Note: I request that the MATLAB scripts used in this project not be reproduced on the course website

Transcription

1 Classification of Breast Tissue Using Electrical Impedance Spectroscopy Michael Nonte Graduate Student Department of Biomedical Engineering University of Wisconsin-Madison Note: I request that the MATLAB scripts used in this project not be reproduced on the course website

2 1. Introduction Breast cancer is typically diagnosed using a tissue biopsy. This is a process by which a sample of suspect tissue is removed from the patient and sent away for histological and chemical analysis. This process typically takes 1 to 2 days, but some samples give inconclusive results and require the patient to have a second biopsy. [1] If a faster method of tissue analysis or a method to determine if a tissue sample is a good candidate for further screening, the cost of screening and stress endured by the patient in awaiting results could be reduced. Electrical Impedance Spectroscopy (EIS) is a method that can used to measure the complex impedance properties of a material. A voltage or current of known frequency and amplitude is applied across the system and the response current or voltage is recorded. The differences in phase and magnitude of the applied stimulus and response are used to determine the complex impedance at that frequency. This is repeated for a range of frequencies to determine how the complex impedance of the system changes with stimulus frequency. Results are often displayed in a nyquist plot, showing the resistive and reactive components of impedance at each frequency measured. Often these plots will have characteristic shapes; for example, figure 1 shows the characteristic curved nyquist plot for a simple RC circuit. Figure 1: Nyquist Plot for a Simple RC Circuit[2] The ability to identify equivalent circuit components when analyzing bulk material properties can help the investigator identify physical properties of the material. For example, biological tissues have distinct impedance properties arising from their relative water content, cell packing density, and several other factors. Figure 2 shows an equivalent circuit model develop by Williams et. al. to explain the physiological significance of impedance properties recorded from subdurally implanted neuroelectrodes.

3 Figure 2: Equivalent Circuit Model of Neuroelectrode-Tissue Interface Impedance and Tissue Impedance[3] The aim of this study is to determine if pattern classification of electrical impedance spectroscopy measurements of breast tissue can be used as a viable means of pre-screening for cancerous tissue and to determine if any relevant physiological properties can be determined based on the strength of different extracted features. 2. Work Performed 2.1 Data Set The EIS data analyzed here was taken from a study by of 106 freshly excised breast tissue samples. EIS was performed in the range of 488 Hz to 1MHz and histology was performed to classify each tissue sample as either carcinoma, fibro-adenoma, mastopathy, glandular, connective, or adipose tissue. [4] This data is available publicly at the UCI Machine Learning Repository. [5] 2.2 Feature Extraction The publicly available data for this study does not include the raw EIS data recorded for each tissue sample. Rather, it contains a nine-attribute feature vector for each tissue sample, consisting of values extracted from the original data. The extracted attributes are as follows: I0: Impedance (ohm) at 0Hz PA500: Phase angle at 500kHz HFS: High-frequency slope of the phase angle DA: Distance between ends of the impedance spectrum AREA: Area under the impedance spectrum A/DA: AREA normalized by DA MAX IP: Maximum of the spectrum DR: Distance between I0 and the real component of the maximum frequency point P: Length of the spectral curve

4 2.3 Feature Selection There are two strategies that can be employed when selecting which features to use for classification: 1) rank each feature by its strength and select some subset of the best features 2) rank each unique combination of features by its strength and select the best combination of features. The first method is preferable in cases where the number of features is sufficiently large to make the task of finding the optimal feature set computationally difficult. The second method is favorable in cases where there a smaller number of features because it allows for the detection of interactions between features that improve classification results. Since there are only 9 features, there are only 511 possible feature vectors. Since this is a relatively low number, I performed an exhaustive search to determine the optimal feature vector from all possible feature vectors. To evaluate the performance of each potential feature vector, I randomly partitioned the data set into approximately equal sized testing and training sets. An extreme learning machine (ELM) with 200 neurons in the hidden layer was trained using the prospective feature vector of the training data, then the output of the test data was computed and the classification rate determined (justification of the use of ELM is discussed in 2.4 below). For each potential feature vector, the data was repartitioned and classification rate was determined 1000 times to ensure the determined performance of each feature vector was not over or under-estimated by a 'lucky' or 'unlucky' partition. 2.4 Classification Figure 3: ELM-SVM Classification Method My first step in classifying the data was to recreate a classification strategy developed by MR Daliri. [6] The chosen feature set is classified by a set of three ELMs with differing numbers of hidden nodes. An ELM is a single-layer perception in which the weights and offsets of connections between the input layer and hidden layer are fixed and randomly assigned. This greatly reduces the training time because only the weights of the output layer need to be computed. This is achieved by solving:

