The Effects of Gender, Level of Co-Contraction, and Initial Angle

on Elbow Extensor Muscle Stiffness and Damping Under a Step Increase

in Elbow Flexion Moment

YUNJU LEE1 and JAMES A. ASHTON-MILLER

1,2,3

1Biomechanics Research Laboratory, Department of Mechanical Engineering, University of Michigan, 3212 G. G. Brown, 2350Hayward St., Ann Arbor, MI 48109-2125, USA; 2Department of Biomedical Engineering, University of Michigan, Ann Arbor,MI 48109-2125, USA; and 3Bone and Joint Injury Prevention and Rehabilitation Center, University of Michigan, Ann Arbor,

MI 48106, USA

(Received 8 November 2010; accepted 31 March 2011; published online 12 April 2011)

Associate Editor Catherine Disselhorst-Klug oversaw the review of this article.

Abstract—Flexion buckling of an arm under the largeground reaction loads associated with arresting a fall to theground increases the risk for head and thorax injuries. Yet,the factors that determine the arm buckling load remainpoorly understood. We tested the hypothesis in 18 healthyyoung adults that neither gender, triceps co-contraction level(i.e., 25, 50, or 75% MVC) nor elbow angle would affect therotational stiffness and damping resistance to step changes inelbow flexion loading. Data on the step response weregathered using optoelectronic markers (150 Hz) and myo-electric activity measurements (2 kHz), and an inversedynamics analysis was used to estimate elbow extensorstiffness and damping coefficients. A repeated-measuresanalysis of variance showed that gender (p = 0.032), elbowflexion angle and co-contraction level (both p< 0.001)affected stiffness, but only the latter affected the dampingcoefficient (p = 0.035). At 25� of initial elbow flexion angleand maximum co-contraction, female stiffness and dampingcoefficients were 18 and 30% less, respectively, than malevalues after normalization by body height and weight. Weconclude that the maximum extensor rotational stiffness anddamping at the elbow is lower in women than in men of thesame body size, and varies with triceps co-contraction leveland initial elbow angle.

Keywords—Elbow, Buckling, Fall, Stiffness, Gender,

Co-contraction.

INTRODUCTION

Falls are a leading cause of injury in the popula-tion.4 One or both upper extremities is often used to

protect the head and thorax in a fall. However, theloads imposed on the upper extremities can be sub-stantial, with the impulsive end-load at each wristreaching one body weight (1*BW) or more in a fall tothe ground.6,23,26 If the upper extremity were toflexion buckle (‘‘give way’’) at the elbow under suchloading then there is an increased risk of the headstriking the ground. Indeed, the elderly are particu-larly prone to fall-related head16,18 and cervical spineinjuries.17 A current knowledge gap includes the fac-tors that determine the threshold load required toflexion buckle the elbow of an end-loaded humanarm.

Direct measurements of the magnitude of the end-load required to initiate arm flexion buckling arecontraindicated because of the risk for stretch-relatedinjury of the elbow extensor muscles, their tendons,and/or their entheses. However, the risk for stretch-related injury of active striated muscle is known toincrease with the product of tensile force and elonga-tion strain in striated muscle.3 Therefore, an indirectapproach to estimating the threshold for flexionbuckling seems warranted. A logical first step, the goalof this article, is to measure the elastic and viscousresistance of the actively contracting elbow extensormuscles to small sudden stretches.

