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Journal of Neuroscience Methods 177 (2009) 80–86
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Dynamic torque during a precision grip task comparable to picking a raspberry Dieter F. Kutz a,∗ , Alexander Wölfel a , Dagmar Timmann b , Florian P. Kolb a a b
Department of Physiological Genomics, Institute of Physiology, University of Munich, Pettenkoferstr. 12, 80336 Munich, Germany Department of Neurology, University of Duisburg-Essen, Hufelandstr. 55, 45138 Essen, Germany
a r t i c l e
i n f o
Article history: Received 19 June 2008 Received in revised form 12 September 2008 Accepted 26 September 2008 Keywords: Prehension Grip force Multi-digit grip Dexterity Disability evaluation Finger strength Rehabilitation Torque
a b s t r a c t Numerous studies have shown torque control to be an important factor in grip-force control. This study introduces a novel task which allows quantification of the dynamics of torque development while increasing grip forces during a task comparable to picking a raspberry. The performance of this task was analysed in two healthy subjects and two cerebellar patients. Individual grip forces and finger positions on a grip rod were analysed using a recently developed technique [Kutz DF, Woelfel A, Timmann D, Kolb FP. Detection of changes in grip forces on a sliding object. J Neurosci Methods 2007;166:250–8]. Levers and torques were derived from grip forces and geometric properties of the grip rod. The analysis of this task performance provides evidence that healthy subjects are able to minimise torque despite increasing grip force, whereas the cerebellar patients tested increased torque disproportionately with increasing grip forces, whereby these high torques were due primarily to the patients’ inability to optimise individual finger positions on the rod. Patients tried to compensate their ataxia-based insecurity by employing higher grip forces, resulting in disproportionately higher torques and increased instability, whereupon they again increased grip force, thus establishing a vicious circle. The analysis of this task suggests that effective rehabilitation strategies must be aimed at interrupting this circle. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Precision grip activities in daily life are performed using multidigital grips involving the thumb and any number of fingers. Most common are tri-digital grips using the thumb, index, and middle fingers. Tri-digital prehension includes holding a small object like a ball or food, writing with a pencil, or unscrewing the cap of a flask (Kapandji, 1995). Multi-digit grips provide flexibility for manipulation, but require a higher degree of control by the central nervous system. The central nervous system must deal with the additional degrees of freedom that arise from the fact that grasp stability can be achieved with many combinations of grip forces. Several studies have addressed grip forces in precision grip tasks in which the thumb is opposed to two or more fingers (for review see Latash et al., 2002; Schieber and Santello, 2004; Castiello, 2005; Nowak and Hermsdorfer, 2006; Flanagan et al., 2006). Earlier studies used grip objects endowed with up to two force transducers and the fingers were changed systematically to grip the object (e.g. Kinoshita et al., 1995; Kinoshita et al., 1996a,b). In the meantime, techniques have been established to measure grip parameters for three or more fingers simultaneously (Flanagan and Tresilian,
∗ Corresponding author. Tel.: +49 89 2180 75230; fax: +49 89 2180 75216. E-mail address:
[email protected] (D.F. Kutz). 0165-0270/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2008.09.031
1994; Flanagan et al., 1999; Burstedt et al., 1999; Baud-Bovy and Soechting, 2001; Zatsiorsky and Latash, 2004; Chau et al., 2006; Pylatiuk et al., 2006; Kutz et al., 2007). Recent studies on finger coordination have shown that the control of torque produced by finger grip forces on an object is a complex task (Flanagan et al., 1999; Burstedt et al., 1999; Zatsiorsky et al., 2002a,b, 2003; Shim et al., 2004, 2005; Gao et al., 2006). These studies have shown that healthy subjects are able to produce adequate and balanced grip forces to compensate torques in static multi-finger prehension. Studies on multi-finger prehension on patients with motor disorders have focussed mainly on grip force (Nowak and Hermsdorfer, 2005, 2006). These studies have revealed that patients with cerebellar disease or cerebellar agenesis produce larger grip forces than healthy subjects (Serrien and Wiesendanger, 1999a,b; Nowak et al., 2002; Rost et al., 2005; Nowak et al., 2007a,b). In this study, a new task was designed in which subjects have to pull a blocked grip rod, which is comparable with picking a raspberry. Picking a raspberry requires perfectly adjusted, increasing grip forces to pull the raspberry off the bush without squeezing it. An advantage of the task in this study is the fact that torques that would deviate the rod from the pull-direction represent losses that subjects try unconsciously to minimise. The aim of this study was to develop a method that allows the dynamics of torque development in multi-finger prehension to be analysed in healthy subjects and in patients with motor disorders.
