### I. Introduction

### II. Methods

### 1. Image Acquisition

### 2. Preprocessing of FAG Images

### 3. Registration of Sequential FAG Images

### 4. Parametric Imaging

_{ROI}(t), of a fluorescein dye in the ROI was modeled using a convolution integral as follows: where RBF is the retinal blood flow-related parameter, C

_{AIF}(t) is the time-intensity curve of the arterial input function (AIF), and R(t) is the residue function which is the relative amount of the fluorescein dye in the ROI. Assuming an idealized case of perfusion where a unit area bolus of a fluorescein dye is instantaneously injected (i.e., R(0) = 1) and subsequently washed out by perfusion (i.e., R(∞) = 0), RBF can be quantified by solving Eq. (1) through deconvolution between C

_{AIF}(t) and C

_{ROI}(t).

_{AIF}(t) and C

_{ROI}(t) need to be fitted to the gamma-variate function. The parameters of the gamma-variate function can be estimated using the Levenberg-Marquardt method for nonlinear regression.

#### 1) Estimation of the arterial input function

_{AIF}(t), was modeled in the form of a gamma-variate function as follows: where t is the elapsed time after injection, K is a constant scale factor, AT is the arrival time of the contrast agent, I

_{Base}is the base intensity, and α and β are shape parameters that depend on the architecture of retinal vasculative and the blood flow, respectively. Here, I

_{Base}can be defined as the average pixel intensity in the ROI prior to the arrival of the contrast agent or a user defined value. As shown in Figure 3B, a representative set of time-intensity data points includes the effects due to the recirculation of the contrast agent.

^{2}was less than 0.01 and the value of χ

^{2}had not increased during the last 8 iterations.

#### 2) Quantification of RBF and MTT with TSVD

_{AIF}(t) and R(t) in Eq. (1) are constant over a short period of time Δt. Eq. (1) is reduced to where RBF

_{x}is the blood flow-related parameter at pixel x, C

_{x}(t) is the concentration of tracer in the venous output, R

_{x}(t) is the residue function, and t

_{i}and N denote the time of the i-th frame and the total number of frames of FAG, respectively. Assuming an idealized case of perfusion, a unit bolus of the contrast agent is injected as an arterial input at the beginning (i.e., R

_{x}(0) = 1), and it begins to leave the vascular network after a finite period (i.e., R drops to zero). If the product of RBF

_{x}and R

_{x}(t) can be estimated, RBF

_{x}can be obtained at t = 0. Here, C

_{x}(t) and C

_{AIF}(t) were estimated at N equally spaced time points t

_{1}, t

_{2}, …, t

_{N}with the time increment Δt. The convolution in Eq. (3) can then be formulated as a matrix equation: where

_{ij}= A

_{i-1,j-1}for all 1≤i, j≤N). Using the standard SVD technique, matrix A can be decomposed to where the orthogonal matrices U and V consist of the left and right singular vectors, i.e., U = (u

_{1}, …, u

_{N}) and V = (v

_{1}, …, v

_{N}). Here, S = diag(s

_{1}, …, s

_{N}) is an N×N diagonal matrix where the diagonal elements si are the corresponding nonnegative singular values of matrix A in non-increasing order, i.e., s

_{1}≥s

_{2}≥…≥s

_{N}≥0. With the inverse matrix A

^{-1}and Eq. (3), matrix b, and consequently R(t), can be calculated as That is, Eq. (6) is used to solve b, which contains the elements of (t). Estimates of RBF

_{x}can be obtained from the maximum of the scaled residue function (t) calculated from Eq. (6), and then MTT can be calculated from (t):

^{-1}, which represents a diagonal matrix that approximates the inverse matrix of S, can be expressed as for i = 0, 1, …, N. Here P

_{SVD}is the cut-off threshold, and it should be noted that the MTT values computed using this technique highly depend on the choice of P

_{SVD}; a large P

_{SVD}results in a smoother residue curve, with the sacrifice of less accurate (usually higher) MTT values, and a small P

_{SVD}will give more accurate MTT values, but the computed residue function will be less smooth. Usually, P

_{SVD}is set in the range of 5%-20% of the maximum singular value of S. In this paper, it is set at 10% of the maximum singular value of S.