Modeling the effect of tilting, passive leg exercise, and functional electrical stimulation on the human cardiovascular system

Abstract Long periods of bed rest negatively affect the human body organs, notably the cardiovascular system. To avert these negative effects and promote functional recovery in patients dealing with prolonged bed rest, the goal is to mobilize them as early as possible while controlling and stabilizing their cardiovascular system. A robotic tilt table allows early mobilization by modulating body inclination, automated passive leg exercise, and the intensity of functional electrical stimulation applied to leg muscles (inputs). These inputs are used to control the cardiovascular variables heart rate (HR), and systolic and diastolic blood pressures (sBP, dBP) (outputs). To enhance the design of the closed-loop cardiovascular biofeedback controller, we investigated a subject-specific multi-input multi-output (MIMO) black-box model describing the relationship between the inputs and outputs. For identification of the linear part of the system, two popular linear model structures—the autoregressive model with exogenous input and the output error model—are examined and compared. The estimation algorithm is tested in simulation and then used in four study protocols with ten healthy participants to estimate transfer functions of HR, sBP and dBP to the inputs. The results show that only the HR transfer functions to inclination input can explain the variance in the data to a reasonable extent (on average 69.8%). As in the other input types, the responses are nonlinear; the models are either not reliable or explain only a negligible amount of the observed variance. Analysis of both, the nonlinearities and the occasionally occurring zero-crossings, is necessary before designing an appropriate MIMO controller for mobilization of bedridden patients.