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# Computer-aided diagnosis for diagnostically challenging breast lesions in DCE-MRI based on image registration and integration of morphologic and dynamic characteristics

- Felix Retter
^{1}, - Claudia Plant
^{4}, - Bernhard Burgeth
^{1}, - Guillermo Botella
^{2}, - Thomas Schlossbauer
^{3}and - Anke Meyer-Bäse
^{2}Email author

**2013**:157

https://doi.org/10.1186/1687-6180-2013-157

© Retter et al.; licensee Springer. 2013

**Received:**15 February 2013**Accepted:**24 July 2013**Published:**17 October 2013

## Abstract

Diagnostically challenging lesions comprise both foci (small lesions) and non-mass-like enhancing lesions and pose a challenge to current computer-aided diagnosis systems. Motion-based artifacts lead in dynamic contrast-enhanced breast magnetic resonance to diagnostic misinterpretation; therefore, motion compensation represents an important prerequisite to automatic lesion detection and diagnosis. In addition, the extraction of pertinent kinetic and morphologic features as lesion descriptors is an equally important task. In the present paper, we evaluate the performance of a computer-aided diagnosis system consisting of motion correction, lesion segmentation, and feature extraction and classification. We develop a new feature extractor, the radial Krawtchouk moment, which guarantees rotation invariance. Many novel feature extraction techniques are proposed and tested in conjunction with lesion detection. Our simulation results have shown that motion compensation combined with Minkowski functionals and Bayesian classifier can improve lesion detection and classification.

## Keywords

- Computer-aided diagnosis
- Breast MRI
- Krawtchouk moments
- Minkowski functional
- Kinetics

## 1 Introduction

Contrast-enhanced magnetic resonance imaging of the breast was reported to be a highly sensitive method for the detection of invasive breast cancer[1]. Different investigators described that certain dynamic signal intensity (SI) characteristics (rapid and intense contrast enhancement followed by a wash-out phase) obtained in dynamic studies are a strong indicator for malignancy[2]. Morphologic criteria have also been identified as valuable diagnostic tools[3]. Recently, combinations of different dynamic and morphologic characteristics have been reported[4] which can reach diagnostic sensitivities up to 97% and specificities up to 76.5%.

Recent clinical research has shown that ductal carcinoma *in situ* (DCIS) with small invasive carcinoma can be adequately visualized in magnetic resonance imaging (MRI)[5] and that MRI provides an accurate estimation of invasive breast cancer tumor size, especially in tumors 2 cm or smaller[6].

However, more than 40% of the false-negative MR diagnosis are associated with diagnostically challenging lesions such as non-mass enhancing lesions (pure DCIs) and with small lesion (foci) size, thus indicating a lower sensitivity of MRI for these cases. It has been shown that double reading achieves a higher sensitivity but is time-consuming; as an alternative, a computer-assisted system was suggested[7]. The success of computer-aided diagnosis (CAD) in conventional X-ray mammography[8–12] motivates furthermore the research of similar automated diagnosis techniques in breast MRI[13, 14].

The goal of this paper is to develop a computer-assisted system and thus improve the quality of breast MRI postprocessing, reducing the number of missed or misinterpreted cases leading to false-negative diagnosis.

Automatic motion correction represents an important prerequisite to a correct automated small lesion evaluation[15]. Motion artifacts are caused either by the relaxation of the pectoral muscle or involuntary patient motion and invalidate the assumption of the same spatial location within the breast of the corresponding voxels in the acquired volumes for assessing lesion enhancement. Especially for small lesions, the assumption of correct spatial alignment often leads to misinterpretation of the diagnostic significance of enhancing lesions[16].

Visual assessment of morphologic properties is a highly inter-observer variable[17], while automated computation of features leads to more reproducible indices and thus to a more standardized and objective diagnosis. In this sense, we research novel mathematical descriptors for both morphology and dynamics and will compare their performance regarding small lesion classification based on novel feature selection algorithms. In addition, we develop and test a novel descriptor, the radial invariant Krawtchouk moments, to capture the morphology of diagnostically challenging lesions.

