Jian-Qiao Sun, Ph.D.
Department of Mechanical Engineering
University of Delaware
Newark, Delaware 19176
INTRODUCTION: Over 40,000 children in this country are affected by cerebral palsy with abnormal gait patterns. Approximately one third of these children need to have surgeries performed in order to improve the efficiency of their gait patterns. The resulting gait patterns rarely resemble those of normal children. Visualization of the predicted changes in the gait pattern prior to surgical intervention can help surgeons in their decision making, and in their explaining the effect of the operation on the post-operative gait patterns to a child s parents. Such a prediction capability may even help to improve the surgical procedure. However, this is a very difficult task and there are no published studies and commercial products that provide the prediction capability of the surgical outcome. This paper presents a method using neural networks for predicting the surgical outcome.
Cerebral palsy (CP) presents a variety of clinical manifestations; and the gait patterns of CP patients have a significant variability. A forward based model for predicting the functional effects of specific surgical procedures on the gait patterns of cerebral palsy patients based on pre- operative kinematic data will require the development of a large database and sophisticated mathematical tools. This is because there are many different patterns of involvement, and the functional effects of specific surgical procedures on the gait patterns often do not render simple mathematical forms and are typically nonlinear. With a large database of pre- and post-operative kinematic measurements as well as EMG information, neural networks become a very attractive tool for discovering the underpinning nonlinear relationship between pre- and post-operative gait patterns for specific surgical procedures.
MATERIALS AND METHODS: Neural networks are composed of many simple elements in parallel mimicking biological systems. Neural networks have been trained to perform very complex functions in a broad range of scientific and engineering disciplines. If a network is well trained, it is able to predict the post-operative gait patterns of new patients. This important property of the network is called generalization and is a key to the present work.
The raw data from the gait analysis must be pre-processed before used as the input and output of neural networks. One common pre-processing in the gait analysis is to change the time scale of gait parameters to the walking cycles. This scaling eliminates the effect of speed with which the child was walking at the time of gait analysis. Since walking is a periodic process, only one cycle of the gait parameters consisting of many data points is needed. The time history of the gait parameters can be expanded in terms of a Fourier series in order to reduce the size of the data. We have found, for example, that the first nine Fourier coefficients of the pre- and post- operative knee flexion/extension angles are adequate to reproduce the original time history of the knee angles by the inverse Fourier transform. Figure 1 shows a couple of examples.
We now have a representation of pre- and post-operative knee flexion/extension angles in terms of a 1X9 vector. We proceed to develop a neural network to predict the 1X9 vectors representing the post-operative knee angles by using the 1X9 vectors representing the pre- operative knee angles of all the patients in the group. The neural network that we used in the example reported herein is a multilayer perception with twelve hidden neurons. The network is trained by using a back-propagation scheme.
RESULTS: 80% percent of the patients in a group was used to train the network and the re maining 20% was used to test the network. The network weights were kept when the error on the test set reached minimum and at the same time, the error on the training set was reasonably small. Some results of prediction are shown in Figure 2. The network can predict the post- operative knee angles of all the patients in the training set, as expected, and it can also give a reasonable estimate of the post-operative knee angles of the patients in the test set. This later finding indicates the ability of the network to make good predictions for a new patient in the future.
DISCUSSION: This study demonstrates the ability of neural networks to predict the post- operative gait patterns by using the pre-operative gait data for a group of CP patients. The neural network must be trained by using data from a patient population that are representative of the group so that it will be able to correctly predict the surgical outcome of a new patient belonging to the same group.
CONCLUSION: Neural networks has been successfully applied to model the pre- and post- operative gait patterns of CP children undergoing rectus transfer surgery. If trained with a representative group of the patients, the networks can predict the surgical outcome of a new patient with a high confidence level. Neural networks can also be used to model many other biological systems undergoing some medical treatments.
Figure 1. The first nine Fourier coefficients (top) of pre- and post-operative right knee flexion and extension angles (middle and bottom) for Patients #1, #8 and #10 (from left to right). The Fourier series reproduction (dash-dot line) of the measurement (solid line) is the worst for Patient #1.
Figure 2. Top: The actual (circles) and predicted (crosses) Fourier coefficients. Bottom: The measured (solid line) and the predicted (dash-dot line) post-operative right knee flexion and extension angles of Patients #1, #8 and #10 (from left to right). Patients #1 and #8 are in the training set and Patient #10 is in the test set.
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