ARTICLE IN PRESS

Journal of Biomechanics 40 (2007) 2846–2856 www.elsevier.com/locate/jbiomech www.JBiomech.com

Using EMG data to constrain optimization procedure improves finger tendon tension estimations during static fingertip force production Laurent Vigourouxa,, Franck Quaineb, Annick Labarre-Vilac, David Amarantinid, Franc- ois Moutete a Laboratoire Mouvement et Perception, UMR 6152, Universite´ de la Me´diterrane´e, Marseille, France Laboratoire GIPSA-lab, de´partement d’Automatique, Equipe Syste`mes Biome´caniques, UMR 5216, Universite´ Joseph Fourier, Grenoble, France c Unite´ ENMG et pathologie neuromusculaire, CHU Grenoble, France d Laboratoire Adaptation Perceptivo-Motrice et Apprentissage, EA 3691, Universite´ Paul Sabatier, Toulouse, France e SOS Main, Unite´ de chirurgie re´paratrice de la main et des bruˆle´s, CHU Grenoble, France

b

Accepted 12 March 2007

Abstract Determining tendon tensions of the finger muscles is crucial for the understanding and the rehabilitation of hand pathologies. Since no direct measurement is possible for a large number of finger muscle tendons, biomechanical modelling presents an alternative solution to indirectly evaluate these forces. However, the main problem is that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint resulting in mathematical under-determinate problems. In the current study, a method using both numerical optimization and the intra-muscular electromyography (EMG) data was developed to estimate the middle finger tendon tensions during static fingertip force production. The method used a numerical optimization procedure with the muscle stress squared criterion to determine a solution while the EMG data of three extrinsic hand muscles serve to enforce additional inequality constraints. The results were compared with those obtained with a classical numerical optimization and a method based on EMG only. The proposed method provides satisfactory results since the tendon tension estimations respected the mechanical equilibrium of the musculoskeletal system and were concordant with the EMG distribution pattern of the subjects. These results were not observed neither with the classical numerical optimization nor with the EMG-based method. This study demonstrates that including the EMG data of the three extrinsic muscles of the middle finger as inequality constraints in an optimization process can yield relevant tendon tensions with regard to individual muscle activation patterns, particularly concerning the antagonist muscles. r 2007 Elsevier Ltd. All rights reserved. Keywords: Biomechanical finger model; Muscle tendon tension; Numerical optimization; Intra-muscular electromyography

1. Introduction Normal finger function is mainly dependant on how force is transmitted from the forearm (extrinsic) and

Corresponding author. Tel.: +33 0 49117 0422; fax: +33 0 49117 2252. E-mail address: [email protected] (L. Vigouroux).

0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.03.010

hand (intrinsic) muscles to the finger joints. To achieve this, the flexor tendon pulley system is critical in maintaining the flexor tendons close to the bone, thus converting force developed in the flexor muscle-tendon into torque at the finger joints. High stress applied on pulleys and tendons results in injuries which are debilitating and require surgical interventions (Gabl et al., 2000; Moutet, 2003; Schweizer, 2001). Because this surgery is complex, an accurate evaluation of the

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

force acting on finger tendons is crucial to assist surgeons in evaluating options for restoring finger function (Valero-Cuevas et al., 1998). Biomechanical models have been widely used to estimate individual finger tendon tensions (Brook et al., 1995; Chao and An, 1978; Harding et al., 1993; Valero-Cuevas et al., 1998; Weightman and Amis, 1982). Unfortunately, the finger musculoskeletal system is redundant in the sense that more muscles cross a joint than there are degrees of freedom at the joint. Mathematically, this produces an under-determinate problem, so there is an infinite number of possible tendon force patterns that can produce the required forces and moments (Chao et al., 1976; Herzog and Leonard, 1991). Numerical optimization techniques are widely used to solve under-determinate problems. These techniques provide solutions that maximize or minimize an objective function related to some physiological criterions based on the hypothesis of minimum energy expenditure. Minimization of muscle stress squared (labelled ‘‘Muscle stress’’ in the current study) is generally used for the estimation of finger muscle and joint forces for both static (Chao et al., 1989; Dennerlein et al., 1998) and dynamic conditions (Brook et al., 1995; Sancho-Bru et al., 2001). Nevertheless, numerical optimization procedures present major limitations since they provide solutions which do not correspond to the muscle activation patterns identified by electromyography (EMG) (Ait-Haddou et al., 2004; Challis and Kerwin, 1993; Jinha et al., 2006; Raikova and Prilutsky, 2001). Particularly, optimization procedures do not take into account that subjects can use different muscle force patterns to produce a similar external fingertip force (Kursa et al., 2006). Moreover, optimization procedures could fail to predict the significant antagonist muscle tensions (Challis, 1997). Consequently, the accuracy of tendon tensions predicted by optimization methods is questionable, particularly for applications in the field of hand function surgery. On the other hand, using the EMG-force relationship to estimate tendon tensions (labelled ‘‘EMG-based’’ method) seems to be an attractive choice since it reflects the individual muscle activation pattern adopted by the subject. EMG muscle activation patterns from the extrinsic muscles of the hand during various finger movements are frequently reported in the literature (Close and Kidd, 1969; Long and Brown, 1964; Long et al., 1970; Maier and Hepp-Reymond, 1995). However, EMG data from the intrinsic muscles remain difficult to acquire and this presents a real experimental challenge since these muscles originate and insert within the hand itself (Burgar et al., 1998). Moreover, establishing the EMG-force relationship imply non-negligible approximations so that the resulting tension values may not respect the mechanical equilibrium (Ketchum et al., 1978; Valero-Cuevas et al., 1998). As a consequence,

