Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory
A mathematical model of cerebral blood flow in the form of a dynamical system is studied.
The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem
and the potential and applicability of the nonlinear control theory techniques are analyzed in this
respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then,
the integrator backstepping approach combined with barrier Lyapunov functions is applied to
construct the control laws that recover the cerebral autoregulation performance of a healthy human.
Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow
autoregulation design. The conducted research should enrich our understanding of the mathematics
behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate
for impaired cerebral autoregulation, e.g., in preterm infants.