**Purpose.**:
Discovery and description of heritable optic nerve head (ONH) phenotypes have been haphazard. In this preliminary study, the authors test the hypothesis that inheritable phenotypes can be discovered and quantified computationally by estimating three-dimensional ONH shape parameters from stereo color photographs from the Twins Eye Study in Tasmania and determining how much of the variability in ONH shape is accounted for by genetic influence.

**Methods.**:
Three-dimensional ONH shape was estimated by an automated algorithm from stereoscopic optic disc color photographs of a random sample of 172 subjects (344 eyes, 45 pairs of monozygotic [MZ] and 41 dizygotic [DZ] twins). Shape resemblances between eyes were quantified with a distance metric. The heritability of the shape resemblance was determined both through the distribution of the discongruence indices and through structural equation modeling techniques (ACE model).

**Results.**:
Significantly different discongruence indices were found for MZ (1.0286; 95% CI, 0.9872–1.0701) and DZ twins (1.4218; 95% CI, 1.2631–1.5804); larger indices for DZ twins indicated that variability was substantially determined by genetic factors. The standardized variances of the A(dditive genetic), C(ommon environmental), and (nonshared) E(nvironmental) components were 0.80, 2.00 × 10^{−15} and 0.20, respectively, for all OD, and 0.79, 3.24 × 10^{−14}, and 0.21 for all OS.

**Conclusions.**:
This preliminary study shows that quantitative phenotyping of the ONH shape from color images leads to phenotypes that can be measured and are largely under genetic control. The association of these inherited phenotypes with genotypes deserves confirmation and further study.

^{ 1,2 }These ONH phenotypes were determined qualitatively in the form of an intuitive Gestalt by human experts and did not allow measurement and quantification.

^{ 3 }Several genes, including

*MYOC*, encoding myocilin,

^{ 4,5 }

*OPTN*, encoding optineurin,

^{ 6 }and the primary congenital glaucoma gene cytochrome P450 1B1 (

*CYP1B1*),

^{ 7 }have been discovered that play a role in the risk for and progression of this disease.

^{ 4,8 }However, the risks attributed to the genes discovered thus far are moderate to small; therefore, the search for additional genes is ongoing. Abnormalities in the shape of the ONH play an essential role in the diagnosis and management of glaucoma. Because the ONH varies substantially between subjects without glaucoma, separating normal variation from glaucomatous change is a challenge.

^{ 9 }

^{ 10 }Phenotypic variability may be attributed to genetic and environmental control using structural equation modeling, also known as the ACE model, for additive genetic effects (A), shared environmental effects (C), and nonshared environmental effects (E).

^{ 11 }Maximum likelihood estimates of these effects determine what proportion of variance in the trait is heritable compared with that attributable to environmental elements.

^{ 12 }

^{ 13 }OCT-based ONH phenotypes would thus be the obvious choice for determining genetic and environmental factors that determine ONH shape. A single horizontal scan of anterior segment optical coherence tomography was collected in the Guangzhou Twin Eye Study to estimate the heritability of the iridotrabecular angle width.

^{ 14 }Unfortunately, it may take years before a sufficient number of three-dimensional OCT data can be obtained from twins to perform twin studies. However, a plethora of stereo color images of the optic disc in twin studies has been collected in the past.

^{ 15 }If we are able to quantify ONH shape from these stereo images, classic twin studies of ONH shape become achievable.

^{ 16 }Stereoscopic optic disc photographs encode the three-dimensional shape of the ONH as disparities between pixel correspondences.

^{ 17 }Shape descriptions using these disparities provide comprehensive information of the underlying structure compared with two-dimensional measurements. Subtle ONH properties, such as neuroretinal rim slope and curvature of the retinal nerve fiber layer (RNFL), which may have significance in assessment of the phenotype, cannot be adequately described by two-dimensional parameters. Therefore, three-dimensional measures of the topography are essential to improve the discriminatory power of computerized ONH analysis.

^{ 15 }and whether some of the shape parameters are under genetic control and, if so, how much of the variability is accounted for by genetic influence.

^{ 2 }The relevant ethics committees of the University of Tasmania and the Royal Victorian Eye and Ear Hospital approved the study, and the protocol adhered to the tenets of the Declaration of Helsinki. The Institutional Review Board of the University of Iowa approved the analysis of the deidentified images, and a waiver of consent was granted. Each subject or his or her respective legal guardian provided written informed consent before participation.

^{ 15 }Zygosity of all twin pairs was confirmed by DNA analysis with polymorphic microsatellite markers. According to the models developed by Nyholt,

^{ 18 }the genotyping protocol falsely classifies a DZ pair as MZ in 1 of 4907 cases.

^{ 2 }

^{ 19 }

^{ 16 }The horizontal disparities between these correspondences form a disparity map relative to the reference image, which contains shape information of the ONH.

^{ 20 }

^{ 21 }Both the metrics of the pixel features and the metrics for the matching correspondences are described in scale space. Pixel features are extracted by encoding the intensity of the reference pixel and its context (i.e., the intensity variations relative to its surroundings and information collected from its neighborhood), using filter banks.