2847

these drawbacks have limited the potential of EMG data as a useful tool for finger tendon tension estimations. In a similar way to recent studies dealing with the estimation of muscular efforts (Amarantini and Martin, 2004; Cholewicki and McGill, 1994; Gagnon et al., 2001), we support the idea that a combination of both EMG data and numerical optimization should be used to estimate tendon tensions. In the current study, such a hybrid method has been developed for biomechanical finger modelling (labelled ‘‘Optimization constrained by EMG’’). The originality of the method consists in introducing inequality constraints estimated via EMG of the extrinsic muscles of the hand (the easiest recordable muscles) in the optimization procedure in order to constrain the space of available solutions. To identify the advantages of this approach, an experimental procedure was performed in order to collect the fingertip force, the EMG and the finger joint postures during a static maximal middle fingertip force production. The computed tendon tensions were compared with those obtained from a classical optimization procedure (‘‘Muscle stress’’ method) and with those estimated from an ‘‘EMG-based’’ method.

2. Materials and methods 2.1. Subjects Six right-handed subjects were tested in this study (age: 27  5:5 years; height 177:4  4:5 cm; body mass 65:6  2:0 kg; Mean  SD). None of the participants had any history of trauma affecting the upper limbs. The procedure was approved by the Consultative Committee for the Protection of Persons in Biomedical Research (CCPPRB, Grenoble, France) and all subjects signed an informed consent. 2.2. Experimental set-up and procedure The subjects sat with the right forearm placed on a horizontal table. The upper arm was at 45 of abduction, the elbow joint flexed at 90 and the wrist placed at 0 of flexion, palm down. The subjects were instructed to hold their middle finger straight without any joint flexion (Fig. 1). A steel plate ð5 mm  10 mm  6 mmÞ fixed to a 3D force sensor was positioned at the centre of the distal phalanx to provide a finger contact area. A digital camera (Sony, CD-S70) located 0.7 m left of the subjects was used to identify the joint angles adopted by the subjects at each test. The longitudinal axis of each segment was defined by two marks placed directly on the skin. The angles of intersection of the longitudinal axis of adjacent segments defined the joint angles. Mean flexion angles were 6:9  5:8 for the DIP joint (y1 Þ, 8:5  6:7 for the PIP joint (y2 Þ and 6:8  5:9 for the MCP joint ðy3 Þ. Subjects were asked to maintain the angle of MCP joint adduction/ abduction at 0 . The task consisted of performing three tests of maximal voluntary fingertip force (MVF) along the vertical axis. As

ARTICLE IN PRESS 2848

L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

Resultant fingertip force (N)

Fig. 1. Finger posture tested in the study. The finger is in a straight position with each joint placed near 0 of flexion. A clamp stabilized the palm of the hand. Subjects were instructed to produce vertical force (white arrow representing the reaction force).

peak force

50 40 30 20 10 0

EMG (m.V)

1000 FDP

500

0 EMG (m.V)

1000 FDS

500

0 EMG (m.V)

1000

EDC

500

0

0

4

8 Time (seconds)

12

Fig. 2. Experimental recording of the resultant fingertip force (N) and rectified EMG signals of the FDP, FDS, EDC muscles during a typical test. The two vertical lines represent the 750 ms window centred on peak force within which the data analysis was performed.

proposed by Valero-Cuevas et al. (1998), subjects were required to increase the force progressively in three steps (10N, 50% MVF, 100% MVF, see Fig. 2). Visual

feedback of the force magnitude (vertical component) was displayed to the subjects in order to control the force production task.

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

2.3. Experimental data

UB TE

UI

ES

2.3.1. Fingertip force A three-axial force sensor (load of range: 0–1 kN, 0.5 N resolution for all axes, ENSIEG, INPG, France) was used to record the fingertip force. The force signals were amplified (PM instrumentation, ref 1965, Orgeval, France) and recorded at 1024 Hz using the MYODATA acquisition system (Mazet Electronique, model Biostim 6082, France).

2849

EDC LU, RI

RB

EDC

FDS FDP

2.3.2. Intra-muscular EMG Monopolar needle electrodes (Medtronic type DCN25, shaft diameter 0.46, core area 0:07 mm2 ) recorded EMG of the extrinsic muscles (Flexor digitorum communis, FDP; Flexor digitorum superficialis, FDS; Extensor digitorum communis, EDC). Electrodes were implanted according to the recommendations of Burgar et al. (1998) and Reilly and Schieber (2003). Raw EMG signals were recorded at 5 kHz with the Keypoint workstation (Medtronic, Skovlunde, Denmark; bandpass from 10 Hz to 5 kHz; amplification to 3 dB; common mode rejection ratio:490 dB). EMG signals were filtered off-line using a zerolag Butterworth filter (order 4, bandpass from 20 to 600 Hz). 2.3.3. Data analysis To compute the tendon tensions at each test, the fingertip force and EMG data were used as inputs into our biomechanical model. Averaged fingertip forces were calculated within a 750 ms window centred on the peak force (Fig. 2). Within this time interval, muscle excitation levels for each extrinsic muscle (em with m ¼ FDP, FDS and EDC) were computed from the EMG data as proposed by Valero-Cuevas et al. (1998): em ¼

