Research Papers

A Low-Dimensional Dissimilarity Analysis of Unilateral and Bilateral Stroke-Impacted Hand Trajectories

[+] Author and Article Information
Jay Ryan U. Roldan

Department of Computer Engineering,
University of California Santa Cruz,
Santa Cruz, CA 95064
e-mail: juroldan@soe.ucsc.edu

Dejan Milutinović

Department of Computer Engineering,
University of California Santa Cruz,
Santa Cruz, CA 95064
e-mail: dejan@soe.ucsc.edu

Zhi Li

Department of Electrical and
Computer Engineering,
Duke University,
Durham, NC 27708
e-mail: zhi.li2@duke.edu

Jacob Rosen

Department of Mechanical Engineering,
University of California Los Angeles,
Los Angeles, CA 90095
e-mail: jacobrosen@ucla.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 6, 2015; final manuscript received May 3, 2016; published online July 13, 2016. Assoc. Editor: Xiaopeng Zhao.

J. Dyn. Sys., Meas., Control 138(11), 111007 (Jul 13, 2016) (8 pages) Paper No: DS-15-1616; doi: 10.1115/1.4033836 History: Received December 06, 2015; Revised May 03, 2016

In this paper, we propose a quantitative approach based on identifying hand trajectory dissimilarities through the use of a multidimensional scaling (MDS) analysis. A high-rate motion capture system is used to gather three-dimensional (3D) trajectory data of healthy and stroke-impacted hemiparetic subjects. The mutual dissimilarity between any two trajectories is measured by the area between them. This area is used as a dissimilarity variable to create an MDS map. The map reveals a structure for measuring the difference and variability of individual trajectories and their groups. The results suggest that the recovery of hemiparetic subjects can be quantified by comparing the difference and variability of their individual MDS map points to the points from the cluster of healthy subject trajectories. Within the MDS map, we can identify fully recovered patients, those who are only functionally recovered, and those who are either in an early phase of, or are nonresponsive to the therapy.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Dariush Mozaffarian, D. , Benjamin, E. J. , Go, A. S. , Arnett, D. K. , Blaha, M. J. , Cushman, M. , de Ferranti, S. , Després, J.-P. , Fullerton, H. J. , Howard, V. J. , Huffman, M. D. , Judd, S. E. , Kissela, B. M. , Lackland, D. T. , Lichtman, J. H. , Lisabeth, L. D. , Liu, S. , Mackey, R. H. , Matchar, D. B. , McGuire, D. K. , Mohler III, E. R. , Moy, C. S. , Muntner, P. , Mussolino, M. E. , Nasir, K. , Neumar, R. W. , Nichol, G. , Palaniappan, L. , Pandey, D. K. , Reeves, M. J. , Rodriguez, C. J. , Sorlie, P. D. , Stein, J. , Towfighi, A. , Turan, T. N. , Virani, S. S. , Willey, J. Z. , Woo, D. , Yeh, R. W. , and Turner, M. B. , 2015, “ Heart Disease and Stroke Statistics 2015 Update: A Report From the American Heart Association,” Circulation, 29(322), pp. e29–e322. [CrossRef]
Stinear, C. , Barber, P. , Smale, P. R. , Coxon, J. P. , Fleming, M. K. , and Byblow, W. D. , 2007, “ Functional Potential in Chronic Stroke Patients Depends on Corticospinal Tract Integrity,” Brain, 130(Pt. 1), pp. 170–180. [PubMed]
Hsieh, C. L. , Hsueh, I. P. , Chiang, F. M. , and Lin, P. H. , 1998, “ Inter-Rater Reliability and Validity of the Action Research Arm Test in Stroke Patients,” Age Ageing, 27(2), pp. 107–113. [CrossRef] [PubMed]
Platz, T. , Pinkowski, C. , van Wijck, F. , Kim, I . H. , Bella, P. D. , and Johnson, G. , 2015, “ Reliability and Validity of Arm Function Assessment With Standardized Guidelines for the Fugl-Meyer Test, Action Research Arm Test and Box and Block Test: A Multicentre Study,” Clin. Rehabil., 19(4), pp. 401–411.
Kopp, B. , Kunkel, A. , Flor, H. , Platz, T. , Rose, U. , Mauritz, K. H. , Gresser, K. , McCulloch, K. L. , and Taub, E. , 1997, “ The Arm Motor Ability Test: Reliability, Validity, and Sensitivity to Change of an Instrument for Assessing Disabilities in Activities of Daily Living,” Arch. Phys. Med. Rehabil., 78(6), pp. 615–620. [CrossRef] [PubMed]
Bohannon, R. W. , and Smith, M. B. , 1987, “ Interrater Reliability of a Modified Ashworth Scale of Muscle Spasticity,” Phys. Ther., 67(2), pp. 206–207. [PubMed]
Cushman, L. A. , and Scherer, M. J. , 1996, “ Measuring the Relationship of Assistive Technology Use, Functional Status Over Time, and Consumer Therapist Perceptions of ATS,” Assistive Technol., 8(2), pp. 103–109. [CrossRef]
Baptiste, S. , Carswell, A. , McColl, M. A. , Polatajko, H. , and Pollock, N. , 2014, “ Canadian Occupational Performance Measure (COPM),” Canadian Association of Occupational Therapists (CAOT), Ottawa, ON, Canada.
Van der Lee, J. H. , Beckerman, H. , Lankhorst, G. J. , and Bouter, L. M. , 2001, “ The Responsiveness of the Action Research Arm Test and the Fugl-Meyer Assessment Scale in Chronic Stroke Patients,” J. Rehabil. Med., 33(3), pp. 110–113. [CrossRef] [PubMed]
