# Calculation of Muscle Activity during Race Walking

###### Contributors (2)

###### Published

###### DOI

**Anne Schmitz**1

Department of Engineering and Technology, University of Wisconsin-Stout, Menomonie, WI

807 3^{rd} Street East

Menomonie, WI 54751

schmitzann@uwstout.edu

**Jaclyn Norberg**

Department of Sport and Movement Science, Salem State, Salem, MA

352 Lafayette Street

Salem, MA 01970

jnorberg@salemstate.edu

**ABSTRACT**

*Joint forces are used as surrogate measures for joint osteoarthritis. These joint contact forces are difficult to measure, and therefore, 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 compare CMC accuracy across different movements. 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**

Contact forces are a variable of interest when investigating joint disease. For example, increased tibiofemoral loading has been shown to be correlated with knee osteoarthritis [1]. This correlation comes from the biological relationship between cartilage properties and mechanical loading [2]. Regions of cartilage that experience high mechanical loads tend to be thicker with more aligned collagen fibers than areas with lower loads [3]. Changes in the location and magnitude of these contact forces shifts these loads to areas maladapted to loading, thus causing cartilage degeneration and eventual osteoarthritis [4].

These joint contact forces are difficult to measure. Therefore, they are calculated using either a serial or cosimulation approach [5]. 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 [6]. Computed muscle control (CMC) is used in these frameworks to calculate muscle activations, which are used to subsequently calculate muscle forces [7].

Since muscle forces are the main contributor to contact forces, accurate contact forces require accurate muscle forces. These muscle forces are impractical to measure experimentally; thus making these difficult to validate when output from simulations. The most current way to check these muscle forces are to compare the calculated muscle activations to experimentally measured electromyography (EMG) data. The literature suggests the accuracy of these activations decreases as motion complexity increases as the CMC algorithm may have difficulty in predicting cocontraction patterns [8]. These activations have been validated for a multitude of movements already in the literature, e.g. single-leg hopping [9], running [8][10], and walking [8][11]. However, since these studies were conducted independently, the relationship between movement type and muscle activation accuracy cannot be ascertained. Therefore, the goal of this study was to determine the relationship between CMC accuracy of muscle activations and movement type. This is an important step in determining the limits of CMC to accurately predict contact forces for use in osteoarthritis prevention, progression, and eventual treatment simulations.

**METHODS**

Instrumented motion capture data (kinematics, kinetics, and electromyography) of a representative subject was used from a previous study [12]. In this study, subjects walked, race walked, and ran at a self-selected pace across a walkway with two embedded forceplates while marker trajectories and electromyography (EMG) were collected. EMG was collected for eight muscles: gluteus medius (GM), rectus femoris (RF), vastus lateralis (VL), adductor longus (AL), semitendinosus (ST), tibialis anterior (TA), gastrocnemius (GM), and peroneus longus (PL). Using a Visual3D (C-Motion, Germantown, MD) to OpenSim [13] pipeline [14], 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 [12][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 [16], were input into OpenSim. Next, these scaling factors were used to scale the OpenSim generic model gait2392 [13]. The generic model in Visual3D and OpenSim were the same in segments used and joint models. However, the OpenSim model additionally contained muscle actuators. Then, the residual reduction algorithm (RRA) was used to create a dynamically consistent system (e.g. [17]). 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 excitations [7].

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

$\ddot{\theta_\ast}\left(t+T\right)-\ddot{\theta_p}\left(t+T\right)=k_v\left[\dot{\theta_p}\left(t\right)-\dot{\theta}\left(t\right)\right]+k_u[\theta_p\left(t\right)-\ \theta\left(t\right)]$

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 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 performs multiple forward dynamics simulations to determine the joint acceleration induced by each musculotendon actuator. These musculotendon actuators are non-linear force generators whereby the force depends of the length of the muscle, muscle excitation, and the shortening/lengthening velocity of the muscle (i.e. the Hill muscle model [18]). Since the number of muscles is greater than the number of joints, the redundant system is treated as an optimization problem. The muscle excitations needed to achieve the overall joint accelerations is determined using the induced acceleration results and by minimizing the summed excitation across all muscles.

CMC simulations were performed for all experimentally measured movements: 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 [9][19], which quantifies the accuracy of CMC to calculate muscle excitations. To investigate 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 [20]. 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).

**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.

As movement difficulty increased with more knee cocontraction, 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 excitations and consequently muscle forces must able be calculated. Therefore, the accuracy of joint forces is dependent on the accuracy of these muscle excitations. Muscle excitations are 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 excitations 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 excitations for movements of varying complexity: walking, race walking, and running. Surprisingly, the CMC tool calculated excitations in reasonable agreement with EMG, regardless of movement complexity (Fig. 2 – Fig. 3).

Overall, the accuracy of the simulations to predict EMG did not vary with movement complexity. This is contrary to suggestions in the literature that the CMC algorithm may have difficulty in predicting cocontraction [8]. CMC uses static optimization where the summed muscle excitations 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 cocontraction. 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 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 [21] (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 [22]). 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. 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. the effect of biarticular muscles on knee and hip coordination).

In summary, we have used the CMC framework to calculate muscle excitations for walking, race walking, and running. The results show these excitations 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.

**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. |

GM | Gastrocnemius muscle. |

PL | Peroneus longus muscle. |

**REFERENCES**

**SUPPLEMENTAL INFO**

Experimentally measured EMG and calculated muscle excitations 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 excitations, measured EMG, and cross-correlation are included for walking (Fig. S1), race walking (Fig. S2), and running (Fig. S3).