A new mathematical model of dynamic cerebral autoregulation based on a flow dependent feedback mechanism

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Abstract
A new mathematical model representing dynamic cerebral autoregulation as a flow dependent feedback mechanism is presented. Two modelling parameters are introduced, λ, the rate of restoration, and τ, a time delay. Velocity profiles are found for a general arterial blood pressure, allowing the model to be applied to any experiment that uses changes in arterial blood pressure to assess dynamic cerebral autoregulation. Two such techniques, thigh cuffs and a lower body negative pressure box, which produce step changes and oscillatory variations in arterial blood pressure respectively, are investigated. Results derived using the mathematical model are compared with data from the two experiments. The comparisons yield similar estimates for λ and τ, suggesting these parameters are independent of the pressure change stimulus and depend only on the main features of the dynamic cerebral autoregulation process. The modelling also indicates that for imposed oscillatory variations in arterial blood pressure a small phase difference between pressure and velocity waveforms does not necessarily imply impaired autoregulation. It is shown that the ratio between the variation in maximum velocity and pressure variation can be used, along with the phase difference, to indicate the nature of the autoregulatory response.