Entropy-based method to quantify limb length discrepancy using inertial sensors

Entropy-based method to quantify limb length discrepancy using inertial sensors

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Limb length is a useful parameter in the assessment of common musculoskeletal disorders such as limb length discrepancy. The measurement variation among rates adversely affects the quantitative aspect of assessments and introduces a greater subjectivity in the course of treatment. Common practise for measuring limb length is based on radiographic imaging techniques which are inconvenient, costly and require clinical knowledge. Direct instruments are difficult to use with patients due to susceptibility to human error in determining the position of the rotational joint. In this study, the determination of limb length is automated using a contemporary algorithm which applies curvature to the measurements from a low-cost and miniaturised inertial sensor, primarily used in the bio-kinematic research. The motion artefacts contribute to the ultimate estimations and, in this approach, a least noise threshold model is employed to address the robustness. The proposed estimation technique was validated with real-data observed from 14 healthy subjects comparing with radiographic and direct measurements. The experimental results indicate greater accuracy compared with manual measurements with low root mean squared error percentages with values ranging from 5.34 to 5.84%. Additionally, the mean limb length difference between our estimator and both radiographic measurements and direct measurement was <1.6 cm.


    1. 1)
      • 1. Gurney, B.: ‘Leg length discrepancy’, Gait Posture, 2002, 15, (2), pp. 195206.
    2. 2)
      • 2. Nguyen, H.T., Resnick, D.N., Caldwell, S.G., et al: ‘Interexaminer reliability of activator method's relative leg-length evaluation in the prone extended position’, J. Manipulative Physiol. Ther., 1999, 22, (9), pp. 565569.
    3. 3)
      • 3. Gibbons, P., Dumper, C., Gosling, C.: ‘Inter-examiner and intra-examiner agreement for assessing simulated leg length inequality using palpation and observation during a standing assessment’, J. Osteopath. Med., 2002, 5, (2), pp. 5358.
    4. 4)
      • 4. Subotnick, S.I.: ‘Limb length discrepancies of the lower extremity (the short leg syndrome)’, J. Orthop. Sports Phys. Ther., 1981, 3, (1), pp. 1116.
    5. 5)
      • 5. Woerman, A.L., Binder-Macleod, S.A.: ‘Leg length discrepancy assessment: accuracy and precision in five clinical methods of evaluation’, J. Orthop. Sports Phys. Ther., 1984, 5, (5), pp. 230239.
    6. 6)
      • 6. Reid, D., Smith, B.: ‘Leg length inequality: a review of etiology and management’, Physiother. Canada, 1984, 36, (4), pp. 177182.
    7. 7)
      • 7. Junker, H., Amft, O., Lukowicz, P., et al: ‘Gesture spotting with body-worn inertial sensors to detect user activities’, Pattern Recognit., 2008, 41, (6), pp. 20102024, doi:
    8. 8)
      • 8. Altun, K., Barshan, B., Tunçel, O.: ‘Comparative study on classifying human activities with miniature inertial and magnetic sensors’, Pattern Recognit., 2010, 43, (10), pp. 36053620, doi:
    9. 9)
      • 9. Avci, A., Bosch, S., Marin-Perianu, M., et al: ‘Activity recognition using inertial sensing for healthcare, wellbeing and sports applications: a survey’. 23rd Int. Conf. Architecture of Computing Systems (ARCS) VDE, 2010, pp. 110.
    10. 10)
      • 10. Amft, O., Tröster, G.: ‘Recognition of dietary activity events using on-body sensors’, Artif. Intell. Med., 2008, 42, (2), pp. 121136, doi:, wearable Computing and Artificial Intelligence for Healthcare Applications.
    11. 11)
      • 11. Tao, Y., Hu, H., Zhou, H.: ‘Integration of vision and inertial sensors for 3d arm motion tracking in home-based rehabilitation’, Int. J. Robot. Res., 2007, 26, (6), pp. 607624.
    12. 12)
      • 12. Zhou, H., Hu, H., Harris, N.D., et al: ‘Applications of wearable inertial sensors in estimation of upper limb movements’, Biomed. Signal Proc. Control, 2006, 1, (1), pp. 2232.
    13. 13)
      • 13. Karunarathne, S.M., Ekanayake, S.W., Pathirana, P.: ‘An adaptive complementary filter for inertial sensor based data fusion to track upper body motion’. 2014 – Seventh Int. Conf. Information and Automation for Sustainability (ICIAfS'14), Colombo, Sri Lanka, 2014.
    14. 14)
      • 14. Olivares, A., Górriz, J., Ramírez, J., et al: ‘Using frequency analysis to improve the precision of human body posture algorithms based on Kalman filters’, Comput. Biol. Med., 2016, 72, pp. 229238, doi:
    15. 15)
      • 15. Scholte op Reimer, W., Niessen, L.W., Huijsman, R., et al: ‘Cost-effectiveness of integrated stroke services’, J. Med., 2005, 98, (6), pp. 415425.
    16. 16)