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2. Subjects, materials, and methods 2.1. Subjects and patients This study was performed with the permission of the ethics committee of the Ludwig-Maximilians-University of Munich. A total of five cerebellar patients and nine healthy subjects participated after giving written informed consent. Characteristic results are shown from two cerebellar patients (CBL1: male, 55 years, right handed, sporadic adult onset ataxia; CBL2: female, 41 years, right handed, spino cerebellar ataxia) and from two healthy subjects: (CTRL1: female, 21 years, right handed; CTRL2: male, 26 years, right handed). 2.2. Grip rod and force-measuring film The grip rod and the force-measuring film have been described elsewhere (Kutz et al., 2007). Briefly, the grip rod is composed of a cylindrical metal bar (10 mm radius) and a linear motor (type: STA2505, Copley Controls, Canton, MA, USA) that can move the grip rod up to 100 mm horizontally. It is equipped with a linear potentiometer to measure the position (type: REM 13-200-K, Megatron Elektronik, Putzbrunn, Germany) and a force transducer to measure the force exerted along the rod (type: U9B, Hottinger Baldwin Messtechnik, Darmstadt, Germany). The maximal force applied by the motor along the rod in the pull or push direction is hardware-limited to 25 N. The motor is controlled by software, custom-written in LabVIEW (v. 8.2, National Instruments, Austin, TX, USA). A force-measuring film (type: 3000/HOT, Tekscan, MA, USA), wrapped around the rod, covers 45 cm2 of the rod surface, 75 mm of grip rod length and 61 mm of the circumference (see Fig. 1A). This assures that force measurements can be made for any number of fingers. It consists of a rectangular array of resistor-based pressure sensors with a distance of 5.08 mm in each direction. The force range of a single sensor is from 890 mN to 13.3 N with a resolution of 100 mN. Force values were stored as an image frame using F-Scan software (v. 5.24, Tekscan) on a desktop computer. The data were sampled at a frequency of 150 frames/s. 2.3. Dynamic torque analysis Grip forces of individual fingers were measured as well as the pull force representing the sum of all tangential forces. Individual fingers exert normal forces to the contact surface of the grip rod. The positions of fingers on the surface are not predetermined but rather unrestrained and freely selectable according to the individual geometric and physiological properties of the subject’s hand. Moreover, digit tips do not adhere to the contact surface and thus, the so-called ‘soft contact model’ (Mason and Salisbury) becomes applicable, approximately without free moments (Zatsiorsky, 2002). The term ‘torque’ is used interchangeably in mechanics, in this study we will use ‘torque’ to designate a force moment resulting from normal finger forces which would tend to deviate the rod from the pulldirection and represent losses that subjects try unconsciously to minimise. Individual grip forces and finger positions were derived from the force-measuring film data as described elsewhere (Kutz et al., 2007). Briefly, force value of individual sensors is seen as pixels of data frame. Pixels of significant grip forces were detected using a modification of Rogerson’s algorithm for change detection in images (Rogerson, 2002). Using the Flood fill algorithm, pixels of coherent areas are marked (see http://en.wikipedia.org/ wiki/Flood fill). In this way significant pixels situated horizontally or vertically adjacent are combined. Finger position was calculated
Fig. 1. Finger position and torque calculation during the “pick the raspberry task”. (A) The grip rod and the attached force-measurement film are shown as well as the finger position during the task. (B) Determination of the rod slice element and calculation of the lever of the three fingers shown in (A), thumb: D1, index finger: D2, middle finger: D3. FD1–3 force vectors given by fingers D1–3 , LD1–3 lever vectors (dashed vector) is the effective lever of LD3 (see Section given by fingers D1–3 , LD3 2.3), CoM: centre of mass. (C) Schema of pull force increase during the raspberry task composed from three phases (see Section 2.4), URR: unpredictable rod release.
