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Journal of Strength and Conditioning Research Publish Ahead of PrintDOI: 10.1519/JSC.0000000000002330

Biomechanical Methods to Quantify Muscle Effort During Resistance Exercise

Loren Z.F. Chiu, PhD, CSCS

Neuromusculoskeletal Mechanics Research Program, Faculty of Physical Education and Recreation,

University of Alberta, Edmonton, AB, Canada

Address for Correspondence:

Loren Z.F. Chiu, PhD, CSCS

3-413 Van Vliet Complex

Faculty of Physical Education and Recreation

University of Alberta

Edmonton, AB Canada T6G 2H9

Phone: 780-248-1263

Fax: 780-248-1891

E-Mail: [email protected]

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Copyright ª 2017 National Strength and Conditioning Association

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ABSTRACT 1

Muscle hypertrophy and strength adaptations elicited by resistance training dependent on the 2

force exerted by active muscles. As an exercise may use many muscles, determining force for individual 3

muscles or muscle groupings is important to understand the relation between an exercise and these 4

adaptations. Muscle effort – the amount of force or a surrogate measure related to the amount of force 5

exerted during a task – can be quantified using biomechanical methods. The purpose of this review was 6

to summarize the biomechanical methods used to estimate muscle effort in movements, particularly 7

resistance training exercises. These approaches include: 1) inverse dynamics with rigid body models, 2) 8

forward dynamics and EMG-driven models, 3) normalized EMG, and 4) inverse dynamics with point 9

mass models. Rigid body models quantify muscle effort as net joint moments. Forward dynamics and 10

EMG-driven models estimate muscle force as well as determine the effect of a muscle’s action 11

throughout the body. Non-linear relations between EMG and muscle force, and normalization reference 12

action selection affect the usefulness of EMG as a measure of muscle effort. Point mass models include 13

kinetics calculated from barbell (or other implement) kinematics recorded using electromechanical 14

transducers or measured using force platforms. Point mass models only allow net force exerted on the 15

barbell or lifter-barbell system to be determined so they cannot be used to estimate muscle effort. Data 16

from studies employing rigid body models, normalized EMG, and musculoskeletal modelling should be 17

combined to develop hypotheses regarding muscle effort; these hypotheses should be verified by 18

training interventions. 19

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Keywords: motion analysis; force; hypertrophy; muscle strength 21

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Word Count: 6,418 23

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INTRODUCTION 25

Resistance exercise is used to improve physical fitness; investigations employing resistance 26

exercise have found increases in muscle size, strength, and endurance, as well as the ability to generate 27

muscle force rapidly (88, 89). Ultimately, these improvements in physical fitness are associated with 28

enhanced physical function in activities of daily living, occupation, recreation, and sport (7, 63, 92, 98, 29

103). Resistance exercise requires muscles to actively generate force; forces acting on a muscle can 30

stimulate physiological processes that elicit adaptations. These adaptations include increases in muscle 31

fiber size, and metabolic enzyme and neural substrate concentrations and activities (44, 88, 93), which 32

increase the ability of a muscle to generate force, as well as the ability to generate force repetitively or 33

for a sustained duration (14). Training adaptations may be dependent on resistance exercise intensity 34

(14, 44, 56). The term intensity as used for exercise is rarely defined and there is debate as to whether 35

intensity refers to a physical or psychological measure (94). In practice, resistance exercise intensity is 36

typically quantified as the load or amount of weight lifted (38). The load lifted can be expressed as a 37

percentage of the maximum amount of weight that can be lifted for one repetition (1 RM), which is the 38

relative intensity (38). 39

Muscles are required to exert force during resistance exercise. The amount of force required 40

from a muscle affects the number and type of motor units and muscle fibers activated (64, 96). As 41

muscle force is an important parameter determining the adaptations elicited, quantifying how much 42

force is required for an exercise is an important objective in resistance exercise research. The load lifted 43

is only one factor affecting the amount of force required from a muscle during an exercise. Other 44

factors include the orientation of bony segments in relation to resistance force vectors, the actions of 45

synergist and antagonist muscles during the exercise, and musculoskeletal geometry (11, 36, 54, 81). 46

Biomechanical methods are commonly used as they are capable of estimating muscle force or providing 47

surrogate measures of muscle force. Technologies for biomechanical analyses are increasingly 48

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accessible, in terms of availability, cost, and ease of use; however, correct use and data interpretation 49

still require understanding of the terms and modelling used. Consequently, there are numerous 50

investigations that have used biomechanical methods to estimate either the force exerted by a muscle 51

or parameters related to the force exerted. Incorrect beliefs may be developed from research if the 52

correct understanding of terms and limitations of these biomechanical methods are not understood. 53

The purpose of this review is to examine and discuss the utility of the biomechanical methods used to 54

investigate muscle effort during resistance exercise. This review will: 1) reflect on the confusing 55

terminology used relating to resistance exercise intensity, 2) propose terminology based on 56

biomechanical measures, and 3) discuss the major biomechanical methods used in resistance exercise 57

research so that strength and conditioning professionals can understand and apply this research. These 58

biomechanical methods include: 1) inverse dynamics with rigid body models, 2) forward dynamics and 59

