# Calculation of Muscle Activity during Race Walking

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**ABSTRACT**

*Race walking has been shown to be a lower impact alternative to running. In fact, lower injury rates are reported in race walkers than runners. This may be due to lower joint forces. However, this theory has not been explicitly tested since joint contact forces are difficult to measure. Therefore, these joint forces are calculated using either a serial or cosimulation approach. In both strategies, a detailed joint model and multibody dynamics model are used in tandem to calculate muscle forces. These muscle forces then contribute to the joint contact forces. Computed muscle control (CMC) is an algorithm that utilizes a proportional-derivative controller, static optimization, and forward dynamics to calculate muscle activations, which are used to subsequently calculate muscle forces. The goal of this study was to investigate the viability of using CMC to calculate muscle activations during race walking, with the intent of using these activations in future studies to calculate joint forces. Instrumented motion capture data (kinematics, kinetics, and electromyography (EMG)) of a representative subject was used from a previous study. In this study, subjects walked, race walked, and ran at a self-selected pace across a walkway with embedded forceplates while marker trajectories and EMG were collected. Muscle actuated forward dynamics simulations (i.e. CMC) were created for each movement. The muscle activations resulting from these CMC simulations were compared to the experimentally measured EMG by performing a cross-correlation. The CMC results were fairly accurate across all muscles (gluteus medius, rectus femoris, vastus lateralis, adductor longus, semitendinosus, tibialis anterior, gastrocnemius, peroneus longus) with correlation coefficients greater than 0.5. There was no apparent relationship between movement type and coefficient. Future work is needed to determine if correlation coefficients of 0.5 are accurate enough for studies looking to accurately quantify joint contact forces.*

**INTRODUCTION**

Race walking has grown in popularity as a lower impact alternative to running. In fact, race walking has been shown to provide similar health benefits at a lower injury rate [1]. This difference in rate of joint injury may be due to the decreased impact loads between the ground and foot seen during race walking as compared to running [2]. Impact loads during race walking and running can travel up the kinetic chain to the knee [3][4]. Since increased tibiofemoral loading has been shown to be correlated with knee osteoarthritis [5], race walking likely induces lower joint contact loads in the knee and may explain the lower injury rate compared to running. However, this mechanistic explanation of lower injury rates cannot be experimentally tested without instrumented knee implants [6].

Joint forces can be calculated using either a serial or cosimulation approach [7]. In both strategies, a detailed joint model and multibody dynamics model are used in tandem to calculate muscle forces. These muscle forces then contribute to the joint contact forces [8]. Computed muscle control (CMC) is one tool used in these frameworks to calculate muscle excitations and activations, which are used to subsequently calculate muscle forces [9].

Since muscle forces are the main contributor to contact forces [10], accurate contact forces require accurate muscle forces. These muscle forces are impractical to measure experimentally; thus making them difficult to validate when output from simulations. These calculated muscle forces are typically validated by comparing the calculated muscle activations with experimentally measured electromyography (EMG) data. These activations have been validated for a multitude of movements already in the literature, e.g. single-leg hopping [11], running [12][13], and walking [12][14]. However, race walking has not been considered in the simulation literature. In order to test the theory that race walking induces lower joint contact loads in the knee than running, the validity of calculated muscle activations that result in muscle forces must first be established. Therefore, the goal of this study is to investigate the viability of using CMC to predict muscle activations for race walking. We hypothesize calculated muscle activations during walking, race walking, and running will be similarly, temporally comparable to measured EMG. All three motions are investigated in order to present a wider context for the race walking results since CMC has been used for running [12][13] and walking [12][14] previously.

**METHODS**

This study is a secondary analysis of data collected for a previous study [15]. Following a protocol approved by an institutional review board (IRB), instrumented motion capture data of an experienced, competitive race walker (mass: 53.2 kg, height: 1.63 m, and age: 31 years) was collected for three motions: walking, race walking, and running at self-selected speeds across a 15 m walkway. The subject walked at 1.25 m/s, race walked at 1.87 m/s, and ran at 3.44 m/s, calculated from a marker placed on the sternum. Ground reaction force data for the stance phase of motion was obtained using two embedded forceplates sampling at 1000 Hz (Bertec Corp., Columbus, OH). Whole body marker trajectories for eighty-five retro-reflective markers were collected at 200 Hz with an 11-camera motion capture system (Motion Analysis Corp., Santa Rosa, CA). A standard marker configuration was used, the details of which are presented elsewhere [15][16]. Electromyography (EMG) (Delsys, Natick, MA) was simultaneously collected for eight muscles: gluteus medius (GM), rectus femoris (RF), vastus lateralis (VL), adductor longus (AL), semitendinosus (ST), tibialis anterior (TA), gastrocnemius (GA), and peroneus longus (PL) using standard SENIAM electrode placements [17][18]. The EMG signals were subsequently postprocessed by creating a linear envelope: (1) low pass, 4th order, zero-lag Butterworth filter with a 100 Hz cutoff frequency, (2) full wave rectified, (3) low pass, 4th order, zero-lag Butterworth filter with an 8 Hz cutoff frequency, and then (4) normalized by maximal voluntary isometric contraction [15][19][20].

