Assessment of blood flow parameters in a hybrid-digital model of the cardiovascular system applying recurrent neural networks

• New technique on recurrent neural network models to predict the conditions in hybrid-digital model of cardiovascular system. • Novel approach to combination of data from a laboratory model and neural network models to correlate the parameters of the cardiovascular system. • Presentation of possible application of the unique hybrid-digital model of cardiovascular system. End-systolic elastance of the left ventricle along with the waveforms of pressure and volumetric blood flow in particular sectors of the circulatory system are of importance in diagnosing various problems like dilated cardiomyopathy, left-ventricular hypertrophy, pulmonary hypertension, or ischemic heart disease. The objective of the paper is to broaden the spectrum of available methods to estimate those parameters since currently accessible techniques are often costly or troublesome. Six models have been developed − three of them estimate end-systolic elastance, two perform regression of volumetric blood flow, and one predicts blood pressure. Training datasets have been collected applying the unique hybrid-digital model. The input of the designed models consists of two or three different waveforms representing pressure and volumetric blood flow in particular areas, including heart ventricles, atria, and pulmonary vessels, in addition to the heart rate value. The basis of each model comprises bidirectional Long Short-Term Memory layers along with the dropout and feed-forward layers. Models that estimate end-systolic elastance achieved various accuracy. One of them performed exceptionally well since the absolute error did not exceed 0.169 m m H g c m 3 which is a negligibly small value. The root-mean-square error (RMSE) of the model predicting pressure waveform reached 0.165 m m H g in the worst case. Regression of the volumetric blood flow resulted in 6.062 c m 3 s worst-case RMSE for the model focusing on the pulmonary valve and 15.979 c m 3 s for pulmonary veins model. Computed results, especially those of the models estimating end-systolic elastance, indicate that it is possible to utilize neural networks to estimate those parameters with sufficient accuracy.