From first principles the flexion buckling load of theend-loaded arm will depend on the rotational elasticand damping resistance of the elbow extensor musclesto forced flexion, the initial elbow angle and initial armextensor co-contraction level,6 their moment armabout the elbow, the segmental lengths and inertiasof the forearm and upper arm, and the magnitude ofthe elbow flexion moment caused by the direction of

Address correspondence to Yunju Lee, Biomechanics Research

Laboratory, Department of Mechanical Engineering, University of

Michigan, 3212 G. G. Brown, 2350 Hayward St., Ann Arbor,

MI 48109-2125, USA. Electronic mail: yunjulee@umich.edu

Annals of Biomedical Engineering, Vol. 39, No. 10, October 2011 (� 2011) pp. 2542–2549

DOI: 10.1007/s10439-011-0308-3

0090-6964/11/1000-2542/0 � 2011 Biomedical Engineering Society

2542

the end-load. The voluntary ‘‘co-contraction’’ of themuscles acting about a joint is associated with anincrease in muscle recruitment of both agonist andantagonist muscle.19 Such co-contraction is known toincrease rotational stiffness at the elbow andknee.15,21,28 For various initial elbow flexion anglesand degrees of elbow extensor muscle co-contraction,one can apply step elbow flexion moments to measurethe kinematic response in elbow flexion. A planar,lumped parameter, model can then be used to estimatethe rotational stiffness and damping resistance of theelbow extensor muscles to resist step elbow flexion, andshow how these depend on muscle co-contraction leveland initial elbow angle.

It is known that there is a significant gender differ-ence in arm extensor strength in healthy adults.5,25

Females have a smaller arm muscle mass than males.12

Therefore, one can hypothesize that the maximalelastic and viscous muscular resistance to forced elbowflexion should also be less in the female, since theresistance to stretch of a muscle depends on the num-ber of cross-bridges in the strongly bound state: at thesame contraction intensity, smaller diameter musclesshould have fewer strongly bound cross-bridges thanlarger muscles with the same architecture. For bothgenders, the non-dominant arm is the most likelyto buckle because its elbow extensor strength (and

stiffness) is typically at least 5% less than the dominantarm.1

The goal of this article, therefore, was to test thethree hypotheses that neither gender, level of tricepsco-contraction nor initial elbow angle affect the rota-tional stiffness or damping coefficients of the extensormuscles acting about the non-dominant elbow inhealthy young adults.

METHODS

Nine healthy young males of mean (SD) age of 25.1(4.4) years and nine healthy young females of 20.3 (2.4)years gave written informed consent to participate inthe study, which was approved by the institutionalreview board. Mean height and mass for the maleswere 1.75 (0.074) m and 76.2 (17.3) kg, respectively,and for the females were 1.61 (0.068) m and 57.3 (8.35)kg, respectively. Subjects were screened by telephoneto exclude any chronic illnesses or upper extremityfractures or sprains within the previous year.

The subject was seated with the left upper armsupported by a pad and with the elbow at either 10�or 25� flexion in the horizontal plane (where 0� isfull elbow extension) (Fig. 1). The horizontal planewas used to obviate gravitational effects on the

FIGURE 1. Experimental setup showing a subject maintaining 10� elbow flexion while resisting the baseline elbow flexionmoment with a specified co-contraction of their elbow muscles using visual biofeedback of their triceps EMG. In the next instantthe weight, W, will be dropped suddenly using the trigger force, T, so that it lands on the weight pan, P, to apply a step elbowflexion moment via the wrist force, Fwrist, applied through load cell, L.

Elbow Extensor Muscle Properties During a Step Change in Flexion Moment 2543

measurements. A strain-gaged load cell (1779 Ncapacity) was attached to the wrist via a wrist cuff andthen connected via aircraft cable to a weight panweighing 1.4 kg. A solenoid-actuated crossbow releasemechanism was used to release a cable to drop a weightof 5.2 kg onto the weight pan in order to cause the stepelbow flexion moment via the wrist cuff.

Bipolar surface electromyographic electrodes,spaced 2 cm apart, were applied to the short head ofthe biceps brachii and the lateral and long heads of thetriceps brachii. The kinematic response of the forearmwas measured at 150 Hz using marker triads and anOptotrak 3020 (Northern Digital, Inc. Waterloo,Canada) optoelectronic camera system. The impactforce was measured by the load cell at 2 kHz. Thekinematic and force data were digitally low-passfiltered (MATLAB 2007a, The MathWorks) with aButterworth filter and cutoff frequencies of 10 and8 Hz, respectively. Integrated surface electromyogra-phy (EMG) data were collected at 2 kHz using anamplifier system (Myosystem 2000, Noraxon Inc.,Scottsdale, AZ, USA).

