On the 12th-16th September 2016 in the University of Glasgow, the Centre for Mathematics Applied to the Life Sciences (CMALS) in conjunction with SofTMech hosted a Mathematics for Industry PhD modelling week. This event gathered PhD students from all over Europe with a variety of backgrounds, with the aim being to give the students a chance to collaborate with others working on a variety of problems arising in the field of biomedical applied mathematics.
The week began with some talks relevant to the various industrial problems followed by more detailed technical talks by the leaders of each group. There were three problems on offer for the week. The first group (supervised by the SofTMech team) was modelling the soft tissue mechanics in the heart. A key issue that arises in this field is that material parameters required for modelling cannot be directly measured but are inferred from medical images. This “inverse modelling” approach involves the combination of mechanistic modelling and statistical parameter inference using Gaussian processes. The other two groups were working on modelling medical devices and protein/molecule interactions.
Medical Devices Problem
The problem I (Niall) worked on involved the modelling of controlled drug release from medical devices, specifically orthopaedic implants. Our group leaders for the week were Dr. Martin Meere from NUI Galway and Dr. Giuseppe Pontrelli from CNR in Rome.
It is believed that the local delivery of drug from an implant may be an ideal way of tackling issues such as infection, inflammation and pain normally associated with the foreign body response when an orthopaedic implant is implemented. Our goal for the week was to develop models of some drug-releasing implants, where the drug can be loaded and released in a controlled optimal manner depending on the situation at hand. A normal problem associated with traditional drug delivery is a large burst of drug can be toxic while a slow release of drug may keep concentrations below an effective threshold.
We were pointed towards an experimental paper by Argarate et al.  in which polymer (PLDL) implant disks were coated with one or two layers containing combinations of drugs and biodegradable polymer (PLLA). There were 9 of us in the group, and we split into 3 smaller sub-groups to work on reproducing 3 different release profiles (amount of drug released vs. time) published in the experimental paper. The first sub-group worked on a pure dissolution problem, where drug is directly loaded onto the implant with no polymer. The other two sub-groups worked on drug release from single and double layer polymer/drug coatings.
Our approach typically involved developing simple mechanistic PDE models accounting for diffusion and convection of the drug molecules then prescribing suitable boundary and initial conditions for the particular case. When we had a grasp on the simpler problem we would then refine the model by reducing the number of assumptions and prescribing more realistic conditions. The skill set of the group was quite varied with some students more comfortable with numerical simulations of the processes and others preferring to seek analytical or approximate solutions. This balance worked well as there was good crossover between the approaches, with students often jumping between subgroups when they thought they could help.
Drug Discovery Problem
I (Paul) worked on the drug discovery problem proposed by GlaxoSmithKlyne. The GSK representative, Dr Armin Sepp, was present throughout the week to provide information and clarification on the problem as required. We were also supported by our academic mentor, Dr Sean McGinty of the University of Glasgow. Our challenge was to develop models for cell signalling, with a view to modelling antibody-mediated interference in signalling. A comprehensive model for this process could have important consequences for the drug discovery and development process, and might be used to decrease the enormous cost expended in drug development.
The team members for our problem came from a variety of backgrounds, including biomedical engineering, applied mathematics, and civil engineering. The varying backgrounds ensured a broad range of perspectives, as each participant drew on their own experience in suggesting how best to tackle the problem.
By the end of the week, we had developed a model incorporating receptor-ligand binding, ligand decay and diffusion, based on mass action kinetics and well-known diffusion models. We then explored various parameter regimes and solved the model equations using analytical and numerical methods. This allowed us to identify some further steps for possible future work, including incorporation of the role of antibodies and their role in interference in the binding process.
The workshop was an excellent opportunity to interact with industry, and it gave me a clear insight into how mathematics and mathematical modelling is applied to industrial problems. The week also presented an invaluable networking opportunity, as we met with other PhD students from all parts of Europe and further afield.
This event was supported by COST Action TD1409, Mathematics for Industry Network (MI-NET).
 Argarate, N., et al., (2014), Biodegradable Bi-layered coating on polymeric orthopaedic implants for controlled release of drugs, Materials Letters, 132: 193-195.
Niall McInerney (University of Limerick) and Paul Greaney (NUI Galway)