Algebraic formulas characterizing an alternative to Guyton's graphical analysis relevant for heart failure

Area of Science:

• Cardiovascular Physiology
• Mathematical Modeling
• Systems Biology

Background:

• Guyton's graphical analysis is a standard tool for understanding heart-vascular interactions.
• The classical Guyton model uses unphysiological assumptions for venous return and cannot predict pulmonary venous pressure.
• Pulmonary venous pressure is crucial for assessing heart failure and pulmonary edema risk.

Purpose of the Study:

• To develop an alternative to Guyton's analysis using a minimal closed-loop mathematical model.
• To address limitations of Guyton's model, including its venous return formula and inability to predict pulmonary venous pressure.
• To provide a more accurate and comprehensive model for cardiovascular equilibrium.

Main Methods:

• Developed a minimal closed-loop mathematical model of the cardiovascular system.
• Partitioned the cardiovascular system to isolate left ventricular function and aggregate blood volumes.
• Linearized end-diastolic pressure-volume relationships and treated arterial pressures as constants for algebraic solutions.

Main Results:

• Predicted variables associated with left ventricular failure morbidities.
• Derived an algebraic formula for left ventricular function based on ventricular properties.
• Derived an algebraic formula for systemic and pulmonary blood flow, accounting for redistribution between circulations.

Conclusions:

• The new model offers an improved alternative to Guyton's analysis for cardiovascular dynamics.
• The model accurately predicts key variables, including pulmonary venous pressure and left ventricular function.
• Despite necessary approximations, the model demonstrates minimal error and provides consistent predictions with reported values.