RMSm , RMSm max

(1)

where RMSm is the EMG root mean square value computed for each test (Basmajian and De Luca, 1985). RMSm max corresponds to the largest root mean square value recorded during the following additional tasks performed for each muscle in the same posture (Chao et al., 1989; Ketchum et al., 1978; Li et al., 2000, 2001). For the EDC muscle, the specific additional isometric task consisted of a maximal extension force with the external force located at the centre of the first phalange. For the FDS muscle, a maximal flexion force was required with the force applied to the middle of the second phalange. In order to exclude the co-activation of the FDP, a quadriga manoeuvre was performed (Schweizer et al., 2003): the subjects kept the index, ring and little fingers extended so that the FDP muscle belly of the middle finger became ineffective. At the same time, the experimenter manually tested that the P3 phalange remained slack at each test ensuring a non-activation of the FDP. No additional specific isometric task was performed for the FDP muscle since the required procedure in the literature corresponds to the MVF carried out in the current study. 2.4. Biomechanical finger model 2.4.1. Mechanical equilibrium equations The biomechanical finger model consists of four rigid segments: proximal, middle, distal phalanx and metacarpal

DIP

PIP

MCP

UI, LU, RI

Fig. 3. Finger muscle tendons (FDP, FDS, EDC, UI, LU, RI) acting on finger joints (DIP, PIP, MCP). The extensor mechanism (adapted from Brook et al., 1995) connects muscle tendons (EDC, UI, LU, RI) and extensor bands (RB, UB, TE, ES) as represented in the upper insert (dorsal view).

bone (Fig. 3). As widely used in the literature (Li et al., 2000, 2001), the segment lengths and the intra-articular lengths were obtained from the anthropometric tables of Buchholz et al. (1992) and An et al. (1979). The Buchholz’table personalizes the segment lengths based on the size of the hand of each subject. DIP and PIP joints were modelled as frictionless hinges with one degree of freedom in flexion/extension. The MCP joint was modelled with two degrees of freedom in flexion/extension and in abduction/adduction. Adapting Newton’s laws of static equilibrium for moments to the four degrees of freedom of the finger model provides a four moment equilibrium equation system: 8 ðMzFDPjDIP þ MzTEjDIP Þ þ MzF ext jDIP ¼ 0; > > > > > ðMzFDPjPIP þ MzFDSjPIP þ MzUBjPIP þ MzRBjPIP > > > > > > þMzESjPIP Þ þ MzF ext jPIP ¼ 0; > < ðMzFDPjMCP þ MzFDSjMCP þ MzLUjMCP þ MzUIjMCP (2) > > > þMzRIjMCP þ MzEDCjMCP Þ þ MzF ext jMCP ¼ 0; > > > > > ðMyFDPjMCP þ MyFDSjMCP þ MyLUjMCP þ MyUIjMCP > > > > : þMyRIjMCP þ MyEDCjMCP Þ þ MyF jMCP ¼ 0; ext

where Mnijj represents the moment of the i tendon (i ¼ FDP, FDS, EDC, lumbrical LU, ulnar interosseus UI, radial interosseus RI, terminal extensor tendon TE, extensor slip ES, radial band RB and ulnar band UB) over the n degree of freedom (n ¼ x; y; z) of the j joint (j ¼ DIP, PIP, MCP). MnF ext jj is the moment of the external fingertip force at the n degree of freedom of the j joint. The moments of each tendon at each joint were computed according to the following cross-product: Mijj ¼ Bi;j ^ ti ,

(3)

where Mijj and Bi;j are, respectively, the moment vector and the moment arm of the i tendon over the j joint, and ti is the tension vector of the i tendon. According to the joint angles (y1 , y2 , y3 ), the moment arms of muscles and tendons were computed for each test. The coordinate points provided by An et al. (1979) in zero degree positions were re-computed

ARTICLE IN PRESS 2850

L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

according to the joint flexion adopted at each test using the Eulerian angles. The moment arms of tendons were defined from these tendon coordinates using the model I of Landsmeer (1961) for the flexor tendons (FDP, FDS, LU, UI, RI) and UB and RB bands and using the model III of Landsmeer (1961) for the extensor tendons (EDC, ES, TE) (An et al., 1983). 2.4.2. Ligaments As proposed by Sancho-Bru et al. (2001), the actions of both ulnar and radial ligaments (UL and RL) acting at the MCP joint were added in the equilibrium equations (Eq. (2)). The tension of each ligament (tlig ) was estimated using a quadratic function relating to the force developed by the ligament to its elongation (Mommersteeg et al., 1996). In order to represent the non-linear behaviour of the ligament, a characteristic constant of the ligament ðKÞ set to 750 N=cm2 (Minami et al., 1985) was included: tlig ¼ K  ðLlig  L0 Þ2 ,

(4)

where Llig is the length of the ligament and L0 is the unstrained length of the ligament. The data for the ligament moment arms and insertion points for the determination of ligament lengths and the ligament moments were obtained from Chao et al. (1989). In our study, the positioning of MCP joint was close to 0 of flexion. This posture induced small ligament moments in comparison to the moments of the external fingertip force ð0:006  0:005 N mÞ. 2.4.3. Extensor mechanism The extensor mechanism (Fig. 3, upper insert) is a deformable tendon hood which connects muscle tendons (LU, RI, UI, EDC) and tendon bands (ES, RB, UB and TE) (Garcia-Elias et al., 1991; Landsmeer, 1961). The model presented by Brook et al. (1995) was used to determine the fraction of force transmitted by each tendon to the extensor bands: 8 tTE ¼ wRB  tRB þ wUB  tUB ; > > > > > > < tRB ¼ aEDC  tEDC þ aLU  tLU þ aRI  tRI ; tUB ¼ aEDC  tEDC þ aUI  tUI ; (5) > > > tES ¼ ð0:944  aUI Þ  tUI þ ð1  aLU Þ  tLU > > > : þð0:314  a Þ  t þ ð1  2a RI RI EDC Þ  tEDC ; where tEDC , tUI , tRI and tLU represent the tendon tensions of EDC, UI, RI and LU, respectively. tTE , tRB , tUB and tES represent, respectively, the tensions of TE, RB, UB and ES. wRB and wUB (computed from An et al., 1979) are cosine terms accounting for the convergence angles of the RB and UB onto the TE. According to Sancho-Bru et al. (2003), the force fraction transmitted by muscle tendons to the extensor mechanism bands (0.944 for UI, 1 for LU and 0.314 for RI) were obtained from Eyler and Markee (1954). The a coefficients were determined together with the unknown tendon tensions using the non-linear optimization process described in the following Section 2.4.4. 2.4.4. Resolution methods The tendon tensions were calculated using three different modes of resolution: (i) ‘‘EMG-based’’ method, (ii) ‘‘Muscle stress’’ method, and (iii) the ‘‘Optimization constrained by EMG’’ method developed in the current study.

