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TECHNICAL PAPERS

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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References

Levy,  A. R., Goldberg,  M. S., Mayo,  N. E., Hanley,  J. A., and Poitras,  B., 1996, “Reducing the Lifetime Risk of Cancer from Spinal Radiographs Among People With Adolescent Idiopathic Scoliosis,” Spine, 21(13), pp. 1540–1548.
Reamy,  B. V., and Slakey,  J. B., 2001, “Adolescent Idiopathic Scoliosis: Review and Current Concepts,” Am. Fam. Physician, 64(1), pp. 111–116.
Pope,  M. H., Stokes,  A. F., and Moreland,  M., 1984, “The Biomechanics of Scoliosis,” Crit. Rev. Biomed. Eng., 11(3), pp. 157–188.
Goldberg,  C. J., Kaliszer,  M., Moore,  D. P., Fogarty,  E. E., and Dowling,  F. E., 2001, “Surface Topography, Cobb Angles, and Cosmetic Change in Scoliosis,” Spine, 26(4), pp. E55–63.
Stokes,  I. A., and Moreland,  M. S., 1989, “Concordance of Back Surface Asymmetry and Spine Shape in Idiopathic Scoliosis,” Spine, 14(1), pp. 73–78.
Thulbourne,  T., and Gillespie,  R., 1976, “The Rib Hump in Idiopathic Scoliosis. Measurement, Analysis and Response to Treatment,” J. Bone Joint Surg. Br., 58(1), pp. 64–71.
Scutt,  N. D., Dangerfield,  P. H., and Dorgan,  J. C., 1996, “The Relationship Between Surface and Radiological Deformity in Adolescent Idiopathic Scoliosis: Effect of Change in Body Position,” Eur. Spine J., 5(2), pp. 85–90.
Theologis,  T. N., Fairbank,  J. C., Turner-Smith,  A. R., and Pantazopoulos,  T., 1997, “Early Detection of Progression in Adolescent Idiopathic Scoliosis by Measurement of Changes in Back Shape with the Integrated Shape Imaging System Scanner,” Spine, 22(11), pp. 1223–1227.
Bunnell,  W. P., 1984, “An Objective Criterion for Scoliosis Screening,” J. Bone Jt. Surg., Am. Vol., 66(9), pp. 1381–1387.
Jaremko,  J. L., Poncet,  P., Ronsky,  J., Harder,  J., Dansereau,  J., Labelle,  H., and Zernicke,  R. F., 2001, “Estimation of Spinal Deformity in Scoliosis from Torso Surface Cross Sections,” Spine, 26(14), pp. 1583–1591.
Jaremko,  J. L., Delorme,  S., Dansereau,  J., Labelle,  H., Ronsky,  J., Poncet,  P., Harder,  J., Dewar,  R., and R. F.,  Zernicke, 2000, “Use of Neural Networks to Correlate Spine and Rib Deformity in Scoliosis,” Computer Methods in Biomechanics and Biomedical Engineering, 3(3), pp. 203–213.
Dayhoff, J. E., 1990, Back-Error Propagation, in Neural Network Architectures: An Introduction, New York, Van Nostrand Reinhold, pp. 58–79.
Dayhoff, J. E., 1990, Neural Network Architectures: An Introduction, Van Nostrand Reinhold, New York.
LeCun, Y., Bottou, L., Orr, G. B., and Muller, K. R., 1998, Efficient Backpropagation, in Neural Networks: Tricks of the Trade, Orr, G. B., and Muller, K. R., eds., New York, Springer-Verlag, pp. 9–50.
Cross,  S. S., Harrison,  R. F., and Kennedy,  R. L., 1995, “Introduction to Neural Networks,” Lancet, 346(8982), pp. 1075–1079.
Friedman,  J., 1991, “Multivariate Adaptive Regression Splines (MARS),” Annals of Statistics, 19, pp.1–141.
Hertz, J., Krogh, A., and Palmer, R. G., 1991, Principal Component Analysis, in Introduction to the Theory of Neural Computation, New York, Addison-Wesley, pp. 204–210.
