A Mathematical Model for the Prediction of Fluid Responsiveness

Fluid therapy is commonly used to improve cardiac output in hemodynamically instable patients in the intensive care unit. However, to predict whether patients will benefit from this intervention (i.e. are volume responsive), is difficult. Dynamic indices, that rely on heart-lung interactions, have shown to be good predictors of fluid responsiveness under strict clinical conditions, but clinical use is still limited. This is due to the lack of understanding of the complex underlying physiology since multiple quantities are involved. We present a physiologically based mathematical model of the interaction between the respiratory and cardiovascular systems incorporating dynamic indices and fluid responsiveness. Our model is based on existing models of the cardiovascular system, its control, and the respiratory system during mechanical ventilation. The model of the cardiovascular system is expanded by including non-linear cardiac elastances to improve simulation of the Frank-Starling mechanism. An original model including five mechanisms for interaction between mechanical ventilation and the circulation is also presented. This model allows for the simulation of these complex relationships and may predict the effect of volume infusion in specific patients in the future. The presented model must be seen as a first step to a bedside clinical decision support system, and can be used as an educational model.