Center for Biomathematical Sciences

Artificial Neural Networks and the
Diagnosis of Ovarian Dysplasia

Methods: Histologic sections from 37 ovaries of which 26 were diagnosed with dysplasia in epithelial inclusion cysts (10 adjacent to carcinoma and 16 incidental) and 11 with benign epithelial inclusion cysts were evaluated by tracing nuclear profiles and assessing measures of nuclear area, shape and texture. These were analyzed using artificial neural networks and also statistically using the Kruskal-Wallis test with the Dunn procedure to compare the morphologic similarity of incidental and adjacent dysplasia.

Results: Neither statistical nor artificial neural network analysis was able to distinguish between incidental and adjacent dysplasia. Both types differed significantly from the control cases.

Conclusions: Neural networks are powerful classification tools when applied to multiple
variables extracted from individual cases. In this study, they helped to substantiate the
similarity between dysplasia found incidentally and that adjacent to ovarian carcinoma. As
dysplasia represents a potential pre-cancerous lesion, its incidental finding may help identify
patients at risk for developing ovarian carcinoma.

This work was supported in part by a traineeship on NIH MSTP Training Grant GM 7280.

An overview of neural networks:
Artificial neural networks (ANNs) are a type of artificial intelligence. As opposed to specifying rules for assigning values to output variables on the basis of input variables, an ANN is presented with a training set of data from which it effectively "learns" such rules while making few assumptions as to the nature of the data. While several neural network designs have been studied and employed for classification, backpropagation networks remain the standard. The fundamental unit of structure in artificial neural networks, like their biological counterparts, is the neuron. A backpropagation ANN has its neurons arranged in a multilayered architecture, with each neuron connected to the neurons in its adjacent layers. There is a layer of input neurons, one or more layers of hidden neurons, and a layer of output neurons. A value is associated with each neuron, and a weight with each connection. In addition, hidden and output neurons have biases associated with them; these may be regarded as weights of special neurons having constant values of one. The value of a hidden or output neuron is computed by passing the biased weighted sum of values from the previous layer through a "transfer function," most typically a sigmoidal function. More formally, let n be the number of layers, n_k be the number of neurons in layer k (k = 1, 2,..., n), w_ijk be the connection weight between the ith neuron in layer k and the jth neuron in layer k-1 (i = 1, 2,..., n_k; j = 1, 2,..., n_k-1; k = 2, 3,..., n), and b_ik and v_ik be the bias and value of the ith neuron in layer k, respectively (i = 1, 2,..., n_k; k = 2, 3,..., n). Then the values v_ik are determined from the formula

The architecture of a typical backpropagation network for use in morphometry is illustrated in the figure below. As is shown, input neurons represent morphometric features, numerical measures of histologic features such as nuclear size and shape, chromatin appearance, and tissue architecture, while output neurons code for the diagnosis. The values taken by output variables are generally constrained to the interval [0, 1]; thus, e.g., a value near one for the "Malignant" neuron is identified with a diagnosis of malignancy.

The classificatory power of neural networks is contained in the weights and biases, known together as the connection matrix. Determination of the optimal connection matrix for a particular set of training facts is a computationally difficult problem; for even very simple networks, the problem has been mathematically demonstrated to be NP-complete (not computable in polynomial time). The approach generally used in ANNs is an adaptive one, in which the weights and biases are "learned" over repeated iterations through the training set. The connection matrix is initially set at random, and the values of hidden and output neurons are computed for a feature vector. Output neuron values are compared with their target values, e.g., (0,1) for malignancy in the example. If the difference between the output value and its target value, known as the error factor, is less than a specified training tolerance, the case represented by the parameter value is regarded to be correctly classified, and the next case is considered. If the error factor is too large, then the connection matrix is modified using some learning rule, most typically the generalized delta rule or a modification thereof. These learning rules reflect factors such as the transfer function, neuron values, error factors, weights, and biases. Initially, output biases and connection weights between output neurons and the last layer of hidden neurons are adjusted. These changes are then backpropagated, one layer at a time, until the whole connection matrix has been modified. Cycling through the training set continues until all cases are correctly classified or, barring this, some other specified stopping point.

Using the final connection matrix, a new set of inputs can be used to predict output values. Numerous factors are incorporated into the design of a neural network, and these may affect its training and ability to generalize. Such factors include network topology, noise, order of training facts, choice of transfer function, initial weights, range specification, learning rate, training tolerance, testing tolerance, and the training set.

Adapted from:
Einstein AJ, Gil J. Classification procedures for diagnosis based on multiple morphometric parameters. Acta Stereologica 1996; 15: 15-24.

This work was supported in part by a traineeship on NIH MSTP Training Grant GM 7280 and by a Hans Elias Bursary.