Malignant lesions have a high tendency to invade their surrounding environment compared to benign ones. This paper proposes a dynamic lesion model and explores the 2nd order derivatives at each image voxel, which reflect the rate of change of image intensity, as a quantitative measure of the tendency. The 2nd order derivatives at each image voxel are usually represented by the Hessian matrix, but it is difficult to quantify a matrix field (or image) through the lesion space as a measure of the tendency. We conjecture that the three eigenvalues contain important information of the Hessian matrix and are chosen as the surrogate representation of the Hessian matrix. By treating the three eigenvalues as a vector, called Hessian vector, which is defined in a local coordinate formed by three orthogonal Hessian eigenvectors and further adapting the gray level occurrence computing method to extract the vector texture descriptors (or measures) from the Hessian vector, a quantitative presentation for the dynamic lesion model is completed. The vector texture descriptors were applied to differentiate malignant from benign lesions from two pathologically proven datasets: colon polyps and lung nodules. The classification results not only outperform four state-of-the-art methods but also three radiologist experts.