In order to find the maximum possible tricepsmuscle root-mean-square (RMS) EMG activity fornormalization purposes, subjects performed three dif-ferent tests with the elbow at 25� flexion. In the firsttest, subjects stood with their back to a wall and slowlyexerted maximum bilateral arm protraction strengthby pushing forward bimanually against a horizontal,2.5 cm diameter, metal bar with hands at shoulderwidth and height; a fixed length of aircraft cableattached each end of the bar to the wall via frictionlesspulleys and a 1799 N load cell. Maximum protractionstrength was recorded. In the second test, the subjectsexerted unilateral maximum protraction strengthagainst resistance provided by an examiner. In thethird test, the subject sat (Fig. 1) and maximallyco-contracted their arm and upper body muscles. Eachsubject performed three 5 s trials separated by 2 minrest intervals. Subsequent EMG data were normalizedby the maximum RMS EMG value found in any ofthese tests.

To determine elbow extensor muscle rotationalstiffness and damping parameters, each subject wasseated with the left upper arm supported and strappedto a special table to prevent it from moving (Fig. 1).The forearm was free to move in the horizontal(gravity-free) plane. A load cell strapped to the sub-ject’s wrist was connected via 3.2-mm diameter aircraftcable and frictionless pulleys to a 1.4 kg weight pan.The subject viewed RMS EMG biofeedback from thelateral triceps brachii and was instructed to keep his/her muscle activation at a specified level prior to andthroughout the entire impact response trial. Test

instructions were ‘‘not to intervene’’ when the arm wasperturbed so the stiffness and damping associated withthe triceps pre-contraction could be measured. Once(s)he had achieved the specified EMG level, a weight of5.2 kg was released after a random delay to fall ontothe weight pan, thereby causing a step increase inelbow flexion angle. Practice trials were performed tofamiliarize the subjects. Then, four trials each wereperformed in each of six conditions with the orderof presentation randomized: at 25, 50, and 75% MVCwith the subject’s initial elbow flexion angle at 10�(where 0� is full extension), and at 25, 50 and75% MVC with the subject’s initial elbow flexionangle at 25�. Extra trials were sometimes indicatedif the required EMG levels were not met satisfactorilyor if there was a technical problem with the dataacquisition.

DATA ANALYSES

A second-order, planar, rotational spring-dampermodel was used to approximate the dynamic propertiesof the elbow joint: T ¼ I€hþ B _hþ Kh; where T is theapplied flexion torque, h is the angular displacement ofthe elbow joint, _h is the angular velocity of the elbowjoint, €h is the angular acceleration of the elbow joint,I is the calculated moment of inertia of the limb(forearm + hand), B is the damping coefficient, and Kis the stiffness coefficient. The moment of inertia wascalculated by measuring the length of the limb andknowing the location of the center of mass of hand andforearm link.5

A deterministic global optimization algorithm(‘‘gclSolve.m’’ in MatlabTM) was used to determine Kand B using the experimental applied flexion moment(torque), the limb inertia, joint angle, angular velocity,and angular acceleration. This was done by minimizingthe square of the paired differences between corre-sponding points on the measured and calculated elbowtorque–angle curves (see Fig. 2). The values of K and Bwere normalized by subject body weight times heightto reduce the effect of body size as a confounder ininter-subject comparisons and make the data moretransferrable to other subjects.

Descriptive statistics were calculated for K and B.A repeated-measures analysis of variance was usedto test for effects of gender, three different muscleco-contraction levels, and two different initial elbowjoint angles on K and B using SAS 9.1 software.A p value of <0.05 was considered statistically sig-nificant for the three main effects (primary hypothe-ses). A Bonferoni correction was used for secondaryhypothesis testing (interactions).