EMG-driven models, 3) normalized electromyography (EMG), and 4) inverse dynamics with point mass 60

models. The information that these methods can provide is illustrated using barbell squats as an 61

example. 62

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TERMINOLOGY 64

While the amount of weight lifted – either absolute weight or percentage of 1 RM – is practical 65

to quantify resistance exercise intensity, this measure provides limited information regarding muscle 66

effort (82). For example, consider a single-joint exercise such as an arm curl, which employs the biceps 67

brachii, brachialis, and brachioradialis. If an 80% 1 RM load were used, it could be expected that each 68

muscle would exert 80% of its maximum force generating capacity. However, this expectation assumes 69

that the load sharing or relative contribution of each muscle is equal, which is not the case. These 70

muscles are activated in a hierarchical manner during an arm curl, where the brachialis is preferentially 71

activated at low resistance force (5). As resistance increases, biceps brachii and brachioradialis are 72

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additionally activated. Similar hierarchical activation of muscles has been found for tasks involving the 73

triceps brachii and anconeus, and quadriceps (97, 109). This supports a hypothesis that there is a force 74

threshold for synergistic muscles at joints, some muscles are maximally activated while others are sub-75

maximally activated, with individual muscle contribution to external force and movement production a 76

complex result of biomechanical and neuromuscular factors. 77

In multi-joint tasks, an external resistance moment of force acts at each joint; the external 78

moment at each joint may vary depending on range of motion and external load (12, 36, 59). Taking 79

into consideration potential hierarchical activation of muscles crossing the same joint and the variation 80

in external resistance moment across multiple joints, each muscle involved in a multi-joint exercise may 81

be required to exert force at different percentages of their maximum force generating ability (12). Thus, 82

in biomechanical studies investigating resistance exercise intensity, the muscles involved should be 83

identified and each muscles’ force quantified. Furthermore, the muscle force required depends on the 84

moment arms of the various muscles involved and the moment arm of the external resistance force (11, 85

34, 36, 82). These moment arms vary with segment and joint angles (76, 104), therefore, muscle force 86

should also be described throughout the exercise’s range of motion. 87

In principle, the most accurate method to quantify a muscle’s force is to measure it directly. 88

Force-sensing transducers, typically implanted during surgical procedures, have been used to directly 89

measure muscle force (37, 39, 46). Fiber optic cables have also been inserted into tendons to measure 90

the force exerted on the tendon by the muscle (35, 40). Both methods are invasive, limited to certain 91

muscles with distinct tendons, and are rarely used in humans. More commonly, indirect methods are 92

employed to estimate or provide surrogate estimates of muscle force. For the purposes of this review, 93

muscle effort is used to describe the force a muscle exerts during a task, or a surrogate estimate that is 94

mechanically (i.e. moment) or statistically (i.e. normalized EMG) related to muscle force. Each indirect 95

method has limitations and assumptions that affect their utility. For example, not all indirect methods 96

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provide the information required to determine all the muscles employed and the force in each of these 97

muscles. 98

99

RIGID BODY MODELS 100

Net Joint Moment 101

Perhaps the most common biomechanical measure of muscle force or effort in multi-joint tasks 102

is the net joint moment (NJM) (16, 36). NJM is calculated using rigid body modelling and inverse 103

dynamics. A typical investigation calculating NJMs will include two- or three-dimensional motion 104

analysis. Force platforms or other force transducers are commonly employed when substantial external 105

forces act on the body, however, are not always necessary (41). Motion analysis data are used to define 106

the body’s segments with the assumptions that segments are rigid bodies, rotating about a frictionless 107

fixed axis, with fixed mass center and moments of inertia. Forces, inertial parameters, and accelerations 108

are entered into equations based on Newton’s Second Law of Motion as shown in the two-dimensional 109

example in Figure 1. Three-dimensional versions of the equations of motion include additional terms. 110

Comparisons of net forces and moments calculated using these methods to measured external forces 111

are quite accurate (<5% error) (8, 25, 86). Briefly, reaction forces acting on the proximal and distal ends 112

of the segment will create a moment that has a tendency to rotate the rigid body. This moment is 113

considered the net external moment, which is countered by moments applied by muscles, ligaments, 114

and bony contact forces. The sum of these moments acting at a joint is the net internal moment or 115

NJM. It should be noted that the NJM and net external moments have equal magnitude but opposite 116

sense. For example, the net external moment at the knee joint, as depicted in Figure 1, has tendency to 117

rotate the leg segment clockwise, while the NJM has a tendency to rotate the leg segment counter-118

clockwise. In many circumstances for the human body, the net muscular moments are the primary 119

contributor to the NJM, therefore, the NJM can be interpreted as net muscular effort for muscle groups 120

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at the joint (87). It is also important for strength and conditioning professionals to remember that the 121

