# Fractal Dimension and Retinal Pathology: A Meta-Analysis
## 3 Results
### Results of Studies Conducting Fractal Analysis on Retinal Images
Glaucoma and Age-related macular degeneration were not significantly associated with FD and an association between diabetic retinopathy and FD was ruled out after multivariate regression analysis [28]. For the studies that looked at myopia [28; 29; 30; 31; 32; 33], hypertension [27; 33; 34], glaucoma, and diabetes [34; 35; 36; 37; 38], all generally observed a mean decrease in fractal dimension relative to the control group or a decreasing trend with respect to increasing disease severity. In contrast, findings from the diabetic retinopathy studies were more mixed. Decreased retinal FD was found to be associated with presence of NPDR [39; 40] and PDR [40]. Retinal FD also showed a decreasing trend with respect to diabetic retinopathy severity ranging from mild NPDR to PDR [37; 38; 41; 42]. However, three studies found that greater retinal FD was associated with early retinopathy signs in young type 1 diabetic patients [43], incidence of referable diabetic retinopathy in urban Malay adults [44], and presence of proliferative diabetic retinopathy in type 2 diabetes [45]. For retinographies from the DRIVE database, no significant change in FD was reported for patients with mild NPDR for the entire retina although a significant difference was found for the macular region [46]. A cohort study [47] also reported no association found between retinal FD and incident diabetic retinopathy in young diabetes patients after a mean (SD) follow-up period of 2.9 (2.0) years. For the studies that examined less common retinal diseases, decreased FD was found for OCTA images of the superficial and deep retinal layers in patients with retinal occlusions [48], an increase in arteriolar/venular FDs was found in NAION patients [49], and FD decreases were found in the deep/superficial retinal plexuses in MacTel2 patients [50]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author (Year)** & **RVPs** & **Imaging Device** & **FD ROI** & **FD Calculation** & **Results** \\ \hline \multirow{4}{*}{[PERSON] et al. (2017)} & \multirow{4}{*}{FDt, vessel density} & \multicolumn{2}{c}{Optovue} & \multirow{4}{*}{Whole area permitted by 3 \(\times\) 3 mm macula scan} & \multirow{4}{*}{\
\begin{tabular}{c} Box-counting \\ method using \\ Fractalves \\ (TheMA, Besancon \\ Cedex, France). \\ \end{tabular} } & \multirow{4}{*}{
\begin{tabular}{c} Myopic eyes had \\ statistically \\ significantly lower \\ and DCP layers. \\ \end{tabular} } \\  & & & & \\ \cline{1-1}  & & & RVPs were calculated for & & \\ \cline{1-1}  & & & the macular and & Segmentation was & FD was found to \\ \cline{1-1}  & & & paramacular regions and & done manually & higher in the \\ \cline{1-1}  & & & also for the entire retina. & using NIH, Adobe & macular region for \\ \cline{1-1}  & & & The image was divided & Photoshop, and & normal patients as \\ \cline{1-1} [PERSON] et al. & \multirow{4}{*}{FDt, grid intersection} & 60\({}^{\circ}\) fundus & into nine square, equal & computerized & opposed to NPDR \\ \cline{1-1}  & & fluorescein & zones with the central & processing. RVPs & patients. FD \\ \cline{1-1}  & & angiography & square denoted the & calculation was & difference in \\ \cline{1-1}  & & & macular region, and the & done using a & paramacular \\ \cline{1-1}  & & & comparacular region being & custom-written & \\ \cline{1-1}  & & & comprised of the five zones & computer & regions were not \\ \cline{1-1}  & & & above, below, and to the & program. & strongly \\ \cline{1-1}  & & & right of the macular region. & & significant. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Outcomes of fractal analysis for retinal pathology. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author (Year)** & **RVPs** & **Imaging Device** & **FD ROI** & **FD Calculation** & **Results** \\ \hline \multirow{6}{*}{ \begin{tabular}{c} (2014) \\ \end{tabular}  } & \multirow{6}{*}{FDt} & \multirow{6}{*}{ \begin{tabular}{c} 45\({}^{\circ}\) digital retinal \\ camera \\ (AFC-230/210) \\ \end{tabular}  } & \multirow{6}{*}{