Y. LEE AND J. A. ASHTON-MILLER2544

RESULTS

Sample elbow flexion moment–angle relationshipsfor a single step elbow response trial in a male and afemale subject, and the corresponding model-predictedresponse, are shown in Fig. 2. The hysteresis is evi-dence of the damping behavior of the elbow extensormusculature. Table 1 shows the mean normalizedvalues of elbow stiffness and damping found duringeach of the six testing conditions (three muscleco-contraction levels and two different initial elbowangles) for each gender. Increasing the initial flexionangle tends to increase stiffness by 15–48%, but not thedamping coefficient, in both male and female subjects.The males mostly had higher stiffness and dampingvalues than the females.

The repeated-measures ANOVA (Table 2) led us toreject all three hypotheses: gender significantly affectednormalized elbow stiffness; stiffness increased signifi-cantly with the muscle co-contraction level and withthe elbow angle. Damping behavior was not signifi-cantly altered by gender or elbow angle, but wasaltered by co-contraction level.

Sample moment–angle relationships show largedifferences at three different triceps co-contractionEMG levels (Fig. 3). The means of normalized stiff-ness of each condition were 0.791 Nm/rad/kg/m for71–90%MVC, 0.534 Nm/rad/kg/m for 51–70%MVC,and 0.267 Nm/rad/kg/m for 31–50% MVC. Themeans of normalized damping are 0.020, 0.011, and0.009 Nms/rad/kg/m, respectively. The stiffness anddamping coefficient values increased with the higherEMG co-contraction levels.

Women reached between 72 and 100% of malestiffness values and 42–76% of male damping values(see Fig. 4 showing mean (SD) absolute values ofstiffness and damping values). At the middle (51–70%MVC) co-contraction EMG level, men had 1.8–2.5times higher absolute values of stiffness and 3.4 timeshigher absolute values of damping. Minimum andmaximum values of non-normalized elbow stiffnesswere 25.8 and 191.7 Nm/rad in males, and 10.3 and106.5 Nm/rad in females, respectively; the corre-sponding values for damping coefficients were 0.47 and11.21 Nms/rad in males, and 0.38 and 3.33 Nms/rad infemales, respectively.

FIGURE 2. Sample measured (broken line) and fitted (solid line) elbow flexion moment vs. elbow flexion displacement relation-ships from one male (left panel, subject BCAB) and one female (right panel, subject BGAA). In this and the following figure datawere taken starting from an initial angle of 25� elbow flexion with triceps muscle co-contracted between 51 and 70%. Modelparameters are also given.

TABLE 1. Means (SD) normalized elbow rotational stiffness and damping coefficients by gender and levelof triceps co-contraction.

Normalized

co-contraction

EMG level

Elbow

angle (�)

Normalized stiffness (Nm/rad/kg/m) Normalized damping (Nms/rad/kg/m)

Males Females Males Females

Mean (SD) Mean (SD) Mean (SD) Mean (SD)

31–50% MVC 10 0.370 (0.160) 0.268 (0.122) 0.019 (0.016) 0.012 (0.005)

51–70% MVC 10 0.419 (0.166) 0.435 (0.218) 0.026 (0.018) 0.013 (0.005)

71–90% MVC 10 0.596 (0.219) 0.459 (0.292) 0.022 (0.015) 0.017 (0.005)

31–50% MVC 25 0.357 (0.100) 0.427 (0.192) 0.017 (0.013) 0.007 (0.004)

51–70% MVC 25 0.622 (0.177) 0.520 (0.189) 0.018 (0.015) 0.012 (0.004)

71–90% MVC 25 0.688 (0.208) 0.564 (0.274) 0.023 (0.018) 0.016 (0.006)

Elbow Extensor Muscle Properties During a Step Change in Flexion Moment 2545

The pattern of least squares means estimates(Fig. 5) and the significant gender by triceps co-contraction (p = 0.014), and gender by initial elbow an-gle (p = 0.016) interactions (Table 2) suggest that stiff-ness was more affected by co-contraction level in malesand by initial elbow angle in females. Gender differenceswere significant, especially at the highest (71–90%MVC)co-contraction level and in the most extended (10�)posture. However, no differences were found in dampingcoefficients between males and females.

