Inverse Problems and Control for Lung Dynamics

Tregidgo, Henry F.J. (2017) Inverse Problems and Control for Lung Dynamics. Doctoral thesis, University of Manchester.

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Abstract

Mechanical ventilation is vital for the treatment of patients in respiratory intensive care and can be life saving. However, the risks of regional pressure gradients and over-distension must be balanced with the need to maintain function. For these reasons mechanical ventilation can benefit from the regional information provided by bedside imaging such as electrical impedance tomography (EIT). In this thesis we develop and test methods to retrieve clinically meaningful measures of lung function from EIT and examine the feasibility of closing the feedback loop to enable EIT-guided control of mechanical ventilation. Working towards this goal we develop a reconstruction algorithm capable of providing fast absolute values of conductivity from EIT measurements. We couple the resulting conductivity time series to a compartmental ordinary differential equation (ODE) model of lung function in order to recover regional parameters of elastance and airway resistance. We then demonstrate how these parameters may be used to generate optimised pressure controls for mechanical ventilation that expose the lungs to minimal gradients of pressure and are stable with respect to EIT measurement errors. The EIT reconstruction algorithm we develop is capable of producing low dimensional absolute values of conductivity in real time after a limited additional setup time. We show that this algorithm retains the ability to give fast feedback on regional lung changes. We also describe methods of improving computational efficiency for general Gauss-Newton type EIT algorithms. In order to couple reconstructed conductivity time series to our ODE model we describe and test the recovery of regional ventilation distributions through a process of regularised differentiation. We prove that the parameters of our ODE model are recoverable from these ventilation distributions apart from the degenerate case where all compartments have the same parameters. We then test this recovery process under varying levels of simulated EIT measurement and modelling errors. Finally we examine the ODE lung model using control theory. We prove that the ODE model is controllable for a wide range of parameter values and link controllability to observable ventilation patterns in the lungs. We demonstrate the generation and optimisation of pressure controls with minimal time gradients and provide a bound on the resulting magnitudes of these pressures. We then test the control generation process using ODE parameter values recovered through EIT simulations at varying levels of measurement noise. Through this work we have demonstrated that EIT reconstructions can be of benefit to the control of mechanical ventilation.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Electrical Impedance Tomography, Control Theory, Lung Dynamics, Mechanical Ventilation
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 49 Calculus of variations and optimal control; optimization
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
Depositing User: Dr Henry F.J. Tregidgo
Date Deposited: 07 Dec 2017 08:45
Last Modified: 07 Dec 2017 08:45
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2603

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