as the weighted centre of force values for each marked area. Then, centres of areas lying inside a given distance (1.645 pixel) are considered to be of the same origin and are combined. In this way combined areas make contact at the corner only. Finger position was recalculated for the combined area (see Fig. 3A in Kutz et al., 2007). From the finger positions, a gripped rod slice element and
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its centre of mass (CoM) were defined. The rod slice element is a part of the rod between the remotest fingers (e.g. rod part between fingers D1 and D3 in Fig. 1B). Levers were derived from the position of individual fingers and the centre of mass of the rod slice element. Individual torques were given by the vector product of finger force and the lever from the position on the rod, where the force is exerted to the centre of mass of the rod slice element. Torques of the individual fingers were calculated at each time point. From these data a total torque function was calculated over time (Eq. (1)). In the following, total torque (M˙ ) is simply named torque. The torque described here would deviate the rod from the pull-axis. However, given that the rod is blocked the torque produces a virtual deviation only. MDi (t) = LDi (t) × FDi (t) M˙ (t) =
MDi (t)
(1)
i
with MDi (t): torque, LDi (t): lever, FDi (t): grip force of individual finger Di and M˙ (t) sum of all torques MDi (t) at time t. For a comparison of the effect of factor lever and factor total grip force on torque, the average torque, average total grip force, and the average of the total effective lever length were calculated for each trial for a 500 ms time window, starting 850 ms before rod release (for details of the task see Section 2.4). Total grip force was calculated as the sum of absolute values of individual finger forces. The total effective lever length was calculated under following considerations. Given that grip forces are normal forces to the contact surface of the grip rod and, hence, are orthogonal to the z-axis and, given that force vector FDi and lever vector LDi are not orthogonal to each other (e.g. FD3 and LD3 in Fig. 1B), the torque produced by vector FDi on the centre of mass is not exerted along the absolute length of vector LDi but, according to vector algebra, along a shorter ). The effective length of lever L is calculated as the length lever (LDi Di of the projection of LDi on the z-axis (pull-axis, e.g. LD3 in Fig. 1B). In cases in which a finger is positioned directly above the centre of mass (e.g. FD2 in Fig. 1B) the effective lever becomes approximately zero and indeed a finger in this position does not contribute to a torque responsible for a virtual deviation out of the pull-axis. The total effective lever length is given by the sum of the absolute values of the lengths of all projected levers of all fingers, i.e. of all effective . LDi 2.4. “Pick the raspberry” task The dynamic torque analysis was performed with a precision grip task, imitating the operation of picking a raspberry. Picking a raspberry requires continuous adjustments of grip forces to pull the raspberry off the bush without squeezing it. Subjects were seated comfortably on a height-adjustable chair in front of the rod. The upper arm was held almost vertical and the forearm was flexed at the elbow joint 90◦ in the sagittal plane. The forearm was in a neutral position between pronation and supination. Subjects were asked to pull the rod horizontally in a fronto-parallel plane from its initial position with a three-finger precision grip (see Fig. 1A). The trials were self-paced by the subjects. The start of a trial was detected when a pull-force velocity threshold of 0.5 N/s was exceeded. After a randomly variable interval (1–5 s) the rod was released (unpredictable rod release/URR; exception for CBL1 with a fixed interval of 2.5 s used). The occurrence of URR was set to zero with negative times preceding it. After rod release (positive time), the rod started to move by the initial pull of subjects. They were asked to stop the pull movement of the rod and the pull force, as at the moment when the “raspberry is picked from the bush”, with as little grip force as possible. The interval from recording start until
