title: Efficient implementation of non-linear valve law and ventricular interaction dynamics in the minimal cardiac model.
abstract: A minimal model of the cardio-vascular system (CVS) with ventricular interaction and inertial effects that accurately captures the physiological trends of a variety of disease states has been developed. However, the physiologically accurate open on pressure, close on flow valve law is computationally heavy to implement, reducing the model's potential clinical benefit. A significantly simpler representation of the valve law using Heaviside functions is derived and the ventricular interaction equations are reformulated to obtain a unique closed form analytical solution. The new formulation is tested and compared with the previous formulation for a healthy human and four clinically significant disease states: mitral and aortic stenosis, pulmonary embolism and septic shock. The new model formulation matches the previous model definition, differing by a mean model response error of no more than 0.2%. Computationally, it is 24 x faster than the previous method. More specifically, a short 20-beat simulation that took 102 s now requires 4.3 s, significantly improving the model's potential for practical use in a diagnostic and/or decision support role in the intensive care unit.
authors.affiliation: Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand. chris.hann@canterbury.ac.nz
authors.forename: C E
authors.initials: CE
authors.lastname: Hann
authors.forename: J G
authors.initials: JG
authors.lastname: Chase
authors.forename: G M
authors.initials: GM
authors.lastname: Shaw
mesh_terms: D002319:Cardiovascular System; D006352:Heart Ventricles / Q000033:anatomy & histology*; D006801:Humans; D008953:Models, Anatomic; D009520:New Zealand; D017711:Nonlinear Dynamics; D016277:Ventricular Function, Left / Q000502:physiology*