5 [6] Where H is the output of the hidden layer, Γ is the weights of the output layer and L is the true class labels. The solution to this problem is: [6] Where H is the generalized inverse of H. This results in a single-step training of the ELM, which greatly improves speed at the cost of reduced accuracy. The ELM layer of this classification method uses three ELMs with 150, 170, and 200 neurons in the hidden layer. The outputs of these ELMs form a feature vector that is classified by a multi-class support vector machine (SVM). Two common ways to extend SVM use to more than two classes are the 1 vs. 1 method and the 1 vs. all method. In the 1 vs. 1 method, binary classification of every combination of two classes is computed for the test data and the outputs are added to a 'voting' matrix where the class with the most vote for each input is chosen as the output class. In the 1 vs. all method, each class is compared against all other classes and the class for which the output function is greatest is chosen for each input. I have chosen to use the 1 vs. 1 method for this project since there are only 6 classes, making this computationally feasible. To determine the classification rate of the ELM-SVM method, I used 3-fold cross validation. The training set was used to train the ELM layer, then the training output of the ELM layer was used to train the multi-class SVM. A simple linear kernel SVM was used to avoid overfitting. The test data was then applied to the ELM layer, then the test output of the ELM layer applied to the SVM. The SVM output was used to calculate classification rate. 3-fold cross validation was repeated 1000 times with a the partition being randomly selected for each repetition; this was done to ensure that the mean classification rate reflected the method of classification rather than an ideal or nonideal partitioning. This entire process was repeated for several of the top-rated feature sets as determined in the feature selection step. Additionally, I performed classification of the data using only the multi-class SVM with the ELM layer omitted. This followed the same 3-fold cross validation with 1000 replicates technique described above. Last, I performed two-class classification using the above techniques (substituting a single linear SVM for the multiclass SVM) where the first class consisted of carcinoma, fibro-adenoma, and mastopathy tissue samples and the second class consisted of glandular, connective, and adipose tissue samples. My reason for doing so is that the first three tissues are all cancerous tissue types while the second three are noncancerous.

6 3. Results 3.1 Feature Selection C l a s s i f i c a t i o n R a t e I O P D A D R A R E A P A P P I O P A # N e u r o n s i n H i d d e n L a y e r Figure 4: Classification Rate as a Function of Neurons in the Hidden Layer for Highest-ranked Feature Sets After determining the strength of every feature vector set using the technique described above, I selected the top three feature vector sets: [PA500, P], [P], and [I0, PA500]. Figure 4 shows the classification rates of these three feature vector sets as a function of number of neurons in the hidden layer for a single ELM. I have included the feature set [I0, P, DA, DR, AREA] because this was determined to be the optimal feature set in a previous study of this data set using analysis of mutual information between individual features and the true class labels. The three best feature vectors determined using the exhaustive search method clearly outperform that determined by the mutual information method.

