Clinicians and imaging scientists interested in the role of tumor microvascular heterogeneity in survival. Intratumoral cellular heterogeneity has been observed in many cancers and associated with treatment resistance, increased metastatic potential, and poor outcomes¹. Radiologic study often reveals microvascular heterogeneity, prompting the development of numerous methods that attempt to quantify spatial and statistical variability in microvascular function. These are often more sensitive to treatment-induced changes than summaries such as median K^trans, and some have shown prognostic value in cervix^2,3 and head and neck⁴ cancer. However no attempt has been made to compare the prognostic value of the available methods across disease and identify which type of heterogeneity (statistical or spatial) is important. A recent review by O’Connor et al.⁵ categorized heterogeneity statistics into four classes: histogram, texture, partitioning, and multispectral. Here we identify heterogeneity statistics that are universally prognostic of disease-free survival (DFS) across cervix, bladder and head and neck cancer.

Pre-treatment DCE-MRI data from 108 patients (locally advanced cancer of the cervix [n = 36], bladder [n = 30], and head and neck [n = 42]) were analyzed. Imaging parameters for each cohort were similar (Table 1). Tumors were delineated on T₂-weighted images by radiologists (7-23 years experience). The two-compartment exchange model⁶ (2CXM) was used to obtain voxel-wise estimates of plasma flow (F_p), permeability surface area product (PS), fractional plasma volume (v_p), and fractional interstitial volume (v_e); voxel-wise estimates of K^trans were computed from F_p and PS. Tracer kinetic modeling was performed in IDL 8.2.2 (Exelis Visual Information Solutions, Boulder, Colorado, USA). Survival data and clinicopathologic variables were obtained (patient age, disease type, treatment type, tumor stage, nodal status, and tumor volume). Local research ethics approvals were obtained. Patients gave written informed consent.

Within each class of heterogeneity statistic identified by O’Connor et al., we selected methods that had: been used by more than one research group, used in more than one disease, and shown previous association with disease stage, treatment efficacy, or survival. We selected the histogram statistics median, standard deviation, skewness, and kurtosis; the texture statistics box-counting dimension⁷ and the Minkowski functionals (MF) area, perimeter, and genus (using a method similar to Canuto et al.⁸; here, the area, perimeter, or genus statistic is computed on a parameter map thresholded at each of a number of thresholds); the multispectral statistics cluster volume fractions and cluster centroids (using a k-means clustering method similar to Berry et al.⁹, with k = 2); and the partitioning statistics enhancing fraction and enhancing volume. All statistics were computed for the five tracer kinetic parameter maps for each patient.

We tested the null hypothesis of no difference in the ability to predict DFS between a null model parameterized by the clinicopathological variables alone and an alternative model parameterized by clinicopathological and heterogeneity statistics. As the number of variables greatly exceeded the number of patients, we used a random survival forest analysis¹⁰ and the variable hunting algorithm¹¹ to automatically and objectively select prognostic variables. Prognostic value of the selected variables was quantified by variable importance (VIMP)¹⁰. To avoid heterogeneity variables coding for disease, variables were converted to intra-disease quantiles prior to modeling. Predictive accuracy was quantified using Harrell’s concordance index in 5-fold cross validation. The null hypothesis was tested using a paired one-sided t-test. Statistical analyses were performed in R 3.1 (R Foundation for Statistical Computing, Vienna, Austria).

Ten variables were identified as universally prognostic across all three diseases (disease type and nine heterogeneity statistics). The heterogeneity statistics selected were (in decreasing order of importance by VIMP): MF perimeter for K^trans (thresholded at quantile 0.1), MF genus for PS (thresholded at quantiles 0.4, 0.6 and 0.8), kurtosis of F_p, largest cluster volume fraction, skewness of F_p, MF genus for K^trans (thresholded at quantile 0.5), and MF perimeter for F_p (threshold at quantile 0.2). Figure 1 shows predicted 3-year DFS probabilities for the selected variables. Figure 2 shows Kaplan-Meier DFS curve estimates for a subset of these variables. Figure 3 shows representative differences in heterogeneity between patients with short and long DFS. Predictive accuracies (concordance indices) for the null and alternative models were 67% and 77% respectively (P < 0.001).We reject the null hypothesis and conclude that an alternative model that uses heterogeneity statistics more accurately predicts DFS. Histogram, texture, and multispectral statistics were selected, suggesting these aspects of heterogeneity are important for predicting DFS (see caption for Figure 3 for interpretation), but partitioning methods (i.e., enhancing fraction) may not be universally predictive.