A hybrid neural ordinary differential equation model of the cardiovascular system.

In the human cardiovascular system (CVS), the interaction between the left and right ventricles of the heart is influenced by the septum and the pericardium. Computational models of the CVS can capture this interaction, but this often involves approximating solutions to complex nonlinear equations numerically. As a result, numerous models have been proposed, where these nonlinear equations are either simplified, or ventricular interaction is ignored. In this work, we propose an alternative approach to modelling ventricular interaction, using a hybrid neural ordinary differential equation (ODE) structure. First, a lumped parameter ODE model of the CVS (including a Newton-Raphson procedure as the numerical solver) is simulated to generate synthetic time-series data. Next, a hybrid neural ODE based on the same model is constructed, where ventricular interaction is instead set to be governed by a neural network. We use a short range of the synthetic data (with various amounts of added measurement noise) to train the hybrid neural ODE model. Symbolic regression is used to convert the neural network into analytic expressions, resulting in a partially learned mechanistic model. This approach was able to recover parsimonious functions with good predictive capabilities and was robust to measurement noise.

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems.

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.