NJM is the resultant from forces of all agonist and antagonist muscles, ligaments, and joint forces; and 122

should not be interpreted as moment solely from a particular muscle group. 123

If a single muscle acts at a joint and this muscle’s moment arm is known, muscular moment can 124

be used to estimate muscle force. While the moment arm is typically not known, normative estimates 125

for moment arms of various muscles are available (76, 100, 104). However, multiple synergist muscles 126

may contribute to the NJM (11, 81, 83). For example, if there is a knee flexor NJM, the biceps femoris 127

long and short heads, semitendinosus, semimembranosus, and gastrocnemius may be involved. As each 128

of these muscles have different moment arms, the relative contribution of each muscle to the knee 129

flexor NJM needs to be known to calculate the force in each muscle (assuming the moment arms are 130

known). Moreover, it is possible that antagonistic muscles are co-contracting. In the case of a knee 131

flexor NJM, quadriceps co-contraction would generate a knee extensor moment. The muscles 132

contributing to the knee NJM can be described mathematically (equation 1), given the previously noted 133

limitations of interpreting a NJM exclusively due to muscle. 134

Equation 1: NJMKnee = MQuadriceps + MHamstrings + MBiceps Femoris Short Head + MGastrocnemius 135

Note that this equation has been simplified by grouping muscles together, even if muscles within a 136

group have different moment arms. If antagonist co-contraction is present, a knee flexor NJM would 137

underestimate the moment generated by the knee flexor muscles. Similarly, a knee extensor NJM 138

would underestimate the quadriceps moment if any knee flexor muscles are co-contracting. 139

Therefore, while the NJM can be used to estimate net muscle effort during single- and multi-140

joint resistance exercise, two limitations inherent to the NJM must be considered when interpreting this 141

parameter. First, the NJM does not provide information about muscular effort for individual muscles. 142

Consequently, assuming no co-contraction occurs, the NJM describes muscular effort for the agonist 143

muscle group acting at a joint. Second, if antagonist co-contraction is present, the NJM describes the 144

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minimum net muscular effort for the agonist muscle group. The actual muscular effort for the agonist 145

muscle group is higher when antagonist muscles co-contract (11, 81). 146

For this reason, NJM are rarely used to directly estimate muscle force, although they have been 147

used in special situations. Some biomechanical studies have captured biomechanical data during an 148

injury. For example, Zernicke et al. (108) recorded a patellar ligament rupture during weightlifting and 149

estimated the force using knee extensor NJM and estimated moment arm. These case studies provide 150

valuable ultimate tissue strength estimates from young or athletic individuals that supplements tissue 151

strength studies conducted on cadaver material, which are usually from elderly donors. 152

In summary, NJM indicates the agonist muscle group involved at a joint during a task and 153

estimates the grouping’s minimum net muscle effort. Additional data, such as EMG, are required to 154

determine if antagonist muscles are co-contracting, which would increase the agonist muscles’ effort. 155

Further, NJM is an absolute indicator of muscle effort and the maximum moment a muscle group can 156

generate will provide context to better interpret NJM. 157

158

Forward Dynamics and EMG-Driven Models 159

Anatomical data can be combined with measured kinematic and kinetic data using 160

musculoskeletal modelling to estimate forces acting on anatomical structures. The use of 161

musculoskeletal modelling in resistance exercise research is increasing, particularly as anatomical data 162

and models are being made available in the public domain (19, 20). Inverse and forward dynamics 163

approaches can be used for musculoskeletal modelling. Inverse dynamics modelling is an extension of 164

NJM analysis (20, 21), which uses assumptions to determine the muscle strategy employed during an 165

exercise (2, 80). A muscle strategy specifies the combination of muscles involved in the NJM (as an 166

example, see equation 1), which, if known allows the moment from each muscle to be estimated. 167

Muscle force can then be estimated by dividing each muscle’s moment by that muscle’s moment arm 168

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given some force sharing assumptions. Muscle electrical activity measured as normalized EMG may be 169

used as inputs to an inverse dynamics model that includes parameters describing mechanical force 170

rise/decay times, muscle force-length and force-velocity relations, and muscle and tendon architectural 171

properties (2, 81, 106). 172

Forward dynamics modelling combines muscle activation dynamics and musculoskeletal 173

geometry to compute muscle forces first, and secondly determine their influence on segment, joint, or 174

whole-body kinematics (27, 107). In addition to estimating muscle forces, this approach may be used to 175

determine a muscle’s role in performing a multi-joint task (45). From an anatomical perspective, muscle 176

actions are described based on the segments to which they attach or the joints they cross. However, 177

muscle actions also result in joint reaction forces that are transferred between segments which can: 1) 178

elicit paradoxical muscle actions and 2) affect motion elsewhere in the body. An example of paradoxical 179

muscle action is the gastrocnemius which is considered an ankle plantar flexor; through joint reaction 180

forces, gastrocnemius may cause ankle dorsiflexion during multi-joint tasks (22, 67). An example of a 181

