Sampling the spatial patterns of cancer: optimized biopsy procedures for estimating prostate cancer volume and Gleason Score

Abstract

Prostate biopsy is the current gold-standard procedure for prostate cancer diagnosis. Existing prostate biopsy procedures have been mostly focusing on detecting cancer presence. However, they often ignore the potential use of biopsy to estimate cancer volume (CV) and Gleason Score (GS, a cancer grade descriptor), the two surrogate markers for cancer aggressiveness and the two crucial factors for treatment planning. To fill up this vacancy, this paper assumes and demonstrates that, by optimally sampling the spatial patterns of cancer, biopsy procedures can be specifically designed for estimating CV and GS. Our approach combines image analysis and machine learning tools in an atlas-based population study that consists of three steps. First, the spatial distributions of cancer in a patient population are learned, by constructing statistical atlases from histological images of prostate specimens with known cancer ground truths. Then, the optimal biopsy locations are determined in a feature selection formulation, so that biopsy outcomes (either cancer presence or absence) at those locations could be used to differentiate, at the best rate, between the existing specimens having different (high vs. low) CV/GS values. Finally, the optimized biopsy locations are utilized to estimate whether a new-coming prostate cancer patient has high or low CV/GS values, based on a binary classification formulation. The estimation accuracy and the generalization ability are evaluated by the classification rates and the associated receiver-operating-characteristic (ROC) curves in cross validations. The optimized biopsy procedures are also designed to be robust to the almost inevitable needle displacement errors in clinical practice, and are found to be robust to variations in the optimization parameters as well as the training populations.

Figure 1

A typical scenario where mis-estimation occurs when using the commonly-adopted estimation criterion for CV. Black solid dots represent the biopsy locations in clinical routines. The red regions represent prostate cancer regions. Please refer to text for more details.

Figure 2

Systematic sketch for the general framework of our approach.

Figure 3

The common prostate space (a) and the histological image of a typical specimen before (b) and after (c) the 3D spatial normalization, in both 3D (top row) and 2D (bottom row) views. Red regions are cancer ground truths labeled by pathologists. The bottom row shows the central slice in the coronal orientation.

Figure 4

Statistical atlases constructed from subpopulations having different (high v.s. low) surrogate marker values. Blue dots represent intuitively-observed biopsy locations where different subpopulations can be differentiated.

Figure 5

Modeling a biopsy needle as a semi-cylinder. (a) A typical biopsy needle – when it is placed into the prostate, the “cut-out” part will extract a piece of prostate tissue; (b) the cut-out part of the biopsy is modeled as a semi-cylinder, with center O, base radius r and semi-length l. The values of r = 1.5mm and l = 6mm are determined by clinical conventions.

Figure 6

Feature extraction step connects each potential needle location u_j with a feature B(u_j). This connection is the basis to the conversion of the problem of selecting optimal biopsy locations into the feature selection formulation.

Figure 7

Optimized biopsy locations for estimating cancer volume (top row) and Gleason Score (bottom row), by using seven needles in both transrectal and transperineal settings.

Figure 8

Estimation accuracy for CV (top row) and GS (bottom row), by the optimized biopsy procedures in transperineal settings. (A1&A2): classification rate as a function of the number of optimal needles. (B1&B2): ROC curve, where 7 needles were used.

Figure 9

Robustness of our approach in estimating GS, with regard to the variations of two major optimization parameters (threshold T and Gaussian kernel σ). (A) T is fixed at 0.5, and σ varies from 1 to 50 (transperineal setting); (B) σ is fixed at 20, and T varies from 0.4 to 0.8 (transrectal setting).

Figure 10

Bootstrapping distribution of the classification rates in 850 simulated populations. The mean and standard deviation is established at 87.18±5.79%, for using transperineal optimized biopsies to estimate GS. Similar results are found in transperineal / transrectal biopsy procedures when estimating CV/GS.