Case studies
CMMB engagement with industry and other end-users has come about through a number of mechanisms, either direct collaboration or supported by a Government scheme such as KTP or CASE studentships. Some examples of successful collaboration are illustrated here.
John King supervised this project by Zofia Jones, PhD student, who was interned with Unilever through the shorter Knowledge Transfer Partnerships scheme coordinated by the Industrial Maths Knowledge Transfer Network. More information is available via the link above.
Modelling the metabolism of fat by the liver
Jonathan Wattis worked on a project with Unilever involving formulating a theoretical description of the competition for LDL receptors on the surface of hepatocytes between LDL particles and larger VLDL particles. The high concentration of such cholesterol rich particles is increasingly being used as an indicator of health as changes in the western diet cause increased incidence ofobesity and type II diabetes. Thus a knowledge of the effect of diet on health is now of interest to the food industry as well as to medical sciences.
The work involved constructing a set of differential equations which described an experimental procedure formulated by food scientists at the University of Reading, where hepatocytes were exposed to a mixtureof LDL and varying types of VLDL particles, containing either polyunsaturated, monounsaturated or saturated fatty acids. The model was able to quantify the extent to which VLDL inhibits the binding of LDL to hepatocytes, and also the reduction in LDL-processing capacity of the liver.
Determining incidence of complications during heart surgery
A local medical device company, Chalice Medical, had been asked by their notified body to conduct a post market clinical follow up (PMCF) study to look at the incidence of a particular possible complication (called transient high pressure drop phenomenon). This phenomenon occurs occasionally when a patient is on the bypass machine during heart surgery and most manufacturers employ a coating on their device to prevent this.
Theo Kypraios worked on this project, with the aim of determining the required sample size of the PMCF study for estimating the proportion of the devices in which the transient high pressure drop phenomenon occurs to within a specified margin of error. The calculations were made using a variety of methodologies ranging from Wald's (approximate) confidence intervals to (exact) Clopper-Pearson ones.
Modelling gas exchange within the Paragon oxygenator
Reuben O'Dea and Paul Houston worked on a project with Chalice Medical comprising theoretical model development and CFD simulation of the blood flow, and associated oxygen and carbon dioxide transport within a Paragon Oxygenator. These devices provide support to patients with respiratory/cardiac failure, finding key use in long-term ECMO/ECLS applications.
Employing a model comprising a combined incompressible Navier-Stokes/Brinkman problem, coupled to partial differential equations describing the concentration of oxygen and carbon dioxide within the blood and gas phases, we provide predictions of the flow profile within the oxygenator device in its current form, and its influence on gas exchange. Furthermore, we provide some preliminary predictions indicating how future changes to the design of the gas exchange unit may influence its performance.
The Figure opposite shows blood flow in an axisymmetric model of the exchanger; arrows and colours indicate flow magnitude and direction.
Providing mathematical evidence of randomness in an electronic circuit
Etienne Farcot and Rod Edwards, a colleague from the University of Victoria in Canada, worked on a project with Rambus, a global company specializing in innovative hardware and software technologies to drive advancements from the data center to the mobile edge. The goal of the project was to demonstrate mathematically that a class of electronic circuits designed and owned by Rambus can be used as a true random number generator (TRNG).
These circuit designs are built using logic gates and for this reason they can be modelled using piecewise linear (PL) differential equations. Almost identical PL models have been used in the literature as mathematical models of biological networks (of genes or neurons). In this context, the two consultants had proved previously that such models could lead to so-called chaotic dynamics. In practical terms chaotic systems, though deterministic, behave in an unpredictable way, making them a good candidate for TRNG functionality.
For this project, specific models for the circuit designs were developed and analysed. Using a combination of analytical and numerical approaches, we were able to provide compelling evidence that the circuits produce a positive entropy (which implies randomness) for robust ranges of physical parameters.