purpose. To describe the development of a technique that enhances spatial resolution of retinal thickness maps of the Stratus OCT (Carl Zeiss Meditec, Inc., Dublin, CA). A retinal thickness atlas (RT-atlas) template was calculated, and a macular coordinate system was established, to pursue this objective.

methods. The RT-atlas was developed from principal component analysis of retinal thickness analyzer (RTA) maps acquired from healthy volunteers. The Stratus OCT radial thickness measurements were registered on the RT-atlas, from which an improved macular thickness map was calculated. Thereafter, Stratus OCT circular scans were registered on the previously calculated map to enhance spatial resolution.

results. The developed technique was applied to Stratus OCT thickness data from healthy volunteers and from patients with diabetic retinopathy (DR) or age-related macular degeneration (AMD). Results showed that for normal, or close to normal, macular thickness maps from healthy volunteers and patients with DR, this technique can be an important aid in determining retinal thickness. Efforts are under way to improve the registration of retinal thickness data in patients with AMD.

conclusions. The developed technique enhances the evaluation of data acquired by the Stratus OCT, helping the detection of early retinal thickness abnormalities. Moreover, a normative database of retinal thickness measurements gained from this technique, as referenced to the macular coordinate system, can be created without errors induced by missed fixation and eye tilt.

^{ 1 }is a frequent manifestation of diabetic retinopathy (DR)

^{ 2 }and age-related macular degeneration (AMD) and is a leading cause of legal blindness in patients with type 2 diabetes.

^{ 3 }Monitoring and mapping

^{ 1 }changes in macular edema over time have provided valuable information to assist in making clinical healthcare decisions.

^{ 4 }

^{ 5 }

^{ 6 }Moreover, monitoring macular edema has been shown to be a useful practice in other circumstances, such as after cataract surgery.

^{ 7 }

^{ 5 }

^{ 8 }

^{ 9 }

^{ 10 }

^{ 11 }

^{ 12 }

^{ 13 }

^{ 14 }

^{ 15 }

^{ 16 }

^{ 17 }

^{ 18 }

^{ 19 }

^{ 20 }

^{ 21 }

^{ 22 }

*IOVS*2003;44:ARVO E-Abstract 4852; Bernardes et al.

*IOVS*2004;45:ARVO E-Abstract 2368). Our initial approach (2003) allowed the integration of any line scans in a user-assisted registration mode, making use of the fundus image provided by OCT. In 2004, a new procedure for the Stratus OCT allowed the integration of line and circle scans, using a data-driven registration by searching for the best match at scan intersections. Although both methods registered OCT scans among themselves, none took into account the location of the scans within the macular area. In 2005, Soerensen et al. (

*IOVS*2005;46:ARVO E-Abstract 2574) followed a different approach by merging two sets of radial line scans, therefore decreasing the step angle from 30° to 15°. To our knowledge, no attempt was made to correct for the location or relative location of the scans, which were thought to cross at the center of the fovea. Finally, in 2006, our group presented the final version of the method, which is described herein in detail (Baptista et al.,

*IOVS*2006;47:ARVO E-Abstract 5728).

^{ 14 }

^{ 15 }

^{ 17 }

^{2}each, with four areas side-by-side and the fifth overlapping the others and centering on the fovea.

^{ 23 }

^{ 24 }

^{ 25 }In this application, atlas construction followed a mixed model in which all individual RTA maps were initially registered into the atlas space. Added to this are 32 RTA maps that were individually registered thereafter to subpixel accuracy. From this second registration process, the final RT-atlas was established.

*a*,

*b*,

*c*, α, β,

*x*

_{0},

*y*

_{0}), the center of the paraboloid allows the translation to be computed (−

*x*

_{0}, −

*y*

_{0}), which brings the foveal depression of the respective RTA map into the origin of the atlas coordinate system in the

*x–y*plane.

*T*

_{ i }for each map such that

*r*

_{ i }is the retinal thickness map

*i*(

*i*= 1…

*K*),

*T*

_{ i }is the corresponding rigid transformation (as defined in equation 3 ),

*f*is a function specifying a bicubic interpolation spline to be sampled into a common grid spacing for the set of

*r̃*

_{ i }maps, and

*r̃*

_{ i }is the translated, rotated, and resampled retinal thickness map to be used to establish the RT-atlas.

*r̃*

_{ i }maps relative to the origin (0, 0). In this way, the built RT-atlas not only establishes a coordinate system, with the origin being the center of the fovea and the horizontal axis the line connecting both the center of the fovea and optic disc, but it also establishes that positive values in the

*x*-axis (the horizontal axis, connecting the fovea to the optic disc) correspond to the nasal macula (fovea-wise) and negative values correspond to the temporal macula (fovea-wise). Similarly, the

*y*-axis (the vertical axis) establishes (fovea-wise) negative and positive values as being in the superior and inferior macula, respectively.

