A minimal cardiac model has been shown to accurately capture a wide range of cardiovascular system dynamics commonly seen in the intensive care unit (ICU). However, standard parameter identification methods for this model are highly non-linear and non-convex, hindering real-time clinical application. An integral-based identification method that transforms the problem into a linear, convex problem, has been previously developed, but was only applied on continuous simulated data with random noise. This paper extends the method to handle discrete sets of clinical data, unmodelled dynamics, a significantly reduced data set theta requires only the minimum and maximum values of the pressure in the aorta, pulmonary artery and the volumes in the ventricles. The importance of integrals in the formulation for noise reduction is illustrated by demonstrating instability in the identification using simple derivative-based approaches. The cardiovascular system (CVS) model and parameter identification method are then clinically validated on porcine data for pulmonary embolism. Errors for the identified model are within 10% when re-simulated and compared to clinical data. All identified parameter trends match clinically expected changes. This work represents the first clinical validation of these models, methods and approach to cardiovascular diagnosis in critical care.