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PARAMETRIC AND NON-PARAMETRIC TECHNIQUES FOR IDENTIFYING IMAGES OF F-ACTIN DISTRIBUTION IN ENDOTHELIAL CELLS WITH APPLIED AGONISTS Kamal J. Khiani1, Sameh M. Yamany1, William D. Ehringer2, Fredrick N. Miller2 and Aly A. Farag1 1 Department of Electrical Engineering and 2 Center for Applied Microcirculatory Research University of Louisville, Louisville, KY 40292. E-mail: [email protected] , Phone: (502) 852-7510, Fax (502) 852-6807 Abstract | This research deals with developing automatic classi cation algorithms for identifying images of F-actin distribution in endothelial cells with dierent treatment of agonists. Parametric and non-parametric classi cation techniques were investigated such as statistical and arti cial neural network classi ers. First and second order features were extracted from the images. Among the statistical classi cation techniques are the Bayes approach and the K-nearest neighbor (K-NN). For the neural network approach, we used the multilayer feedforward and the functional link network. All of these techniques provide adequate results with the neural methods performing with higher accuracy reaching above 97% classi cation. Keywords | Endothelial cells, F-actin, Permeability, Pattern recognition, Statistical classi ers, Bayes rule, K-NN, Neural classi ers, Functional link.

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I. Introduction

NDOTHELIAL cells line the internal cavities of the vasculature. These cells contain a brous matrix which is called the cytoskeleton. This matrix is composed of actin. In polymerized form, it is called F-actin and in molecular form it is called G-actin. Endothelial cells play a direct role during in ammation by increasing permeability [1]. The permeability refers to the passage of a substance. There are drugs or agonists which cause this increase in permeability on the endothelial cells. These drugs include -thrombin and histamine. The permeability results in and/or accompanies rearrangement of the F-actin which induces pores in the cytoskeletal matrix. -Thrombin causes a greater rearrangement and distribution of the F-actin as compared to the histamine. Understanding the molecular mechanism of these agonists is important for the study of other agonists that may model the same mechanisms. Developing an automatic classi cation scheme could be used as a screening process for the other agonists. This screening would indicate either a similar \-thrombin like" or a \histamine like" mechanism. This would decrease the number of experiments needed to be performed on determining the mechanisms of permeability. II. Methods

and images were collected from each class after treatment with agonists. Images were digitized by use of a Carl Zeiss Axiovert 100 Microscope equipped with a mercury lamp and a rhodamine lter set. Various preprocessing steps were conducted to eliminate experimental variations [2]. On the resulting images (30 images from each class), rst-order features (using the gray level histogram) and second-order features (using the gray level co-occurrence matrix) were extracted [3]. Four features provided the best discrimination. Two were from the gray level histogram (1st percentile and mean gray level) and two from the cooccurrence matrix (entropy and correlation). These features were used in the design and testing of the classi ers. For each class, 15 images were used to train the design and the other 15 images were used in the testing.

Method 1:

The statistical classi ers are also divided into parametric and non-parametric. The Bayes approach, which is parametric, is based on the assumption that all the relevant probability values are known such as the a priori probability P (w ). The a posteriori probabilities P (! j x~) may be calculated from the a priori probabilities P (! ) and the conditional density functions p(~x j ! ) using Bayes' theorem (equation 1). (1) P (! j x~) = p(~x j p!(~x))P (! ) where 3 (2) p(~x) = p(~x j ! )P (! ) i

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We followed the Bayes decision rule for classi cation assuming Gaussian distributions. Decide ! for maxfP (! j x~)g for (i = 1; 2; 3) (3) Because the covariance matrices are dierent for the three classes, the Bayes classi er becomes a quadratic discriminant function. i

Method 2:

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Along with the two classes of agonist treatments, there The K-nearest neighbor (K-NN) is a non-parametric stawas another class of untreated or control endothelial cells. tistical classi er which means that no probability distribuThe classi cation becomes a three class problem as shown tion was assumed. The rule classi es a sample by assigning in gure 1. A controlled imaging environment was designed it the label most frequently represented among the k nearThe following are the steps. This work has been partially supported by grants from the Whitaker est1.samples. Obtain distances between the test sample and all the Foundation and the Center for Applied Microcirculatory Research, samples in the design set. the University of Louisville.

