Aims: This paper discusses three-dimensional hemodynamic control problems (left atrial pressure, cardiac output, and mean blood pressure), which is a major challenge in treating heart failure via drug therapy. We analyze the effectiveness and challenges of one of the nonlinear control methods called input-output linearization for this control challenge.
Methods: In modeling, first, the output functions of three-dimensional hemodynamics were analytically derived as the nonlinear functions of four cardiovascular parameters: vascular resistance, cardiac contractility, heart rate, and stressed blood volume. Next, a drug library was introduced to model the pharmacological effects against these four variables. Assuming multiple drug infusion as the system inputs, these four cardiovascular parameters as the system state, and hemodynamics as system outputs, the system structure was mathematically formulated. In the control design, a nonlinear control method based on differential geometry called input-output linearization was applied to linearize this hemodynamic system. This transformed the original system into a new system representation in which the control inputs can be designed independently for each output function, thanks to decoupling the inter-dependency. For evaluation, the performance of the hemodynamic controller was evaluated in simulation.
Results: While some simulations resulted in desirable controlled responses, others showed control failures depending on the initial conditions and control objectives. It was suggested that this was due to the singularities that exist in the nonlinear coordinate transformation when input-output linearization is applied. Moreover, considering drug input can not be negative, the input constraint is suggested to be a theoretical challenge in this design method.
Conclusion: We found that input-output linearization is useful in adjusting the hemodynamic response independently. However, theoretical issues were also highlighted, such as the problem of singularities due to the linear dependent relationship among output functions.