muscle influencing motion elsewhere in the body is the soleus, which is the primary contributor to 182

accelerating the body upwards and forwards during walking and running, despite this muscle only 183

attaching to the leg and foot segments (49). 184

Estimating muscle forces using musculoskeletal modelling accomplishes the objectives of 185

identifying the muscles involved and quantifying each muscle’s force patterns given various 186

assumptions. However, the assumptions made in modelling procedures are important to consider when 187

interpreting these muscle forces. For muscle effort in resistance exercise, there are two important 188

considerations that may influence the accuracy of estimates. The first is the assumptions made to 189

determine muscle strategy and the second in the accuracy of the anatomical data employed in the 190

model. These assumptions will be introduced here, however, it is beyond the scope of this paper to 191

explore the validity of these assumptions in detail. 192

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Normalized EMG is often used to aid in determining muscle strategy (81). EMG is measured 193

during the tasks itself as well as during a reference task, typically a maximal voluntary isometric action. 194

Task EMG is expressed as a percentage of the EMG during the reference task. These data are used 195

under the premise that there is a positive linear relation between EMG and muscle force (this inaccurate 196

assumption is discussed further later). EMG data from multiple muscles are combined to estimate how 197

much each muscle contributes to the NJM, however, it is not usually possible to obtain EMG from all 198

muscles for these models. Most of these models are driven with the major agonist and antagonist 199

muscles that can be recorded with surface EMG. Another method to determine muscle strategy in 200

modelling is the use of optimization criteria. As show in equation 1, there are multiple combinations of 201

muscle moments that will add up to the NJM. An optimization criterion sets a defined objective, such as 202

minimizing energy expenditure or muscle stress (68, 80). A software program is tasked to find the 203

combination that meets this objective. Certain activities allow for specific optimization criteria to be 204

used. In vertical jumping studies, a model may be optimized to find the muscle strategy that allows the 205

greatest vertical jump height to be achieved (9, 10). 206

A relatively new method to determine muscle strategy is to rule out strategies where one or 207

more muscles require forces greater than their maximum strength. This approach has been employed in 208

gait studies, where it has been found that many strategies are possible as few muscles operate near 209

their maximum force capacity (89, 91). This is not surprising as, in healthy adults, gait is a low intensity 210

activity. The same premise was employed by Bryanton et al. (11) to study barbell squats. The major 211

muscles contributing to the hip extensor NJM during squats are the gluteus maximus and hamstrings. 212

As the hamstrings generate both hip extensor and knee flexor moments, the hamstrings are antagonists 213

to the quadriceps at the knee. Greater hamstrings contribution to the hip extensor NJM would result in 214

a larger knee flexor moment, requiring larger quadriceps moment. Different combinations of gluteus 215

maximus and hamstrings contributions to the hip extensor NJM were considered by examining their 216

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effect on the quadriceps moment. Bryanton et al. (11) found that the only hip extensor strategy where 217

quadriceps moment did not exceed quadriceps maximum strength was one were gluteus maximus was 218

near-maximally active and hamstrings were less active. These results were consistent with EMG studies 219

reporting low hamstring activation in weighted back squats, where biceps femoris and semitendinosus 220

EMG are approximately one half of that during leg curls and stiff-leg deadlifts (105). 221

Anatomical data used in musculoskeletal modelling studies may be from normative data sets or 222

directly measured in participants (3, 19). As it is economically costly and time-intensive to measure 223

anatomical information, most musculoskeletal modelling studies use normative data sets. The 224

anatomical information used in musculoskeletal modelling may include – depending on model 225

complexity – muscle moment arms, muscle attachment site coordinates, and muscle architectural 226

properties. These parameters are not constant; they vary depending on the orientation of body 227

segments. Accordingly, it is important to determine these parameters with segments oriented in 228

various positions (76, 104). This may be an issue for resistance exercise modelling, due to the large 229

range of motion that occurs for many segments (18). In contrast, range of motion is muscle smaller 230

during gait, which is the most commonly modelled task (89, 91). As an example, anatomical parameters 231

are available for the hip and knee up to 90⁰ of flexion (where 0⁰ is anatomical position for each joint) 232

(76, 104). Hip and knee flexion angles during squats are reported to exceed 100⁰ and 130⁰, respectively. 233

For accurate modelling, it will be necessary to obtain anatomical data throughout the range of motion in 234

which resistance exercise tasks are performed (101). 235

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Relative Muscular Effort 237

Both NJM and muscle force determined using musculoskeletal models provide absolute muscle 238

effort estimates. However, further information is required to interpret these estimates in regards to 239

potential strength training effects. Specifically, knowledge of the maximum muscular effort is required. 240

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For example, resistance exercise intensity is typically described as a percentage of 1 RM in practice. 241

Absolute muscle effort can be related to maximum muscle strength. This parameter has been called 242

relative muscular effort (RME), functional demand, and muscular utilization ratio (6, 12, 72, 85). To 243

determine RME, NJM are estimated as previously described and expressed relative to the maximum 244

moment measured during maximal voluntary strength testing using isokinetic dynamometry. 245

