Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T04:44:57.064Z Has data issue: false hasContentIssue false

A Team Approach to Undergraduate Research in Biomathematics: Balance Control

Published online by Cambridge University Press:  05 October 2011

J. Milton*
Affiliation:
Joint Science Department of Claremont McKenna, Pitzer and Scripps Colleges
A. Radunskaya
Affiliation:
W. M. Keck Science Center, 925 N. Mills Ave. Claremont, CA 91711, USA
W. Ou
Affiliation:
Department of Mathematics, Pomona College, 610 North College Ave., Claremont, CA 91711 USA
T. Ohira
Affiliation:
Joint Science Department of Claremont McKenna, Pitzer and Scripps Colleges
*
Corresponding author. E-mail: jmilton@jsd.claremont.edu
Get access

Abstract

The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of relevant mathematical models. An in–house laboratory component ensures that students have the opportunity to directly compare prediction to observation and motivates the development of projects that push the boundaries of the subject. The projects, by their nature, readily lend themselves to the formation of inter–disciplinary student research teams. Thus students have the opportunity to learn skills essential for success in today’s workplace including productive team work, critical thinking, problem solving, project management, and effective communication.

Type
Research Article
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

D. Acheson. From Calculus to Chaos: An introduction to dynamics. Oxford University Press, New York (1998).
A. Armenti, Jr., editor. The Physics of Sports. American Institute of Physics, New York (1992).
Y. Asai, Y. Tasaka, K. Nomura, T. Nomura, M. Casidio, P. Morasso A model of postural control in quiet standing: Robust compensation of delay–induced instability using intermittent activation of feedback control. PLoS ONE 4 (2009), e6169.
G. L. Baker, J. A. Blackburn. The pendulum: a case study in physics. Oxford University Press, New York, 2005.
H. C. Berg. Random walks in biology. Princeton University Press, New Jersey (1993).
Bottaro, A., Yasutake, Y., Nomura, T., Casidio, M., Morasso, P.. Bounded stability of the quite standing position: An intermittent control model. Human Movement Science 27 (2008), 473495. CrossRefGoogle Scholar
Bormann, R., Cabrera, J. L., Milton, J. G., Eurich, C. W.. Visuomotor tracking on a computer screen: An experimental paradigm to study dynamics of motor control. Neurocomputing 58–60 (2004), 517-523. CrossRefGoogle Scholar
Boulet, J., Balasubramiam, R., Daffertshofer, A., Longtin, A.. Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics. Phil. Trans. Roy. Soc. A 368 (2010): 423-438. CrossRefGoogle ScholarPubMed
Cabrera, J. L., Milton, J. G.. On–off intermittency in a human balancing task. Phys. Rev. Lett. 89 (2002), 158702. CrossRefGoogle Scholar
Cabrera, J. L., Milton, J. G.. Human stick balancing: Tuning Lévy flights to improve balance control. CHAOS 14 (2004): 691. CrossRefGoogle ScholarPubMed
Cabrera, J. L., Bormann, R., Eurich, C., Ohira, T., Milton, J.. State–dependent noise and human balance control. Fluct. Noise Lett. 4 (2004), L107-L118. CrossRefGoogle Scholar
Campbell, S. A., Crawford, S., Morris, K.. Friction and the inverted stabilization problem. J. Dyn. Syst. Meas. Control. 130 (2008), 054502. CrossRefGoogle Scholar
Chiel, J. J., Beer, R. D.. The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. TINS 20 (1997), 553557. Google Scholar
Cluff, T., Balasubramania R., R.. Motor learning characterized by changing Lévy distributions. PLoS One 4 (2009): e5998. CrossRefGoogle ScholarPubMed
de Silva, V., Tenenbaum, J. B., Langford, J. C.. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000), 23192323. Google Scholar