Therefore, the goal of our paper is to evaluate quantitatively based on automated classification the utility of novel feature extraction approaches to breast lesion detection such as foci and non-mass enhancing lesions.

## 2 Materials and methods

### 2.1 Patients

A total of 63 patients, all females with an age range of 42 to 73 years, with 66 solid breast tumors were examined. All patients had histopathologically confirmed diagnosis from needle aspiration/excision biopsy and surgical removal.

Histologic findings were malignant in 30 and benign in 36 lesions. Tumors were classified as diagnostically challenging lesions for both foci and non-mass enhancing lesions. Lesion size was derived from mammography images. Mean size of malignant lesions was 1.3 cm (median = 1.2 cm, range = 0.4 to 3.8 cm), and mean size of benign lesions was 1.2 cm (median = 1.0 cm, range = 0.3 to 3.0 cm).

### 2.2 Magnetic resonance imaging

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 prone position. First, transversal images were acquired with short TI inversion recovery sequence (TR = 5,600 ms, TE = 60 ms, FA = 90°, IT = 150 ms, matrix size 256 × 256 pixels, slice thickness 4 mm). A dynamic T1-weighted gradient echo sequence (3D fast low-angle shot sequence) was performed (TR = 11 ms and TR = 9 ms, TE = 5 ms, FA = 25°) in transversal slice orientation with a matrix size of 256 × 256 pixels and an effective slice thickness of 4 or 2 mm.

The dynamic study consisted of six measurements with an interval of 83 s. The first frame was acquired before injection of a paramagnetic contrast agent (gadopentetate dimeglumine, 0.1 mmol/kg body weight, Magnevist™, Schering, Berlin, Germany), which was immediately followed by five other measurements. The initial localization of suspicious breast lesions was performed by computing difference images, i.e., subtracting the image data of the first from the fourth acquisition. As a pre-processing step to clustering, each raw gray level time series *S*(*τ*),*τ* ∈ {1,…,6} was transformed into a signal time series of relative signal enhancement *x*(*τ*) for each voxel, the pre-contrast scan at *τ* = 1 serving as reference; in other words,$x(\tau )=\frac{x(\tau )-x(1)}{x(1)}$. Thus, we ensure that the proposed method is less sensitive to changing between different MR scanners and/or protocols.

## 3 Motion compensation and lesion segmentation

*u*, in an image sequence

*f*

_{1},

*f*

_{2}with movement in between the image acquisitions:

*u*
_{
i
},*i* ∈ {*x*,*y*,*z*} describes the movement in the corresponding direction.

The method is based on two typical assumptions for variational optical flow methods: the brightness and smoothness assumption. Additionally, we enforce a divergence-free flow field.

*f*

_{0}is pre-processed and convolved with a Gaussian

*K*

_{ σ }of a standard deviation

*σ*:

where the spatial domain Ω represents a spatiotemporal domain. The data term (*M*(*D*
^{
k
}
*f*,*u*)) describes a brightness constancy assumption, the first part of the regularizer (*S*(∇*f*,∇*u*)) penalizes deviations from piecewise smoothness, and the second part of the regularizer *D*(div*u*) penalizes non-divergent-free flow fields. The weight terms *μ* > 0 and *λ* represent the regularization parameters, the so called Lamé constants, where larger values correspond to more simplified flow fields. This technique is a global method where the filling-in-effect yields dense flow fields, and no subsequent interpolation is necessary as with the technique proposed in[19]. This method works within a single variational framework. This technique overcomes the aperture problem, provides sub-pixel accuracy, and can be easily enhanced and adapted.

The optimal motion correction results were achieved for motion compensation in two directions for mostly small standard deviations of the Gaussian kernel and smoothing parameter. Consistent with the only study known for evaluating the effect of motion correction algorithms[16], the proposed motion compensation technique improved the tumor diagnosis by having a strong impact on the enhancement curves.

Motion compensation is followed by image segmentation where each MR image has to be segmented into two regions, the region of interest, i.e., the voxels belonging to the tumor, and the background. We are using an interactive region growing algorithm that creates a binary mask for the tumor and its surroundings. The image used for the region growing algorithm was the difference image of the second post-contrast image and the native pre-contrast image.