Muscle strength is the maximum force or moment that can be exerted by a muscle group under 246

specified conditions (61, 65). These conditions include muscle length, action type (eccentric, isometric, 247

or concentric), and velocity; ideally, these conditions should be matched between the exercise studied 248

and the maximum strength test (6). Single-joint isometric and isokinetic dynamometry have been used 249

to estimate muscle strength (6, 12), however, the moment measured in these tests may underestimate 250

the true maximum moment-generating ability (48). One limitation of single-joint dynamometry is that 251

individual muscles cannot be isolated; this is the same limitation present in calculating the NJM. Since 252

antagonist co-contraction is often present in movement and maximal strength expression, the moment 253

measured will be less than the moment generated by the agonist muscles. A second limitation is that 254

muscle activation may not be maximal, either because not all motor units are activated or motor unit 255

firing frequency is too low (53). When a muscle or muscle group is not maximally activated, the 256

measured moment will be less than the maximum those muscles could generate. In healthy adults, the 257

amount of inactivation is approximately 2-7% (32, 62, 77), although it is important to recognize that this 258

does not correspond directly to the force deficit from inactivation (53). Due to some muscle 259

inactivation, the moment measured using single-joint dynamometry may underestimate the true 260

maximum strength potential for the muscle group of interest. This is demonstrated in investigations 261

where the moment measured during single-joint dynamometry is less than the NJM during the task, 262

resulting in an RME greater than 100% (85). Thus, RME may overestimate the actual amount of muscle 263

group strength used during a task. 264

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Consequently, RME should not be interpreted as an exact value. An RME of 80% indicates that 265

approximately 80% of the muscle group’s maximum strength is required, however, the true amount is 266

likely lower due to underestimation of the muscle group’s actual maximum strength. The value of RME 267

is to provide context to evaluate NJM or muscle force estimates. For example, two muscles may have 268

different NJM during an exercise. However, each muscle may have the same RME if the muscles have 269

different maximum strength capacities; the exercise would be equally challenging for both muscles. As 270

maximum strength varies across muscle groups, RME provides greater detail as to how hard a muscle 271

group operates during a task than absolute muscular effort (11, 12, 73). 272

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Application to Barbell Squats 274

Barbell squats are a common multi-joint resistance exercise and numerous biomechanical 275

studies have been conducted on variations of squat exercise. There are several controversies regarding 276

squats, such as to what depth (knee flexion angle) should squats be performed, where should the 277

barbell be placed, and how should the feet be positioned. As primary objectives of resistance exercise 278

include increasing muscle size and strength, the best evidence for the effectiveness of an exercise is a 279

training study. Two investigations have compared the effectiveness of partial versus full squats, where 280

squats were performed to 60⁰ and 120⁰ knee flexion, respectively (where 0⁰ is knee extension) (7, 51). 281

Collectively, these studies found that full squats elicited greater increases in lower extremity strength, 282

knee extensor strength, quadriceps size and vertical jump height than partial squats. Moreover, 283

investigations where training was performed with squats to 90⁰ knee flexion found minimal increases in 284

quadriceps size (69, 99). Thus, to increase quadriceps size and strength, as well as vertical jump height, 285

squats should be performed to a minimum depth of 120⁰ knee flexion. 286

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Biomechanical investigation of barbell squats can provide insight into why this squat depth may 288

be required. Several studies have established that the major muscle groups involved in barbell squats 289

are the hip extensors, knee extensors, and ankle plantar flexors (16, 34, 36). Moreover, squat depth and 290

barbell load have been reported to influence the NJM required from each of these muscle groups, 291

although the effect of each varies depending on muscle group (36). Bryanton et al. (12), using 3D 292

motion analysis and isometric dynamometry, determined hip extensor, knee extensor, and ankle plantar 293

flexor RME during squats at different depths with varying barbell loads. Ankle plantar flexor RME was 294

invariant to squat depth but increased with barbell load, reaching 71% of maximum strength at 90% 1 295

RM. Knee extensor RME increased primarily as a function of squat depth, reaching 57% of maximum 296

strength at 105⁰-119⁰ knee flexion (0⁰ is knee extension) with 90% 1 RM. Hip extensor RME increased 297

both with barbell load and squat depth, reaching 76% of maximum strength at 105⁰-119⁰ knee flexion 298

with 90% 1 RM. From these data, it was hypothesized that while using heavy loads may be effective to 299

train the ankle plantar flexors and hip extensors, the knee extensors would be best trained during squat 300

exercise by using greater squat depths as described by knee flexion angle. 301

A follow-up report estimated the actual quadriceps RME, as hamstrings co-contraction at the 302

knee would result in the knee extensor NJM being an underestimate of the quadriceps moment 303

required (11). Using a musculoskeletal model, quadriceps moment and RME were estimated under the 304

assumptions that either: 1) gluteus maximus and hamstrings activation were equal or 2) gluteus 305

maximum activation was maximal and hamstrings activation was minimized. Quadriceps RME increased 306

with both squat depth and barbell load, reaching 120% of maximum strength using the first assumption 307

and 87% of maximum strength using the second assumption for squats to 105⁰-119⁰ knee flexion at 90% 308

