Characterization of movement patterns using unsupervised learning neural networks: Exploring a novel approach for monitoring athletes during sidestepping.

The monitoring of athletes is crucial to preventing injuries, identifying fatigue or supporting return-to-play decisions. The purpose of this study was to explore the ability of Kohonen neural network self-organizing maps (SOM) to objectively characterize movement patterns during sidestepping and their association with injury risk. Further, the network's sensitivity to detect limb dominance was assessed. The data of 67 athletes with a total of 613 trials were included in this study. The 3D trajectories of 28 lower-body passive markers collected during sidestepping were used to train a SOM. The network consisted of 1247 neurons distributed over a 43 × 29 rectangular map with a hexagonal neighbourhood topology. Out of 61,913 input vectors, the SOM identified 1247 unique body postures. Visualizing the movement trajectories and adding several hidden variables allows for the investigation of different movement patterns and their association with joint loading. The used approach identified athletes that show significantly different movement strategies when sidestepping with their dominant or non-dominant leg, where one strategy was clearly associated with ACL-injury-relevant risk factors. The results highlight the ability of unsupervised machine learning to monitor an individual athlete's status without the necessity to reduce the complexity of the data describing the movement.

Implications of the choice of distance-based measures in assessing and investigating tumble turn performance.

Although the tumble turn in swimming has been studied extensively, no consensus exists about which measure is best suited to capture its performance. The aim of this study was to better understand the implications of choosing a particular distance-based performance measure for assessing and investigating tumble turn performance in freestyle swimming. To this end, a large set of retrospective turn data consisting of 2,813 turns performed by 160 swimmers was analyzed statistically in three steps. First, a mixed-effects model was derived for the entire data set, which showed that both performance level and sex had clear effects on the distance-based performance measures and performance determining variables studied in the literature. Second, repeated measures correlations were calculated for the entire data set and four performance level- and sex-based subgroups to determine the level of association between the performance measures. This analysis revealed that the performance measures were strongly correlated (r > 0.84 and p < 0.05 for all possible pairs), largely independent of performance level and sex. This finding implies that the choice of performance measure is not very critical when one is interested solely in the overall performance. In the third and last step, mixed-effects models were derived for the performance measures of interest to establish the importance of different turn-related actions for each measure, again for both the entire data set and the four subgroups separately. The results of this analysis revealed that performance measures with short(er) distances are more sensitive to changes in the adaptation time and reflect the wall contact time better than performance measures with long(er) distances, which in contrast are more useful if the focus is on the approach speed prior to the turn. In this final analysis, various effects of performance level and sex were found on the technical execution of the tumble turn.

Breaking new grounds in injury risk screening in soccer by deploying unsupervised learning with a special focus on sex and fatigue effects.

In injury prevention, a vertical drop jump (DJ) is often used for screening athletes at risk for injury; however, the large variation in individual movement patterns might mask potentially relevant strategies when analysed on a group-based level. Two movement strategies are commonly discussed as predisposing athletes to ACL injuries: a deficient leg axis and increased leg stiffness during landing. This study investigated the individual movement pattern of 39 female and male competitive soccer players performing DJs at rest and after being fatigued. The joint angles were used to train a Kohonen self-organising map. Out of 19,596 input vectors, the SOM identified 700 unique postures. Visualising the movement trajectories and adding the latent parameters contact time, medial knee displacement (MKD) and knee abduction moment allow identification of zones with presumably increased injury risk and whether the individual movement patterns pass these zones. This information can be used, e.g., for individual screening and for feedback purposes. Additionally, an athlete's reaction to fatigue can be explored by comparing the rested and fatigued movement trajectories. The results highlight the ability of unsupervised learning to visualise movement patterns and to give further insight into an individual athlete's status without the necessity of a priori assumptions.

Improving tumble turn performance in swimming-the impact of wall contact time and tuck index.

Race time can be shortened by improving turn performance in competitive swimming, but this requires insight into the optimal turn technique. The aim of the present study was to examine the effect of Wall Contact Time (WCT) and Tuck Index on tumble turn performance and their interrelations by experimentally manipulating both variables, which has not been done in previous research. Eighteen Dutch national level swimmers (FINA points 552 ± 122) performed tumble turns with three different WCTs (shorter, preferred, longer) and three different Tuck Indices (higher, preferred, lower), which were recorded by four underwater cameras and a wall-mounted force plate. Linear kinematic and kinetic variables, including the approach velocity (Vin), wall adaptation time (Tadapt), percentage of active WCT (aWCT), peak push-off force (FPeak) and exit velocity (Vexit), were extracted from the recordings and analyzed statistically, using the 5 m round trip time (5mRTT) as performance measure. The results indicated that the WCT should be sufficiently long to generate a high push-off force at the end of wall contact when the body is in a streamlined position. This led to a significantly shorter 5mRTT than a shorter or longer WCT. A linear mixed effect model yielded negative significant effects of WCT (-4.22, p < 0.001), FPeak (-2.18, p = 0.04), Vin (-4.83, p = 0.02), Tadapt (-2.68, p = 0.002), and Vexit (-9.52, p < 0.001) on the 5mRTT. The best overall turning performance was achieved with a Tuck Index of 0.7, which suggests that some of the participating swimmers could benefit from adapting their distance to the wall while turning, as was exemplified by calculating the optimal Tuck Index for individual swimmers. These results underscore the importance of WCT and Tuck Index vis-à-vis tumble turn performance, as well as their interrelations with other performance determining variables in this regard.