Van der Lee, J. H. , Beckerman, H. , Knol, D. L. , de Vet, H. C. , and Bouter, L. M. , 2004, “ Clinimetric Properties of the Motor Activity Log for the Assessment of Arm Use in Hemiparetic Patients,” Stroke, 35(6), pp. 1410–1414. [CrossRef] [PubMed]
Poole, J. L. , and Whitney, S. L. , 1988, “ Motor Assessment Scale for Stroke Patients: Concurrent Validity and Interrater Reliability,” Arch. Phys. Med. Rehabil., 69(3Pt. 1), pp. 195–197. [PubMed]
Mathiowetz, V. , Weber, K. , Kashman, N. , and Volland, G. , 1985, “ Adult Norms for the Nine Hole Peg Test of Finger Dexterity, OTJR: Occupation,” Participation Health, 5(1), pp. 24–38. [CrossRef]
Morris, D. M. , Uswatte, G. , Crago, J. E. , Cook, E. W. , and Taub, E. , 2001, “ The Reliability of the Wolf Motor Function Test for Assessing Upper Extremity Function After Stroke,” Arch. Phys. Med. Rehabil., 82(6), pp. 750–755. [CrossRef] [PubMed]
Gladstone, D. , Daniels, C. , and Black, S. , 2002, “ The Fugl-Meyer Assessment of Motor Recovery After Stroke: A Critical Review of Its Measurement Properties,” Am. Soc. Neurorehabil., 16(3), pp. 232–240.
Duncan, P. , Propst, M. , and Nelson, S. , 1983, “ Reliability of the Fugl-Meyer Assessment of Sensorimotor Recovery Following Cerebrovascular Accident,” Phys. Ther., 63(10), pp. 1606–1610. [PubMed]
Simkins, M. , Al-Refai, A. , and Rosen, J. , 2014, “ Upper Limb Joint Space Modelling of Stroke Induced Synergies Using Isolated and Voluntary Arm Perturbations,” IEEE Trans. Neural Syst. Rehabil. Eng., 22(3), pp. 491–500. [CrossRef] [PubMed]
Krakauer, J. , 2006, “ Motor Learning: Its Relevance to Stroke Recovery and Neurorehabilitation,” Curr. Opin. Neurol., 19(1), pp. 84–90. [CrossRef] [PubMed]
Levin, M. , Kleim, J. , and Wolf, S. , 2009, “ What Do Motor ‘Recovery’ and ‘Compensation’ Mean in Patients Following Stroke?” Neurorehabil. Neural Repair, 23(4), pp. 313–319. [CrossRef] [PubMed]
Borg, I. , Groenen, P. , and Mair, P. , 2013, Applied Multidimensional Scaling, Springer, New York.
Borg, I. , and Groenen, P. , 2005, Modern Multidimensional Scaling (Theory and Applications), Springer, New York.
Kuiken, C. , DeJong, J. , Baan, E. , Keulen, W. , Tersmette, M. , and Goudsmit, J. , 1992, “ Evolution of the v3 Envelope Domain in Proviral Sequences and Isolates of Human Immunodeficiency Virus Type 1 During Transition of the Viral Biological Phenotype,” J. Virol., 66(7), pp. 4622–4627. [PubMed]
Bedford, T. , Suchard, M. , Lemey, P. , Dudas, G. , Gregory, V. , Hay, A. J. , McCauley, J. W. , Russell, C. A. , Smith, D. J. , and Rambaut, A. , 2014, “ Integrating Influenza Antigenic Dynamics With Molecular Evolution,” Elife, 3, p. e01914. [CrossRef] [PubMed]
He, J. , and Deem, M. , 2010, “ Low-Dimensional Clustering Detects Incipient Dominant Influenza Strain Clusters,” Protein Eng. Des. Sel., 23(12), pp. 935–946. [CrossRef] [PubMed]
Smith, D. , Lapeded, A. , de Jong, J. , Bestebroer, T. M. , Rimmelzwaan, G. F. , Osterhaus, A. D. , and Fouchier, R. A. , 2004, “ Mapping the Antigenic and Genetic Evolution of Influenza Virus,” Sci. Mag., 305, pp. 371–376.
Vicon Industries, 2015, “ Motion Capture on the WWW,” http://www.vicon.com/
Vicon, 2015, “ Vicon BodyBuilder Manual,” Vicon Industries, Oxford, UK.
Harley, L. , 2011, “ Stages in Learning Motor Synergies: A View Based on the Equilibrium-Point Hypothesis,” Ph.D. thesis, School of Applied Physiology, Georgia Institute of Technology, Atlanta, GA.
Ada, L. , Canning, C. , and Low, S. , 2003, “ Stroke Patients Have Selective Muscle Weakness in Shortened Range,” Brain, 126(Pt. 3), pp. 724–731. [CrossRef] [PubMed]
Bohannon, R. , 2007, “ Muscle Strength and Muscle Training After Stroke,” J. Rehabil. Med., 39(1), pp. 14–20. [CrossRef] [PubMed]
Dewald, J. , Pope, P. , Given, J. , Buchanan, T. S. , and Rymer, W. Z. , 1995, “ Abnormal Muscle Co-Activation Patterns During Isometric Torque Generation at the Elbow and Shoulder in Hemiparetic Subjects,” Brain, 118(Pt. 2), pp. 495–510. [CrossRef] [PubMed]
Dewald, J. , and Beer, R. , 2001, “ Abnormal Joint Torque Patterns in the Paretic Upper Limb of Subjects With Hemiparesis,” Muscle Nerve, 24(2), pp. 273–283. [CrossRef] [PubMed]
Ada, L. , Canning, C. , Carr, J. H. , Kilbreath, S. L. , and Shepherd, R. B. , 1994, “ Task Specific Training of Reaching and Manipulation,” Adv. Psychol., 105, pp. 239–265.
Cirstea, C. , Ptito, A. , Forget, R. , and Levin, M. F. , 2000, “ Arm Motor Improvement in Stroke Patients May Depend on Type of Training,” Soc. Neurosci. Abstr., 26(1–2).
Roby-Brami, A. , Feydy, A. , Combeaud, M. , Biryukova, E. V. , Bussel, B. , and Levin, M. F. , 2003, “ Motor Compensation Recovery for Reaching in Stroke Patients,” Acta Neurol. Scand., 107(5), pp. 369–381. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 5

