Positive pressure mechanical ventilation is a crucial therapy for patients with respiratory failure in the intensive care unit. The progression of disease and condition of the lung both influence mechanical behaviour of the respiratory system. Guiding mechanical ventilation treatment with respiratory mechanics allows a patient-specific approach to treatment, which can lead to improved alveolar recruitment, less ventilator induced lung injury and improved patient outcomes. Mathematical models of respiratory mechanics that can integrate this data into real-time, patient-specific respiratory mechanics parameters to monitor and guide treatment. Thus mathematical models can play an increasingly necessary role in implementing patient-specific mechanical ventilation therapy.

This research tests and optimises respiratory mechanics models across a range of clinical data, predominantly from the pilot phase of the Clinical Utilisation of Respiratory Elastance (CURE) trials. A key issues in any such models is the trade-off of elastance and resistance, where poor models of resistance skew the results and utility of elastance and estimate and make the model unusable. This research presents a model that allows resistance to vary linearly with pressure. It offers similar performance to a more complex viscoelastic model in increasingly common pressure support modes, and improvements in volume control modes of ventilation. The variable resistance model suggests that resistance increases with pressure during inspiration.

Existing models for respiratory mechanics do not perform well in the presence of patient effort. However, patient effort is increasingly common in the increasingly preferred ventilation support modes. Patient effort can be measured, but adds significant invasiveness and cost, and this is not clinically feasible. This research explores the impact of patient effort on respiratory mechanics, and how to maintain stable and accurate estimations of respiratory mechanics when patient effort is unknown, variable in time and effort, and significantly affects identified model results. A pressure reconstruction algorithm, and a polynomial model of patient effort are developed to allow stable estimations of respiratory mechanics in the presence of patient effort. A comparison of five different models and reconstruction methods tests their ability to provide consistent and correct estimates of respiratory mechanics in different volume control datasets with and without patient effort. An iterative pressure reconstruction method combined with stacking of small groups of reconstructed breaths in moving windows is shown to be the best method for consistent and accurate respiratory mechanics estimation.

Methods are also presented for automated asynchrony detection, and while they achieve promising results, there is need for more accuracy before they are clinically useful. In particular it is difficult for automated methods of monitoring asynchronous patient effort to be highly accurate, and there is a need for a broader set of patient data to further develop any such methods. Overall, this thesis evaluates the ability of mathematical models to assess respiratory mechanics for monitoring and clinical decision support in mechanical ventilation, and especially addresses this issue in the presence of patient effort.