# Relationship between the amplitudes of cerebral blood flow velocity and intracranial pressure using linear and non-linear approach

## TL;DR

This study explores how brain blood flow and pressure interact in traumatic brain injury patients using linear and nonlinear methods during a breathing test.

## Contribution

The study introduces RAMP and JSA indices to better understand vascular-parenchymal interactions in TBI.

## Key findings

- RAMP index was significantly higher at baseline compared to during hypocapnia.
- JSAsym frequency decreased during hypocapnia compared to baseline.
- Grouped-averaged AmpCBFV and AMP showed no significant correlation at baseline or during hypocapnia.

## Abstract

Intracranial pressure (ICP), cerebral blood flow and volume are affected by craniospinal elasticity and cerebrospinal fluid dynamics, interacting in complex, nonlinear ways. Traumatic brain injury (TBI) may significantly alter this relationship. This retrospective study investigated the relationship between the vascular and parenchymal intracranial compartments by analysing two amplitudes: cerebral blood flow velocity (AmpCBFV) and ICP (AMP) during hypocapnia manoeuvre in TBI patients. Twenty-nine TBI patients hospitalised at Addenbrooke’s Hospital, whose ICP and CBFV were monitored during mild hypocapnia, were included. A linear metric of the relationship was defined as a moving-window correlation (R) between AmpCBFV and AMP, named RAMP. Nonlinear metrics were based on the Joint Symbolical Analysis (JSA) algorithm, which transforms AmpCBFV and AMP into sequences of symbols (‘words’) using a binary scheme with word lengths of three. The mean AmpCBFV and AMP were not significantly correlated at baseline (r = − 0.10) or during hypocapnia (r = − 0.19). However, the RAMP index was significantly higher at baseline (0.64 ± 0.04) compared to hypocapnia (0.57 ± 0.04, p = 0.035). The relative frequency of symmetrical word types (JSAsym) describing the AmpCBFV–AMP interaction decreased during hypocapnia (0.35 ± 0.30) compared to baseline (0.44 ± 0.030; p = 0.004). Our results indicate that while the grouped-averaged AmpCBFV and AMP were not significantly correlated, either at baseline or during hypocapnia, significant changes were observed when using RAMP and JSA indices. Further validation of these new parameters, which reflect the association between the vascular and parenchymal intracranial compartments, is needed in a larger cohort.