Two 3D trajectories with the same number of points. The coordinates of the kth sample point of the ith and jth trajectories are (xki,yki,zki) and (xkj,ykj,zkj), respectively. The measure of difference between the trajectories is based on the area between the trajectories (shaded).

Grahic Jump Location
Fig. 4

Area ratio calculated as the ratio of the areas above and below the trajectory: S axis represents the traveled distance in the xy-plane, and ΔSk are increments of the traveled distance between trajectory data points

Grahic Jump Location
Fig. 3

Sample of the collected trajectory data relative to the motion-capturing system coordinate frame. The relative position and orientation of the target workspace with respect to the chair on which the subjects sat were kept unchanged. (a) Unilateral mode trajectory data of subject 2 from the control group. Both right and left trajectories are shown. (b) Bilateral mode trajectory data of subject 2 from the control group. (c) Unilateral mode trajectory data of subject 1 from the hemiparetic group. Both healthy (light gray) and unhealthy (dark gray) trajectories are shown. (d) Bilateral mode trajectory data of subject 1 from the hemiparetic group.

Grahic Jump Location
Fig. 2

Target workspace setup: (a) front and (b) top view of the target workspace. The left workspace is composed of targets L1–L5, and the right one is composed of targets R1–R5. (c) The subject's shoulders are aligned with the center of the left and right workspaces.

Grahic Jump Location
Fig. 1

Marker placement: (a) nine reflective markers are attached to each of the left and right arms (light gray circles). Four markers are attached to the torso (dark gray circles). (b) Subject holds a T-shaped pointer with a marker attached at the tip.

Grahic Jump Location
Fig. 6

Approximations of the area between two trajectories: (a) the area is approximated as a sum of two triangles sharing the side connecting (xkj,ykj,zkj) and (xk+1i,yk+1i,zk+1i) and (b) the area is approximated as a sum of two triangles sharing the side connecting (xki,yki,zki) and (xk+1j,yk+1j,zk+1j)

Grahic Jump Location
Fig. 9

The MDS maps for all the trajectories for targets 1–5 are depicted in (a)–(e), respectively: the ellipse with the shaded area describes the 95% area for the cluster of the trajectories of healthy subjects, and the points corresponding to the trajectories of hemiparetic subjects in unilateral (▽) and bilateral (°) reaching modes

Grahic Jump Location
Fig. 7

Boxplots of the area ratio per target for two reaching modes and two groups of subjects. A ratio less than one means that there is an upward motion at the start of the trajectory followed by a forward motion toward the target.

Grahic Jump Location
Fig. 8

The polynomial order per target for the trajectories from two reaching modes and two groups of subjects

Grahic Jump Location
Fig. 10

The distances of the centers of points corresponding to the unilateral and bilateral hemiparetic trajectories to the center of the healthy subject cluster (a) and the standard deviation (b) of the distance to the center of the healthy trajectory cluster. The bar graphs show the distances and standard deviation per type of the trajectory and target.

Grahic Jump Location
Fig. 11

Subject 2 map for all the targets are shown in (a)–(e). (▽) represents the bilateral trajectories, and (°) represents the unilateral reaching trajectories of subject 2. The dashed lines illustrate the separation between the unilateral and bilateral trajectories. The ellipses with the shaded areas describe the 95% area for the cluster of healthy trajectories.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In