Three-dimensional OCT image sets of the endocardial surface of an isolated right ventricular free wall (RVFW) preparation from a New Zealand white rabbit were used in this study. The protocol was approved by the Institutional Animal Care and Use Committee at Washington University. The experimental procedures have been previously described.10
The RVFW was dissected, stretched, and pinned epicardial side down onto a silicon disk. The sample was placed in 3.7% formaldehyde for one day and 20% sucrose solution for an additional two days. This dehydration step improves the visibility of the fibers under OCT imaging.
A microscope-based OCT system11
was used to image volumes of the sample. The axial and lateral resolution of the system was approximately 10 µm (in air). The three data sets presented in this work vary in structural complexity . Each volume was 4.5 mm × 4.5 mm × 3.16 mm, corresponding to a pixel size of 11.25 µm × 11.25 µm × 4.86 µm. To calculate fiber orientation from 2-D OCT images, a modification of the intensity-based gradient algorithm described by Karlon et al.5
Fig. 1 3-D OCT data sets of the right ventricular free wall (RVFW). (a) 3-D OCT images of the RVFW, data sets (a1) RVFW1, (a2) RVFW2, and (a3) RVFW3. The arrow in A1 points to cross-sectional (en face) slices. (b) View of three en face slices in depth within (more ...)
Within en face OCT images , uneven sample surface topology (e.g., RVFW1) and shadows cast by trabeculations (e.g., RVFW2 and RVFW3) cause low spatial frequency changes in the background intensity. These artifacts introduce unwanted intensity gradients within the image. A 2-D second-order Butterworth high-pass filter was used under the assumption that the surface topology and shadowing artifacts have lower spatial frequency components compared to visible fiber structures. The high-pass filter was convolved with the en face OCT image to suppress variations in background intensity. The high-pass filtered en face OCT image was convolved with a Wiener filter for noise reduction.
Two-dimensional 3 × 3 Sobel filters were used to estimate local gradients in the image. Gx
are defined as the convolution of the horizontal and vertical Sobel filters with the 2-D en face
filtered OCT images. For each pixel, the magnitude of the gradient,
and the gradient direction, θ′ = atan(Gy
), was calculated.
Within a small local window of the image, W
, the dominant local direction of the gradient was computed by taking the maximum of the angular distribution function,
, a function of G
) and θ′(i
), as described by Karlon et al.5
The angular distribution function is a fit of a radial normal distribution to the distribution of angles within the local window.
The directions of the cardiac fibers were assigned as perpendicular to the direction of the dominant local gradients. Two criteria were used to reject invalid fiber orientation assignments. First, the algorithm identified windows with no tissue present by using a threshold on the average pixel intensity within the window. Second, to measure the confidence in fiber orientation measurements produced by the automated algorithm, a D’Agostino-Pearson κ2 (normality) test was conducted on the angular distribution of calculated orientations within each window. High values of κ2 indicate that the angular distribution function is not a normal distribution, and therefore, the confidence in the fiber orientation assignment in that window is low. Threshold values for κ2 (0.02) and average intensity values within a window (80, 1.5 times the noise floor) were selected. The automated algorithm was implemented using the software package matlab 184.108.40.2067 R2006b (© 1984–2006, The Mathworks, Inc.).
In order to validate the method quantitatively, an investigator blinded to the results of the automated algorithm manually measured fiber orientation angles on the en face OCT images analyzed by the automated algorithm. En face images were analyzed in increments of 25 µm in depth for all three data sets. Results from the automated algorithm were compared to manual measurements by analyzing the mean and standard deviation of fiber orientation assignments for each depth and orientation as a function of depth. This comparison was made using several window sizes, but the mean of the absolute difference was the lowest for a window size of 563 µm × 563 µm (almost four myocytes in length, assuming that an adult cardiac myocyte has an average length of 150 µm). Results using a 563 µm × 563 µm window were resampled to obtain 256 vectors per image. Under these settings, the 2-D fiber orientation algorithm runs in less than 7 s per image using a Workstation with an Intel processor running at 2.66 GHz and 2-GB SDRAM memory, 533 MHz with Windows.