Dijkstra, T. M. H., Katsumata, H., Sternad, D.. The dialogue between data and model: passive stability and relaxation behavior in a ball bouncing task. Nonlinear Studies 11 (2004), 319344. Google Scholar
B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems. SIAM, Philadelphia (2002).
Eurich, C. W., Milton JG, J. G.. Noise-induced transitions in human postural sway. Phys. Rev. E 54 (1996): 6681-6684. CrossRefGoogle ScholarPubMed
C. W. Eurich, K. Pawelzik. Optimal control yields power laws. In Artificial Neural Networks: Formal Models and Their Applications, Springer Lecture Notes in Computer Science Vol. 3697, edited by W. Duch, J. Kacprzyk, E. Oja and S. Zadronzny (Springer–Verlag, Berlin, 2005), pp. 365–370.
Foo, P., Kelso, J. A. S., de Guzman, G. D.. Functional stabilization of fixed points: Human pole balancing using time to balance information. J. Exp. Psychol. Hum. Percept. Perform. 26 (2000), 1281-1297. CrossRefGoogle ScholarPubMed
Guckenheimer, J.. A robust hybrid stabilization strategy for equilibria. IEEE Trans. Automatic Control 40 (1995), 321326. CrossRefGoogle Scholar
Insperger, T.. Stick balancing with reflex delay in case of parametric forcing. Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 21602168. CrossRefGoogle Scholar
Kamimura, A., Ohira, T.. Group chase and escape. New J. Physics 12 (2010), 053013.
Kuiken, T. A., Miller, L. A., Lipschutz, R. D., Lock, B. A., Stubblefield, K., Marasso, P. D., Zhou, P., Dumanian, G. A.. Targeted reinnervation for enhanced prosthetic arm function in a woman with a proximal amputation: a case study. Lancet 369 (2007), 371380. CrossRefGoogle Scholar
Kuo, A. D.. The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective. Hum. Mov. Sci. 26 (2007), 617656. CrossRefGoogle ScholarPubMed
S. S. Lafon. Diffusion Maps and Geometric Harmonics. PhD thesis, Yale University, 2004.
Landry, M., Campbell, S. A., Morris, K., Aguilar, C. O.. Dynamics of an inverted pendulum with delayed feedback control. SIAM J. Appl. Dyn. Sys. 4 (2005), 333351. CrossRefGoogle Scholar
Lockhart, D. B., Ting, L. H.. Optimal sensorimotor transformations for balance. Nat. Neurosci. 10 (2007), 13291336. CrossRefGoogle ScholarPubMed
Loram, I. D., Lackie, M.. Human balancing of an inverted pendulum: position control by small, ballistic–like, throw and catch movements. J. Physiol. (London) 540 (2002), 1111-1124. CrossRefGoogle ScholarPubMed
Loram, I. D., Maganaris, C. N., Lakie, M.. Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J. Physiol. (London) 564 (2005), 295-311. CrossRefGoogle ScholarPubMed
J. Maynard Smith. Mathematical Ideas in Biology. Cambridge University Press, New York (1968).
T. A. McMahon. Muscles, Reflexes and Locomotion. Princeton University Press, New Jersey (1984).
Mehta, B., Schaal, S.. Forwards models in visuomotor control. J. Neurophysiol. 88 (2002), 942953. Google Scholar
Milton, J. G., Small, S. S., Solodkin, A.. On the road to automatic: Dynamic aspects in the development of expertise. J. Clin. Neurophysiol. 21 (2004), 134143. CrossRefGoogle ScholarPubMed
Milton, J. G., Cabrera, J. L., Ohira, T.. Unstable dynamical systems: Delays, noise and control. Europhys. Lett. 83 (2008), 48001. CrossRefGoogle Scholar
Milton, J. G., Ohira, T., Cabrera, J. L., Fraiser, R. M., Gyorffy, J. B., Ruiz, F. K., Strauss, M. A., Balch, E. C., Marin, P. J., Alexander, J. L.. Balancing with vibration: A prelude for “drift and act” balance control. PLOS One 4 (2009), e7427. CrossRefGoogle Scholar
Milton, J., Cabrera, J. L., Ohira, T., Tajima, S., Tonosaki, Y., Eurich, C. W., Campbell, S. A.. The time–delayed inverted pendulum: Implications for human balance control. Chaos 19 (2009), 026110. CrossRefGoogle ScholarPubMed