Using a Visual3D (C-Motion, Germantown, MD) to OpenSim [21] pipeline [22], muscle actuated forward dynamics simulations were created for each movement (Fig. 1).

First, Visual3D was used to process the raw motion capture data (in .c3d format) to produce scaling factors and perform inverse kinematics [15][16]. A description of the bone-embedded reference frames and inverse kinematics algorithm is described in more detail elsewhere [15]. Then, these scaling factors, which were calculated as ratios between the bone lengths in the generic model and bone lengths of the actual subject [23], were input into OpenSim version 3.2. Next, these scaling factors were used to scale the OpenSim generic model gait2392 [21]. The generic model in Visual3D and OpenSim used the same anatomical segments, anthropometrics, and biomechanical joint models. However, the gait2392 OpenSim model additionally contained 92 musculotendon actuators. Then, the residual reduction algorithm (RRA) was used to create a dynamically consistent system (e.g. [24]). RRA creates a dynamically consistent system by slightly changing the mass properties of the bones of the scaled model and the inverse kinematics data so Newton’s equation of motion can be satisfied (ΣF = ma). Since *F* is force applied to the body as measured via the ground reaction forces (i.e. forceplate data), mass, *m*, is modeled from anthropometric studies, and acceleration, *a*, of the body segments is also measured from marker trajectories (i.e. derivative of inverse kinematics), Newton’s equation of motion is often inconsistent due to measurement errors. RRA modifies the *m* and *a* variables so the equals sign can be realized. This modified model and marker data is used by the computed muscle control (CMC) tool to calculate muscle forces [9].

CMC first uses a proportional-derivative (PD) controller to calculate the accelerations needed to move a model towards an experimental data trajectory (Eq. 1 [9]):

In this equation, $\ddot{\theta_{*}}$ are the desired joint angular accelerations calculated after a time interval T; *θ̇* and *θ* are the angular velocity and position of the joints reached by the model due to muscle forces, respectively; the subscript *p* denotes variables that are the kinematic variables of the prescribed motion (i.e. experimentally measured motion); k_{v} and k_{u} are the velocity and position feedback constants of the PD controller. This means that if the model is behind where the experimental kinematics are at time *t*, the controller will accelerate the model until *t + T* and reassess if the model is on track yet. If the model is ahead, the controller will decelerate the joints in the same way. Once the desired joint accelerations are computed, the CMC algorithm integrates muscle activation and contraction dynamics forward from *t* to *t + T* for a range of muscle excitations to determine the maximum and minimum forces that can be achieved by the muscles at time *t + T.* These musculotendon actuators are non-linear force generators whereby the force depends on the length of the muscle, muscle excitation, and the shortening/lengthening velocity of the muscle (i.e. the Hill muscle model [25]). Since the number of muscles is greater than the number of joints, the redundant system is treated as an optimization problem. Therefore, static optimization is used to calculate the musculotendon forces that lie within the previously calculated bounds, produce the desired accelerations from the PD controller, and minimize the summed excitation across all muscles (i.e. a surrogate measure for muscle energy expenditure) [9].

CMC simulations were performed for a representative trial of each experimentally measured movement: walking, race walking, and running. The muscle activations resulting from these CMC simulations were compared to the experimentally measured EMG by performing a cross-correlation in Matlab (MathWorks, Natick, MA). The variables of interest extracted were the maximum value of the correlation coefficient and the phase delay [11][26]. These variables were used to quantify the accuracy of CMC to calculate muscle activations.

To better understand the relationship between movement type and CMC accuracy, a cocontraction index was used to quantify the complexity of each movement. The cocontraction index was calculated as the ratio between the rectus femoris and semitendinosus activity (Eq. 2 [27]):

EMGS/EMGL * (EMGS + EMGL)

In this equation, EMGS is the EMG activity for the less active muscle while EMGL is the activity of the more active muscle. Linear regressions were then used to quantify the relationship between CMC accuracy (i.e. maximum correlation coefficient, phase delay) and movement type (maximum cocontraction index). Cocontraction was used as a surrogate of movement complexity and type because CMC may have difficulty in predicting coordination that involves coactivation. This comes from the optimization step of the CMC framework where the sum of muscle activations squared is minimized. Coactivation, which is clinically considered activation of antagonistic joint pairs [28], would cause an increase in the cost function and hence not be chosen by the CMC algorithm as a preferred coordination pattern.

**RESULTS**

The maximum cross-correlation coefficient between the calculated muscle excitations and experimentally measured EMG were greater than 0.5 for walking, race walking, and running (Fig. 2). The maximum correlation coefficients averaged across all muscles were 0.5 for normal walking, 0.68 for race walking, and 0.7 for running. The phase delay averaged across all muscles was 22% stance for normal walking, 32% for race walking, and 28% for running. The time traces of the calculated muscle excitations, measured EMG, and cross-correlations can be found in the supplemental information.