2. Sort the obtained distance values in ascending order. 3. Consider the subset of the rst k distances in the sorted array. Knowing the class membership of each of these samples, assign the test sample to the majority class in this subset if exists, otherwise the result is considered inconclusive. 4. Estimate the error rate by comparing the classi cation results with actual class memberships.

Method 3:

The arti cial neural network methods are nonparametric. For the multilayer feedforward network there is one input layer, one or more hidden layers and one output layer. The basic element of the network is called the neuron [4]. Each neuron consists of a set of weights, one for each input, and an activation function. The neuron computes the weighted sum of the inputs and passes this value to an activation function which generates an output. A 4-3-3 (input ? hidden ? output) multilayer feedforward network was investigated. With neural networks, training is a process by which the network is conditioned to Fig. 1. The three class of images control (top left), -thrombin (top right) and histamine (bottom ) yield a particular response to a speci c input. The training sample consists of a pair of data consisting of an input TABLE I vector and its corresponding desired output vector. DurResults of the different classifiers ing training, the network weights are adjusted until some maximum error criterion is satis ed. The training was acCLASSIFIER % CORRECT complished with the error back-propagation training algoBayes (Method 1 ) 95.5% rithm (EBPTA) [4]. This is a supervised learning algorithm which performs a gradient descent on a squared error enK-NN (Method 2 ) 95.5% ergy surface to arrive at a minimum. Multilayer NN (Method 3 ) 97.7%

Method 4:

Functional link neural networks are single-layer networks that are able to handle linearly non-separable classes due to increasing the dimensions of the inputs by using nonlinear combination of the input parameters. In the so-called tensor model the additional input terms are obtained for each of the input feature vectors as the product x x for 8i; j 2 [1; D] where D is the dimension of the input vector. With the additional inputs, a 10-3 (input ? output) architecture was implemented for the four feature vectors. The input/output mapping was learned using the simple delta learning rule instead of the generalized delta rule [5]. Although no new information is explicitly inserted in the process, the input representation has been enhanced and the linear separability can be achieved in the extended space [4]. The key idea behind this method is to nd a suitably enhanced representation of the input data. i

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III. Results

Table 1 shows the results of the classi cation of the both the statistical and neural approaches. The results demonstrate that both methods classify the three class of images well. The Bayes and K-NN classi ers reached classi cation rates above 95%. The arti cial neural network implementations seems to classify just as well and in some cases better. The highest classi cation rate was 97.7%. Current work is concerned with correlating the features with the physical phenomena in the images.

Func. Link NN (Method 4 )

95.5%

IV. Conclusions

Classi cation of the F-actin distribution in endothelial cells treated with agonists was accomplished using dierent classi cation techniques. Based on the results obtained, the neural network classi er proved to be the best among the others in terms of speed, accuracy and ease of implementation. In conclusion, it is feasible to discriminate the dierent F-actin distributions from the types of treatments on endothelial cells. This enables further investigation of other agonists which may resemble the same types of organization of the F-actin bers and hence imply similar mechanisms. Additional details are in [2]. References

[1] William D. Ehringer, Michael J. Edwards and Frederick N. Miller, \Mechanisms of -Thrombin, Histamine, and Bradykinin Induced Endothelial Permeability," Journal of Cellular Physiology, 1996. [2] K.J. Khiani, \Classi cation of F-actin distribution under treatment of drugs in endothelial cells," MENG Thesis, University of Louisville, Louisville KY, 1996. [3] K.J. Khiani, S.M. Yamany, W.D. Ehringer, F.N. Miller and A.A. Farag, \Classi cation of the eects of F-actin under treatment of drugs in endothelial cells," ANNIE 1996 (submitted). [4] J.M. Zurada, Introduction to Arti cial Neural Systems, St. Paul, MN: West Publishing Company, 1992. [5] Y.H. Pao, Adaptive Pattern Recognition and Neural Networks, Addison Wesley pub. 1989.