Abstract
The variability in dependent biological data (measured as forces at the human foot during pedalling) was reduced, by principal components analysis, to two major components which, combined, accounted for 46% of the variability observed in sets of 26 observations per cycle. On the basis of weighting over the cycle, the components were interpreted as due to Power Production and to Phase Switch from powergeneration to recovery. Force measurements were made for three frequencies of leg pedalling (1.00, 1.66, and 2.33 Hz at 10 N ergometer resistance). For each principal component, the mean (or summed) deviation over 75 consecutive cycles was found to increase linearly (p<0.05) with velocity of leg movement, by 7% and 85% respectively. Analysis of autocorrelations over cycles of movement showed that, in contrast to the strong interconnections of force measures within a cycle of movement, between-cycle dependence was very low. The statisticaltechnique described provides a useful descriptive and inferential method for analyzing dependent cyclic data. The resulting model of the locomotor forces generated at the foot implies that control of power output is substantially for one cycle of a limb and that variability of force increases at the point when the leg switches from power-generation to recovery.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson O, Grillner S (1983) Peripheral control of the cat's step cycle. II. Entrainment of the central pattern generators for locomotion by sinusoidal hip movements during “fictive” locomotion. Acta Physiol Scand 118:229–239
Boylls CC, Zomlefer MR, Zajac FE (1984) Kinematic and EMG reactions to imposed interlimb phase alterations during bipedal cycling. Brain Res 324:342–345
Brooke JD, Hoare H, Rosenrot P, Triggs R (1981) Computerized system for measurement of force exerted within each pedal revolution during cycling. Physiol Behav 26:139–143
Brooke JD, Chapman A, Fischer L, Rosenrot P (1984) A note on stability in force applied to control a repetitive task with the legs. J Mot Behav 16:313–319
Brooke JD, McIlroy WE (1985) Locomotor limb synergism through short latency afferent links. Electroencephalogr Clin Neurophysiol 60:39–45
Brooke JD, Boyce DE, McIlroy WE, Robinson T, Wagar D (1986a) Modulation of phase relations of myoelectric activity and propulsive force in human bipedality at different speeds and resistances. Electromyogr Clin Neurophysiol (in press)
Brooke JD, Boyce DE, McIlroy WE, Robinson T, Wagar D (1986b) Transfer of variability from electromyogram to propulsive force in human locomotion. Electromyogr Clin Neurophysiol (in press)
Chatfield C (1975) The analysis of time series: theory and practice. Chapman and Hall, London, p 23
Dillon WR, Goldstein M (1984) Multivariate analysis: methods and applications. Wiley, New York
Feldman AG (1980) Superposition of motor programs. I. Rhythmic forearm movements in man. Neuroscience 5:81–90
Freund HJ (1983) Motor unit and muscle activity in voluntary motor control. Physiol Rev 63:387–436
Grillner S (1972) A role for muscle stiffness in meeting the changing postural and locomotor requirements of force development by the ankle extensors. Acta Physiol Scand 86:92–108
Grillner S, Zangger P (1979) On the central generation of locomotion in the low spinal cat. Exp Brain Res 34:241–261
Hines WGS, Hurnik JF, Mullen K (1983/84) Analysing qualitative behavioural data: A Markov chain aid. Appl Anim Ethol 11:111–121
Hoaglin DC, Mosteller F, Tukey JW (eds) (1983) Understanding robust and exploratory data analysis. Wiley, New York, p 82
Huynh H, Feldt LS (1970) Conditions under which mean square ratios in repeated-measurement designs have exact F-distributions. J Am Stat Assoc 65:1582–1589
Huynh H, Feldt LS (1976) Estimation of the Box correction for degrees of freedom from sample data in the randomized block and split-plot designs. J Educ Statist 1:69–83
Humphrey DR, Reed DJ (1983) Separate cortical systems for control of joint movement and joint stiffness: reciprocal activation and coactivation of antagonist muscles. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Raven Press, New York, pp 347–372
Kearnell D (1983) Functional properties of spinal motoneurons and gradation of muscle force. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Raven Press, New York, pp 213–225
Llolgen H, Graham T, Sjogaard G (1980) Muscle metabolites, force, and perceived exertion bicycling at varying pedal rates. Med Sci Sports Exerc 12:435–451
Mortimer JA, Webster DD (1983) Dissociated changes of short-and long-latency myotatic responses prior to a brisk voluntary movement in normals, in karate experts and in Parkinsonian patients. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Raven Press, New York, pp 541–554
Shik ML, Orlovsky GN (1976) Neurophysiology of locomotor automatism. Physiol Rev 56:465–501
Snedecor GW, Cochran WG (1980) Statistical methods, 7th ed. Iowa State University Press, Ames, Iowa
Steel RGD, Torrie JH (1960) Principles and procedures of statistics. McGraw-Hill, New York, p 157
Winter DA (1984) Kinematic and kinetic pattern in human gait. J Hum Move Sci 3:51–56
Winer BJ (1970) Statistical principles in experimental design. McGraw-Hill, New York, p 122
Author information
Authors and Affiliations
Additional information
Research supported in part by NSERC (Canada) Grants A6187 and A0025 to W.G.S.H. and J.D.B. respectively
Rights and permissions
About this article
Cite this article
Hines, W.G.S., O'Hara-Hines, R.J. & Brooke, J.D. A multivariate solution for cyclic data, applied in modelling locomotor forces. Biol. Cybernetics 56, 1–9 (1987). https://doi.org/10.1007/BF00333062
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00333062