Mechanical ventilation (MV) is one of the most difficult, costly and variably delivered therapies for Acute Respiratory Distress Syndrome (ARDS) and respiratory failure patients in the intensive care unit (ICU). These patients experience severe widespread breathing problems and require MV for breathing support. However, conventional MV does not provide enough real-time information to guide or individualize therapy, and suboptimal MV settings increase the risk of further lung injury and complications. In particular, positive end expiratory pressure (PEEP) is applied during MV to aid recovery by improving gas exchange and prevent de-recruitment of lung units. However, selection of patient-specific, optimal PEEP remains widely debated, as no standard approaches exist for setting MV. Clinicians often use general approaches or experience to select PEEP, increasing the variability and risk of care, while reducing or eliminating any patient-specific aspect of care. Thus, physiological mathematical lung models of respiratory mechanics are required, if they are suitable to be used to optimise MV settings to improve critically ill patient outcomes. The aims of this research are to investigate and develop new, extended models of lung mechanics for ARDS and respiratory failure patients. In particular, to create model-based measures of the potential impact to healthy lung units of changing MV therapy parameters. This goal requires rapid forms of parameter identification to define patient-specific model parameters from clinical data that can be used as complementary metrics in guiding and individualising MV. The first model, an airway branching model (ABM) was developed based on classical fluid mechanics models that are commonly used. Typically, they are not feasible for real-time applications. Thus, there is a need to develop an accurate, effective, yet simpler, ABM model that can be applied at the bed-side. To address this issue, a patient-specific airway branching (ABMps) model is developed to measure the airway pressure drop at every physiological airway branch with an extended patient-specific physiological dimension that is unique for each patient and can evolve over time with new data. With this patient-specific dimension (α), the ABMps is able to provide clinical insight on patient-specific physiological conditions. Using the retrospective clinical data from the Christchurch Hospital, it was found that α ranges from 0.45-0.66 for ARDS patients, which is smaller than normal healthy people indicating severity of condition. Hence, the airway condition of a patient can be characterised and evolve over time to provide useful patient-specific clinical guidance. Next, a model using only the expiratory data of the breathing cycle is developed and presented that is potentially useful during clinical respiratory mechanics monitoring to guide MV. In particular, the expiratory time constant parameter, (K), can provide unique information related to respiratory system elastance in MV patients. In this thesis, the extended model is tested using clinical data from ARDS patients and investigates the relationship between the expiratory time constant and model-based inspiratory respiratory system elastance. The goal is to use this relation to titrate patient-specific PEEP, which can help prevent the risk of lung over-distension and ventilation-induced injury. The third model extends the time varying elastance model to investigate the variability of this respiratory system elastance for MV patients. In this case, in Christchurch Hospital. With the proposed metric, a deeper understanding can be achieved that provides clinicians with more information on how respiratory elastance varies between patients, PEEP, and ventilation time. This information is patient-specific and can be updated overtime, as well as used as a marker of patient condition. Estimating respiratory mechanics of MV patients is unreliable when patients exhibit spontaneous breathing (SB) efforts on top of any form of ventilator support. Most well-known developed models are thus only suitable for fully sedated patients. Monitoring respiratory mechanics of SB patients requires invasive clinical protocols and equipment that are clinically too intensive to carry out. In this research, it was found that the variability of lung elastance in SB patients is due to an effective negative elastance produced by the SB effort that is created by the SB effort, but cannot be modelled directly. Thus, by extending the non-invasive time-varying elastance model to capture negative elastance, it can provide more consistent monitoring for SB patients by reviewing the distribution of negative elastance. This work thus extends capabilities of these models and quantified the level of SB efforts. Finally, due to the asynchrony, also known as reverse triggering, airway pressure can assume an unusual and unmodelled M-wave shaped airway pressure during the MV. This M-wave airway pressure is also due to the SB efforts, exhibited by patients, even when they are fully sedated. Hence, a model-based method to reconstruct the affected airway pressure curve is introduced that enables estimation of the true underlying respiratory mechanics of these patients, as well as quantifying SB efforts. Results show that this pressure wave reconstruction method was able to accurately identify the respiratory elastance, assess the level of SB effort, and quantify the incidence of SB effort without invasive protocols or interruption to care. Hence, this method is clinically useful for clinicians in determining optimal ventilator settings to improve patient care. Overall, these tools and methods provide significant new ways to clinically manage MV patients in the ICU. Model-based methods offer the opportunity to protocolize and individualize care. Thus, the main outcomes of this work provide a step forward towards better, more consistent and patient-specific MV.