Analytical Representation of Four-dimensional Hemodynamics for Drug Therapy Simulation in Acute Heart Failure Treatment

Acute heart failure imperils multiple organs, including the heart. Elucidating the impact of drug therapies across this multidimensional hemodynamic system remains a challenge. This paper proposes a simulator that analyzes the impact of drug therapies on four dimensions of hemodynamics: left atrial pressure, cardiac output, mean arterial pressure, and myocardial oxygen consumption. To mathematically formulate hemodynamics, the analytical solutions of four-dimensional hemodynamics and the direction of its change are derived as functions of cardiovascular parameters: systemic vascular resistance, cardiac contractility, heart rate, and stressed blood volume. Furthermore, a drug library which represents the multi-dependency effect of drug therapies on cardiovascular parameters was identified in animal experiments. In evaluating the accuracy of our derived hemodynamic direction, the average angular error of predicted versus observed direction was 18.85[deg] after four different drug infusions for acute heart failure in animal experiments. Finally, the impact of drug therapies on four-dimensional hemodynamics was analyzed in three different simulation settings. One result showed that, even when drug therapies were simulated with simple rules according to the Forrester classification, the predicted direction of hemodynamic change matched the expected direction in more than 80% in 963 different AHF patient scenarios. Our developed simulator visualizes the impact of drug therapies on four-dimensional hemodynamics so intuitively that it can support clinicians' decision-making to protect multiple organs.