the detected trial start is termed the grip-phase, the following interval until the URR is here termed the pull-phase and the last interval is termed the pick-phase. If during the pull-phase the velocity (i.e. the pull-force rate) exceeded an upper limit (5 N/s) subjects were informed by a red LED in front of them. The inter-trial-interval was minimally 10 s. Prior to recording, subjects were allowed at least 10 trials for practice. The time course of the task and the requested increase of the pull force is shown in Fig. 1C. 3. Results The aim of this study was to introduce a novel task in which the differences in dynamics of torque development in multi-finger prehension of healthy subjects and cerebellar patients can be analysed. It is for the analysis of a task, analogous to picking a raspberry which requires perfectly adjusted, increasing grip forces orthogonal to the rod surface. Unbalanced grip forces would deviate the gripped rod slice element from the pull-direction and hence are losses which subjects try to minimise unconsciously. 3.1. Dynamic torque analysis Fig. 2 shows the results of an individual healthy subject CTRL1 (CTRL, Fig. 2A–C) and a cerebellar patient CBL1 (CBL, Fig. 2D–F) during a single trial of the “pick the raspberry” task. CTRL1 showed a linearly increasing pull force (blue line in Fig. 2A) until the unpredictable rod release (URR) and an abrupt decrease after the release. The torque (black line in Fig. 2A) showed a small increase after initial pull increase and remained stable (below 0.01 Nm) until the URR with a small increase afterwards. The total grip force (black line in Fig. 2B) as well as individual finger grip forces (D1: blue line, D2: green line, D3: red in Fig. 2B) increased continuously until the URR similar to the increased pull force (mean pull-/grip-force ratio = 0.66). After URR grip forces reached a maximum due to the fact that subject tried to stop the pull movement. The increased finger grip forces after URR caused the small increase of the torque shown in Fig. 2A (black line). The absolute lengths of levers LDi of the individual finger positions are shown in Fig. 2C. During the grip-phase, i.e. after initial contact with the rod (approximately 1.35 s after trial start) transient peak levels were reduced immediately to a constant length of approximately 10 mm. This represents the optimal length (radius of rod) indicating that the fingers are positioned on the surface of a narrow rod slice element (mean width = 3.4 ± 1.3 mm) around the centre of mass, resulting in a small torque (see Fig. 2A). A completely different picture is shown by CBL1. Torque and pull force (black line and blue line in Fig. 2D, respectively) increased abruptly to a high level (over 0.1 Nm and 10 N, respectively) and remained so up to the URR. Torque increased further after rod release. Total grip and the individual finger grip forces were more complex (Fig. 2E). After an initial strong and step-like increase, which was contemporaneous to the pull-force increase, grip forces increased approximately linearly until the URR. This shows that this patient was able to produce increasing grip forces but was unable to establish a pull-force increase from these grip forces (compare the black line in Fig. 2E with the blue line in Fig. 2D, mean pull-/gripforce ratio = 0.42). In addition, CBL1 occasionally used a four-finger grip rather than the requested three-finger grip (D4: magenta line in Fig. 2E and F). After rod release grip forces reached a maximum of twice the total grip force in respect to the values at URR. The absolute lengths of lever LDi also showed a different picture. After initial contact, only thumb and middle finger reached an approximately optimal lever (blue line and red line in Fig. 2F, respectively) whereas index and ring finger produced a lever twice as large as thumb or
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Fig. 2. Torque, pull force, grip forces, and finger positions during the “pick the raspberry task” of the healthy subject CTRL1 (CTRL, A–C) and the cerebellar patient CBL1 (CBL, D–F). (A and D) Torque (black line) and pull force (blue line) over time; note the two different scales for torque (left) and pull force (right) in both panels. (B and E) Total (black line) and single grip forces of fingers (thumb: blue line, index finger: green line, middle finger: red line, ring finger: magenta line). (C and F) Absolute values of the lengths of levers of the fingers, same convention as in (B and E). All recordings are aligned to the unpredictable rod release (URR, t = 0).
