Abstract
Accurate control of forces produced by the fingers is essential for performing object manipulation. This study examines the indices of finger interaction when accurate time profiles of force are produced in different directions, while using one of the fingers or all four fingers of the hand. We hypothesized that patterns of unintended force production among shear force components may involve features not observed in the earlier studies of vertical force production. In particular, we expected to see unintended forces generated by non-task fingers not in the direction of the instructed force but in the opposite direction as well as substantial force production in directions orthogonal to the instructed direction. We also tested a hypothesis that multi-finger synergies, quantified using the framework of the uncontrolled manifold hypothesis, will help reduce across-trials variance of both total force magnitude and direction. Young, healthy subjects were required to produce accurate ramps of force in five different directions by pressing on force sensors with the fingers of the right (dominant) hand. The index finger induced the smallest unintended forces in non-task fingers. The little finger showed the smallest unintended forces when it was a non-task finger. Task fingers showed substantial force production in directions orthogonal to the intended force direction. During four-finger tasks, individual force vectors typically pointed off the task direction, with these deviations nearly perfectly matched to produce a resultant force in the task direction. Multi-finger synergy indices reflected strong co-variation in the space of finger modes (commands to fingers) that reduced variability of the total force magnitude and direction across trials. The synergy indices increased in magnitude over the first 30% of the trial time and then stayed at a nearly constant level. The synergy index for stabilization of total force magnitude was higher for shear force components when compared to the downward pressing force component. The results suggest complex interactions between enslaving and synergic force adjustments, possibly reflecting the experience with everyday prehensile tasks. For the first time, the data document multi-finger synergies stabilizing both shear force magnitude and force vector direction. These synergies may play a major role in stabilizing the hand action during object manipulation.
Similar content being viewed by others
References
Danion F, Schöner G, Latash ML, Li S, Scholz JP, Zatsiorsky VM (2003) A force mode hypothesis for finger interaction during multi-finger force production tasks. Biol Cybern 88:91–98
de Freitas PB, Jaric S (2009) Force coordination in static manipulation tasks performed using standard and non-standard grasping techniques. Exp Brain Res 194:605–618
Flanagan JR, Wing AM (1993) Modulation of grip force with load force during point-to-point arm movements. Exp Brain Res 95:131–143
Gao F, Latash ML, Zatsiorsky VM (2005) Control of finger force direction in the flexion–extension plane. Exp Brain Res 161:307–315
Gorniak SL, Duarte M, Latash ML (2008) Do synergies improve accuracy? A study of speed-accuracy trade-offs during finger force production. Mot Control 12:151–172
Gorniak SL, Zatsiorsky VM, Latash ML (2009) Hierarchical control of static prehension: II. Multi-digit synergies. Exp Brain Res 194:1–15
Gysin P, Kaminski TR, Gordon AM (2003) Coordination of fingertip forces in object transport during locomotion. Exp Brain Res 149:371–379
Ingram JN, Körding KP, Howard IS, Wolpert DM (2008) The statistics of natural hand movements. Exp Brain Res 188:223–236
Jaric S, Russell EM, Collins JJ, Marwaha R (2005) Coordination of hand grip and load forces in uni- and bidirectional static force production tasks. Neurosci Lett 381:51–56
Johansson RS, Westling G (1984) Roles of glabrous skin receptors and sensorimotor memory in automatic control of precision grip when lifting rougher or more slippery objects. Exp Brain Res 56:550–564
Johnston JA, Winges SA, Santello M (2009) Neural control of hand muscles during prehension. Adv Exp Med Biol 629:577–596
Kilbreath SL, Gandevia SC (1994) Limited independent flexion of the thumb and fingers in human subjects. J Physiol 479:487–497
Kim SW, Shim JK, Zatsiorsky VM, Latash ML (2008) Finger interdependence: linking the kinetic and kinematic variables. Hum Move Sci 27:408–422
Latash ML, Zatsiorsky VM (2009) Multi-finger prehension: control of a redundant motor system. Adv Exp Med Biol 629:597–618
Latash ML, Scholz JF, Danion F, Schöner G (2001) Structure of motor variability in marginally redundant multi-finger force production tasks. Exp Brain Res 141:153–165
Latash ML, Scholz JF, Danion F, Schöner G (2002a) Finger coordination during discrete and oscillatory force production tasks. Exp Brain Res 146:412–432
Latash ML, Li S, Danion F, Zatsiorsky VM (2002b) Central mechanisms of finger interaction during one- and two-hand force production at distal and proximal phalanges. Brain Res 924:198–208
Latash ML, Scholz JP, Schöner G (2007) Toward a new theory of motor synergies. Mot Control 11:275–307
Latash ML, Friedman J, Kim SW, Feldman AG, Zatsiorsky VM (2010) Prehension synergies and control with referent hand configurations. Exp Brain Res (in press)
