Automated detection and diagnosis of small lesions in breast MRI represents a challenge for the traditional computeraided diagnosis (CAD) systems. The goal of the present research was to compare and determine the optimal feature sets describing the morphology and the enhancement kinetic features for a set of small lesions and to determine their diagnostic performance. For each of the small lesions, we extracted morphological and dynamical features describing both global and local shape, and kinetics behavior. In this paper, we compare the performance of each extracted feature set for the differential diagnosis of enhancing lesions in breast MRI. Based on several simulation results, we determined the optimal feature number and tested different classification techniques. The results suggest that the computerized analysis system based on spatiotemporal features has the potential to increase the diagnostic accuracy of MRI mammography for small lesions and can be used as a basis for computeraided diagnosis of breast cancer with MR mammography.
Breastcancer is one of the most common cancers among women. Contrastenhanced MR imaging of the breast was reported to be a highly sensitive method for the detection of invasive breast cancer [
As an important aspect remains the fact that many of these techniques were applied on a database of predominantly tumors of a size larger than 2 cm. In these cases, MRI reaches a very high sensitivity in the detection of invasive breast cancer due to both morphological criteria as well as characteristic timesignal intensity curves. However, the value of dynamic MRI and of automatic identification and classification of characteristic kinetic curves is not well established in small lesions when clinical findings, mammography, and ultrasound are unclear. Recent clinical research has shown that DCIS with small invasive carcinoma can be adequately visualized in MRI [
Visual assessment of morphological properties is highly interobserver variable [
More than 40
In the present study, we design and evaluate a computerized analysis system for the diagnosis of small breast masses with an average diameter of <1 cm.
The automated evaluation is a multistep system which includes global and local features such as shape descriptors, dynamical features, and spatiotemporal features combining both morphology and dynamics aspects. Different classification techniques are employed to test the performance of the complete system. Summarizing, in the present paper, a multifactorial protocol, including image registration, and morphologic and dynamic criteria are evaluated in predominantly small lesions of 1.0 cm or less as shown in Figure
Diagram of a computerassisted system for the evaluation of small contrast enhancing lesions.
A total of 40 patients, all females having an age range 42–73, with indeterminate small mammographic breast lesions were examined. All patients were consecutively selected after clinical examinations, mammography in standard projections (craniocaudal and oblique mediolateral projections) and ultrasound. Only lesions BIRADS 3 and 4 were selected where at least one of the following criteria was present: nonpalpable lesion, previous surgery with intense scarring, or location difficult for biopsy (close to chest wall). All patients had histopathologically confirmed diagnosis from needle aspiration/excision biopsy and surgical removal. Breast cancer was diagnosed in 17 out of the total 31 cases. The average size of both benign and malignant tumors was less than 1.1 cm.
MRI was performed with a 1.5 T system (Magnetom Vision, Siemens, Erlangen, Germany) with two different protocols equipped with a dedicated surface coil to enable simultaneous imaging of both breasts. The patients were placed in a prone position. First, transversal images were acquired with a STIR (short TI inversion recovery) sequence (TR = 5600 ms, TE = 60 ms, FA = 90°, IT = 150 ms, matrix size 256
The dynamic study consisted of 6 measurements with an interval of 83 s. The first frame was acquired before injection of paramagnetic contrast agent (gadopentetate dimeglumine, 0.1 mmol/kg body weight, Magnevist, Schering, Berlin, Germany) immediately followed by the 5 other measurements. The initial localization of suspicious breast lesions was performed by computing difference images, that is, subtracting the image data of the first from the fourth acquisition. As a preprocessing step to clustering, each raw gray level timeseries
Automatic motion correction represents an important prerequisite to a correct automated small lesion evaluation [
We tested motion compensation for two and three directions and found the optimal motion compensation results in two directions [
The small lesion evaluation is based on a multistep system that includes a reduction of motion artifacts based on a novel nonrigid registration method, an extraction of morphologic features, dynamic enhancement patterns as well as mixed features for diagnostic feature selection and performance of lesion evaluation. Figure
The complexity of the spatiotemporal tumor representation requires specific morphology and/or kinetic descriptors. We analyzed geometric and Krawtchouk moments and geometrical features as shape descriptors, provided a temporal enhancement modeling for kinetic feature extraction and the scaling index method for the simultaneous morphological and dynamics representation.