## 4 Kinetic and morphologic features

### 4.1 Features describing the enhancement kinetics

*dynamic contrast-enhanced magnetic resonance*(DCE-MR) examination for each image voxel represents one of the major steps in designing CAD systems for breast MRI. In[2], it was shown that the shape of the time-signal intensity curve represents an important criterion in differentiating benign and malignant enhancing lesions in DCE-MR imaging. The results indicate that the enhancement kinetics, as represented by the time-signal intensity curves visualized in Figure2, differ significantly for benign and malignant enhancing lesions and thus represent a basis for differential diagnosis. In cancerous breast tissue, plateau or washout time courses (type II or III) prevail. Steadily progressive signal intensity time courses (type I) are exhibited by benign enhancing lesions, albeit these enhancement kinetics are shared not only by benign tumors but also by fibrocystic changes.

*l*=

*a*

*t*+

*b*to the data of the last three time scans of every pixel. The distance that

*l*is supposed to minimize with respect to the data is the sum of the squared errors which leads to the well-known problem of least squares. Since we only need the slope

*a*, it is sufficient to compute for the last three post-contrast scans:

where *l*
_{
ij
} is the relative enhancement${l}_{\mathit{\text{ij}}}:=\frac{{f}_{\mathit{\text{ij}}}-{f}_{0j}}{{f}_{0j}}$, *n* corresponds to the number of voxels we consider, and$\stackrel{\u0304}{\xb7}$ denotes the mean.

Since this feature has already proven its descriptive power, we are using it in the evaluation of motion correction.

### 4.2 Features describing the lesion morphology

Morphological characteristics contain valuable information about a lesion’s type. Combined with kinetic properties, one could expect a higher accuracy. Furthermore, non-mass enhancing lesions such as DCIS or ICS can be better differentiated based on morphologic properties[20]. In the previous work[21], we have considered features that describe the geometric characteristics of the shape and local moments such as that of Krawtchouk to identify the non-smooth surface.

#### 4.2.1 Minkowski functionals

Another family of characteristics that capture morphologic attributes is generated by Minkowski functionals (MFs)[22]. MF can characterize geometrical and topological space concepts such as shape, convexity, and connectivity and represent a simple yet precise tool for the analysis of geometrical structures in tumors. The most important MF for three-dimensional (3D) tumors is the Euler characteristic.

*V*, surface area

*S*, mean breadth

*B*, and Euler characteristic

*χ*. The meaning of

*V*and

*S*are immediately clear, and the Euler characteristic is the number of regions of connected white voxels plus the number of completely enclosed regions of black voxels minus the number of black tunnels through white regions, remembering that in our data, the tumor is shown as a white object in a black area. The mean breadth is proportional to the integral mean curvature

*H*of the tumor

*A*which is defined as

with *κ*
_{
1
},*κ*
_{
2
} as the principal curvatures and *d* *f* as the area element of *A*.

The *N* denotes the number of voxels in the tumor when we assume a voxel size of one.

#### 4.2.2 Krawtchouk moments

The (discrete) Krawtchouk polynomials represent a set of functions that are related to the binomial distribution. Their descriptive power was shown in[24]. Since they are defined over a discrete set, their application is well suited in image processing.

*n*th order is the hypergeometric function

*p*∈ (0,1),

*x*,

*n*= 0,1,…,

*N*,

*N*> 0.

_{2}

*F*

_{1}is defined as

*a*)

_{ k }which is

*ρ*(

*n*;

*p*,

*N*) and their weight function

*w*(

*x*;

*p*,

*N*) are associated:

*n*+

*m*+

*l*)th order for an image of size

*N*×

*M*×

*L*as

For example, the Krawtchouk moments have successfully been used for content-based search by Mademlis et al.[26].

