Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Nonlinear Analysis

Objective: As an extension to our study comparing a putative compartmental and data-based model of linear dynamic cerebral autoregulation (CA) and CO₂-vasomotor reactivity (VR), we study the CA-VR process in a nonlinear context. Methods: We use the concept of principal dynamic modes (PDM) in order to obtain a compact and more easily interpretable input-output model. This in silico study permits the use of input data with a dynamic range large enough to simulate the classic homeostatic CA and VR curves using a putative structural model of the regulatory control of the cerebral circulation. The PDM model obtained using theoretical and experimental data are compared. Results: It was found that the PDM model was able to reflect accurately both the simulated static CA and VR curves in the associated nonlinear functions (ANFs). Similar to experimental observations, the PDM model essentially separates the pressure-flow relationship into a linear component with fast dynamics and nonlinear components with slow dynamics. In addition, we found good qualitative agreement between the PDMs representing the dynamic theoretical and experimental CO₂-flow relationship. Conclusion: Under the modeling assumption and in light of other experimental findings, we hypothesize that PDMs obtained from experimental data correspond with passive fluid dynamical and active regulatory mechanisms. Significance: Both hypothesis-based and data-based modeling approaches can be combined to offer some insight into the physiological basis of PDM model obtained from human experimental data. The PDM modeling approach potentially offers a practical way to quantify the status of specific regulatory mechanisms in the CA-VR process.