(i) ‘‘EMG-based’’ method: This method allows the estimation of tendon tensions of the extrinsic muscles only (FDP, FDS and EDC) since no EMG was recorded for the intrinsic muscles. The tendon tensions (tm EMG , with m ¼ FPD, FDS and EDC), were obtained from the product of the physiological cross-sectional areas of the muscles (PCSAm ), the maximum isometric muscle stress (smax ) and the muscle excitation level (em ), as follows (Cholewicki and McGill, 1994; Valero-Cuevas et al., 1998): tm EMG ¼ em  smax  PCSAm ,

(6)

2

smax was fixed to 35 N cm (Valero-Cuevas et al., 1998; Zajac, 1989), PCSAm as defined by An et al. (1983) and em was obtained from EMG data of the extrinsic muscles (Section 2.3.3 Data analysis). (ii) ‘‘Muscle stress’’ method: This method used the muscle stress squared criterion (Eq. (7)) to select a solution (Dennerlein et al., 1998; Sancho-Bru et al., 2003). The optimization process is summarized as follows: find: ti (i ¼ fFDP; FDS; LU; UI; RI; EDCg) and aEDC , aLU , aUI , aRI , that minimize: 2 i  X ti , (7) GðtÞ ¼ PCSAi 1 subject to the equality constraints of mechanical equilibrium contained in Eqs. (2), (4) and (5) and subject to the inequality constraints: PCSAi  smax Xti X0, 0paLU p1;

0paUI p0:944;

(8) 0paRI p0:314,

0p2:aEDC p1.

ð9Þ

Eq. (8) was added to obtain positive tendon tensions below the theoretical maximal muscle force. Eq. (9) states that the proportion of force transmitted by the tendons to the extensor mechanism bands ranges from 0 to 1 for the LU and the EDC muscles, 0–0.944 for the UI muscle and 0–0.314 for the RI muscle. (iii) ‘‘Optimization constrained by EMG’’ method: This method consists in using the muscle stress squared criterion (Eq. (7)) to select a solution. In addition, inequality constraints associated with EMG recordings were added to constrain the FDP, FDS and EDC tendon tension estimations (Eq. (6)). The optimization process consists of: find: ti (i ¼ fFDP; FDS; LU; UI; RI; EDCg) and aEDC , aLU , aUI , aRI that minimizes Eq. (7) subject to the mechanical equilibrium equality constraints of Eqs. (2), (4) and (5), subject to the inequality constraints contained in Eqs. (8) and (9) and subject to the EMG inequality constraints: ð1  mÞtm EMG ptm pð1 þ mÞtm EMG .

(10)

Eq. (10) represents the inequality constraints based on the EMG data, where tm EMG was computed from Eq. (6). Then Eq. (10) was applied to each of the three extrinsic muscles. A coefficient (m) was added in order to weight the ‘‘EMG-based’’ results which could be inconsistent.

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

As an initial condition, the m coefficient was set to 0 implying that the estimated tendon tensions (i.e. tFDP , tFDS , tEDC ) strictly equalled those computed from EMG data (i.e. tFDP EMG , tFDS EMG , tEDC EMG ). When the optimization process did not converge towards a solution (i.e. mechanical equilibrium cannot be reached with such constraints), m was iteratively increased in steps of 0.05 until a solution was provided. Thus, high m values indicate discrepancies between the determinate solutions and the EMG estimations, whereas low m values indicate concordant estimations. The results of the tendon tensions obtained with all the three methods were compared for all tests.

2851

Table 1 Fingertip force (F ext , Newton), FDP, FDS, EDC muscle excitation levels ðeFDP ; eFDS ; eEDC Þ and the m coefficient for the three tests of each subject F ext

eFDP

eFDS

eEDC

m

Subject 1 43.2 40.2 34.9

0.59 1 0.46

1 0.56 0.54

0.20 0.30 0.21

0.15 0.1 0.45

Subject 2 46.9 49.0 53.0

0.88 0.76 1

0.74 0.69 1

0.28 0.25 0.50

0.5 0.75 0.35

Subject 3 41.3 42.0 38.9

0.62 1 0.69

1 0.93 0.96

0.62 1 0.56

0.15 0 0.05

Subject 4 52.4 51.7 51.4

0.74 0.74 1

0.81 0.98 1

0.59 0.50 0.57

0.35 0.2 0.3

Subject 5 55.3 43.8

1 0.70

1 0.92

0.20 0.22

0.7 0.25

3.1. Fingertip force, muscle excitation level (em ) and m coefficient

Subject 6 39.0 41.6 32.8

1 0.64 0.63

0.71 0.55 0.50

0.14 0.13 0.13

0 0 0.05

Fingertip force, muscle excitation level (em ) and m coefficient are presented for each test and each subject in Table 1. The fingertip forces averaged 44:0  7:4 N. Over the whole subjects, muscle excitation level was 0:79  0:18 for the FDP and 0:82  0:19 for the FDS (ranging from 0.46 to 1 for the FDP and from 0.50 to 1 for the FDS). The EDC muscle excitation level averaged 0:38  0:23 (ranging from 0.13 to 1). The m coefficients averaged 0:26  0:24 (ranging from 0 to 0.75). This means that the tendon tensions estimated by the ‘‘Optimization constrained by EMG’’ method were included, on average, in a 26% interval of the tensions predicted by the EMG. In four tests, coefficients over 0.4 were calculated whereas in 10 tests the m coefficients were lower or equal to 0.25.