There was no significant relationship between cocontraction and rectus femoris correlation (p = 0.86), rectus femoris phase delay (p = 0.94), or semitendinosus phase delay (p = 0.61) (Fig. 3). Although, as cocontraction increased, the maximum semitendinosus correlation coefficient did significantly increase linearly (p = 0.01).

**DISCUSSION**

Joint forces are an important variable of interest when studying joint degeneration, specifically osteoarthritis. To calculate these contact forces, muscle activations and consequently muscle forces must be calculated. Therefore, the accuracy of joint forces is dependent on the accuracy of these muscle activations. Muscle activations can be calculated using a computed muscle control (CMC) algorithm consisting of a proportional-derivative controller, static optimization, and forward dynamics. This framework has been verified by comparing calculated muscle activations to experimentally measured EMG. Although, this has been done for a limited number of movements. This study has expanded on the literature by evaluating the performance of the CMC tool in predicting muscle activations for race walking. Ultimately, the CMC tool calculated activations for race walking in reasonable agreement with EMG, similar to the accuracy found in walking and running (Fig. 2 – Fig. 3).

Overall, the accuracy of the simulations to predict EMG did not vary with movement type (i.e. walking, race walking, and running). This is contrary to suggestions in the literature that the CMC algorithm may have difficulty in predicting cocontraction [12][11]. CMC uses static optimization where the summed muscle activations across all muscles is minimized. This cost function cannot mathematically account for cocontraction. However, the coordination of walking, race walking, and running may not be true clinical cocontraction where cocontraction is typically considered activating antagonistic joint pairs [28]. For example, to produce knee flexion, the CMC algorithm would activate the hamstrings (Fig. 4). If hip flexion accompanies this knee flexion, CMC would also activate the rectus femoris (Fig. 4). This coordination of a biarticular muscle would show up clinically as cocontraction.

Hip flexion and knee flexion simultaneously occur during all three type of gait (walking, race walking, and running) during early stance to loading response and pre- to initial swing phases [29] (Fig. 5). At early stance, a knee flexion moment is produced by the hamstring muscles to absorb the contact forces during initial contact of all three gaits, with less during race walking due to the nature of the gait (i.e. knee extended from heel strike until the body is in full vertical upright position [30]). While this is occurring, a hip flexor moment is created by the rectus femoris to bring the leg forward for initiation of stance phase. Similarly, as the foot comes off the ground (i.e. toe off) during early swing, the hip joint moves from hip extension to hip flexion creating a hip flexion moment and the knee joint moves from knee extension to knee flexion creating a knee flexion moment to prepare for the next contact (i.e. heel strike). These events occur simultaneously where the hamstrings and the rectus femoris, all of which are biarticular muscles, are producing muscle activity at the same time to produce cocontraction.

There are some study design choices to consider when interpreting the results of this study. First, only knee cocontraction was considered. Hip and ankle cocontraction was not considered since the muscles at these joints require indwelling EMG electrodes. This was beyond the scope of the initial study. Second, the same optimization strategy was used for all three gaits where the sum of muscle activations squared (i.e. a surrogate measure of muscle energy expenditure) was minimized in calculating muscle activations. It is unclear if the same coordination strategy is truly utilized during all three movements *in vivo*; although we would expect the same results if various optimization strategies were used for each movement (i.e. CMC versus static optimization).

In summary, we have used the CMC framework to calculate muscle activations for walking, race walking, and running. The results show these activations agree fairly well with measured EMG, regardless of the motion. We theorize CMC can calculate muscle cocontraction patterns for biarticular muscles, although not for uniarticular muscles since CMC uses a static optimization tool. This is an important first step in determining the usefulness of CMC to be used in simulations calculating joint contact forces for osteoarthritis simulations. The next step is to determine if the correlations found in this study are accurate enough to calculate reasonable joint contact forces during race walking.

**NOMENCLATURE**

CMC | Computed muscle control. An algorithm, which includes a proportional-derivative controller, used to calculate muscle forces. |

EMG | Electromyography. Measurement of muscle excitations. |

RRA | Residual reduction algorithm. Used to make dynamically consistent simulations. |

GM | Gluteus medius muscle. |

RF | Rectus femoris muscle. |

VL | Vastus lateralis muscle. |

AL | Adductor longus muscle. |

ST | Semitendinosus muscle. |

TA | Tibialis anterior muscle. |

GA | Gastrocnemius muscle. |

PL | Peroneus longus muscle. |

**SUPPLEMENTAL INFO**

Experimentally measured EMG and calculated muscle activations are a function of time. To quantify the relationship between these time varying signals, cross-correlation was used. To present a complete picture of the time varying data, plots of the calculated muscle activations, measured EMG, and cross-correlation are included for walking (Fig. S1), race walking (Fig. S2), and running (Fig. S3).