1 RM; the first assumption was deemed to be not feasible. Collectively, these findings indicate that 309

gluteus maximus and quadriceps RME increase as a function of both squat depth and barbell load. 310

Based on these results, it could be hypothesized that squats to at least 105⁰-119⁰ knee flexion would be 311

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better to elicit gluteus maximus and quadriceps size and strength adaptations compared to squats 312

where less knee flexion is achieved. This hypothesis, at least in regards to quadriceps cross-sectional 313

area and isometric knee extensor strength, has been confirmed (7). 314

The association between squat depth and likely knee extensor muscular effort is consistent with 315

other studies where weighted squats were performed. In the clean and power clean, the barbell is 316

caught on the shoulders in a front squat. Moolyk et al. (74) observed greater knee extensor NJM in 317

cleans, which had 131⁰ knee flexion (0⁰ is knee extension), versus power cleans, which had 90⁰ knee 318

flexion. A recent study of squat exercise biomechanics reported knee extensor NJM was greater at 319

120⁰-134⁰ and 135-149⁰ knee flexion than at 105⁰-119⁰ knee flexion (18). Although these studies did 320

not investigate RME, maximal knee extensor moment is generated at knee flexion angles between 60⁰ 321

and 90⁰. Maximal knee extensor moment decreases with knee flexion angles greater than 60⁰-75⁰ (54); 322

thus, it can be hypothesized that the larger knee extensor NJM with increasing squat depth would result 323

in greater knee extensor RME with these greater squat depths. 324

325

EMG 326

In addition to NJM, EMG is commonly assumed to be a good estimate of muscle effort. The 327

physiologic principles of EMG analysis, as well as the general assumptions and limitations associated 328

with EMG have been discussed at length (55, 57). For this review, the issues most pertinent to using 329

EMG as a measure of muscle effort during resistance exercise are considered. EMG amplitude is the 330

electrical potential difference measured from activated motor units near the surface or fine-wire 331

electrodes recording electrodes. Surface electrodes are non-invasive and have a larger recording area 332

than fine-wire electrodes, at the expense of greater potential for crosstalk and electrode movement 333

relative to the underlying muscle (57). Fine-wire electrodes are better for selectively recording the same 334

motor units within a single muscle, however, can record fewer total motor units (57). 335

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The measured electrical potential difference is specific to the muscle and the impedance 336

between the recording electrodes and the muscle (57). This impedance varies based on the distance 337

between the muscle and the electrodes, the distance between the electrodes, electrode size, biological 338

tissue composition, and several other factors (26, 43, 57). While some factors can be controlled for, 339

others cannot. Therefore, the electrical potential difference may be valid only for a specific muscle on a 340

specific day. This means that the EMG signal cannot be compared between different muscles, to the 341

same muscle on different days, or between different persons. To permit these comparisons, rectified 342

and processed EMG amplitude during an activity is normalized to EMG amplitude during a reference 343

action (4, 28). When the reference action is a maximal voluntary effort, this is interpreted the same as 344

NJM normalized to moment during maximum strength testing or RME. Normalized EMG should not be 345

interpreted, as has been discussed for RME, as an exact percentage of maximum muscle strength. One 346

study has directly compared these electrophysiological versus mechanical methods. For a bodyweight 347

squat at 90⁰ knee flexion, normalized EMG underestimated muscle effort compared to normalized NJM 348

(i.e. RME) (52). Thus, there may not be direct correspondence between EMG normalized to a maximal 349

voluntary effort and RME. 350

A further benefit of normalizing EMG is that it reduces the effect of amplitude cancellation (58). 351

Motor unit action potentials include both positive and negative phases. The action potentials from 352

motor units sum, increasing or decreasing (when negative voltages cancel positive voltages) EMG 353

amplitude. As muscle activation and muscle force exerted increase, EMG amplitude cancellation also 354

increases. Mathematical simulations predict that absolute EMG amplitude may be reduced by as much 355

as 62% at maximum muscle force (58). Normalizing EMG reduces the effect of amplitude cancellation to 356

less than five percent (58). 357

358

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The premise behind interpreting normalized EMG is that a linear relation exists between EMG 359

and mechanical measures of muscle effort (55, 79). However, linear and curvilinear relations between 360

normalized EMG and mechanical measures of muscle effort have been reported (28, 71, 110). For 361

purposes of normalization, most investigations record the reference EMG at a single effort level, which 362

is insufficient to establish the relation with muscle effort. Consequently, muscle effort may be 363

incorrectly estimated from normalized EMG. 364

An additional problem for interpreting normalized EMG is the reference action selected. To 365

estimate muscle effort as a percentage of maximum, maximal voluntary isometric efforts have been 366