Mean

3. Results In one test, subject 5 did not perform according to the task requirements (the DIP joint was hyper-extended) and so this test was removed from the study.

3.2. Tendon tensions The estimations of FDP tendon tensions calculated using the three methods are presented in Fig. 4. For the methods and the tests, the FDP tendon tensions ranged from 65.3 to 185.7 N. In each test, the estimations differed according to the method employed. The ‘‘Optimization constrained by EMG’’ method provided higher values than the others methods (þ41:8% on average) in four tests (the three tests of subjects 2 and the 3rd test of the subject 4), whereas the ‘‘Muscle stress’’ method provided lower values (31:9% on average) in three tests (the 2nd tests of subjects 1 and 3 and the 1st test of subject 6) and a higher value in the 1st test of subject 1 ðþ35:9%Þ. In the other tests, the three methods provided estimations in a similar range. For all the subjects, except subjects 5 and 2, the estimations obtained with the ‘‘Optimization constrained

44:0  7:4 0:79  0:18 0:82  0:19 0:38  0:23 0:26  0:24

The F ext ; eFDP ; eFDS and eEDC represent experimental data and the m coefficient represents the manner in which the EMG data have been taken into account in the ‘‘Optimization constrained by EMG’’ method.

by EMG’’ method consistently matched those obtained with the ‘‘EMG-based’’ method, reflecting the test-bytest variation. This correspondence was not observed with the ‘‘Muscle stress’’ method. Fig. 5 presents the estimations of FDS tendon tensions. They globally ranged from 72.8 to 245.7 N. Results show that the ‘‘Muscle stress’’ method gave estimations superior to those of the other methods (þ43:0% on average) in 11 tests (the three tests of subjects 2, 4 and 6 and the 2nd and 3rd tests of subject 1). For all tests, the ‘‘EMG-based’’ method gave the lowest estimations. Similarly to the FDP results, the estimations from the ‘‘Optimization constrained by EMG’’ method matched the estimations of the ‘‘EMGbased’’ procedure, except in subject 5. Estimations of EDC tendon tensions are shown in Fig. 6. They fell within the global range of 0 to 60 N. The ‘‘Muscle stress’’ method set the estimations to 0 N in all tests excluding the two tests of subject 5 and the 3rd test of subject 4. In contrast, the results of the ‘‘Optimization constrained by EMG’’ method were similar to those of the ‘‘EMG-based’’ method in each test. Concerning the intrinsic muscles, no estimation was possible with the ‘‘EMG-based’’ method since no EMG was registered from these muscles. Averaged intrinsic muscle forces estimated using the ‘‘Muscle stress’’ method and the ‘‘Optimization constrained by EMG’’ method are indicated in Fig. 7. Tendon tensions of LU

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

2852

200

Subject 4

Subject 1

Force (N)

150 100 50 0 Subject 5

Subject 2

200

Force (N)

150 100 50 0 200

Subject 3

Subject 6

Force (N)

150 100 50 0

1

2 Tests

3

1

2

3

Tests

Fig. 4. FDP tendon tensions estimated in the three tests of the six subjects: & represents the results of the ‘‘EMG-based’’ method,  represents the estimations of the ‘‘Muscle stress’’ method and m the estimations of the new ‘‘Optimization constrained by EMG’’ method.

muscle were set to 0 N with both the ‘‘Optimization constrained by EMG’’ method and the ‘‘Muscle stress’’ method. Concerning the UI muscle tendon tensions, the ‘‘Optimization constrained by EMG’’ method provided tensions averaging 56:8  27:3 N and the ‘‘Muscle stress’’ method gave an average of 32:4  8:3 N. Finally, RI muscle tendon tensions averaged 38:5  26:5 N and 13:5  7:9 N with the ‘‘Optimization constrained by EMG’’ and the ‘‘Muscle stress’’ methods, respectively.

4. Discussion Identifying finger tendon tensions is crucial for applied anatomists and kinesiologists in order to understand finger biomechanics. Several methods using biomechanical simplifications (Fowler and Nicol, 2000; Harding et al., 1993; Li et al., 2001; Weightman and Amis, 1982), EMG-based estimations (Valero-Cuevas et al., 1998) and numerical optimization (Dennerlein et al., 1998) give an approximation of these variables. However, these methods do not allow the simultaneous evaluation of the tensions in antagonist muscles and the

agonist muscle activation sharing patterns. In the current study, we propose to use a numerical optimization procedure which includes additional inequality constraints computed from EMG data. To constitute the additional constraints, a m coefficient was determined incrementally for each test. For 14 of the 17 tests, the m coefficient was increased from 0.1 to 0.75 meaning that no satisfactory mechanical solution could be found from the ‘‘EMG-based’’ estimations. This fact was due to the probable discrepancies in EMG measurements and/or in muscle characteristics (PCSAm ; smax ) taken into account into the EMG-based calculation. The m coefficient quantifies thus the differences between the determinate solutions and the ‘‘EMG-based’’ estimations. In addition, using only one m coefficient for the three extrinsic muscles presents several other advantages for finger modelling. Firstly, it allows estimates of all muscle forces without requiring an EMG recording of each muscle (in particular intrinsic muscles). Secondly, the m coefficient avoids the alternative of combining both an EMG criterion and the muscle stress criterion in the optimization procedure (i.e. using a multi-cost function) which supposes the use of arbitrary weights for each criterion.