In the six males and five females for whom strengthdata were available, the correlations between bilat-eral arm protraction strength and unilateral meanstiffness, K, and damping, B, values at the highestco-contraction condition (71–90% MVC) did notreach significance (Fig. 6). While, a trend toward agender difference in stiffness is observed (Fig. 6, left),none is evident for damping (Fig. 6, right).

DISCUSSION

This study provides the first experimental evidencethat the pre-activated elbow extensor musculature ofmales exhibits greater elastic and viscous resistance tostretch than females under a standardized step elbowflexion loading. This was true both in terms of absolutevalues as well as after normalization by body size(body weight times stature). This gender difference isconsistent with the functional result of 12% less elbowdeflection in males when they manually arrest anoncoming ballistic pendulum at chest level.9 Thesegender differences in upper extremity responses areconsistent with similar differences in the resistance ofthe active musculature of the lower extremities tostretch,14 even in size-matched young men andwomen.28

In the present study, women exhibited 72–100% ofmale stiffness values and 42–76% of male dampingvalues. These gender differences are consistent with thegender differences found in the literature for otherjoints. For example, the absolute active rotational kneestiffness in women has been found to be 56–73% ofthat in men, and female damping values ranged from36 to 63% of male damping values.14 If the elbowextensor muscles, the triceps brachii, which are ago-nists during elbow extension, are assumed to be pre-activated at the same volitional level, a reasonableexplanation for the gender difference found in thepresent study is the greater arm muscle mass (seeIntroduction) and elbow extensor strength of males.7

The present findings in active muscle extend those ofLin et al.22 who studied the stretch behavior of passivehuman elbow muscle; however, the gender differencein normalized elbow muscle stiffness or damping inpassive muscles did not achieve significance.

The present absolute values of elbow stiffness anddamping are slightly higher than published valuesmeasured under a variety of testing conditions(Table 3) in upper extremities. This trend may reflectthe higher muscle activation levels used in the presentstudy. For example, it is the elbow stiffness values of10.3 Nm/rad for the female subjects and 25.8 Nm/radfor the male subjects, measured at the lowest ‘‘Nor-malized Co-contraction EMG Level’’ (Table 1), thatcorrespond with published stiffness values. Our resultsalso corroborate the published values that wereobtained under ‘‘comfortable’’ maximal co-contractionconditions.24 On the other hand, our damping valueswere systematically larger than those reported byPopescu et al.24 particularly for fully activated malemuscle (Table 3). This may again reflect differences inthe levels of triceps muscle activation during the test-ing. Older women are less likely to involve their armsin arresting a fall, or they fail to appropriately use their

TABLE 2. ANOVA tables for the main effect and interactionfor normalized elbow stiffness and damping coefficients.

Stiffness Damping

F p F p

Main effect

Gender 5.58 0.032* 2.66 0.124

Co-contraction 26.44 <0.001* 8.28 0.004*

Elbow angle 30.56 <0.001* 4.22 0.058

Factor interaction

Gender 9 co-contraction 5.76 0.014* 0.2 0.819

Gender 9 elbow angle 7.32 0.016* 1.18 0.294

Co-contraction 9 elbow angle 1.64 0.227 4.22 0.035*

Gender 9 co-contraction 9

elbow angle

1.3 0.301 0.83 0.454

* p < 0.05.

FIGURE 3. Sample plots showing the effect of three differentlevels of triceps muscle co-contraction on the applied flexionmoment vs. elbow angular displacement starting from an initialangle of 10� flexion. The trials are from male subject BCAI.

