Statistical Deformation Model of the Optic Disk

Statistical Deformation Model of the Optic Disk

Bock, Rüdiger; Hornegger, Joachim; Michelson, Georg
Statistical deformation model of the optic disk
Investigative Ophthalmology & Visual Science (IOVS), 2010, 51, ARVO E-Abstract 1774 (Poster as PDF, ARVO E-Poster)

Background and Purpose

Quantitative glaucoma indices commonly rely on geometric parameters of the optic nerve head (ONH) such as disk area or cup volume.

However, the ONH is too complex structure to be accurately analyzed by geometric morphometry because of:

  • Sparse sampling of ONH
  • Lack of mathematically derived and biologically interpretable ONH descriptions [2]

We provide dense descriptions of the ONH variability in glaucomatous cases presented by tissue deformations.

Data

Erlangen Glaucoma Registry

  • Color fundus photographs (Kowa non-myd, FOV 22.5°, ONH centered)
  • Gold standard for glaucoma diagnosis is present
    • Diagnosis by an experienced ophthalmologist
    • Complete ophthalmological examination
      (ophthalmoscopy, visual field test, IOP, FDT, HRT II) 

Dataset characteristics

  • Mean age 55.4 ± 10.9 years
  • ONH area 2.2 ± 0.5 mm2 (Macro ONH not included)
  • 149 glaucoma cases Ig (FDT test time 67.4 ± 35.6 s)
  • 246 controls Ic

 

Methods

Fundus image preprocessing

Normalized optic nerve head images by eliminating disease independent variations such as

  • illumination inhomogeneities
  • ONH normalization
  • vessel structures.

Non rigid image registration

Characterization of inter subject ONH variability by dense deformation fields calculated between one reference image and image samples

  • Variational multilevel approach D(R(U), T) + s * S(U) →U min
  • Distance measure D: Sum of squared differences
  • Smoother S: Diffusion regularizer

 

Deformation based reference ONH

ONH reference image R that is characterized by the minimal average residual deformation over a sample set I is calculated by an iterative procedure:

  1. Reference R: Selection of initial estimate as the average of sample set I
  2. Calculation of deformation fields between samples and current reference
  3. Average all deformation fields to average deformation field
  4. Deformation of reference by average deformation field 

 

Statistical deformation model (SDM) of ONH

to provide a mathematically derived and biologically interpretable description of ONH variability in glaucomatous optic atrophy.

  • PCA model on deformations of
    • control samples Ic
    • glaucomatous cases Ig 
  • Supervised attribute selection on modes

→ Identification of modes most discriminating between controls and glaucomatous

 

Results and Discussion

Deformation based reference ONH

Comparison of pixel wise averaging (left) and deformation based averaging
(right) of ONH reflectance images of controls.

Pixel wise averages are too smooth to indentify local structures. Deformation based averaging clearly shows the naturally shaped appearance of the cup (central bright spot).

 

Statistical Deformation Model of ONH in glaucoma

First four PCA modes most discriminating between control and glaucoma
providing a mathematically derived and biologically interpretable description of ONH deformations: (first row) Simultaneous deformation of the cup and rim, (second row) local extension of the cup (red: high magnitude, blue: low magnitude of deformation vector).

  • Discriminative modes identify patterns of variation
  • Intuitive visualization of ONH deformation (Figure 4)
  • Mathematically derived influence of rim and cup

→ Biologically interpretable descriptions of ONH deformation in case of glaucoma

Conclusion

Statistical deformation modelling of ONH provides

  • intuitive representation of ONH variability
  • main modes of glaucomatous deformations
  • identification of abnormal deformations.


Deformation based morphometry of ONH shows a potential to be a future technique to gain novel insights into glaucomatous changes of the ONH.