      • 16. Madgwick, S., Harrison, A., Vaidyanathan, R.: ‘Estimation of IMU and MARG orientation using a gradient descent algorithm’. IEEE Int. Conf. Rehabilitation Robotics (ICORR), 2011, pp. 17, doi: 10.1109/ICORR.2011.5975346.
    17. 17)
      • 17. Madgwick, S.O.: ‘An efficient orientation filter for inertial and inertial/magnetic sensor arrays’. Report x-io, University of Bristol, UK.
    18. 18)
      • 18. Saiyi, L., Ferraro, M., Caelli, T., et al: ‘A syntactic two-component encoding model for the trajectories of human actions, biomedical and health informatics’, IEEE J., 2014, 18, (6), pp. 19031914, doi: 10.1109/JBHI.2014.2304519.
    19. 19)
      • 19. Karunarathne, S.M., Li, S., Ekanayake, S.W., et al: ‘A machine-driven process for human limb length estimation using inertial sensors’. 2015 IEEE Tenth Int. Conf. Industrial and Information Systems (ICIIS) (ICIIS'2015), Peradeniya, Sri Lanka, 2015.
    20. 20)
      • 20. Šimšk, D., Karchňák, J., Jobbágy, B., et al: ‘Design of inertial module for rehabilitation device’. 11th Int. Symp. Applied Machine Intelligence and Informatics, 2013, pp. 3336.
    21. 21)
      • 21. Woodman, O.J.: ‘An introduction to inertial navigation’. Technical Report UCAMCL-TR-696, University of Cambridge, Computer Laboratory, 2007, vol. 14, p. 15.
    22. 22)
      • 22. Flenniken, W., Wall, J., Bevly, D.: ‘Characterization of various IMU error sources and the effect on navigation performance’. Institute of Navigation Global Navigation Satellite System, 2005, pp. 967978.
    23. 23)
      • 23. Marschollek, M.: ‘A method to find generic thresholds for identifying relevant physical activity events in sensor data’, J. Med. Syst., 2016, 40, (1), pp. 18.
    24. 24)
      • 24. Richman, J.S., Lake, D.E., Moorman, J.: ‘Sample entropy’, in Abelson, John N., , Simom, Melvin I. (EDs.): ‘Numerical computer methods, part E, methods in enzymology’, vol. 384 (Academic Press, California, 2004), pp. 172184, doi:
    25. 25)
      • 25. Richman, J.S., Moorman, J.R.: ‘Physiological time-series analysis using approximate entropy and sample entropy’, Am. J. Physiol. Heart Circulatory Physiol., 2000, 278, (6), pp. H2039H2049.
    26. 26)
      • 26. Chen, X., Solomon, I., Chon, K.: ‘Comparison of the use of approximate entropy and sample entropy: applications to neural respiratory signal’. Conf. Proc. Annual Int. Conf. the IEEE Engineering in Medicine and Biology Society2004, vol. 4, pp. 42124215.
    27. 27)
      • 27. Grecu, V., Grecu, L., Demian, M., et al: ‘A virtual system for simulation of human upper limb’. Proc. World Congress on Engineering (WCE), London, UK, 2009.
    28. 28)
      • 28. Clauser, C.E., McConville, J.T., Young, J.W.: ‘Weight, volume, and center of mass of segments of the human body’. Technical Report, DTIC Document, 1969.
    29. 29)
      • 29. Ekanayake, S.W., Morris, A.J., Forrester, M., et al: ‘Biokin: an ambulatory platform for gait kinematic and feature assessment’, Healthc. Technol. Lett., 2015, 2, (1), pp. 4045.
    30. 30)
      • 30. Mannini, A., Intille, S.S., Rosenberger, M., et al: ‘Activity recognition using a single accelerometer placed at the wrist or ankle’, Med. Sci. Sports Exercise, 2013, 45, (11), p. 2193.
    31. 31)
      • 31. Karunarathne, M., Li, S., Ekanayake, S., et al: ‘An adaptive orientation misalignment calibration method for shoulder movements using inertial sensors: a feasibility study’. Int. Symp. Bioelectronics and Bioinformatics (ISBB), 2015, pp. 99102, doi: 10.1109/ISBB.2015.7344933.
    32. 32)
      • 32. De Luca, C.J., Gilmore, L.D., Kuznetsov, M., et al: ‘Filtering the surface EMG signal: movement artifact and baseline noise contamination’, J. Biomech., 2010, 43, (8), pp. 15731579.
    33. 33)
      • 33. Lazennec, J.Y., Brusson, A., Rousseau, M.A., et al: ‘Do patient's perceptions of leg length correlate with standing 2- and 3-dimensional radiographic imaging?’, J. Arthroplasty, 2016, 31, (10), pp. 23082313.
    34. 34)
      • 34. Tamura, T., Maeda, Y., Sekine, M., et al: ‘Wearable photoplethysmographic sensors–past and present’, Electronics, 2014, 3, (2), pp. 282302.
    35. 35)
      • 35. Goldberger, A.L., Peng, C.-K., Lipsitz, L.A.: ‘What is physiologic complexity and how does it change with aging and disease?’, Neurobiol. Aging, 2002, 23, (1), pp. 2326.
    36. 36)
      • 36. Boonstra, M.C., van der Slikke, R.M., Keijsers, N.L., et al: ‘The accuracy of measuring the kinematics of rising from a chair with accelerometers and gyroscopes’, J. Biomech., 2006, 39, (2), pp. 354358.
    37. 37)
      • 37. Karunarathne, M.S.: ‘Segmentation of shoulder movements using inertial sensors and entropy’. Int. Conf. Computational Modeling & Simulation 2017 (ICCMS 2017), 2017, pp. 241244.
    38. 38)
      • 38. Frank, J., Mannor, S., Precup, D.: ‘Activity and gait recognition with time-delay embeddings’. Association for the Advancement of Artificial Intelligence, 2010.

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