# Predicting the Aqueductal Cerebrospinal Fluid Pulse: A Statistical Approach
## 4 Discussion
Chief amongst these is the presence of compliance in the system, as indicated by the presence of an AVD between the arterial blood entering the cranium and the venous blood leaving it (Table 1), which in healthy adults has been reported as 89 \(\pm\) 40 ms [29], very similar to the value of 87.7 \(\pm\) 78.8 ms observed in our study (p = 0.97). Although intracranial compliance is not fully understood, it is thought that it is strongly influenced by compliance in the spinal column [34] and also by the characteristics of the cerebral venous drainage system [12; 35; 36; 37]. Although the cranium contains incompressible fluids and gels, it is not a closed system, because venous blood can freely exit the cranium via the IJVs and VVs--something that imparts a functional compliance to the whole system. However, if the venous drainage pathways become constricted, then blood will tend to accumulate in the cerebral veins [17] causing the brain parenchyma to become stiffer [2] and intracranial compliance to decrease. Given also that constricted IJVs have been associated with increased aCSF pulsatility [2], it is perhaps not surprising that the variable importance analysis (Table 4) found the cervical venous flow rate signal to be the best predictor of the aCSF pulse. As such, this supports the findings of [PERSON] et al. [20] who observed that the motion of the aCSF pulse was strongly correlated with accumulation of venous blood in the cranium. It also reinforces the opinion [12; 38] that the cerebral veins play an important role in the regulation of the dynamic intracranial equilibrium. While most of the subjects in our study exhibited similar characteristics with regard to the performance of the linear model, it is noticeable that for a couple of individuals (subjects 5010 and 5031) the explained variance (i.e., the adjusted \(r^{2}\) value) was much lower than the median adjusted \(r^{2}\) value for the whole study cohort. For example, with subject 5031 the GLM was only able to explain 29.5% of the variance in the aCSF pulse, which was much less than that explained in the other subjects. If we compare subject 5031 (a 21 year old female--Figure 4) with a typical individual such as subject 5005 (a 38 year old male--Figure 2), for whom the model explained 88.4% of the variance, it can be seen that the arterial systolic peak was much greater in subject 5031 than in subject 5005. Also the venous flow rate profile in subject 5031 was atypical, with the venous diastolic 'peak' (i.e., the minimum value in the inverted venous signal shown in Figures 2G and 4A) occurring much earlier in the CC in subject 5031 compared with subject 5005. Furthermore, subject 5031 exhibited a somewhat atypical aCSF flow rate profile (Figure 4B) compared with subject 5005 (Figure 2H), who was more representative of the study cohort. Having said this, both subjects exhibited venous morphologies that appeared normal (Figure 1B,C; and Figure 4C). Noticeably however, the AVD for subject 5031 was 151.6 ms, while it was only 89.9 ms for subject 5005, indicating that intracranial compliance was much greater in the former compared with the latter. While the increase in intracranial compliance provides a plausible explanation for the poor prediction performance of the model in subject 5031, it should be noted that we found no correlation between AVD and model adjusted \(r^{2}\) value in the study cohort as a whole. Therefore, we cannot be certain that the observed model performance in subject 5031 is directly attributable to the increase in the AVD as other unobserved factors might be at work. Interestingly, while for most subjects the cervical venous flow rate signal was the best predictor of aCSF pulse, for subjects 5010 and 5031 (the two subjects with the lowest adjusted r\({}^{2}\) values) it was the cCSF signal that was the dominant predictor (Table 4). As such, this suggests that venous anomalies might have contributed to the lower r\({}^{2}\) values observed for these subjects.