A multi-scale modelling framework for airway hyper-responsiveness and remodelling in asthma

Asthma is a disease that affects the airways that carry air in and out of the lungs. During an asthmatic attack, triggered by irritants such as dust or smoke, the muscle cells that line the walls of the airways, contract and tighten so that the airway becomes narrower. The lining of the airways becomes inflamed and sticky mucus or phlegm is produced. All these reactions cause the airways to become narrower and irritated - leading to the symptoms of asthma such as coughing and wheezing. Over time, repeated episodes of asthma can cause the number of muscle cells to increase resulting in the airway wall getting thicker. There is currently no cure for asthma, and although it can be managed with regular medication, complications can still arise.


Considerable research is currently being undertaken to identify the factors that cause asthma - from genetic to environmental factors. Other research is aimed at understanding why asthmatic airways narrow so much and so fast, and at identifying the factors that cause the airway walls to thicken. Much of the research has been carried out on very specific aspects of the disease. For instance, one research group will look very closely at the chemicals that are released inside the muscle cell as a result of inhaling the irritant. Another group may focus on the components in the muscle cell that cause it to contract. Yet another group might look at how the muscle cells together (the tissue) responds to manipulations such as stretching. All these different things, however, interact during an asthmatic attack, but it is not easy to work out what the effect of these interactions are, just by looking at the individual measurements.


The intention of this work is to create a new mathematical framework that combines physics, mathematics and biological information from on-going experiments. The research will bridge the gaps between the different levels (cells to tissues) as well as develop new models at each level. This framework will thus help us to understand how the processes involved in asthma interact with each other, and so to understand what might happen if we could disrupt one of the processes. For instance, does the mathematical model predict a lessening of symptoms? Or does it predict a shuffle-around of the interactions, thus compensating for the disruption? Answers to these important questions will help scientists move closer towards finding new, more effective, therapies.

Asthma is a chronic inflammatory disease, responsible for significant societal and economic burdens worldwide. It is characterised by airway hyper-responsiveness, inflammation and remodelling. The underlying biological mechanisms responsible for these characteristics continue to be debated.


The aim of the work proposed here is to develop a novel multi-scale mathematical modelling framework that explicitly couples the molecular level interactions in the airway smooth muscle (ASM) cell to acute contractile biomechanical response at the tissue level in an airway as well as long-term airway remodelling. The theoretical models will be informed by, and validated by, findings from experimental groups that focus on cellular level observations (e.g. cytoskeletal mechanical properties in response to stretch) as well as macroscopic observations of airway calibre changes in agonist-initiated precision-cut lung slice experiments during which intracellular calcium signals can also be measured.


Development of the mathematical models will require the use of a number of different theories including continuum approaches that account for the glass-like rheology of biological tissue to quantify the local stress environment of the ASM cell and response time-scales involved, non-linear dynamics and reaction-diffusion models of intracellular calcium and cross-bridge muscle mechanics within the cell to predict force generation. All of these are linked (with feedback) through the functional processes involved. Furthermore the effect of repeated stress challenges on ASM and the potential for remodelling to be initiated over long time-scales will also be accounted for within the material constitutive laws. The coupling of the different models is challenging mathematically because the biological processes and dynamics have to span multiple spatial and temporal scales with the need to transfer key information across the scales.


The mathematical framework will provide an important first step towards identification of key interactions from sub-cellular to tissue level events involved in asthma. This in turn will provide the basis for a computational platform (in the long term) for the assessment of new hypotheses on the system as a whole, and allow predictions of the effect of potential new therapies.