Tumor heterogeneity estimation for radiomics in cancer

Abstract

Radiomics is an emerging field of medical image analysis research where quantitative measurements are obtained from radiological images that can be utilized to predict patient outcomes and inform treatment decisions. Cancer patients routinely undergo radiological evaluations when images of various modalities including computed tomography, positron emission tomography, and magnetic resonance images are collected for diagnosis and for evaluation of disease progression. Tumor characteristics, often referred to as measures of tumor heterogeneity, can be computed using these clinical images and used as predictors of disease progression and patient survival. Several approaches for quantifying tumor heterogeneity have been proposed, including intensity histogram-based measures, shape and volume-based features, and texture analysis. Taking into account the topology of the tumors we propose a statistical framework for estimating tumor heterogeneity using clustering based on Markov random field theory. We model the voxel intensities using a Gaussian mixture model using a Gibbs prior to incorporate voxel neighborhood information. We propose a novel approach to choosing the number of mixture components. Subsequently, we show that the proposed procedure outperforms the existing approaches when predicting lung cancer survival.

Keywords: Markov random fields; cancer imaging; computed tomography; image segmentation; machine learning.

Figure 1:

Left column: 2D slices of CT scans of two patients. The tumor is enclosed in a red box. Middle column: histograms showing the intensities of tumor voxels. Right column: 3D surface renditions of respective tumors.

Figure 2:

Barplots showing the distribution of clinical variables. Histology provides a description of the tumor based on the abnormality of tumor cells observed using a microscope. Overall stage of cancer indicated the size of the tumor and its spread by a number I, II, IIIa, and IIIb, where a higher number implies larger and more spread cancer. T1, T2, T3, and T4 refer to the size and extent of the tumor. The higher the number the larger or more extensive the tumor. N1, N2, and N3 refer to the number and location of lymph nodes that contain cancer (the higher the number the more lymph nodes), N0 indicates there are no nearby lymph nodes, NX implies that cancer in nearby lymph nodes is not measurable.

Figure 3:

Top left: An axial slice of the CT for one patient. Top right: Four of the tumor surface vertices (in red) marked by the radiologist. Bottom left: All tumor surface points marked by the radiologist. Bottom right: The full area of the tumor identified by interpolation of surface points and identification of tumor interior points.

Figure 4:

Results of clustering the voxel intensities using k-means, GMM, and our proposed MRF-GMM. The true images as well as the estimated cluster segmentations by each of the three algorithms are shown on rows 1 and 3. Each of these rows are followed by a row of boxplots showing the results of the four cluster comparison measures (overlap, Jaccard index, mutual information (MI) and adjusted Rand index) for 100 runs of the simulations. Within each boxplot figure, the first three boxplots correspond to the first added noise setting (σ = 1 and σ = 2 for true images 1 and 2 correspondingly) while the second set of three boxplots corresponds to the second added noise setting (σ = 2 and σ = 3 for true images 1 and 2 correspondingly).

Figure 5:

True images used in the simulations to evaluate ranking of image heterogeneity.

Figure 6:

ROC curves comparing the six predictive methods using the proposed collections of tumor heterogeneity measures for 3-year survival.

Figure 7:

Boxplots of AUCs from 10-fold cross-validation for each model and the corresponding estimation method for 3-year survival.