recommended (90). However, maximum EMG amplitude may not occur during these tasks as maximum 367

muscle activation may not occur and amplitude cancellation is high (58). Normalized EMG values much 368

greater than 100% have been reported (47), which may be explained by a reference task that does not 369

allow maximum EMG amplitude to be obtained. The use of dynamic tasks, such as sprint running or 370

jumping, has been proposed for EMG normalization as absolute EMG amplitudes are higher compared 371

to single-joint isometric actions (95). However, this is problematic for interpretation as NJM and 372

estimated muscle forces during sprint running and jumping may also be sub-maximal (31, 75), therefore, 373

these tasks do not provide an adequate reference point for maximum muscle effort. An ideal reference 374

task would involve both maximum muscle effort and maximum EMG amplitude. 375

A final potential problem is EMG variation as a function of joint angle. Some research has 376

reported that EMG amplitude is dependent on joint angle (1, 33), while others have found that EMG 377

amplitude does not change with joint angle (13, 66). If there is a relation between EMG amplitude and 378

joint angle, joint angle specific EMG normalization is required (33). The conflicting results between 379

investigations may be a result of how data are analyzed. In general, studies assessing the relation 380

between EMG amplitude and joint angle have averaged data across multiple subjects before 381

determining the relation (1, 33, 66). This ignores that the relation may be different for each subject (60). 382

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Additionally, there is large variability in EMG amplitude for actions performed both within and between 383

days (13, 60, 90). EMG amplitudes from a single effort, or the average of multiple efforts, will not reflect 384

the range of possible EMG amplitudes. By ignoring this range, incorrect relations between EMG 385

amplitude and joint angle may be established. 386

The utility of EMG as an estimate of muscle effort requires the actual relation between 387

normalized EMG and mechanical measures of muscle effort should be established. Moreover, a 388

reference task for normalization should be selected that requires maximum muscle effort and results in 389

maximum EMG amplitude. 390

391

POINT MASS MODELS 392

Barbell Kinematics & Kinetics 393

Mechanical systems can be idealized as point mass or rigid body models. Point mass models 394

idealize an object to have mass but no geometry; the forces exerted on an object act at the center of 395

mass. An individual performing an exercise can be represented using a point mass model by examining 396

the forces exerted on the individual or on a manipulated object like a barbell. Free body diagrams 397

illustrating the forces exerted on an individual performing a barbell squat and the forces exerted on the 398

lifter-barbell system using a point mass model are shown in Figure 2. In a barbell squat, three external 399

forces – gravitational attraction on the lifter’s mass, force from the barbell and the ground reaction 400

force – act on the lifter. The sum of these forces is proportional to the acceleration of the lifter’s center 401

of mass along the same axis. Both the forces exerted by the barbell and the ground can be measured. 402

For simplicity, only the vertical forces are shown, however, horizontal forces may also be exerted. This 403

example is not specific to barbell squats and can be used to represent any exercise where an external 404

resistance exerts vertical force on an individual. 405

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Based on Newton’s third law, the force exerted by the barbell on the lifter is equal in magnitude 406

but opposite in sense (or direction along the axis) to the force exerted by the lifter on the barbell. The 407

vertical force exerted on the barbell is calculated using equation 2. 408

Equation 2: FY = m*g + m*aY; where FY: vertical force, m: mass, g: gravitational acceleration, a: 409

vertical acceleration 410

Mass multiplied by gravitational acceleration is weight, which is used in practice to quantify resistance 411

exercise intensity. However, in dynamic exercise, vertical barbell acceleration is not zero, and vertical 412

force exerted on the barbell is greater and lower than the barbell’s weight as the barbell has positive 413

and negative vertical acceleration, respectively. Acceleration can be directly measured using 414

accelerometers or calculated from displacement. Displacement has been measured using two- or three-415

dimensional motion analysis, or electromechanical transducers, such as linear position transducers and 416

optical encoders. 417

Electromechanical transducers are relatively inexpensive and are commonly employed to 418

quantify resistance exercise intensity. Methods for accurate kinetic calculations using these 419

technologies have been discussed in previous papers (23, 24); one key consideration is relevant for this 420

review. Specifically, it is important to recognize that the kinematics measured by these devices are 421

representative of the barbell (or implement the device is attached to) and may not be representative of 422

the lifter-barbell system (17). These technologies only permit measurement of the barbell kinematics 423

and not the lifter-barbell kinematics. In some cases, such as for a bench press, the primary resistance is 424

provided by the barbell and the mass of the upper extremity is relatively small and can be ignored (42). 425

In contrast, for exercises such as squats or cleans, both the barbell and the lifter’s mass provide 426

considerable resistance to movement (17, 42). Some studies have calculated force – and other kinetic 427

parameters – using barbell kinematics and the mass of the lifter-barbell system (17, 50). This approach 428

is only accurate if the barbell kinematics and the lifter-barbell system are identical (17). Any 429