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middle finger (green line and magenta line in Fig. 2F, respectively). These different levers were due partly to this patient’s incapacity to grip the rod from the front side (e.g. Fig. 1A) but from above. The resulting mean width of rod slice element was 10.7 ± 7.1 mm in this patient. The development of torque for all trials recorded from CTRL1 and from CBL1 are shown in Fig. 3. In general, CTRL1 produced low torques and was able during practice to reduce the torque to a minimum (Fig. 3A) resulting in a low average torque with small standard deviations (Fig. 3B). In contrast, CBL1 produced higher torques and was unable to reduce them, despite having a considerably larger number of practice trials (Fig. 3E). On average, this patient (CBL1) produced torques six-fold as large as that of CTRL1 before URR (compare Fig. 3B with F). It is interesting to note that this patient’s total grip force was in the same range as that of the healthy subject (see Fig. 3C and G). This indicates that the differences in grip force most likely did not contribute for the differences in torque values. Main differences can be seen in the average total effective lever (Fig. 3D and H). Both produced initially larger levers but only the healthy subject was able to minimise the average total effective lever and its standard deviation during the pull-phase (Fig. 3D). In contrast, CBL1 was unable to position the fingers well and remained at URR with eight-fold larger total effective lever values and larger standard deviations than CTRL1 (Fig. 3H), producing larger mean torques (Fig. 3F). 3.2. Comparison of total grip force and length of total effective lever as factors for torque development The data presented above show that CTRL1 was able to produce decreasing, low torques during the pull-phase whereas CBL1 produced increasing, high torques. Since torque is given by the vector product of factor lever and factor grip force, the question arises as to whether the differences in torques are due mainly to the higher grip forces produced by CBL1 or the larger total effective lever length. Average torque, average total grip force, and average of the total effective lever length were calculated for a 500-ms time window starting 850 ms before the URR. During this time window grip forces and finger positions were sufficiently established (see grey areas in Fig. 3) and adequately detectable. Fig. 4 shows the results of both healthy subjects (blue and cyan tetrahedrons) and both patients (red and yellow spheres). Healthy subjects showed a low variation in the total effective lever length and the variation of torques is in good relationship to the total grip forces exerted. In contrast patients showed strong variation in the total effective lever length and the total grip force. Comparison of patients and healthy subjects results show that the variation of torque in patients’ data is mainly due to their total effective lever length (compare Fig. 3H with D). This indicates that patients were unable to position their fingers appropriately on a narrow rod slice element to reduce the total effective lever during the task. 4. Discussion This study introduces a new task which allows a quantification of the dynamics of torque development in multi-finger prehension tasks with increasing grip forces, comparable to picking a raspberry, by healthy subjects and patients with motor disorders. Levers and torques were derived from grip forces and geometric properties of the grip rod used. An advantage of the task is that torques that would tend to deviate the rod from the pull-axis are losses that subjects try to minimise unconsciously. Our results show that the healthy subjects are able to minimise torque despite increasing grip force, whereas cerebellar patients increase torque dispropor-
tionately with increasing grip forces. The main factor of torque increase was the effective lever. Before URR, patient (e.g. CBL1) used an eight-fold larger total effective lever length than CTRL1. This is due to the fact that this patient did not place the fingers accurately on a narrow rod slice element around the centre of mass (10.7 ± 7.1 mm vs. 3.4 ± 1.3 mm of the subject). Hence, cerebellar patients produced less pull force than control subjects (mean pull/grip-force ratio 0.55 vs. 0.80, respectively) although both produced grip forces within the same range (Fig. 3C and G). It can be presumed that cerebellar patients suffer from the lack of control of co-contraction of flexor and extensor muscle to position the fingers appropriately to produce well-balanced grip forces. Indeed, it seems that patients try to compensate their ataxia-based insecurity by developing higher grip forces, resulting in disproportionately higher torques and increased instability, resulting in increasing grip force, thus establishing a vicious circle. Further results should provide effective rehabilitation strategies which are aimed to interrupt the above described vicious circle. Our measurements are based on the soft contact model (Mason and Salisbury, 1985). In this model, a free moment (Zatsiorsky, 2002) about the direction of a normal force is possible only due to the friction between the digit tip and the contact surface. An attempt to generate such a moment will result in a digit-tip rolling on the contact surface (Zatsiorsky, 2002). In our experimental task finger movements are allowed (see Section 