Title : Resolution of the CSF-SBP phase paradox: A mathematical framework for cerebral pressure dynamics
Abstract:
Objective: To resolve the clinical paradox where CSF pressure peaks before systolic blood pressure yet both drop to zero simultaneously during cardiac arrest.
Backgroud: CSF pressure demonstrates 50-100ms phase lead over systolic blood pressure during normal cardiac cycles, yet both pressures zero simultaneously during cardiac arrest. This paradox lacks theoretical explanation. Previous models invoking temporal delays explain phase relationships but not simultaneous collapse, while direct coupling models explain zeroing but not phase lead.
Design/Methods: We developed a geometric energy conservation framework incorporating the Monro-Kellie doctrine. Through energy partitioning among arterial, transverse, and CSF components with normalization constraints, we derived pressure relationships. Geometric factors K = (PT/PL)(VT /Vc) and k = (VL/Vc)[1 + mk(Pt/PL)] emerge from fundamental conservation principles.
Results: The linear relationship Pc = PL(K−k) resolves both paradoxical observations. Time derivatives show dPc/dt = (dPL/dt)(K − k) + PL[d(K − k)/dt], where the second term creates phase lead through geometric factor evolution. During cardiac arrest, as PL → 0, then Pc → 0 simultaneously, explaining instantaneous coupling. The framework predicts measurable coupling constants and compliance-related changes.
Conclusion: This geometric energy conservation framework provides the first unified resolution of the CSF-SBP phase paradox. The linear coupling relationship explains both phase lead and simultaneous zeroing through geometric factors rather than temporal delays. Clinical applications include non-invasive ICP estimation and personalized pressure management based on individual coupling constants.