To represent the shape of the tumor contour, the tumor voxels having nontumor voxel as a neighbor were extracted to represent the contour of the tumor. In this context, neighbor voxels include diagonally adjacent voxels, but not voxels from a different transverse slice. Due to the different grid sizes in the three directions of the MR images and possible gaps between transverse slices, the tumor contour in one transverse slice does not necessarily continue smoothly into the next transverse slice. Considering tumor contours between transverse slices therefore introduces contour voxels that are completely in the tumor interior in one slice. This is illustrated in Figure
Example of contour computation.
Figure
Left to right: tumor in adjacent transverse slices of a 512
The contour in each slice was stored as an 1D chain of the 3D position of each contour voxel, constituting a “walk” along the contour. The chains of several slices were spliced together end to end to form a chain of 3D vectors representing the contour of the tumor.
Next, the center of mass of the tumor was computed as
Knowing the center of mass, for each contour voxel
From the chain of floating point values
The entropy
From the radius,
An additional measurement describing the compactness of the tumor, which was also used as a feature, is the number of contour voxels, divided by the number of all voxels belonging to the tumor.
The spatial and morphological variations of a tumor can be easily captured by shape descriptors. We analyze two modalities as shape descriptors based on moments: the geometric and Krawtchouk moments.
We will employ loworder threedimensional geometrical moment invariants as described in [
Global and local shape description represents an important field in 3D medical image analysis. For breast lesion classification, there is a stringent need to describe properly the huge data volumes stemming from 3D images by a small set of parameters which captures the morphology (shape) well. However, very few techniques have been proposed for both global and local shape description. We employed Krawtchouk moments [
Krawtchouk moments represent a set of orthonormal polynomials associated with the binomial distribution [
We assume that
The tumor can be represented by Krawtchouk moments since it is expressed as a function
Lesion differential diagnosis in dynamic protocols is based on the assumption that benign and malignant lesions exhibit different enhancement kinetics. In [
Schematic drawing of the timesignal intensity (SI) curve types [
Computing the average signal intensity of the tumor before contrast agent administration (SI) and after contrast agent administration (
To capture the slope of the curve of relative signal intensity enhancement (RSIE) versus time in the late postcontrast time, we computed the line
The solutions to these equations are given by
The scaling index method [
Mathematically, the scaling index represents the 2D image as a set of points in a threedimensional state space defined by the coordinates
For each of the three time scans
The following section gives a description of classification methods applied to evaluate the effect of spatiotemporal features in breast MR images.
Discriminant analysis represents an important area of multivariate statistics and finds a wide application in medical imaging problems. The most known approaches are linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and Fisher’s canonical discriminant analysis.
Let us assume that
The Bayes classification [
This classification method assigns each new sample to the group with the highest a posterior probability. Thus, the classification rule becomes
There are two cases to be distinguished regarding the covariance matrices: if the covariance matrices are different for each class, then we have a QDA (quadratic discriminant analysis) classifier, while if they are identical for the different classes, it becomes an LDA (linear discriminant analysis) classifier.
The underlying idea of Fisher’s linear discriminant analysis (FLDA) is to determine the directions in the multivariate space which allow the best discrimination between the sample classes. FLDA is based on a common covariance estimate and finds the most dominant direction and afterwards searches for “orthogonal” directions with the same property. The technique can extract at most
This technique identifies the first discriminating component based on finding the vector
In the following, we will explore the results of the previously described features’ sets from different classification techniques. The results will elucidate the descriptive power of several tumor features for small lesion detection and diagnosis.
The Krawtchouk moments describe a representation of local shape parameters and can thus describe the differences in morphology between benign and malignant tumors. Since the obtained number of Krawtchouk moments is very high (>200), we reduced their dimension based on principal component analysis (PCA). Table
Classification results based on Krawtchouk moments for different principal components (PC). Abbreviations: linear discriminant analysis (LDA), naive Bayes linear discriminant analysis (N.B.LDA), quadratic discriminant analysis (QDA), naive Bayes quadratic discriminant analysis (N.B.QDA), and Fisher’s linear discriminant (FLDA).
PC  Correctly classified (%)  

