Evaluation of Liver Fibrosis Using Texture Analysis on Combined-Contrast-Enhanced Magnetic Resonance Images at 3.0T

Purpose. To noninvasively assess liver fibrosis using combined-contrast-enhanced (CCE) magnetic resonance imaging (MRI) and texture analysis. Materials and Methods. In this IRB-approved, HIPAA-compliant prospective study, 46 adults with newly diagnosed HCV infection and recent liver biopsy underwent CCE liver MRI following intravenous administration of superparamagnetic iron oxides (ferumoxides) and gadolinium DTPA (gadopentetate dimeglumine). The image texture of the liver was quantified in regions-of-interest by calculating 165 texture features. Liver biopsy specimens were stained with Masson trichrome and assessed qualitatively (METAVIR fibrosis score) and quantitatively (% collagen stained area). Using L 1 regularization path algorithm, two texture-based multivariate linear models were constructed, one for quantitative and the other for quantitative histology prediction. The prediction performance of each model was assessed using receiver operating characteristics (ROC) and correlation analyses. Results. The texture-based predicted fibrosis score significantly correlated with qualitative (r = 0.698, P < 0.001) and quantitative (r = 0.757, P < 0.001) histology. The prediction model for qualitative histology had 0.814–0.976 areas under the curve (AUC), 0.659–1.000 sensitivity, 0.778–0.930 specificity, and 0.674–0.935 accuracy, depending on the binary classification threshold. The prediction model for quantitative histology had 0.742–0.950 AUC, 0.688–1.000 sensitivity, 0.679–0.857 specificity, and 0.696–0.848 accuracy, depending on the binary classification threshold. Conclusion. CCE MRI and texture analysis may permit noninvasive assessment of liver fibrosis.


Introduction
Image texture, defined as a "function of the spatial variation in pixel intensities" (1), is used in this study to detect the presence of liver fibrosis and predict its severity. On combined contrast enhanced (CCE) magnetic resonance (MR) images of the liver, image texture within regions of interest (ROIs) were objectively quantified using texture analysis. The five texture classes considered in this study were statistics of the pixel intensity histogram, Gaussian-mixture model (2), autocorrelation (3), gray-level co-occurrence matrices (4), and Voronoi polygons (5). This appendix discusses technical and computational details. The choice of these texture classes and their calculation methods was made in consideration for the expected mathematical and morphological properties of the liver fibrosis texture. Desired texture features for CCE images would characterize high intensity reticulations, low intensity nodules, and the contrast between these two areas. The texture features would be locally uniform, invariant under linear transformations of the intensity value, and invariant under certain spatial transformations of the ROI (e.g. translation, reflection, rotation). Based on these expectations, the following calculations were performed.

Image Normalization
Each source ROI image was normalized as follows. First, the rectangular ROI was rotated such that the rectangle's edges were parallel to Cartesian coordinate axes. Then, the rotated images were re-gridded and interpolated at 0.5mm pixel resolution. To correct for spatial drift in pixel intensity within the ROI, bi-linear trend was estimated and removed using 2D linear regression. The pixel intensity scale was corrected to the standardized range [0 1]. This normalization was necessary to ensure that the calculated texture features are comparable across different ROIs, acquisitions, and subjects.

Image Transformations
Each normalized, source ROI image was transformed as follows. Let F(i,j), the pixel intensity at i-th column and j-th row, be the standardized source ROI image. The gradient image G(i,j) was calculated as the magnitude of the gradient vector at each pixel location, G=|∇F|, where ∇ denotes the gradient operator. Similarly, the Laplacian image L(i,j) was calculated as L=∇ 2 F, where ∇ 2 is the "del" operator. The gradient and Laplacian images are also referred to "edge-enhanced" and "zero-crossing" images of the original ROI images. These have visually distinct (but related) patterns from the original image (Error! Reference source not found.) and thus may be helpful in characterize fibrosis textures.

Gaussian--Mixture Models
The intensity histogram was fitted to two distribution models, (1) single Gaussian and (2) a mixture of two Gaussians. The two-Gaussian model considers a histogram h(x) as a sum of two normal populations (lower and higher intensity populations), each with its own mean and variance h(x) = p L g L (x; µ L ,σ L ) + p H g H (x; µ H ,σ H ) where h(x) is the overall probability density function for intensity value x, g is the normal density function with mean µ and standard deviation (std) σ. The mixing proportion p indicates the relative abundance of the lower and higher intensity populations. For each histogram, the model parameters (p L , µ L , σ L and p H , µ H , σ H ) were estimated (T10-15), and the Mahalanobis distance (T16) between g L and g H , as well as Akaike information criterion (AIC) of the fit, were calculated using the Gaussian-Mixture Model (GMM) package in MATLAB statistical toolbox. The AIC for the single-Gaussian model fit was also calculated, and the goodness-of-fit of the two-vs. one-Gaussian models was compared by the ratio AIC 2 /AIC 1 (T17).

Autocorrelation
The 2-dimensional autocorrelation function of the ROI image was calculated within ±10mm spatial offsets in xand y-directions as: where N is the number of pixels in the ROI, and i' and j' are the offsets in the x-and y-directions. This range of offsets [-10mm, +10mm] was chosen under the assumption that the spatial structure of fibrosis has scales <10mm. On the calculated autocorrelation map, the iso-contour loci of value 1/e were fitted to an ellipse. The long-and short-axes length (T18, 19), average axes length (T20), and the long-short axis ratio (T21) were calculated to assess the spatial scale and orientation of the autocorrelation.

Voronoi Polygons
The vertices of Voronoi polygons were chosen at 2D local intensity minima of the ROI image. Using these vertices as seeds, a tessellation of Voronoi polygons were generated to fill the ROI using a MATLAB Voronoi algorithm. The average and the STD of number of edges (T42, 43), length of edges (T44, 45), seed density (T46, 47), and edge density (T48-49) were computed. The polygon's 0 th to 3 rd -degree inertial moments (T50-55) were also computed using a previously described algorithm (7).

Summary
For each ROI location, three ROI images were generated (F, G, and L). For each ROI image, 55 texture features were computed as detailed above. Thus, a total of 165 texture features were computed per ROI location. These texture features were averaged across five non-overlapping ROI locations within the subject's liver. The average 165 texture features of the individual subject served as the input variables for the multiple regression model described in the main text.