Leijnse JN, Snijders CJ, Bonte JE, Landsmeer JM, Kalker JJ, Van Der Meulen JC, Sonneveld GJ, Hovius SE (1993) The hand of the musician: the kinematics of the bidigital finger system with anatomical restrictions. J Biomech 10:1169–1179
Leijnse JN, Carter S, Gupta A, McCabe S (2008) Anatomic basis for individuated surface EMG and homogeneous electrostimulation with neuroprostheses of the extensor digitorum communis. J Neurophysiol 100:64–75
Li ZM, Latash ML, Newell KM, Zatsiorsky VM (1998a) Motor redundancy during maximal voluntary contraction in four-finger tasks. Exp Brain Res 122:71–78
Li ZM, Latash ML, Zatsiorsky VM (1998b) Force sharing among fingers as a model of the redundancy problem. Exp Brain Res 119:276–286
Li S, Danion F, Latash ML, Li Z-M, Zatsiorsky VM (2000) Characteristics of finger force production during one- and two-hand tasks. Hum Move Sci 19:897–924
Li ZM, Pfaeffle HJ, Sotereanos DG, Goitz RJ, Woo SL-Y (2003) Multi-directional strength and force envelope of the index finger. Clin Biomech 18:908–915
Li ZM, Dun S, Harkness DA, Brininger TL (2004) Motion enslaving among multiple fingers of the human hand. Mot Control 8:1–15
Li ZM, Kuxhaus L, Fisk JA, Christophel TH (2005) Coupling between wrist flexion–extension and radial-ulnar deviation. Clin Biomech 20:177–183
Milner TE, Dhaliwal SS (2002) Activation of intrinsic and extrinsic finger muscles in relation to the fingertip force vector. Exp Brain Res 146:197–204
Ohtsuki T (1981) Inhibition of individual fingers during grip strength exertion. Ergonomics 24:21–36
Pataky TC, Latash ML, Zatsiorsky VM (2007) Finger interaction during maximal radial and ulnar deviation efforts: experimental data and linear neural network modeling. Exp Brain Res 179:301–312
Poliakov AV, Schieber MH (1999) Limited functional grouping of neurons in the motor cortex hand area during individuated finger movements: a cluster analysis. J Neurophysiol 82:3488–3505
Reilly KT, Hammond GR (2006) Intrinsic hand muscles and digit independence on the preferred and non-preferred hands of humans. Exp Brain Res 173:564–571
Rouiller EM (1996) Multiple hand representations in the motor cortical areas. In: Wing AM, Haggard P, Flanagan JR (eds) Hand and brain. The neurophysiology and psychology of hand movements. Academic Press, San Diego, pp 99–124
Santello M, Fuglevand AJ (2004) Role of across-muscle motor unit synchrony for the coordination of forces. Exp Brain Res 159:501–508
Santello M, Soechting JF (2000) Force synergies for multifingered grasping. Exp Brain Res 133:457–467
Schieber MH (1991) Individuated finger movements of rhesus monkeys: a means of quantifying the independence of the digits. J Neurophysiol 65:1381–1391
Schieber MH, Santello M (2004) Hand function: peripheral and central constraints on performance. Appl Physiol 96:2293–2300
Schieber MH, Lang CE, Reilly KT, McNulty P, Sirigu A (2009) Selective activation of human finger muscles after stroke or amputation. Adv Exp Med Biol 629:559–575
Scholz JP, Schöner G (1999) The uncontrolled manifold concept: identifying control variables for a functional task. Exp Brain Res 126:289–306
Shim JK, Latash ML, Zatsiorsky VM (2003) The central nervous system needs time to organize task-specific covariation of finger forces. Neurosci Lett 353:72–74
Shim JK, Olafsdottir H, Zatsiorsky VM, Latash ML (2005) The emergence and disappearance of multi-digit synergies during force production tasks. Exp Brain Res 164:260–270
Shim JK, Huang J, Hooke AW, Latash ML, Zatsiorsky VM (2007) Multi-digit maximum voluntary torque production on a circular object. Ergonomics 50:660–675
Sosnoff JJ, Jordan K, Newell KM (2005) Information and force level interact in regulating force output during two and three digit grip configurations. Exp Brain Res 167:76–85
Vaillancourt DE, Slifkin AB, Newell KM (2002) Inter-digit individuation and force variability in the precision grip of young, elderly, and Parkinson’s disease participants. Mot Control 6:113–128
Valero-Cuevas FJ, Zajac FE, Burgar CG (1998) Large index fingertip forces are produced by subject-independent patterns of muscle excitation. J Biomech 31:693–703
Winges SA, Kornatz KW, Santello M (2008) Common input to motor units of intrinsic and extrinsic hand muscles during two-digit object hold. J Neurophysio. 99:1119–1126
Yokogawa R, Hara K (2002) Measurement of distribution of maximum index-fingertip force in all directions at fingertip in flexion/extension plane. J Biomech Eng 124:302–307
Zatsiorsky VM, Latash ML (2008) Multi-finger prehension: an overview. J Mot Behav 40:446–476
Zatsiorsky VM, Li ZM, Latash ML (1998) Coordinated force production in multi-finger tasks: finger interaction and neural network modeling. Biol Cybern 79:139–150
Zatsiorsky VM, Li ZM, Latash ML (2000) Enslaving effects in multi-finger force production. Exp Brain Res 131:187–195
Zatsiorsky VM, Gregory RW, Latash ML (2002) Force and torque production in static multi-finger prehension: biomechanics and Control. Part I. Biomechanics. Biol Cybern 87:50–57
Zatsiorsky VM, Gao F, Latash ML (2003a) Finger force vectors in multi-finger prehension. J Biomech 36:1745–1749
Zatsiorsky VM, Gao F, Latash ML (2003b) Prehension synergies: effects of object geometry and prescribed torques. Exp Brain Res 148:77–87
Acknowledgments
The study was in part supported by NIH grants AG-018751, NS-035032, and AR-048563.