7 3.2 Classification Table 1: Summary of results of the 6-class problem Feature Vector [I0 P DA DR AREA][PA500 P][I0 PA500] [P] All 9 Features Mean CR(ELM/SVM) Mean CR(SVM) CR Std Dev (ELM/SVM) CR Std Dev (SVM) Mean Time (ELM/SVM) Mean Time (SVM) Time std (ELM/SVM) Time std(svm) The SVM-only classification method outperformed the ELM-SVM method for all feature sets. Additionally, the SVM-only classification method was faster than the ELM-SVM method for all feature vectors except for the one containing all features. While the SVM-only method took longer to compute for this feature vector, it yielded the highest classification rate of the 6-class problem. Table 2: Summary of results of the 2-class problem Feature Vector [I0 P DA DR AREA][PA500 P][I0 PA500] [P] All 9 Features Mean CR(ELM/SVM) Mean CR(SVM) CR Std Dev (ELM/SVM) CR Std Dev (SVM) Mean Time (ELM/SVM) Mean Time (SVM) Time std (ELM/SVM) Time std(svm) Both classification techniques show improvement in classification rate for the 2-class problem compared to the 6-class problem. Again, the SVM-only technique outperforms the ELM-SVM technique for all feature vectors. Additionally, the SVM-only technique requires a much shorter computation time compared to the ELM-SVM technique. 4 Discussion Performance of the feature vectors selected by exhaustive search outperformed the previously selected feature vector in the ELM-SVM method, but all feature vectors showed similar performance for the SVM-only approach. The justification for using a non-exhaustive feature selection technique is

8 typically to save time. In a clinical application of breast tissue classification using EIS, the feature selection step would be performed when developing the system for classification rather than in-clinic. As such, the amount of time it takes to perform feature selection is unimportant as long as it can be achieved in a finite amount of time. When performing the exhaustive feature selection for 9 features, it took less than 10 minutes to determine the ideal feature vectors; the improvement in classification performance more than made up for this minor inconvenience in computation time. If classification of breast tissue using EIS is ever used as a clinical pre-screening process, it is my recommendation that an exhaustive search of possible feature vectors be used, so long as the set of possible features remains relatively small. The ELM-SVM method took longer on average to compute and had a lower classification rate than the SVM-only method. The low classification rate of the ELM layer resulted in a loss of information and gain in computation time for the ELM-SVM method. Based on these results, it seems that a SVM-only approach would be preferable to the ELM-SVM approach for clinical classification of breast tissue. Based on this data set, the ability to determine exact tissue type does not have a high enough classification rate to replace the need for histological and chemical screening of tissue samples. However, results of the two-class approach indicate that classification using EIS may be useful as a pre-screening process to determine if an excised sample is appropriate for further screening. This would reduce the chance that a sample sent for further screening results in an inconclusive result. While the classification rate is only ~80% for the two-class problem; this is based on a relatively small number of tissue samples. If a large-scale study of EIS properties of breast tissue were performed, it is possible that classification rate could be greatly improved. One of the aims of this study was to determine if there is any physiological significance to the strength of different features. In the two-class problem, the inclusion of I0 caused considerable improvement in the ELM-SVM classification. I0 is a measure of the real impedance (non-capacitive); it is possible that cancerous tissue and regular tissue differ in water content and/or ionic strength and thus have different real impedance properties. Future work could improve the accuracy of classification and our understanding of the physiological basis of tissue impedance properties by including equivalent circuit component values in the feature vector. The potential benefit of immediate tissue classification, or at least improved pre-screening of tissue could reduce the cost of screening and the amount of time a patient needs to wait before receiving their results. Before this technique can be used clinically, the classification rate must be greatly improved to prevent the occurrence of false positives.

9 References [1] American Cancer Society. [ ndcytologyspecimensforcancer/testing-biopsy-and-cytology-specimens-for-cancer-how-long-doestesting-take] Accessed 15 Dec [2] Lvovich, V. F. (2012). Impedance spectroscopy: applications to electrochemical and dielectric phenomena. John Wiley & Sons. [3] Williams, J. C., Hippensteel, J. A., Dilgen, J., Shain, W., & Kipke, D. R. (2007). Complex impedance spectroscopy for monitoring tissue responses to inserted neural implants. Journal of neural engineering, 4(4), 410. [4] Jossinet, J. (1996). Variability of impedivity in normal and pathological breast tissue. Medical and Biological Engineering and Computing, 34(5), [5] UCI Machine Learning Repository. [ Accessed 7 Dec [6] Daliri, M. R. (2013). Combining extreme learning machines using support vector machines for breast tissue classification. Computer methods in biomechanics and biomedical engineering, (ahead-ofprint), 1-7.