Workshop on Mathematical Modeling of Blood Flow and the Baroreflex System

A pulse oximeter is a device that measures the oxygen saturation of the blood. Typically it functions by shining two lights, of different wavelength (but both close to infra-red)  through a translucent part of the body. The different wavelength lights are absorbed to differing degrees by the oxygenated and deoxygenated haemoglobin and so the ratio of oxygenation to deoxygenation may be calculated. Since arterial blood vessels respond to pressure changes (due to the heart pumping) the signal is time-dependent and so the output of the pulse oximeter may also be used to monitor the heart rate. In fact this variation in the signal is essential to the functioning of the device since, to distinguish the light absorption from the blood and surrounding tissue, the pulse oximeter only uses the varying part of the signal.

Standard uses for the pulse oximeter include medical monitoring of oxygenation and heart rate and also the diagnosis of sleep disorders. In general, the output of the pulse oximeter exhibits very similar behaviour to the output from the catheter, so it has the potential to also provide a continuous  supply of information on the blood pressure. Currently there exist two standard methods for measuring blood pressure:

1)      The sphygmomanometer — this is the familiar cuff which is inflated, usually on the upper arm. In general it is manually operated and requires a quiet environment. It is a very old technology (from the 1800s) and is prone to operator error. It also provides data only for a short period and so may miss rapid events. Whilst digital cuffs exist these can be highly inaccurate.

2)      The intra-arterial catheter — this is inserted into an artery and can provide continuous accurate data. However, it is an invasive technique primarily used on bed-ridden and intensive care patients. These patients are particularly susceptible to infections and sepsis and ischaemia are complications frequently associated with these devices.

The specific goal of this meeting is to develop and adapt mathematical models to describe blood pressure measurements obtained via a pulse oximeter with the goal of relating the output to the true pressure value and also to ascertain any other information that can be extracted from the data. The primary focus will be on ODE approaches, such as the baroreflex model of Ottesen (J. Math Biol. 1997) but, in keeping with a workshop mentality, other methods may also be considered.

Tim Myers, Centre de Recerca Matemàtica (coordinator)

Michelle De Decker, Centre de Recerca Matemàtica

Francesc Font, Centre de Recerca Matemàtica

Andrew Fowler, Oxford University and Limerick University

Jonathan Low, Centre de Recerca Matemàtica 

Adam Mahdi, University of North Carolina

Mark McGuinness, University of Wellington, Victoria

Sarah Mitchell, University of Limerick

Vicent Ribas Ripoll, Sabirmedical

Anna Saez de Tejada, Sabirmedical

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