Author information
Authors and Affiliations
Corresponding author
Appendix: Computation of the two components of variance
Appendix: Computation of the two components of variance
To compute the index of multi-finger synergies stabilizing the force vector magnitude and direction, two components of the across-trials variance were computed in the space of commands to fingers, finger modes. This analysis involved the following steps.
To eliminate the co-variation of finger forces due to enslaving, finger forces were transformed into another set of variables, finger modes (Zatsiorsky et al. 1998; Latash et al. 2001; Danion et al. 2003):
\( d{\bf m} = {\bf E}^{ - 1} \, d{\bf F} \) (assuming that E is an invertible matrix) where d F is the change in force produced, E is a 4 × 4 enslaving matrix, and d m is the change in mode magnitudes.
Rather than taking the regular matrix inverse, the pseudoinverse was calculated, using the singular value decomposition:
The pseudoinverse was then calculated from:
where S * is the reciprocal of the non-zero elements in S. However, small values in elements of S (below 0.01) were set to zero before calculating S *. For most cases, the result was equivalent to taking the regular matrix inverse, but the removal of small values in S prevented very large values of the inverse of the enslaving matrix in a small number (<10%) of extreme cases.
Before calculating variance, the forces in each direction were normalized with respect to the maximum task force in that direction, i.e., the force magnitude in each direction, which the subject was asked to produce. The components of the task force were always considered for each direction separately.
In our study, two performance variables were considered. The first was the sum of the forces (F TOT ) produced by the four fingers in a given task-relevant direction (Z, and either X or Y): F TOT,k = F Ik + F Mk + F Rk + F Lk, where F Ik is the force produced by the index finger in the k direction (X, Y or Z).
The Jacobian defines the transformation between small changes in the individual finger force magnitudes and changes in FTOT:
where dF jk is the change in force produced by j finger in k direction (X, Y or Z).
In the space of finger modes, we can express this relationship as:
The UCM was approximated linearly as the null-space of J spanned by basis vectors, e i from the following equation:
We calculated f || as the sum of mean-free mode vectors projected onto the UCM:
where n = 4 is the number of elemental variables and k = 1 corresponds to the one-dimensional performance variable. f ⊥ is the component of mode vectors perpendicular to the null space:
Then the variance per degree-of-freedom (DOF) within the UCM, i.e. V UCM was computed as follows:
Similarly, V ORT, i.e. variance per DOF orthogonal to the UCM was calculated as follows:
Further, to allow comparison across subjects, an index, ΔV was computed as the difference between the variance within UCM and the variance orthogonal to UCM, divided by the total variance (all computed per DOF).
ΔV indices were computed separately for each of the two relevant directions for each task (Z and X or Y) and each subject separately. Positive ΔV would indicate a multi-finger synergy stabilizing the performance variable, while zero or negative ΔV would mean no such synergy.
The second performance variable considered was the ratio between the two vector components reflecting the direction of the vector. It was defined as the force in the non-Z task direction k (i.e., X or Y) divided by the force in the Z direction:
This ratio represents the tangent of the force direction angle. In this analysis, forces were used, rather than modes, to ensure that the units are the same for the numerator and denominator. In this case, the performance variable was R; it depended on eight elemental variables, the eight force components of the four finger force vectors.
For forces in a non-Z direction, the elements of the Jacobian were:
The elements of the Jacobian for the forces in Z direction were:
Thus, the Jacobian matrix was:
The remainder of the analysis was equivalent to the procedure described earlier. Briefly, the null-space of the Jacobian was used to approximate the UCM. For each sample over the 5-s trial, mean-free finger forces were projected onto the UCM and onto the orthogonal complement. Variance was computed within both sub-spaces and normalized per degree-of-freedom (the UCM is 7-dimensional and the orthogonal sub-space in one-dimensional). These indices, V UCM and V ORT , were used to compute the index of multi-finger synergy (ΔV) stabilizing force vector direction.
Rights and permissions
About this article
Cite this article
Kapur, S., Friedman, J., Zatsiorsky, V.M. et al. Finger interaction in a three-dimensional pressing task. Exp Brain Res 203, 101–118 (2010). https://doi.org/10.1007/s00221-010-2213-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00221-010-2213-7