Milton, J., Townsend, J. L., King, M. A., Ohira, T.. Balancing with positive feedback: the case for discontinuous control. Phil. Trans. Roy. Soc. A 367 (2009), 1181-1193. CrossRefGoogle ScholarPubMed
J. Milton, J. Gyorffy, J. L. Cabrera, T. Ohira. Amplitude control of human postural sway using Achilles tendon vibration. 16th US National Congress of Theoretical and Applied Mechanics (2010). State College, PA (USNCTAM2010–791).
Milton, J. G., Radunskaya, A. E., Lee, A. H., de Pillis, L. G., Bartlett, D. F.. Team research at the biology–mathematics interface: Project management perspectives. CBE–Life Sciences Education 9 (2010), 316-322. CrossRefGoogle Scholar
Milton, J., Naik, P., Chan, C., Campbell, S. A.. Indecision is neural decision making models. Math. Model. Nat. Phenom. 5 (2010), 125145. CrossRefGoogle Scholar
J. Milton, J. Lippai, R. Bellows, A. Blomberg, A. Kamimura, T. Ohira. Visuomotor tracking tasks with delayed pursuit and escape. 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control (2011). Washington, D. C. (DETC2011-47312).
P. J. Nahin PJ. Chases and escapes: The mathematics of pursuit and evasion. Princeton University Press, Princeton, New Jersey (2007).
T. Ohira, J. Milton. Delayed random walks: Investigating the interplay between noise and delays. In: Delay Differential Equations: Recent Advances and New Directions, edited by B. Balachandran, T. Kalmár–Nagy and D. E. Gilman, Springer–Verlag, New York, pp. 305–335 (2009).
Patzelt, F., Riegel, M., Ernst, U., Pawelzik, K.. Self-organized critical noise amplification in human closed loop control. Front. Comp. Neurosci. 1 (2007), Article 4, 19. Google Scholar
Pinter, I. J., von Swigchem, R., Knoek van Soet, A. J., Rozendaal, L. A.. The dynamics of postural sway cannot be captured using a one-segment inverted pendulum model: A PCA on segment rotations during unperturbed stance. J. Neurophysiol. 100 (2008), 31973208. CrossRefGoogle ScholarPubMed
Pippard, A. B.. The inverted pendulum. Eur. J. Physics 8 (1987), 203206. CrossRefGoogle Scholar
Scott, S. H.. Optimal feedback control and the neural basis of volitional motor control. Nature Rev, Neurosci. 5 (2004), 534546. CrossRefGoogle ScholarPubMed
Stirling, J. R., Zakynthinaki, M. S.. Stability and the maintenance of balance following a perturbation from quiet stance. Chaos 14 (2004), 96105. CrossRefGoogle ScholarPubMed
Stepan, G.. Delay effects in the human sensory system during balancing. Phil. Trans. Roy. Soc. A 367 (2009), 11951212. CrossRefGoogle ScholarPubMed
Stepp, N.. Anticipation in feedback–delayed manual tracking tracking of a chaotic oscillator. Exp. Brain Res. 198 (2009), 521525. CrossRefGoogle ScholarPubMed
A. Straw. An open–source library for realtime visual stimulus generation. Frontiers Neuroinformatics 11 (2008): doi: 10.3389.neuro.11.004:2008.
A. D. Straw, M. H. Dickinson. Motmot, an open–source toolkit for realtime video acquisition and analysis. Source Code for Biology and Medicine (2010). doi: 10.1186/1751-0473-4-5.
Vicsek, T.. Closing in on evaders. Nature 466 (2010), 4344. CrossRefGoogle Scholar
S. Vogel. Comparative Biomechanics: Life’s physical world. Princeton University Press, New Jersey (2003).
Voss, H. U.. Anticipating chaotic synchronization. Phys. Rev. E 61 (2000), 51155119. CrossRefGoogle ScholarPubMed
Winter, D. A., Patla, A. e., Prince, F., Ishac, M., Gielo–Perczak, K.. Stiffness control in quiet standing. J. Neurophysiol. 80 (1998), 1211-1221. Google Scholar
Zakynthinaki, M. S., Madera Milla, J. M., López de Durana, A., Cordent Martinez, C. A., Rodriguez Romo, G., Stillero Quintana, M., Samperd Molinuevo, J.. Rotated balance in humans due to repetitive rotational movement. Chaos 20 (2010), 013118. CrossRefGoogle ScholarPubMed
V. Zatsiorsky. Biomechanics in Sports: Performance enhancement and injury prevention. Blackwell Science, Malden, MA (2000).