#### 4.2.3 Radial invariant Krawtchouk moments

*f*(

*r*,

*θ*). In an image of a size

*N*×

*N*, the radius

*r*varies from 0 to

*N*/2 and the angle

*θ*varies from 0 to 2

*π*in steps of

*ν*. Therefore,${\theta}_{c}=\frac{2\pi c}{\nu},\phantom{\rule{2.77626pt}{0ex}}c=0,\dots ,\nu -1$. Given this representation, the radial Krawtchouk moments are defined as

*r*. If the image is rotated by an angle

*α*, we get

Hence, the *ϕ*
_{
mn
} are rotationally invariant.

*R*∈

*S*

*O*(3) by three consecutive rotations of angle Ψ ∈ [0,2

*π*], Θ ∈ [0,

*π*] and Φ ∈ [0,2

*π*] around three predefined axes. For convenience, let us choose the three axes as the coordinate axes

*Z*,

*X*,

*Z*:

The rotation is uniquely defined for every choice of angles with Θ ≠ 0. If Θ = 0, we get a rotation of angle Ψ + Φ around the *Z*-axis which can be achieved by an infinite combination of values for Ψ and Φ. We avoid this in our discretization by shifting the values of Θ by half of the step size of the discretization.

*f*(

*r*,Φ,Θ,Ψ) denote the image in the Euler coordinates, which means the vector (

*r*,0,0)

^{ T }is rotated by

*R*

_{Φ,Θ,Ψ}and its three components describe the pixel at the corresponding

*x*,

*y*and

*z*coordinates (of course, the origin of the coordinate system

*x*,

*y*,

*z*refers to the center of the image), then the radial Krawtchouk moments in 3D are defined as

*α*,

*β*,

*γ*such that the moment${R}_{\mathit{\text{klmn}}}^{\prime}$ (10) becomes

## 5 Classification techniques

The following section gives a description of classification methods applied to evaluate the effect of motion compensation to breast MRI 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 **x** describes a K-dimensional feature vector, that there are *J* classes, and there are *N*
_{
j
} samples available in group *j*. The mean in group *j* is given by *μ*
_{
j
}, and the covariance matrix is given by Σ_{
j
}.

### 5.1 Bayes classification based on LDA and QDA

The Bayes classification[28] is based on estimating the prior probabilities *π*
_{
i
} for each class which describe the prior estimates about how probable a class is.

where *μ*
_{
j
} represents the means of the classes and Σ_{
j
} is the corresponding covariance matrix. The assignment to a certain class *j* for a certain pattern is made based on the smallest determined value of *C*
_{
j
}.

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 classifier, while if they are identical for the different groups, it becomes a LDA classifier.

### 5.2 Fisher’s linear discriminant analysis

The underlying idea of Fisher’s linear discriminant analysis (FLDA) is to determine the directions in the multivariate space that allow the best discrimination between the sample classes[29]. 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 *J* - 1 components, and for visualization purposes, scores of the first component are plotted against that of the second one, thus yielding the optimal separation among the classes.

with *B* denoting the inter-class sum-of-squares matrix and *W* the intra-class sum-of-squares matrix.

### 5.3 Support vector machines

*H*=

*a*

*v*+

*b*that separates the feature vectors${\overrightarrow{v}}_{i},i=1,\dots ,n$ in their

*d*dimensional domain in two classes${\overrightarrow{v}}_{i}\in \{M,B\}$. First, let us assume that our data set is linearly separable and that we can find a pair$(\overrightarrow{w},b)$ that fulfills

*θ*

_{ i },

*i*= 1,…,

*n*which leads us to a minimization of$L(\overrightarrow{w})=\frac{\parallel \overrightarrow{w}\parallel}{2}+\alpha {\sum}_{i=1}^{n}{\theta}_{i}$ subject to

An additional challenge appears if there is a non-linear function that separates the variable since the common approach would fail under these circumstances. Aizerman et al. refined this method using non-linear kernel functions instead of the scalar product which maps the variables onto another space. The optimal hyperplane computed corresponds to a non-linear function in the original feature space.

## 6 Results

In the following, we will explore the applicability of the previously described motion compensation algorithm under different motion compensation parameters and features’ sets as well as different classification techniques. The results will elucidate the applicability of motion compensation as an artifact correction method and also the descriptive power of several tumor features with and without motion correction.

