulate after six to eight months of simulated hypercholesterolemia. A sensitivity analysis revealed the strong influence of LDL oxidation rate on the risk of FC creation, which was exploited to model the antioxidant effect of statins. Combined with an empirical simulation of the drug ability to decrease the level of LDL, the virtual statins treatment led to reductions of oxidized LDL levels similar to reductions measured in vivo. AVAILABILITY AND IMPLEMENTATION: An Open source software was used to develop the agent-based model of early AS. Two different concentrations of LDL agents were imposed in the intima layer to simulate healthy and hypercholesterolemia groups of 'virtual patients'. The interactions programmed between molecules and cells were based on experiments and models reported in the literature. A factorial sensitivity analysis explored the respective effects of the less documented model parameters as (i) agent migration speed, (ii) LDL oxidation rate and (iii) concentration of autoantibody agents. Finally, the response of the model to known perturbations was assessed by introducing statins agents, able to reduce the oxidation rate of LDL agents and the LDL boundary concentrations. CONTACT: [email protected] information: Supplementary data are available at Bioinformatics online.

Intervertebral disc metabolic transport is essential to the functional spine and provides the cells with the nutrients necessary to tissue maintenance. Disc degenerative changes alter the tissue mechanics, but interactions between mechanical loading and disc transport are still an open issue. A poromechanical finite element model of the human disc was coupled with oxygen and lactate transport models. Deformations and fluid flow were linked to transport predictions by including strain-dependent diffusion and advection. The two solute transport models were also coupled to account for cell metabolism. With this approach, the relevance of metabolic and mechano-transport couplings were assessed in the healthy disc under loading-recovery daily compression. Disc height, cell density and material degenerative changes were parametrically simulated to study their influence on the calculated solute concentrations. The effects of load frequency and amplitude were also studied in the healthy disc by considering short periods of cyclic compression. Results indicate that external loads influence the oxygen and lactate regional distributions within the disc when large volume changes modify diffusion distances and diffusivities, especially when healthy disc properties are simulated. Advection was negligible under both sustained and cyclic compression. Simulating degeneration, mechanical changes inhibited the mechanical effect on transport while disc height, fluid content, nucleus pressure and overall cell density reductions affected significantly transport predictions. For the healthy disc, nutrient concentration patterns depended mostly on the time of sustained compression and recovery. The relevant effect of cell density on the metabolic transport indicates the disturbance of cell number as a possible onset for disc degeneration via alteration of the metabolic balance. Results also suggest that healthy disc properties have a positive effect of loading on metabolic transport. Such relation, relevant to the maintenance of the tissue functional composition, would therefore link disc function with disc nutrition.