Genetic Algorithm–Neural Network Estimation of Cobb Angle from Torso Asymmetry in Scoliosis

[+] Author and Article Information
Jacob L. Jaremko, Philippe Poncet, Janet Ronsky, James Harder, Ronald F. Zernicke

Dept. of Surgery Faculty of Medicine, University of Calgary, 3330 Hospital Dr. NW, Calgary, AB, T2N 4N1

Jean Dansereau

Dept. of Mechanical Engineering, Ecole Polytechnique, C.P. 6079, Succ. Centre–Ville, Montreal, PQ H3C 3A7

Hubert Labelle

Ste. Justine Hospital, 3175 Cote Ste-Catherine, Montreal PQ H3T 1C5

J Biomech Eng 124(5), 496-503 (Sep 30, 2002) (8 pages) doi:10.1115/1.1503375 History: Received July 01, 2001; Revised June 01, 2002; Online September 30, 2002
Copyright © 2002 by ASME
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Artificial neural network (ANN) architecture. The input layer accepted indices of torso asymmetry. In the hidden or processing layers, each node produced an output if the sum of inputs from connected links, multiplied by the link weights, was sufficiently large. Bias nodes functioned as constant terms in the ANN, like y-intercepts in linear regression models. Use of hidden layers enabled nonlinear calculations recognizing features of the input data. The ANN output in this study was an estimate of the Cobb angle.
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Calculation of selected torso asymmetry indices. (a) Cross-sections were cut through the torso surface model. PSIS axis=line joining skin markers on posterior superior iliac spines. (b) The quasi-Cobb angle (θ) was computed for each index of asymmetry between the most appropriate pair of points of inflection on the index-curve. (c) Angles of principal axis (PAX) rotation (θ1), back surface rotation (BSR, θ2), and the difference between BSR and PAX rotation (θ3) were recorded relative to the PSIS axis along with the “rib hump” (dL–dR). (d) Half-areas were cut relative to the PAX reference axis. Asymmetry of half-centroids CL and CR was measured in the antero-posterior (dXC) and lateral (ZCL vs. ZCR) directions. The angle of rotation of the line joining the half-centroids (θ), and the difference between aspect ratios (dAP/dLat) between left and right half-areas were also computed.
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Genetic algorithm for selection of neural-network (ANN) input indices. (1) The population was initialized by creating a set of “chromosomes” containing a “gene” for each available input index, randomly set to zero (“do not use”) or one (“ok to use”). (2) The fitness of each chromosome was the accuracy of Cobb-angle predictions from an ANN using only the indices whose genes have non-zero values for that chromosome. (3) A new population of the same size as the original one was created by selecting chromosomes as if spinning a roulette wheel, with the chance of a chromosome being selected for the new population being proportional to that chromosome’s fitness. (4) These selected chromosomes then “reproduced” via mutation and cross-over. (5) The algorithm repeated, starting a new “generation” with the updated population. Over time, the population “evolved” towards optimal fitness.
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Genetic algorithm (GA) training showing typically rapid convergence. This example GA tested 20 individuals each with chromosomes of 24 input indices. Fitness was already high in the initial population due to “seeding” of the population with individuals whose indices correlated well to the Cobb angle.
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Actual Cobb angle vs. ANN-estimate of Cobb angle, in (a) training set and (b) test set. ANN results were better in the training set; this “over-fitting” would be reduced by use of a larger data set.
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Sensitivity (SN) and specificity (SP) of the prediction that a patient’s Cobb angle would be greater than the specified minimum value, as fractions of the maximum possible value of 1.0. From the prevalence line (the proportion of the data set having Cobb angles greater than a given value) it is clear that 70% of our patients had curves between 20°–50°. In this zone, both SN and SP were greater than 0.7, each peaking near 0.95 at thresholds of 25°–35°. Estimation of severe curves >50° was also highly sensitive and specific.




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