Y. LEE AND J. A. ASHTON-MILLER2546

arm to arrest the fall: both these behaviors carry ahigher risk for head impact than males.27 It is possiblethat with their age-related loss in strength, which theythemselves instinctively may be aware of, older womenfear flexion buckling of the elbow and thus are unableto avoid injury. They are caught on the horns of adilemma. If they choose to avoid flexion buckling bylanding with a straight elbow joint then they risk aColles fracture of the wrist; but if they permit flexionbuckling of their elbow then they risk head or cervical

spine injury.8 The present results show that this latterscenario is a reasonable fear. The lower maximal elbowextensor stiffness in women would lead one to predict asmaller capacity to prevent elbow flexion bucklingunder fall-related impact scenarios than in males ofsimilar body size. This underlines the importance ofmaintaining elbow extensor strength with age. This isespecially salient for those with obesity becausethe extra weight reduces the arm extensor strength-to-body weight ratio.

FIGURE 4. Mean absolute values of elbow rotational stiffness (top panels: a, b) and damping coefficients (bottom panels: c, d) atan initial angle of 10� (left panels: a, c) and 25� (right panels: b, d) as a function of triceps co-contraction level. The bars denote onestandard deviation.

FIGURE 5. Least squares means estimate for normalized stiffness suggesting gender/triceps muscle co-contraction interactioneffect (left panel) and gender/elbow angle interaction effect (right panel).

Elbow Extensor Muscle Properties During a Step Change in Flexion Moment 2547

This study has several limitations. One limitation ofthe study design is the relatively modest sample sizewhich limited statistical power to <80% for the effectof gender on the damping coefficient (Table 2). Asecond limitation is that the study of gender differenceswould have been stronger had we recruited men andwomen of similar size (body height and weight).28

Therefore, to counter bias due to the larger size of themales and their upper extremities (see Introduction),we only tested the three hypotheses using data thatwere normalized by body size. A third limitation is thatthe flexion moment due to the ~51 N step force wasless than that would be induced by the 745–880 N end-load known to act on the hand/wrist during a naturalfall arrest.6 On the other hand, it was of a similar orderof magnitude to that induced during a ‘‘stiff arm’’ fallarrest strategy,6,7 given that the elbow deflection wassimilar in both cases. This helps validate the presentexperimental design as being promising for testingmiddle-aged or even older adult elbow elastic andviscous properties.

A fourth limitation is the relatively weak correlationfound between bilateral maximum arm protractionstrength and maximum unilateral values of elbowextensor stiffness and damping (Fig. 6). Blanpied andSmidt2 found fairly strong linear correlations betweenankle plantar flexion strength, stiffness, and damping.One reason for our weak correlations could be the

method for testing arm extensor strength: this relied onsubjects having to stabilize their shoulder and wristmuscles in order to exert a maximum arm protractioneffort. It is possible that the requirement for the subjectto exert significant contractions of their shoulderadductor and flexor muscles, as well as their wristflexor and hand power grip muscles, caused variabilitythat weakened the correlations. In retrospect, lessscatter might have been obtained had subjects exerteda unilateral single joint test of elbow extensor strength,rather than a bilateral multi-joint test of arm protrac-tion strength. It is also possible that better correlationsmight have been found had we recruited only athletesbecause of their better body awareness, motor control,and coordination abilities.

A fifth limitation was the use of just two differentinitial angles of elbow (10� and 25�) when a largerrange of elbow initial angles has been observed inforward fall arrests.6 Future studies might explore theeffect of greater initial flexion angles to place the tri-ceps muscle at longer fiber lengths. This would be ex-pected to reduce the resistance found when the muscleis stretched beyond its short range stretch.10 However,one ethical concern is that larger stretches at highercontraction forces also increase the risk of injury,3 solarge stretches are contraindicated. While the subjectonly monitored triceps activity, and triceps stiffnesscan theoretically only affect the rising (elbow flexion)

FIGURE 6. Scattergrams showing the correlation between bilateral arm protraction strength and unilateral mean stiffness (left)and damping (right) parameter values.