*r̃*

_{ i }thickness maps, with each map considered to be an independent variable. Hence, for each coordinate in the space defined by transformation (equation 2) , a set of thickness data exists.

*K*largest spreads of the cluster, all being orthogonal among themselves and therefore being the data uncorrelated in this new set of axes.

^{ 26 }

*A*matrix composed of the eigenvectors of the covariance matrix (

*C*) of the original data. This covariance matrix is built by considering each retinal thickness map as an independent variable with the dimension

*K*×

*K*and is computed as

*x*

_{ m }and x̄

_{ m }are, respectively, the retinal thickness and the average retinal thickness of map

*m*, and

*E*{ · } is the expectation.

**v**and scalars λ, respectively, eigenvectors and eigenvalues, that is, the nontrivial solution of

*A*is given by

*A*line

*i*is the transpose of vector

**v**

_{ i }(eigenvector

*i*) to which corresponds the eigenvalue λ

_{ i }, being λ

_{1}≥ λ

_{2}≥… ≥ λ

_{ K }≥ 0.

*C*form an optimal orthogonal basis for the entire set of retinal thickness maps. Because the set of retinal thickness maps (i.e., multiple views of retinas of healthy volunteers), is correlated, the vector associated with the larger eigenvalue represents the entire set of information with the least expansion error compared with other orthogonal expansions.

_{1}≥ λ

_{2}≥… ≥ λ

_{ K }≥ 0).

*K*original retinal thickness maps in the established

*PCA*

_{1}, resorting to an optimization process, and repeated the procedure, with the PCA now applied to compute a new set of eigenvectors and eigenvalues. The final RT-atlas (Fig. 1)was computed as before, with all maps registered to subpixel accuracy to the initial atlas (

*PCA*

_{1}).

*PCA*

_{1}) and the final (RT-atlas) computed atlases, after their normalization to the range (0,1), is 3.2%. Five RTA maps were rejected due to the application of a validation criterion to the estimated parameters (

*x*,

*y*for translation and θ for rotation); that is, a map was rejected if any one of these was not within 1.75 standard deviations from its mean, which accounts for more than 90% of the cases for a normal distribution.

*x*- and

*y*-axes, that minimize the error (err) given by

*N*= 6 is the number of radial scans,

*O*

_{ i }is the low-pass filtered thickness measurements of OCT scan

*i*,

**R**is a thickness vector computed from the RT-atlas, and E{ · } is the expectation of the dot product between Ω (a vector of weights) and the squared differences between

*O*

_{ i }and

**R**on their overlapping areas.

_{1}= (

*x*,

*y*) such that

*x*| ≤ δ

_{1}and |

*y*| ≤ δ

_{1}.

_{1}by adding a new degree of freedom that allows the scan set to rotate as a whole, while simultaneously fine tuning its global position based on the previous optimization step. That is, we wanted to estimate Γ

_{2}= (

*x*,

*y*,θ) with (

*x*

_{0},

*y*

_{0}), the starting point, made equal to Γ̂

_{1}and θ

_{0}= 0. Hence, in this second optimization step, both the global position and global rotation adjusted themselves. For this step, the constraint |θ| ≤ δ

_{2}was added.

*DC*component (

*dc*) to accommodate an average difference between retinal thickness measurements, a gain factor (

*g*) to accommodate for different retinal thickness measurements, and a sampling rate (spacing) factor (

*sr*) to accommodate the difference in the sample spacing.

_{3}, = (

*dc*,

*g*,

*sr*) with (

*dc*

_{0},

*g*

_{0},

*sr*

_{0}) = (0,1,1) and Γ̂

_{2}, the result of the previous optimization step. Constraints also applied, with |

*dc*| ≤ δ

_{3}, δ

_{4}≤

*g*≤ δ

_{5}, and δ

_{6}≤

*sr*≤ δ

_{7}.

*i*= 1…

*N*). Therefore, we had to perform

*N*individual optimizations; that is, for each one, we had to estimate Γ

_{4}

^{ i }subject to |Δx

_{i}|≤δ

_{8}, |Δy

_{i}|≤δ

_{8}, and |Δθ

_{i}|≤δ

_{9}.

^{ 27 }with the OCT-registered data points as control points. This approach allows defining a surface passing through every control point while presenting the least bent surface for the entire space (minimum bending energy surface).

