A computational model to generate simulated three-dimensional breast masses

Abstract

Purpose: To develop algorithms for creating realistic three-dimensional (3D) simulated breast masses and embedding them within actual clinical mammograms. The proposed techniques yield high-resolution simulated breast masses having randomized shapes, with user-defined mass type, size, location, and shape characteristics.

Methods: The authors describe a method of producing 3D digital simulations of breast masses and a technique for embedding these simulated masses within actual digitized mammograms. Simulated 3D breast masses were generated by using a modified stochastic Gaussian random sphere model to generate a central tumor mass, and an iterative fractal branching algorithm to add complex spicule structures. The simulated masses were embedded within actual digitized mammograms. The authors evaluated the realism of the resulting hybrid phantoms by generating corresponding left- and right-breast image pairs, consisting of one breast image containing a real mass, and the opposite breast image of the same patient containing a similar simulated mass. The authors then used computer-aided diagnosis (CAD) methods and expert radiologist readers to determine whether significant differences can be observed between the real and hybrid images.

Results: The authors found no statistically significant difference between the CAD features obtained from the real and simulated images of masses with either spiculated or nonspiculated margins. Likewise, the authors found that expert human readers performed very poorly in discriminating their hybrid images from real mammograms.

Conclusions: The authors' proposed method permits the realistic simulation of 3D breast masses having user-defined characteristics, enabling the creation of a large set of hybrid breast images containing a well-characterized mass, embedded within real breast background. The computational nature of the model makes it suitable for detectability studies, evaluation of computer aided diagnosis algorithms, and teaching purposes.

FIG. 1.

Process of generating a simulated mass model and embedding it into an existing mammogram.

FIG. 2.

GRS surface with the introduction of two low-frequency modifications: A Gaussian bump (left side) and a spike irregularity (right side), exaggerated here for illustration purposes.

FIG. 3.

Flowchart for the generation of the initial set of simulated spicule segments.

FIG. 4.

Spatial interpretation of an initial parent segment (superscript 0) and child segments (superscript 1) generated in the branching algorithm.

FIG. 5.

An example mass with various spiculation structures added. The parameters defining the spiculation growth for these examples are shown in the table below the images.

FIG. 6.

Flowchart for the generation of the iterative branching structure.

FIG. 7.

Example of a generated mass phantom (a) without horizontal stretching and (b) with horizontal stretching.

FIG. 8.

Process of embedding a simulated mass in a real mammogram: (a) Original mammogram; (b) Fat tissue approximation obtained using thin-plate splines: the gray values correspond to absorption produced by a fixed attenuation coefficient of fat tissue; (c) Hybrid image with real mammogram containing a simulated tumor; and (d) Simulated tumor projection.

FIG. 9.

Examples showing the results of embedding the simulated mass phantoms into digitized mammograms. Each of these patients had one normal breast and one breast containing a true mass. The locations of the simulated and actual masses are indicated by white arrows. (a)–(f) The normal breast is shown in the left image; the center image shows the normal image with a simulated mass embedded; the right image shows the opposite breast image containing a real mass. (g) and (h) Detail in the mammograms where the simulated (left) and normal (right) masses were embedded for spiculated and nonspiculated examples, respectively.

FIG. 10.

Overall outline of the validation study, based on the generation of image pairs, with one image exhibiting a real mass and the other containing a matched, simulated mass.

FIG. 11.

Corresponding pairs of (a) real and (b) simulated masses for a nonspiculated tumor (left pair) and (c) real and (d) simulated masses for a spiculated tumor (right pair). The tumor locations are indicated by arrows.

FIG. 12.

Examples of simulated tumors with matched simulated and real mammogram regions. The first three columns show examples of nonspiculated masses; the last three columns show spiculated masses. Each row shows (from left to right) a 3D representation of the simulated tumor, a region of interest in which the simulated tumor has been embedded, and a corresponding region of interest from the opposite breast containing a real tumor with similar characteristics.

FIG. 13.

Region of interest in hybrid mammogram, indicating various findings as described in Ref. .

FIG. 14.

Rating distribution for each radiologist in the reader study. Error bars indicate 95% confidence intervals.

FIG. 15.

Example representation of an individual segment and its projection.