TABLE 3. Ranges of non-normalized elbow stiffness and damping coefficients found in the literature.

Stiffness (Nm/rad) Damping (Nms/rad) Movement condition Muscle condition Literature

10.3–191.7 0.38–11.2 Voluntary motion Active Current study

17–55 0.5–1.8 0.5 and 1 Hz voluntary motion Active Xu and Hollerbach29

26.8–46.8 – Reaching movement Active Flash11

5–21 – Ballistic, voluntary motion Active Gomi and Kawato13

5–200 0.2–2.6 Voluntary extension motion Active Popescu et al.22

42.9–168.8 3.92–9.09 Time-varying motion

(catching a ball)

Active Lacquaniti et al.18

2.26–2.62 0.53–0.73 Pendulum test Passive Lin et al.20

Y. LEE AND J. A. ASHTON-MILLER2548

phase of the response in Figs. 2 and 3, it is possiblethat the magnitude of biceps contraction might haveaffected the elbow stiffness on the descending (elbowextension) limb of that curve. However, there was nosignificant difference in the overall results whether oneanalyzed the ascending limb alone, or combined theascending and descending limbs together. Hence, itappears as if the triceps muscle activation and itsmechanical properties dominated the measured elbowdynamic response. Finally, joint stiffness can vary withtime during a step response,20 so it might be worthinvestigating whether time-varying stiffness and/ordamping constants would have given a better fit to thedata than our assumption of constant stiffness anddamping parameters.

ACKNOWLEDGMENTS

Support of PHS grant P30 AG 024824 is gratefullyacknowledged.

REFERENCES

1Askew, L. J., K. N. An, B. F. Morrey, and E. Y. S. Chao.Isometric elbow strength in normal individuals. Clin.Orthop. Relat. Res. 222:261–266, 1987.2Blanpied, P., and G. L. Smidt. The difference in stiffness ofthe active plantar flexors between young and elderlyhuman females. J. Gerontol. A Biol. 48:M58–M63, 1993.3Brooks, S. V., E. Zerba, and J. A. F. Faulkner. Injury tomuscle fibres after single stretches of passive and maxi-mally stimulated muscles in mice. J. Physiol. 488:459–469,1995.4CDC. CDC Injury Research Agenda 2009–2018. http://www.cdc.gov/injury/ResearchAgenda/CDC_Injury_Research_Agenda-a.pdf, p 12, 2009.5Chaffin, D. B., G. B. J. Andersson, and B. J. Martin.Occupational Biomechanics. New York, NY: John Wiley& Sons, 2006.6DeGoede, K. M., and J. A. Ashton-Miller. Fall arreststrategy affects peak hand impact force in a forward fall.J. Biomech. 35:843–848, 2002.7DeGoede, K. M., and J. A. Ashton-Miller. Biomechanicalsimulations of forward fall arrests: effects of upperextremity arrest strategy, gender and aging-related declinesin muscle strength. J. Biomech. 36:413–420, 2002.8DeGoede, K. M., J. A. Ashton-Miller, and A. B. Schultz.Fall-related upper body injuries in the older adult: a reviewof the biomechanical issues. J. Biomech. 36:1043–1053,2003.9DeGoede, K. M., J. A. Ashton-Miller, A. B. Schultz, andN. B. Alexander. Biomechanical factors affecting the peakhand reaction force during the bimanual arrest of a movingmass. J. Biomech. Eng. 124:107–112, 2002.

10Edman, K. A. P., G. Elzinga, and M. I. M. Noble.Enhancement of mechanical performance by stretch duringtetanic contractions of vertebrate skeletal muscle fibres.J. Physiol. 281:139–155, 1978.

11Flash, T. The control of hand equilibrium trajectory inmulti-joint arm movements. Biol. Cybern. 57:257–274,1987.

