# Predicting the Aqueductal Cerebrospinal Fluid Pulse: A Statistical Approach
## 3 Results
### Data Analysis Results  
The results of the correlation analysis, which are presented in Table 3, reveal a strong negative correlation (mean (SD) r = \(-\)0.837 (0.126)) between the arterial and cCSF flow rates over the CC. Conversely; a strong positive correlation (mean (SD) r = 0.763 (0.266)) was observed between the venous and aCSF flows. Moderate correlations were also found between the venous and cCSF (mean (SD) r = 0.621 (0.178)), and venous and arterial (mean (SD) r = \(-\)0.601 (0.293)) flow rates, while the remaining correlations were weaker.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Signal**} & **Mean Flow** & **Median Flow** & **Caudal Peak** & **Cranial Peak** & **Pulsatility Index** \\  & **Rate (mL/s)** & **Rate (mL/s)** & **(mL/s)** & **(mL/s)** & **Mean (SD)** \\  & **Mean (SD)** & **Mean (SD)** & **Mean (SD)** & **Mean (SD)** & **Mean (SD)** \\ \hline Arterial flow rate & 12.34 (2.06) & 11.31 (2.01) & 8.36 (1.55) & 19.58 (4.51) & 0.91 (0.22) \\ Venous flow rate & \(-\)12.33 (2.02) & \(-\)12.26 (1.98) & \(-\)15.71 (2.86) & \(-\)8.89 (2.25) & 0.56 (0.23) \\ cCSF flow rate & 0.08 (0.10) & 0.59 (0.45) & \(-\)2.70 (1.05) & 1.72 (0.58) & 3.85 (129.86) \\ aCSF flow rate & 0.00 (\(>\)0.01) & 0.00 (0.01) & \(-\)0.10 (0.06) & 0.09 (0.05) & 31.28 (86.47) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean, minimum and maximum flow rates (with the computed pulsatility indices) for the cervical arterial, venous and CSF flows, together with aqueductal CSF flow, aggregated for all subjects.  
Figure 3: Ensemble mean arterial, venous, cervical CSF and aqueductal CSF signals for all subjects aggregated together. Error bars represent one standard deviation. (NB. The venous signal has been inverted for comparison purposes.).  
Multiple linear regression analysis (Table 4) revealed that it was possible with a high degree of accuracy (mean (SD) adjusted r\({}^{2}\) = 0.794 (0.184)) to predict the aCSF flow rate signal using the arterial, venous and cCSF signals as predictors (p \(<\) 0.001 for all models except that for subject 5031 which was p = 0.004). Partial adjusted r\({}^{2}\) values were: arterial (mean r\({}^{2}\) = 0.342 (SD = 0.278)); venous (mean r\({}^{2}\) = 0.641 (SD = 0.260)); and cCSF (mean r\({}^{2}\) = 0.408 (SD = 0.264)). However, no correlation was observed between AVD values and the model adjusted r\({}^{2}\) values (r = -0.041; p = 0.893). No significant difference (p = 0.658) was observed between the adjusted r\({}^{2}\) values for the male (mean (SD) adjusted r\({}^{2}\) = 0.830 (0.165)) and female (mean (SD) adjusted r\({}^{2}\) = 0.778 (0.198)) subjects.  
The relative importance weights of the aCSF signal predictor variables are presented in Table 4. These reveal that the venous flow rate was the strongest predictor (F = 7.86 (df = 2 & 36), p = 0.001). Post-hoc t-tests subsequently revealed that the relative weight of the venous flow rate (48.886 \(\pm\) 20.415) was significantly higher compared to that of the arterial (20.721 \(\pm\) 22.027, p = 0.001) and cCSF signals (30.393 \(\pm\) 10.705, p = 0.030).