Natale,  C. Di, Macagnano,  A., D’Amico,  A., and Davide,  F., 1997, “Electronic-Nose Modelling and Data Analysis Using a Self-Organizing Map,” Measurements in Science & Technology, 8, pp. 1236–1243.
Dayhoff, J. E., 1990, The Kohonen Feature Map, in Neural Network Architectures: An Introduction, New York, Van Nostrand Reinhold, pp. 163–191.
Naes,  T., Kvaal,  K., Isaksson,  T., and Miller,  C., 1993, “ANNs in Multivariate Calibration,” Journal of Near-Infrared Spectroscopy, 1, pp. 1–11.
Forrest,  S., 1993, “Genetic Algorithms: Principles of Natural Selection Applied to Computation,” Science, 261(5123), pp. 872–878.
Holland, J. H., 1975, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, Michigan.
Dybowski,  R., Weller,  P., Chang,  R., and Gant,  V., 1996, “Prediction of Outcome in Critically Ill Patients Using Artificial Neural Network Synthesized By Genetic Algorithm,” Lancet, 347(9009), pp. 1146–1150.
Jefferson,  M. F., Pendleton,  N., Lucas,  S. B., and Horan,  M. A., 1997, “Comparison of a Genetic Algorithm Neural Network with Logistic Regression for Predicting Outcome After Surgery for Patients with Nonsmall Cell Lung Carcinoma,” Cancer, 79(7), pp. 1338–1342.
Jefferson,  M. F., Pendleton,  N., Mohamed,  S., Kirkman,  E., Little,  R. A., Lucas,  S. B., and Horan,  M. A., 1998, “Prediction of Hemorrhagic Blood Loss with a Genetic Algorithm Neural Network,” J. Appl. Physiol., 84(1), pp. 357–361.
Jefferson,  M. F., Pendleton,  N., Lucas,  C. P., Lucas,  S. B., and Horan,  M. A., 1998, “Evolution of Artificial Neural Network Architecture: Prediction of Depression After Mania,” Methods Inf. Med., 37(3), pp. 220–225.
Poncet,  P., Delorme,  S., Ronsky,  J. L., Dansereau,  J., Harder,  J., Clynch,  G., Dewar,  R. O., Labelle,  H., Gu,  P. H., and Zernicke,  R. F., 2000, “Reconstruction of Laser-Scanned 3D Torso Topography and Stereo-Radiographical Spine and Rib-Cage Geometry in Scoliosis,” Computer Methods in Biomechanics & Biomedical Engineering, 4(1), pp. 59–75.
Labelle,  H., Dansereau,  J., Bellefleur,  C., and Jequier,  J. C., 1995, “Variability of Geometric Measurements from Three-Dimensional Reconstructions of Scoliotic Spines and Rib Cages,” Eur. Spine J., 4(2), pp. 88–94.
Jaremko,  J. L., Poncet,  P., Ronsky,  J. L., and Zernicke,  R. F., 2000, “Estimation of Vertebral Levels from Torso Surface Data,” Arch. Physiol. Biochem., 108(1–2), pp. 198.
Houck, C. R., Joines, J., and Kay, M., 1996, “A Genetic Algorithm for Function Optimization: A Matlab Implementation,” ACM Transactions on Mathematical Software, http://www.ie.ncsu.edu/gaot.
Demuth, H., and Beale, M., 2000, Neural Network Toolbox User’s Guide (v. 4.0 for Matlab v. 6.0), The Math Works, Natick, MA.
Weinstein,  S. L., and Ponseti,  I. V., 1983, “Curve Progression in Idiopathic Scoliosis,” J. Bone Jt. Surg., Am. Vol., 65(4), pp. 447–455.
Drerup,  B., and Hierholzer,  E., 1996, “Assessment of Scoliotic Deformity from Back Shape Asymmetry Using an Improved Mathematical Model,” Clin. Biomech. (Los Angel. Calif.), 11(7), pp. 376–383.

Figures

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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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