LDA  N.B.LDA  QDA  N.B.QDA  FLDA  
1  71.0  71.0  64.5  64.5  71.0 
2  71.0  74.2  58.1  64.5  74.2 
3  64.5  67.7  67.7  58.1  67.7 
4  64.5  64.5  74.2  71.0  64.5 
5  64.5  64.5  74.2  64.5  64.5 
6  61.3  64.5 

64.5  61.3 
7  67.7  74.2  74.2  67.7  71.0 
8  71.0  74.2  74.2  67.7  71.0 
9  61.3  74.2  71.0  67.7  61.3 
10  61.3  74.2  74.2  67.7  61.3 
11  58.1  67.7  71.0  67.7  58.1 
We now examine not anymore every single feature but group the features together in specific classes that contain the features described in the previous sections. Table
Combined classification of the feature groups and different classification methods. Abbreviations: linear discriminant analysis (LDA), naive Bayes linear discriminant analysis (N.B.LDA), quadratic discriminant analysis (QDA), naive Bayes quadratic discriminant analysis (N.B.QDA), and Fisher’s linear discriminant (FLDA).
Features  Correctly classified (%)  

LDA  N.B.LDA  QDA  N.B.QDA  FLDA  
Contour features  64.5  74.2  67.7  77.4  64.5 
Scaling index features  67.7  71.0  61.3  51.6  67.7 
Tumor RSIE features  64.5  74.2  74.2  77.4  64.5 
Contour RSIE features  64.5  74.2  54.8  54.8  64.5 
Geometric moments  51.6  54.8  51.6  64.5  51.6 
Krawtchouk moments  71.0  74.2 

71.0  74.2 
We perform receiver operating characteristic (ROC) analysis to determine the sensitivity, specificity, and area under the curve (AUC) of the CAD system. The results of the sensitivity and specificity for the current data set based on specific features selected based on their discrimination capability and also in combination are shown in Table
Sensitivity and specificity for specific features alone and in combination based on linear naive Bayes classification.
Features  True positive (%)  True negative (%) 

Contour feature (radius standard deviation)  70.5  85.7 
Scaling index features (entropy) 

57.1 
Tumor RSIE features (entropy (time scan 4))  76.4  71.4 
Contour RSIE features (entropy (time scan 4))  76.4  71.4 
Slope of RSIE  76.4  64.3 
Geometric 5th moment  71.6 

Bayes classification without geometric moments  76.4  78.5 
Bayes classification with geometric moments  88.2  78.5 
The best AUCvalues for single features as well as for all features combined can be found in Table
AUC values for selected single features and all features combined based on an FLDA classification.
Features  AUC (%) 

Contour feature (radius mean) 

Scaling index features (mean)  79.6 
Tumor RSIE features (entropy (time scan 3))  81.5 
Contour RSIE features (entropy (time scan 4))  81.3 
Slope of RSIE  72.7 
FLDA classification with all features 

The AUCvalues demonstrate that the contour features are very powerful descriptors and are able to capture the spatiotemporal behavior of small lesions.
The goal of the presented study was the introduction of new techniques for the automatic evaluation of dynamic MR mammography in
Several novel lesion descriptors such as morphological, kinetic and spatiotemporal are applied and evaluated in context with benign and malignant lesion discrimination. Different classification techniques were applied to the classification of the lesions. A surprisingly low number of eight features proved to contain relevant information and achieved for both Fisher’s LDA and LDA good classification results. Krawtchouk moments proved to capture both the local and global shape features and represent thus in term of classification the best shape descriptors. In terms of spatiotemporal features, the scaling index entropy yields the highest sensitivity demonstrating that the enhancement pattern in small lesions has to be analyzed both in terms of spatial and temporal information. The benign characteristics are best described by geometric moments. The AUCvalues demonstrate that the contour features can capture very well the spatiotemporal behavior of these small lesions.
The results suggest that quantitative diagnostic features can be employed for developing automated CAD for small lesions to achieve a high detection and diagnosis performance. The performed ROCanalysis shows the potential of increasing the diagnostic accuracy of MR mammography by improving the sensitivity without reduction of specificity for the data sets examined.
The research was supported by NIH Grant 5K25CA10679905 and by an Alexander von Humboldt Fellowship.