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

250

Subject 1

Subject 4

Subject 2

Subject 5

Subject 3

Subject 6

2853

Force (N)

200 150 100 50 0 250

Force (N)

200 150 100 50 0 250

Force (N)

200 150 100 50 0

1

2 Tests

3

1

2 Tests

3

Fig. 5. FDS tendon tensions estimated in the three tests of the six subjects: & represents FDP tendon tension estimations of the ‘‘EMG-based’’ method,  represents the estimations of the ‘‘Muscle stress’’ method and m the estimations of the new ‘‘Optimization constrained by EMG’’ method.

The results of the EMG muscle excitation levels show that subjects adopted different extrinsic muscles coordination patterns to produce similar fingertip forces. This has already been observed by several authors during the application of sub-maximal forces (Close and Kidd, 1969; Long and Brown, 1964; Long et al., 1970; Maier and Hepp-Reymond, 1995). Thus, our EMG results confirm that the finger biomechanical models must necessarily be sensitive to the various muscular coordinations adopted by the subjects. This is not the case with the ‘‘Muscle stress’’ method. In contrary, the ‘‘Optimization constrained by EMG’’ method yields tendon tension values consistent with the EMG patterns of the extrinsic muscles. In particular, this method produces accurate estimations of the partici pation of the antagonist muscles as shown by the reliable EDC tendon tension values. These findings constitute an important advance in the field of finger biomechanics since the determination of the antagonist tendon tensions is seen as a recurrent problem (Harding et al., 1993; Li et al., 2001; Weightman and Amis, 1982).

To satisfy the mechanical equilibrium constraints, the ‘‘Muscle stress’’ method provided agonist tendon tension estimations proportional to the fingertip force intensity and tensions equalled to zero in the antagonist muscles. The ‘‘Muscle stress’’ method reflects thus the only fingertip force test-by-test variability whatever the EMG activities. Although these estimations are consistent with the static equilibrium conditions, they are inconsistent with the EMG recordings of FDP, FDS and EDC muscles. Conversely, the ‘‘EMG-based’’ method reflects the EMG test-by-test variability but does not permit to reach the mechanical equilibrium. The ‘‘Optimization constrained by EMG’’ yields coherent solutions in view of the mechanical equilibrium (fingertip force test-by-test variability is thus reflected) and takes into account the EMG test-by-test variability thanks to the additional inequality constraints. As a consequence, the results of the ‘‘Optimization constrained by EMG’’ are thus a compromise which responds to the two natures of variability. This feature is essential to improve finger surgery. For example, the estimation of accurate FDS and FDP tendon tensions is

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

2854

Force (N)

60

Subject 1

Subject 4

Subject 2

Subject 5

Subject 3

Subject 6

40 20 0

Force (N)

60 40 20 0

Force (N)

60 40 20 0

1

2

3

1

2

Tests

3

Tests

Fig. 6. EDC tendon tensions estimations during the three tests of the six subjects: & represents EDC estimations of the ‘‘EMG-based’’ method,  the estimations of the ‘‘Muscle stress’’ method and m the estimations of the developed ‘‘Optimization constrained by EMG’’ method.

100

Force (N)

80 60 40 20 0

UI

LU

Fig. 7. Mean intrinsic muscle forces for UI and RI muscles (n ¼ 6 subjects) computed from the ‘‘Optimization constrained by EMG’’ method (’) and the ‘‘Muscle stress’’ method ( ). LU muscle forces were estimated to 0 N with both optimization methods. No estimation was available with the ‘‘EMG-based’’ method since no EMG recording was performed on intrinsic muscles.

crucial to quantify finger pulley forces, since pulley forces are directly related to tendon forces (Hume et al., 1991; Roloff et al., 2006). This knowledge could be especially important for surgeons to properly choose the tissue for reconstruction (Bunnel, 1944; Karev et al., 1987; Widstrom et al., 1989) and to take an accurate size and shape of graft (Lister, 1985). The ‘‘Optimization

constrained by EMG’’ procedure may represents a reliable solution to this problem. In the current study we use the EMG of the three extrinsic muscles (FDS, FDP and EDC). More consistent results are provided with this method than without EMG measurement. Including EMG measurements from the three extrinsic muscles is therefore a