_{1}= (

*x*

_{c},

*y*

_{c}) to minimize the error given by

*M*is the number of circular scans,

*O*

_{ i }is the low-pass filtered thickness measurements of OCT scan

*i*,

**R**′ is a thickness vector computed from the OCT map built based on the Fast Macular Protocol scans (the TPS surface of the previous section), and

*E*{ · } is the expectation of the squared differences between

*O*

_{ i }and

**R**′ on their overlapping areas.

_{1}= (

*x*

_{c},

*y*

_{c}) as

_{c}|≤γ

_{1}, |y

_{c}|≤γ

_{1}, and

*M*= 5.

_{1}instead of using Γ̂

_{1}, comes from the fact that the Fast Macular and Fast RNFL Protocols are performed independently, which means two acquisitions at two instances in time, therefore eliminating values computed for the Fast Macular Protocol. The second step for the Fast RNFL Protocol is the same as the one performed for the Fast Macular Protocol (i.e., adding a rotation parameter to Ψ

_{1}to become Ψ

_{2}= (

*x*

_{c},

*y*

_{c}, θ

_{c}). Similarly, both the global position and global rotation are left to adjust themselves. For this step the constraint |θ

_{c}|≤γ

_{2}is added. Since we were registering OCT measurements on a map built on OCT measurements (i.e., similar data from the same instrumentation), there was no need to compute scaling parameters as before.

*M*individual optimizations, whereby we estimated

*i*= 1…

*M*, subject to

*x*- and

*y*-axes, consisting of estimating

_{11}≤

*s*

_{ xi }≤ γ

_{12}, γ

_{13}≤

*s*

_{ yi }≤ γ

_{14}, γ

_{15}≤

*s*

_{ hxi }, ≤ γ

_{16}, and γ

_{17}≤

*s*

_{ hyi }, ≤ γ

_{18}.

^{ 27 }(see the last paragraph of the OCT to RT-atlas Registration section in Methods), relatively high values would be found for AMD eye maps compared with those for healthy or DR eyes, resulting from the pathologic condition and not from registration and/or thickness measurement errors.

^{ 23 }

^{ 26 }to capture the major shape characteristics of the retinal thickness and therefore the ones that best represent the average population.

*x–y*plane represents the origin of the macular coordinate system (located at the center of the fovea) and the vertical axis is the resulting thickness from the first component of the PCA (i.e., the one corresponding to the higher eigenvalue and therefore having the largest spread of data. It should be noted that this surface represents the average shape of a healthy retina’s thickness and not the average thickness). It also clearly shows the asymmetric depression on the temporal side relative to the nasal side, which results from the careful registration of the RTA maps.

^{ 27 }surface passing through each of these data points is defined by a total of 13,443 parameters.

*n*= 12 eyes) before and after registration through the RT-atlas is 5.93 ± 1.60 and 4.17 ± 1.06 μm, respectively, which demonstrates the added value of the registration procedure. There was a 30% reduction of the mean and a 34% reduction of the SD.

*n*= 44). The average OCT thickness difference at scan intersection was computed, and the mean ± SD of these average values was reduced 28% ± 24% due to the registration procedure; these reductions were 35% ± 43% for the DR patient group and 26% ± 25% for the AMD patient group.

_{1}(Eq. 12)and ψ̂

_{2}were not performed, at the expense of having larger γ

_{3}and γ

_{4}degrees of freedom for the estimation of Ξ

_{1}

^{1}, Ξ

_{2}

^{1}, and Ξ

_{3}

^{1}. The application of the developed methodology to a 30-year-old healthy volunteer’s right eye can be seen in Figure 6 , which shows a map that achieved a score of good and a mean ± SD of 5.16 ± 4.23 μm. Although a high average was presented for the differences in retinal thickness at scan intersections, it should be noted that this map was calculated based on a different acquisition protocol (non–fast circular scans). Nevertheless, this value is within 1 SD of the average distribution in the healthy volunteers’ group.

**Figure 1.**

**Figure 1.**

Group | Poor | Insufficient | Sufficient | Good | Group Average |
---|---|---|---|---|---|

Healthy volunteers | 4.61/1.22 (n = 4) | 3.95/0.89 (n = 8) | 4.17/1.06 (n = 12) | ||

Diabetic retinopathy | 8.78/2.55 (n = 2) | 6.12/1.54 (n = 6) | 4.50/0.94 (n = 10) | 5.51/1.98 (n = 18) | |

Age-related macular degeneration (AMD) | 23.67/18.46 (n = 11) | 9.64/2.59 (n = 13) | 8.89/3.70 (n = 2) | 15.52/14.05 (n = 26) | |

Grade average | 23.67/18.46 (n = 11) | 9.52/2.60 (n = 15) | 6.08/2.45 (n = 12) | 4.25/0.96 (n = 18) |

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

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