### 6.1 Experimental results

**Numerical code of features**

Numerical code | Feature |
---|---|

1. | Minkowski functionals (MF) |

1.1 | Volume |

1.2 | Surface |

1.3 | Curvature |

1.4 | Euler characteristic |

2 | Normed Minkowski functionals (independent oftumor size) |

2.1 | Surface |

2.2 | Curvature |

2.3 | Euler characteristic |

3 | Krawtchouk moments (Reduction to 28 dimensions) |

3.1 | Standard Krawtchouk moments |

3.2 | Radial Krawtchouk moments |

4 | Slope of RSIE (without motion compensation) |

**Classifiers employed for lesion classification**

Classifier | Description |
---|---|

LDA | Linear discriminant analysis |

NLDA | Naive Bayes linear discriminant analysis |

QDA | Quadratic discriminant analysis |

NQDA | Naive Bayes quadratic discriminant analysis |

FLD | Fisher’s linear discriminant analysis |

PK | SVM Classification with a polynomial kernel |

RBF | SVM Classification with a radial basis function |

PUK | SVM Classification with a Pearson VII universal function kernel |

AUC | Area under the ROC curve |

AUC for the classifiers applied to single features from Table1

LDA | NLDA | QDA | NQDA | FLD | PK | RBF | PUK | |
---|---|---|---|---|---|---|---|---|

1.1 | 0.74 | 0.74 | 0.72 | 0.72 | 0.79 | 0.78 | 0.78 | 0.77 |

1.2 | 0.75 | 0.75 | 0.72 | 0.72 | 0.78 | 0.75 | 0.75 | 0.72 |

1.3 | 0.75 | 0.75 | 0.76 | 0.76 | 0.75 | 0.79 | 0.79 | 0.78 |

1.4 | 0.78 | 0.78 | 0.80 | 0.80 | 0.82 | 0.80 | 0.80 | 0.80 |

2.1 | 0.70 | 0.70 | 0.70 | 0.70 | 0.75 | 0.72 | 0.72 | 0.69 |

2.2 | 0.78 | 0.78 | 0.81 | 0.81 | 0.82 | 0.82 | 0.82 | 0.79 |

2.3 | 0.85 | 0.85 | 0.87 | 0.87 | 0.84 | 0.85 | 0.85 | 0.84 |

3.1 | 0.82 | 0.78 | 0.78 | 0.75 | 0.66 | 0.82 | 0.54 | 0.90 |

3.2 | 0.64 | 0.64 | 0.58 | 0.57 | 0.58 | 0.66 | 0.54 | 0.61 |

4 | 0.76 | 0.76 | 0.75 | 0.75 | 0.73 | 0.75 | 0.77 | 0.76 |

## 7 Discussion

Breast MRI reading is often impeded by motion artifacts of different grades. Motion correction algorithms become a necessary correction tool in order to improve the diagnostic value of these breast MR images. We applied a new motion compensation algorithm based on the Horn and Schunck method for motion correction and determined the optimal parameters for lesion classification. At the same time, we described the lesions based on morphologic and kinetic features and determined the descriptive power of single features. In addition, we developed and tested a novel descriptor, the radial invariant Krawtchouk moment. The highest AUC value was achieved for the normed Euler characteristic showing that this topological measure captures well the shape of the tumor. Different classification techniques were applied to the classification of the lesions.

## 8 Conclusions

A novel CAD system was proposed for the detection of diagnostically challenging lesions. This system comprised a novel motion compensation algorithm based on the optical flow method, segmentation, morphological and kinetic feature extraction, and classification as an evaluation method for the extracted features from the lesions. Three new morphologic features (Minkowski functional, Krawtchouk moments, and invariant Krawtchouk moments) for the discrimination of diagnostically challenging lesions have been proposed in this article and compared with the standard enhancement kinetic features. The simulation results have shown that morphologic feature descriptors such as the Minkowski functional appear to be more adequate than kinetic descriptors for descriptors for diagnostically challenging lesions.

## Declarations

### Acknowledgements

This research was supported in part by the NIH grant 5K25CA106799-04.

## Authors’ Affiliations

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