ARTICLE IN PRESS L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

substantial advance in the domain of finger modelling. We have chosen not to include the EMG of the intrinsic muscles since their measurements are very difficult to perform and could be at the origin of large imprecision (Burgar et al., 1998). In spite of this, intrinsic muscles are introduced into the mathematical formulation of the model and contribute to the stabilization of the joints. The ‘‘Optimization constrained by EMG’’ method and the ‘‘Muscle stress’’ method gave different UI and RI muscle force estimates. This means that the additional EMG inequality constraints introduced in the ‘‘Optimization constrained by EMG’’ method influenced the intrinsic muscles force estimates despite the fact that these constraints were based on the EMG of extrinsic muscles. Consequently, it could be supposed that the intrinsic muscle forces estimated with the ‘‘Optimization constrained by EMG’’ method were more consistent since they were evaluated according to the EMG excitation level of the other muscles crossing the joints. As a limitation, the consideration of a more precise muscle model including the Hill model could give a better estimate of tendon tensions from the ‘‘EMGbased’’ method and could reduce the values of m coefficients (Hoy et al., 1990; Anderson and Pandy, 2001). However, little information is available on finger muscle characteristics (e.g. pennation angle, tendon stiffness, optimal muscle length) making this improvement difficult (Valero-Cuevas et al., 1998). At this stage, it appears that the ‘‘Optimization constrained by EMG’’ method provides consistent results with respect to both the mechanical constraints of the task and the physiological behaviour of the subject. Such reliability of the results is obtained neither from the ‘‘EMG-based’’ model nor from the ‘‘Muscle stress’’ model. However, it should be considered that a simultaneous ‘‘in vivo’’ measurement of tendon tensions would be the only way to validate completely our estimates. Unfortunately, direct measurement of the six finger muscles is technically impossible given the current state of knowledge. To conclude, a new method has been introduced to estimate the six finger tendon tensions in agreement with different external measurements (i.e. EMG, external force and kinematics data). Evidence has been shown that this technique improves the consistency of the provided results and could have a large panel of clinical evaluations. Adaptations of the present method to the modelling of other musculo-skeletal systems should be envisaged in further studies.

Aknowledgement Authors thank the University Joseph Fourier for the financial support of this research (BQR-UJF, 2004). Authors also thank T. Coyle for her assistance.

2855

References Ait-Haddou, R., Jinha, A., Herzog, W., Binding, P., 2004. Analysis of the force-sharing problem using an optimization algorithm. Mathematical Biosciences 191, 11–122. Amarantini, D., Martin, L., 2004. A method to combine numerical optimization and EMG data for the estimation of joint moments under dynamic conditions. Journal of Biomechanics 37, 1393–1404. An, K.N., Chao, E.Y., Cooney, W.P., Linscheid, R.N., 1979. Normative model of human hand for biomechanical analysis. Journal of Biomechanics 12, 775–788. An, K.N., Ueba, Y., Chao, E.Y., Cooney, W.P., Linscheid, R.L., 1983. Tendon excursion and moment arm of index finger muscles. Journal of Biomechanics 16, 419–425. Anderson, F.C., Pandy, M.G., 2001. Dynamic optimization of human walking. Journal of Biomechanical Engineering 123, 381–390. Basmajian, J.V., De Luca, C.J., 1985. Muscles Alive. Williams & Wilkins, Baltimore. Brook, N., Mizrahi, J., Shoam, M., Dayan, J., 1995. A biomechanical model of index finger dynamics. Medical Engineering and Physics 17, 54–63. Buchholz, B., Armstrong, T.J., Goldstein, S.A., 1992. Anthropometric data for describing the kinematics of the human hand. Ergonomics 35, 261–273. Bunnel, S., 1944. Surgery of the Hand. JB Lippincott, Philadelphia. Burgar, C.G., Valero-Cuevas, F.J., Hentz, V.R., 1998. Fine-wire electromyographic recording during force generation. American Journal of Physical Medicine & Rehabilitation 76, 494–501. Challis, J.H., 1997. Producing physiologically realistic individual muscle force estimations by imposing constraints when using optimization techniques. Medical Engineering and Physics 19, 253– 261. Challis, J.H., Kerwin, D.G., 1993. An analytical examination of muscle force estimations using optimization techniques. Proceedings of the Institution of Mechanical Engineers 207, 139–148. Chao, E.Y., An, K.N., 1978. Graphical interpretation of the solution to the redundant problem in biomechanics. Journal of Biomechanics 100, 159–167. Chao, E.Y., Opgrande, J.D., Axmear, F.E., 1976. Three-dimensional force analysis of finger joints in selected isometric hand functions. Journal of Biomechanics 9, 387–396. Chao, E.Y., An, K.N., Cooney, W.P., Linscheid, R.L., 1989. Biomechanics of the Hand. World Scientific, Singapore. Cholewicki, J., McGill, S.M., 1994. EMG assisted optimization: a hybrid approach for estimating muscle forces in an indeterminate biomechanical model. Journal of Biomechanics 27, 1287–1289. Close, J.R., Kidd, C., 1969. The functions of the muscles of the thumb, the index, and long finger. The Journal of Bone and Joint Surgery 51, 1601–1620. Dennerlein, J.T., Diao, E., Mote, C.D., Rempel, D.M., 1998. Tensions of the flexor digitorum superficialis are higher than a current model predicts. Journal of Biomechanics 31, 295–301. Eyler, D.L., Markee, J.E., 1954. The anatomy and function of the intrinsic musculature of the fingers. Journal of Bone and Joint Surgery 36, 1–18. Fowler, N.K., Nicol, A.C., 2000. Interphalengeal joint and tendon forces: normal model and biomechanical consequences of surgical reconstruction. Journal of Biomechanics 33, 1055–1062. Gabl, M., Reinhart, C., Lutz, M., Bodner, G., Angermann, P., Pechlaner, S., 2000. The use of a graft from the second extensor compartment to reconstruct the A2 flexor pulley in the long finger. Journal of Hand Surgery—British Volume 25, 98–101. Gagnon, D., Lariviere, C., Loisek, P., 2001. Comparative ability of EMG, optimization, and hybrid modelling approaches to predict