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19

discrepancies between barbell versus lifter-barbell system kinematics would create error when 430

calculating force in this manner (17). 431

Even if the force for the lifter-barbell system can be calculated using these kinematic methods, 432

this force would be the same as that obtained from a force platform (17). This is illustrated in Figure 2. 433

Thus, using parameters derived from barbell or barbell-lifter system kinematics has the same utility as 434

measuring force platform data, which is discussed in the next section. 435

436

Force Platforms 437

Typically, force platforms are used to measure ground reaction forces and moments during tasks 438

where an individual stands, walks, or runs over the platform (15, 78). However, other configurations 439

have been employed, such as placing the hands on the platform during a push up or mounting a bench 440

press on the platform (30, 102). Force platforms are a convenient method to obtain biomechanical 441

parameters due to their relatively low cost and ease of use, which includes data processing. For 442

biomechanics research, multi-component force platforms that measure forces along and moments 443

about three axes are typically used. Single-component force platforms marketed for physics classes that 444

measure vertical ground reaction force are also available and at a much lower cost than multi-445

component force platforms. 446

In addition to force, impulse can be calculated by integrating the force data with respect to 447

time. Forward dynamics equations can be used to calculate acceleration, change in velocity, and change 448

in position. Work is calculated by integrating force with respect to displacement, while power is 449

calculated by multiplying force and velocity. However, these parameters only describe the kinematics 450

and kinetics of the body’s or system’s center of mass as a point mass model interacting with the force 451

platform. It is questionable whether these parameters are useful measures of muscle effort. 452

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20

The force measured by a force platform is the net force exerted on the platform by an 453

individual. The net force exerted increases when forces sum and decreases when forces cancel, 454

therefore, high muscle efforts may not result in high forces exerted on the force platform. Using 455

musculoskeletal modelling, Mills et al. (70) found that ground reaction forces could be reduced during 456

jump landings if hip extensor, knee extensor, and ankle plantar flexor muscle forces increased. Changing 457

countermovement depth in vertical jumps changes the peak vertical ground reaction force, but did not 458

affect peak hip extensor, knee extensor, and ankle plantar flexor NJM (29). Salem et al. (84) reported 459

that knee peak extensor NJM was lower and peak hip extensor NJM was higher in the involved versus 460

non-involved limb of individuals who had had anterior cruciate ligament reconstructive surgery within 461

the past year. However, there were no differences in the peak vertical ground reaction force between 462

limbs. 463

Taken together, these scenarios demonstrate that ground reaction force alone cannot be used 464

to infer hip extensor, knee extensor, and ankle plantar flexor muscle efforts. As ground reaction force is 465

directly proportional to a system’s center of mass acceleration along the same axis, any methodologies 466

based on center of mass kinematics are also not appropriate to quantify muscle effort. 467

468

SUMMARY 469

An understanding of how resistance exercise acts as a stimulus to elicit neural and muscular 470

adaptations requires knowledge of muscle forces or related estimates of muscle effort, such as 471

moments and normalized EMG. Currently, only indirect methods have been used to estimate muscle 472

effort as opposed to direct measurement of muscle force in vivo. Several biomechanical methods have 473

been employed, however, only some of these methods estimate muscle effort. Point mass models, such 474

as using force platforms and linear position transducers, are commonly employed due to the relatively 475

low cost and ease of use of the methodology involved. However, point mass models only quantify the 476

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net force exerted on the lifter, barbell, or lifter-barbell system; this parameter is inadequate for 477

quantifying muscle effort. Inverse dynamics using a rigid body model can be used to calculate the NJMs 478

during exercises that may be interpreted as muscle group effort using RME. Musculoskeletal modelling, 479

some driven with normalized EMG as inputs to estimate load sharing between specific muscles, can 480

estimate muscle forces. RME can also be determined using NJM or muscle force by normalizing to 481

maximum muscle strength. Considering limitations of NJM, musculoskeletal modelling, and normalized 482

EMG, muscle effort estimates can be used to hypothesize application in resistance training. These 483

hypotheses, however, should be verified through training studies. 484

485

ACKNOWLEDGEMENTS 486

The author would like to express his appreciation to two anonymous reviewers who provided 487

important insight and feedback in the review process. 488

489

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27

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762

763

764

List of Figures and Figure Footnotes 765

766

Figure 1: Free body diagrams for rigid body modelling to calculate net joint moments acting on the thigh 767

leg and foot segments. Dynamics equations are shown for the leg segment only. F – force; M – 768

moment; m – mass; a – acceleration; g – gravitational acceleration; α – angular acceleration; I – moment 769

of inertia; X – X-axis; Y – Y-axis; Z – Z-axis; T – thigh; L – leg; Ft – foot; H – hip; K – knee; A – ankle; G – 770

ground. 771

772

Figure 2: Point mass model free body diagrams showing the lifter and barbell (left) and lifter-barbell 773

system (right) during squat exercise. F – force; m – mass; a – acceleration; g – gravitational acceleration; 774

X – X-axis; Y – Y-axis; Z – Z-axis. 775

ACCEPTED


ACCEPTED


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