Quantifying local tumor morphological changes with Jacobian map for prediction of pathologic tumor response to chemo-radiotherapy in locally advanced esophageal cancer

Abstract

We proposed a framework to detect and quantify local tumor morphological changes due to chemo-radiotherapy (CRT) using a Jacobian map and to extract quantitative radiomic features from the Jacobian map to predict the pathologic tumor response in locally advanced esophageal cancer patients. In 20 patients who underwent CRT, a multi-resolution BSpline deformable registration was performed to register the follow-up (post-CRT) CT to the baseline CT image. The Jacobian map (J) was computed as the determinant of the gradient of the deformation vector field. The Jacobian map measured the ratio of local tumor volume change where J < 1 indicated tumor shrinkage and J > 1 denoted expansion. The tumor was manually delineated and corresponding anatomical landmarks were generated on the baseline and follow-up images. Intensity, texture and geometry features were then extracted from the Jacobian map of the tumor to quantify tumor morphological changes. The importance of each Jacobian feature in predicting pathologic tumor response was evaluated by both univariate and multivariate analysis. We constructed a multivariate prediction model by using a support vector machine (SVM) classifier coupled with a least absolute shrinkage and selection operator (LASSO) for feature selection. The SVM-LASSO model was evaluated using ten-times repeated 10-fold cross-validation (10 × 10-fold CV). After registration, the average target registration error was 4.30 ± 1.09 mm (LR:1.63 mm AP:1.59 mm SI:3.05 mm) indicating registration error was within two voxels and close to 4 mm slice thickness. Visually, the Jacobian map showed smoothly-varying local shrinkage and expansion regions in a tumor. Quantitatively, the average median Jacobian was 0.80 ± 0.10 and 1.05 ± 0.15 for responder and non-responder tumors, respectively. These indicated that on average responder tumors had 20% median volume shrinkage while non-responder tumors had 5% median volume expansion. In univariate analysis, the minimum Jacobian (p = 0.009, AUC = 0.98) and median Jacobian (p = 0.004, AUC = 0.95) were the most significant predictors. The SVM-LASSO model achieved the highest accuracy when these two features were selected (sensitivity = 94.4%, specificity = 91.8%, AUC = 0.94). Novel features extracted from the Jacobian map quantified local tumor morphological changes using only baseline tumor contour without post-treatment tumor segmentation. The SVM-LASSO model using the median Jacobian and minimum Jacobian achieved high accuracy in predicting pathologic tumor response. The Jacobian map showed great potential for longitudinal evaluation of tumor response.

Figure 1

Main framework for Jacobian feature extraction.

Figure 2

Conceptual illustration of Jacobian map. Red contour simulates GTV in the baseline image. Top row: smaller follow-up sphere illustrates shrinkage of a tumor. The DVF converge towards the tumor center (sink) resulting in a Jacobian map with shrinkage (blue). Bottom row: larger follow-up sphere simulates expansion of a tumor resulting in a diverging DVF (source) and a Jacobian map with expansion (red).

Figure 3

Responder case: Baseline, follow-up, DVF and Jacobian images in axial, sagittal and coronal views. Red contour is GTV and white arrows indicate shrinking esophageal wall.

Figure 4

Non-Responder case: Baseline, follow-up, DVF and Jacobian images in axial, sagittal and coronal views. Red contour is GTV and white arrows indicate expanding esophageal wall.

Figure 5

Box plots of the Median Jacobian and Minimum Jacobian features inside the tumor. × indicates average value.

Figure 6

Scatter plot of the Median and Minimum Jacobian and the classification line by the SVM-LASSO model.

Figure 7

(a) baseline CT containing air cavity in GTV (red contour). (b) follow-up CT filled with soft tissue. (c) DVF using default registration parameters. (d) DVF using masked optimized registration. (e) Jacobian map using default registration parameters. (f) Jacobian map using masked optimized registration.