ARTICLE IN PRESS 2856

L. Vigouroux et al. / Journal of Biomechanics 40 (2007) 2846–2856

trunk muscle forces and lumbar spine loading during dynamic sagittal plane lifting. Clinical Biomechanics 16, 359–372. Garcia-Elias, M., An, K.N., Berglund, L.J., Linshield, R.L., Cooney, W.P., Chao, E.Y., 1991. Extensor mechanism of the finger. I. A quantitative geometric study. Hand Surgery 16, 1130–1136. Harding, D.C., Brandt, K.D., Hillberry, B.M., 1993. Finger joint force minimization in pianists using optimisation techniques. Journal of Biomechanics 26, 1403–1412. Herzog, W., Leonard, T., 1991. Validation of optimization models that estimate the forces exerted by synergistic muscles. Journal of Biomechanics 24, 31–39. Hoy, M.G., Zajac, F.E., Gordon, M.E., 1990. A musculoskeletal model of the human lower extremity: the effect of muscle tendon and moment arm on the moment-angle relationship of musculotendon actuators at the hip knee and ankle. Journal of Biomechanics 23, 157–169. Hume, E.L., Hutchinson, D.T., Jaeger, S.A., Hunter, J.M., 1991. Biomechanics of pulley reconstruction. Journal of Hand Surgery— American Volume 16, 722–730. Jinha, A., Ait-Haddou, R., Herzog, W., 2006. Predictions of cocontraction depend critically on degrees of freedom in the musculoskeletal model. Journal of Biomechanics 39, 1145–1152. Karev, A., Stahl, S., Taran, A., 1987. The mechanical efficiency of the pulley system in normal digits compared with a reconstructed system using he belt loop technique. Journal of Hand Surgery— American Volume 12, 596–601. Ketchum, L.D., Thompson, D.E., Pocock, G., Wallingford, D., 1978. A clinical study of the forces generated by the intrinsic muscles of the index finger and the extrinsic flexor and extensor muscles of the hand. Journal of Hand Surgery 6, 571–578. Kursa, K., Diao, E., Lattanza, L., Rempel, D., 2006. In vivo forces generated by finger flexor muscles do not depend on the rate of fingertip loading during an isometric task. Journal of Biomechanics 38, 2288–2293. Li, Z.M., Zatsiorsky, V.M., Latash, M.L., 2000. Contribution of the extrinsic and intrinsic hand muscles to the moment in finger joints. Clinical Biomechanics 15, 203–211. Li, Z.M., Zatsiorsky, V.M., Latash, M.L., 2001. The effect of finger extensor mechanism on the flexor force during isometric tasks. Journal of Biomechanics 34, 1097–1102. Lister, G., 1985. Indications and techniques for the repair of the finger flexor tendon sheath. Hand Clinics, 85–95. Long, C., Brown, M.E., 1964. Electromyographic kinesiology of the hand. Muscles moving the long finger. Journal of bone and joint surgery 46, 1683–1706. Long, C., Conrad, P.W., Hall, E.A., Furler, S.L., 1970. Intrinsicextrinsic muscle control of the hand in power grip and precision handling. Journal of Bone and Joint Surgery 52, 853–867.

Maier, M.A., Hepp-Reymond, M.C., 1995. EMG activation patterns during force production in precision grip. I. Contribution of 15 finger muscle to isometric force. Experimental Brain Research 103, 108–122. Minami, A., An, K.N., Cooney, W.P., Linsheid, R.L., Chao, E.Y., 1985. Ligament stability of the MCP joint: a biomechanical study. Journal of Biomechanics 29, 255–260. Mommersteeg, T.J.A., Blankevoort, L., Huiskes, R., Kooloos, J.G.M., Kauer, J.M.G., 1996. Characterization of the mechanical behaviour of human knee ligaments: a numerical-experimental approach. Journal of Biomechanics 29, 151–160. Moutet, F., 2003. Flexor tendon pulley system: anatomy, pathology, treatment. Chirurgie de la Main 22, 1–12. Raikova, R.T., Prilutsky, B.I., 2001. Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses. Journal of Biomechanics 34, 1243–1255. Reilly, K.T., Schieber, M.H., 2003. Incomplete subdivision of the human multitendoned finger muscle flexor digitorum profundus: an electromyographic study. Journal of Neurophysiologie 90, 2560– 2570. Roloff, I., Scho¨ffl, V.R., Vigouroux, L., Quaine, F., 2006. Biomechanical model for the determination of the forces acting on the pulley system. Journal of Biomechanics 39, 915–923. Sancho-Bru, J.L., Perez-Gonzalez, A., Vergara-Monedero, M., Giurintan, D.J., 2001. A 3-D dynamic model of human finger for studying free movements. Journal of Biomechanics 34, 1491–1500. Sancho-Bru, J.L., Perez-Gonzalez, A., Vergara, M., Giurintan, D.J., 2003. A 3D biomechanical model of the hand for power grip. Journal of Biomechanical Engineering 125, 78–83. Schweizer, A., 2001. Biomechanical properties of the crimp grip position in rock climbers. Journal of Biomechanics 34, 217–223. Schweizer, A., Franck, O., Ochsner, P.E., Jacob, H.A.C., 2003. Friction between human finger flexor tendons and pulleys at high loads. Journal of Biomechanics 36, 63–71. Valero-Cuevas, F.J., Zajac, F.E., Burgar, C.G., 1998. Large indexfingertip forces are produced by subject-independent patterns of muscle excitation. Journal of Biomechanics 31, 693–703. Weightman, B., Amis, A.A., 1982. Finger joint force predictions related to design of joint replacements. Journal of Biomedical Engineering 4, 197–205. Widstrom, C.J., Doyle, J.R., Johnson, G., Manske, P.R., McGee, R., 1989. A mechanical study of six digital pulley reconstruction techniques: Part II. Strength of individual reconstructions. Journal of Hand Surgery—American Volume 14, 826–829. Zajac, F.E., 1989. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering 17, 359–411.