## 4 Discussion  
The average cumulative segmentation algorithm had a sensitivity of 0.997 \(\pm\) 0.008 and a specificity of 0.9998 \(\pm\) 0.001. This high level of accuracy demonstrates the benefit of using a manual input to initialize automatic segmentation. Using manual segmentation alone would be too time intensive to be used in a practical healthcare setting, while utilizing only an automatic segmentation approach would not provide sufficient segmentation accuracy to delineate and quantify the diameters of the smaller arteriolar (<10 micrometers) cerebral blood vessels. The proposed segmentation algorithm combines the accuracy of manual segmentation with the benefit of automated and less time intensive approach and provides segmentation with a high degree of accuracy while also minimizing the required time and effort. Almost all the state-of-the-art algorithms that were used to detect blood vessels were only suitable for healthy blood vessels as they usually assume the vascular linearity and/or circular cross-sections which is not the case in pathological vessels [23]. The proposed segmentation algorithm, however, did not impose any assumptions on blood vessels, and it can delineate both healthy and pathological vessels efficiently. However, the focus in this study was the investigation of the correlation between hypertension development and changes in cerebral vascular diameter. So, the change in a vessel diameter was the only studied diagnostic factor so far. In future work, we would introduce more investigation on more diagnostic factors which in turn would help in diagnosing various vascular-based disease such as strokes. The high degree of sensitivity and specificity of our approach in accurately delineating blood vessels from surrounding brain tissue enables the quantification of cerebrovascular changes. The PDFs indicate the total blood vessel diameter change in time from day 0 and day 700. Below the circle of Willis, there is a statistical correlation between PDFs and  
Figure 6: Applying a 3D growing algorithm to the volume of binary segmented images allows for visualization of the automatically segmented MRA data. Day 0 of patient C (top left). Day 700 of patient C (top right). Day 0 of patient D (bottom left). Day 700 of patient D (bottom right). The correlation between the CDF and MAP was not found in these patients. Some apparent differences between vascular constructions in areas below the circle of Willis are highlighted. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Patient** & \multicolumn{2}{c}{**Day 0**} & \multicolumn{2}{c}{**Day 700**} \\ \hline  & **Systolic BP** & **Diastolic BP** & **MAP** & **Systolic BP** & **Diastolic BP** & **MAP** \\ \hline A & 120 & 80.5 & 93.7 & 103.5 & 66.5 & 78.8 \\ B & 130.5 & 83 & 98.8 & 143.5 & 94 & 110.5 \\ C & 118 & 80.5 & 93 & 105.3 & 69 & 81.1 \\ D & 114 & 84.5 & 94.3 & 120 & 88 & 98.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: BP measurements of patients A, B, C, and D.  
systemic BP (\(p\)-value = 0.0007), demonstrating that increased MAP is related to decreased average vessel diameter and PDF. The BP and MAP measurements correlate well with most patients' non-invasive mean PDF diameter measurements below the circle of Willis. Since cerebral changes have been hypothesized to precede systemic hypertension [9; 10; 26], our methodology may present a tool for potentially initiating early treatment to prevent or optimize management of systemic HBP in conjunction with other approaches including cognitive testing. This finding is important as it suggests that the remodeling of vessels due to increasing blood pressure occurs prior to the onset of diagnosed essential hypertension. Individuals in the current study were explicitly selected to have pre-hypertensive values of blood pressure. Of equal importance, the methodology can determine the relationship of cerebrovascular remodeling to cortical small vessel disease and lacunar lesions known to occur with advanced hypertensive disease and with implications for stroke and dementia [27; 28].