12Gallagher, D., M. Visser, R. E. De Meersman, D.Sepulveda, R. N. Baumgartner, R. N. Pierson, T. Harris,and S. B. Heymsfield. Appendicular skeletal muscle mass:effects of age, gender, and ethnicity. J. Appl. Physiol.83:229–239, 1997.

13Gomi, H., and M. Kawato. Equilibrium-point controlhypothesis examined by measured arm stiffness duringmultijoint movement. Science 272:117–120, 1996.

14Granata, K. P., D. A. Padua, and S. E. Wilson. Genderdifferences in active musculoskeletal stiffness. Part I.Quantification in controlled measurements of knee jointdynamics. J. Electromyogr. Kinesol. 12:119–126, 2002.

15Granata, K. P., S. E. Wilson, A. K. Massimini, andR.Gabriel. Active stiffness of the ankle in response to inertialand elastic loads. J.Electromyogr.Kinesol. 14:599–609, 2004.

16Kannus, P., S. Niemi, J. Parkkari, M. Palvanen, and H.Sievanen. Alarming rise in fall-induced severe head injuriesamong elderly people. Injury 38:81–83, 2007.

17Kannus, P., M. Palvanen, S. Niemi, and J. Parkkari.Alarming rise in the number and incidence of fall-inducedcervical spine injuries among older adults. J. Gerontol. ABiol. 62:180–183, 2007.

18Kannus, P., M. Palvanen, S. Niemi, J. Parkkari, A. Natri,I. Vuori, and M. Jarvinen. Increasing number and inci-dence of fall-induced severe head injuries in older adults.Am. J. Epidemiol. 149:143–150, 1999.

19Kearney, R. E., and I. W. Hunter. System identification ofhuman joint dynamics. Crit. Rev. Biomed. Eng. 18:55–87,1990.

20Lacquaniti, F., M. Carrozzo, and N. A. Borghese. Time-varying mechanical behavior of multijointed arm in man.J. Neurophysiol. 69:1443–1464, 1993.

21Lacquaniti, F., F. Licata, and J. F. Soechting. Themechanical behavior of the human forearm in response tothe transient perturbations. Biol. Cybern. 44:35–46, 1982.

22Lin, C. C. K., M. S. Ju, and H. W. Huang. Gender and ageeffects on elbow joint stiffness in healthy subjects. Arch.Phys. Med. Rehab. 86:82–85, 2005.

23Lo, J., G. N. McCabe, K. M. DeGoede, H. Okuizumi, andJ. A. Ashton-Miller. On reducing hand impact force inforward falls: results of a brief intervention in young males.Clin. Biomech. 18:730–736, 2003.

24Popescu, F., J. M. Hilder, and W. Z. Rymer. Elbowimpedance during goal-directed movements. Exp. BrainRes. 152:17–28, 2003.

25Stobbe, T. J. The Development of a Practical StrengthTesting Program for Industry. PhD Thesis, University ofMichigan, Ann Arbor, MI, 1982.

26Tan, J. S., J. J. Eng, S.N.Robinovitch, andB.Warnick.Wristimpact velocities are smaller in forward falls than back-ward falls from standing. J. Biomech. 39:1804–1811, 2006.

27Vellas, B. J., S. J. Wayne, P. J. Garry, and R. N. Baum-gartner. A two-year longitudinal study of falls in 482community-dwelling elderly adults. J. Gerontol. A Biol.53:M264–M274, 1998.

28Wojtys, E. M., L. J. Huston, J. S. Harold, J. P. Boylan,and J. A. Ashton-Miller. Gender differences in muscularprotection of the knee in torsion in size-matched athletes.J. Bone Joint Surg. Am. 85:782–789, 2003.

29Xu, Y., and J. M. Hollerbach. A robust ensemble datamethod for identification of human joint properties duringmovement. Biomed. Eng. 46:409–419, 1999.

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