^{ 19,22,23 }The result is a multiscale pixel feature vector.

^{ 24,25 }The representation of the three-dimensional structure of the ONH as a disparity map made objective quantification of its three-dimensional shape possible.

*N*dimensional feature space.

^{ 26 }Disparity maps were first normalized to have zero mean and unit variance, and the projection was then chosen to maximize the “scatter” of all disparity maps in the reduced feature space, represented as a linear transformation matrix with orthonormal columns. These columns, which we call eigen-disparity maps, are the set of eigenvectors corresponding to the

*N*largest eigenvalues of the covariance matrix of all disparity maps. The eigen-disparity maps can also be seen as the primary features or characteristics of the ONH map, expressing such features as, for example, temporal versus nasal prominence of the ONH. New

*N*-dimensional feature vectors were formed accordingly by projection of each disparity map through the transformation matrix.

*N*components. The next step was to determine whether there was a discrepancy in the shape between eyes and, if so, whether this discrepancy was larger, on average, between DZ than between MZ twins.

*d*(

*I*

_{1},

*I*

_{2}), to provide a quantitative assessment of the resemblance of two disparity maps,

*I*

_{1}and

*I*

_{2}. Given the distance of the ONH shape between any two disparity maps

*d*(

*I*

_{1},

*I*

_{2}), a discrepancy index between a pair of twins is then calculated to indicate their resemblance in terms of ONH shape.

*A*and

*B*. ONH disparity maps estimated from OS and OD stereoscopic photographs of both subjects are denoted as

*A*

_{OS},

*A*

_{OD}and

*B*

_{OS},

*B*

_{OD}, respectively. The discrepancy index between the twin pair

*D*(

*A*,

*B*) is then defined as the ratio of the average inter-twin distances to the intra-twin distances of the four involved disparity maps: Inter-twin distances refer to the ONH shape differences between eyes of different subjects, and intra-twin distances refer to the differences between both eyes of the same subject. Thus, the phenotype of the eyes of two subjects with shared genetic influences is compared with the eyes of the same subject with shared genetic and environmental influences. If the shape of the ONH is primarily genetically determined and eye laterality is relatively less important in ONH embryogenesis, the inter-twin distances on the numerator should not be larger than the intra-twin distances on the denominator in cases of MZ twins because they share 100% of their genes. Any dissimilarity between the members of a MZ twin pair provides evidence for nonshared environmental influences. DZ twins share only 50% of their genes but are usually more similar than expected from this genetic basis because of shared environmental factors.

^{ 27 }On the other hand, if we take account of the measurement error and the existence of nonshared environmental factors, both MZ and DZ correlations may have the tendency to decrease proportionally from their population values.

^{ 12 }Thus, if ONH shape is at least partially under genetic influence, MZ twins are expected to have a discrepancy index close to 1, with a narrow distribution, whereas DZ twins are expected to have a discrepancy index larger than 1 with a wider distribution.

^{ 11 }SEM has the ability to construct these latent variables by explicitly capturing measurement error in the model and allowing the structural relations between latent variables to be accurately estimated.

^{ 28 }

^{ 27 }Environmental effects are assumed to be independent of a person's genotype. The correlations reflecting the similarity of MZ and DZ twins were calculated and expressed in terms of the A, C, and E components of the model.

^{ 12 }We used the OpenMx package for R language,

^{ 29 }which is widely used to maximize the likelihood estimates of components over the entire sample that best reproduce the observed variance-covariance matrices for the MZ and DZ twins.

^{ 27 }In practice, positive correlations for MZ and DZ twins are predicted by the ACE model. Specifically, the DZ correlation is expected to be half the MZ correlation if it fits a pure AE model without any shared environmental influences (C) and to be the same if it fits a pure CE model without any additive genetic influences (A).

^{ 12 }

^{ 30 }

^{ 16 }and were analyzed, estimating the ONH shape of both eyes from 172 subjects (Fig. 1).

*N*= 25) eigen-disparity maps were chosen (Fig. 2) using appearance-based feature selection

^{ 26 }to summarize the statistical properties of the structure in the test population, which accounted for 86.66% of its ONH shape variation.

^{ 26 }The first eigen-disparity map represented the average shape in the entire dataset, and, as expected, variance explained dropped off rapidly after the 25th eigen-disparity map. Figure 3 is an attempt to interpret the morphology of the eigen-disparity maps by which vertical and horizontal tilts of the optic disc seem to be visible in the second and third eigen-disparity maps (Fig. 2) and temporal and nasal components in the fourth map (Fig. 3 top right), whereas the fifth eigen disparity map seemed to show the size variation of cupping (Fig. 3, bottom left).

^{−15}, and 0.20, respectively, for all OD and were 0.79, 3.24 × 10

^{−14}and 0.21 for all OS. The full ACE model suggested that a substantial portion of the variation in ONH shape was caused by genetic effects (A), with minor nonshared environmental effects (E) and shared environmental effects (C) negligible. When the C component was removed from the model, the resultant, more restricted AE model explained almost the entire observed variance-covariance for MZ and DZ twins.

^{ 2 }