2.4) resulting in changed finger positions. This component could be disregarded, since it does not contribute to the torque. For the calculation of overall torque during multi-digit prehension, Zatsiorsky and colleagues introduced the principle of superposition in studies of human prehension (Zatsiorsky et al., 2004) extending the idea of virtual fingers (Baud-Bovy and Soechting, 2001). The calculation is based on a fixed arrangement of finger positions with the thumb opposed in centre to the other fingers. Under these conditions the corresponding calculation can be simplified (see Eq. (1) of Zatsiorsky et al., 2004). Measurement systems with fixed finger positions are applicable for studies with healthy subjects, but not for patients with motor disorders. For the latter, measurement systems with enlarged contact area and reduced finger aperture are necessary (e.g. Nowak and Hermsdorfer, 2005, 2006; Kutz et al., 2007). The advantage of the present system is that it allows unrestrained arms and completely free finger positions, i.e. physiological conditions, to measure individual grip forces of any number of fingers, even though they are not positioned in a prismatic grip as shown for a patient with motor disorder (see Fig. 4 in Kutz et al., 2007). This required a change in the algorithm for calculation of torque produced by normal forces. We determined first the position of fingers and from that values the rod slice element touched and covered by the fingers exerting forces, and its centre of mass was derived. Levers were derived from the position of individual fingers and the centre of mass of the rod slice element resulting in the total torque which is calculated directly following Eq. (1) (see Section 2). On the other hand our system does not provide individual tangential forces at the individual finger positions whereas the total sum of all tangential forces is measured as pull force. From that point of view a direct comparison of our results with Zatsiorsky and colleagues must be incomplete (e.g. Zatsiorsky et al., 2002a, 2004; Zatsiorsky and Latash, 2004). In our task moreover, subjects pulled an initially fixed object whereas in other studies object were lifted (e.g. Flanagan and Tresilian, 1994; Flanagan et al., 1999; Burstedt et al., 1999; Nowak et al., 2002; Zatsiorsky et al., 2002a, 2004; Zatsiorsky and Latash, 2004; Nowak and Hermsdorfer, 2005, 2006). Thus, in our task, the torque produced by unbalanced grip forces does not produce a deviation of the object from the pull-axis which would compensate the torque. However, a reduction of this torque is obtained by optimising the finger positions.
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Fig. 3. Stack plots and average responses of torque, grip force and total effective lever length of the healthy subject CTRL1 (CTRL, A–D) and the cerebellar patient CBL1 (CBL, E–H). (A and E) Stack graphs of torque development of all trials, arrows indicating single trials shown in Fig. 2. (B and F) Average torque ± standard deviation. (C and G) Average total grip force ± standard deviation. (D and H) Average total effective lever length ± standard deviation. All recordings are aligned to the unpredictable rod release (URR, t = 0). The gradual change in the total effective length of lever over time shown in (D and H) is due to the dispersion in time as a result of the trial-by-trial variability of the pull-phase (see Section 2.4).
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Fig. 4. Three dimensional scatterplot of mean torque, total grip force, and total effective lever length of all trials of both healthy subjects and both cerebellar patients: mean values were calculated for a 500-ms time window starting 850 ms before the unpredictable rod release (see dark grey areas in Fig. 3). Healthy subjects: blue and cyan tetrahedrons and blue and cyan triangles in the projection plane torque over force and torque over total effective lever length, respectively. Cerebellar patients: red and yellow spheres and red and yellow circles in the projection plane torque over force and torque over lever, respectively. The blue and red coloured data are from CTRL1 and from CBL1 shown in Figs. 2 and 3, respectively.
The novel task introduced in this study provides evidence that healthy subjects reduce their torque unconsciously, whereas cerebellar patients fail (see Fig. 3D and H). It can be assumed that the inaccurate grip-force scaling observed in cerebellar patients (Serrien and Wiesendanger, 1999a; Nowak et al., 2002) is at least partly the outcome of unbalanced grip forces and not necessarily a preceding erroneously determined scale factor. This assumption, however, needs further investigation of torque dynamics with the described raspberry task. Acknowledgments The authors would like to thank Dr. J. Davis for critically reading the manuscript and T. Meindl and M. Bruckmeier for assistance during the experiments and preparing the figures. The study was supported by the “Else Kröner-Fresenius-Stiftung” (A12/07) and the Friedrich-Baur-Foundation (0006/2003; 0005/2004, 0004/2005). References Baud-Bovy G, Soechting JF. Two virtual fingers in the control of the tripod grasp. J Neurophysiol 2001;86:604–15. Burstedt MKO, Flanagan JR, Johansson RS. Control of grasp stability in humans under different frictional conditions during multidigit manipulation. J Neurophysiol 1999;82:2393–405.
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