(416e) Computational Modeling of Tuberculosis Granuloma Activation

Tuberculosis (TB) is one of the most common infectious diseases and deadliest diseases worldwide. It is estimated that one-third of the world's population is infected with TB, and 1.5 million TB-related deaths were reported in 2014. TB is spread by aerosol droplets containing Mycobacterium tuberculosis (Mtb). The Mtb bacteria enter through the respiratory system and are attacked by the immune system in the lungs. The bacteria are clustered and contained by aveolar macrophages into cellular aggregates called granulomas. These granulomas can hold the bacteria dormant for long periods of time in a condition called latent TB. The bacteria can be activated when the granulomas are compromised by other immune response events in a host, such as cancer, HIV, or aging. MMP-1 dysregulation has been recently implicated in TB activation through experimental studies, but the mechanism is not well understood. Animal and human studies currently cannot probe the dynamics of activation, so a computational approach is proposed to fill this gap. The overall objective of the study is to predict TB cavity formation (a hallmark of activation) in response to the dynamics of MMP-1 dysregulation.

A previously developed mathematical model of the immune response to Mtb in the lungs [1] is used as the basis for this work. This previous model can track the levels of T cells, bacteria, cytokines and chemokines and can simulate the possible outcomes of the infection: clearance, latency, and reactivation. The infection outcome of interest in this work is latency. The previous model is a system of 16 ordinary differential equations (ODEs). To model the effect of MMP-1 dysregulation, 2 additional ODEs for the concentration of MMP-1 and collagen were developed, and a term was added to a preexisting ODE to represent the leakage of extracellular bacteria. The preexisting model and new ODEs were incorporated into a Python class, and an ode solver included in the Scipy package was used to solve the system of ODEs. A global sensitivity analysis using SALib’s implementation of Saltelli sampling and Sobol analysis was done on the model.

With the new equations to the model, a long term progression towards a leaking case is possible. Using a set of parameters that generates a latent case in the previous model, the new model at first starts to tend towards the latent case. After the bacterial population establishes itself, production of MMP-1 is increased. This drives the degradation of collagen, which allows bacteria to escape the granuloma. The case ultimately tends towards a steady state with a constant rate of bacterial leakage.

The model proposed here is intended to provide a possible mechanism for the link between MMP-1 dysregulation and TB activation. The new equations added into the model serve to add a leaking case that represents the formation of a necrotic cavity, which is characteristic of activation after a period of latency. Further work includes validating individual model parameters, sensitivity analysis, and model results under other conditions.

References: [1] Sud, Bigbee, Flynn & Kirschner. 2006. The Journal of Immunology, 176 (7), 4296–4314.

Acknowledgments: This work is supported in part by the Oklahoma Center for Respiratory Infectious Diseases, supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number P20GM103648.