A majority of patients admitted to the Intensive Care Unit (ICU) require some form of respiratory support. In the case of Acute Respiratory Distress Syndrome (ARDS), the patient often requires full intervention from a mechanical ventilator. ARDS is also associated with mortality rate as high as 70%. Despite many recent studies on ventilator treatment of the disease, there are no well established methods to determine the optimal Positive End-Expiratory Pressure (PEEP) or other critical ventilator settings for individual patients. A model of fundamental lung mechanics is developed based on capturing the recruitment status of lung units. The main objective of this research is to develop a minimal model that is clinically effective in determining PEEP. The model was identified for a variety of different ventilator settings using clinical data. The fitting error was between 0.1% and 4% over the inflation limb and between 0.3% and 13% over the deflation limb at different PEEP settings. The model produces good correlation with clinical data, and is clinically applicable due to the minimal number of patient specific parameters to identify. The ability to use this identified patient specific model to optimize ventilator management is demonstrated by its ability to predict the patient specific response of PEEP changes before clinically applying them. Predictions of recruited lung volume change with change in PEEP have a median absolute error of 1.87% (IQR: 0.93-4.80%; 90% CI: 0.16-11.98%) for inflation and a median of 5.76% (IQR: 2.71-10.50%; 90% CI: 0.43-17.04%) for deflation, across all data sets and PEEP values (N=34predictions). This minimal model thus provides a clinically useful and relatively simple platform for continuous patient specific monitoring of lung unit recruitment for a patient.