Control strategies during fast turning manoeuvers - the free moment and its contribution to body rotation and joint loading.

The purpose of this study was to identify the relationship between ACL relevant knee joint loading and the free (reaction) moment during 90° sidestepping task. It was hypothesized that the specific movement strategy of an athlete will impact this relationship and therefore contribute to joint loading. Functional principal component and canonical correlation analysis were used to understand the nature of free moments and their interaction with 3D joint loading in 52 athletes. It was observed that the orientation of either a positive or negative free moment is associated with different orientations and location of the foot segment at initial touch down. This impacted the rotational moment that is transferred to the knee joint: A higher internal reaction moment is observed when athletes were exposed to a positive free reaction moment, which potentially increases the load on the ACL. Furthermore, the free moment predicted joint moments and joint reaction forces. The interpretation of the principal components identified the function of the free moment to control body rotation. Free moments of different orientation were generated during the same movement, which highlights the importance of investigating individual movement strategies to understand potential injury risk and control factors.

Fatigue Induced by Repeated Changes of Direction in Élite Female Football (Soccer) Players: Impact on Lower Limb Biomechanics and Implications for ACL Injury Prevention.

BACKGROUND: The etiology of Anterior Cruciate Ligament (ACL) injury in women football results from the interaction of several extrinsic and intrinsic risk factors. Extrinsic factors change dynamically, also due to fatigue. However, existing biomechanical findings concerning the impact of fatigue on the risk of ACL injuries remains inconsistent. We hypothesized that fatigue induced by acute workload in short and intense game periods, might in either of two ways: by pushing lower limbs mechanics toward a pattern close to injury mechanism, or alternatively by inducing opposed protective compensatory adjustments. AIM: In this study, we aimed at assessing the extent to which fatigue impact on joints kinematics and kinetics while performing repeated changes of direction (CoDs) in the light of the ACL risk factors. METHODS: This was an observational, cross-sectional associative study. Twenty female players (age: 20-31 years, 1st-2nd Italian division) performed a continuous shuttle run test (5-m) involving repeated 180°-CoDs until exhaustion. During the whole test, 3D kinematics and ground reaction forces were used to compute lower limb joints angles and internal moments. Measures of exercise internal load were: peak post-exercise blood lactate concentration, heart rate (HR) and perceived exertion. Continuous linear correlations between kinematics/kinetics waveforms (during the ground contact phase of the pivoting limb) and the number of consecutive CoD were computed during the exercise using a Statistical Parametric Mapping (SPM) approach. RESULTS: The test lasted 153 ± 72 s, with a rate of 14 ± 2 CoDs/min. Participants reached 95% of maximum HR and a peak lactate concentration of 11.2 ± 2.8 mmol/L. Exercise duration was inversely related to lactate concentration (r = -0.517, p < 0.01), while neither%HR max nor [La-] b nor RPE were correlated with test duration before exhaustion (p > 0.05). Alterations in lower limb kinematics were found in 100%, and in lower limb kinetics in 85% of the players. The most common kinematic pattern was a concurrent progressive reduction in hip and knee flexion angle at initial contact (10 players); 5 of them also showed a significantly more adducted hip. Knee extension moment decreased in 8, knee valgus moment increased in 5 players. A subset of participants showed a drift of pivoting limb kinematics that matches the known ACL injury mechanism; other players displayed less definite or even opposed behaviors. DISCUSSION: Players exhibited different strategies to cope with repeated CoDs, ranging from protective to potentially dangerous behaviors. While the latter was not a univocal effect, it reinforces the importance of individual biomechanical assessment when coping with fatigue.

Prediction of ground reaction force and joint moments based on optical motion capture data during gait.

The standard camera- and force plate-based set-up for motion analysis suffers from the disadvantage of being limited to laboratory settings. Since adaptive algorithms are able to learn the connection between known inputs and outputs and generalise this knowledge to unknown data, these algorithms can be used to leverage motion analysis outside the laboratory. In most biomechanical applications, feedforward neural networks are used, although these networks can only work on time normalised data, while recurrent neural networks can be used for real time applications. Therefore, this study compares the performance of these two kinds of neural networks on the prediction of ground reaction force and joint moments of the lower limbs during gait based on joint angles determined by optical motion capture as input data. The accuracy of both networks when generalising to new data was assessed using the normalised root-mean-squared error, the root-mean-squared error and the correlation coefficient as evaluation metrics. Both neural networks demonstrated a high performance and good capabilities to generalise to new data. The mean prediction accuracy over all parameters applying a feedforward network was higher (r = 0.963) than using a recurrent long short-term memory network (r = 0.935).

Artificial Neural Networks in Motion Analysis-Applications of Unsupervised and Heuristic Feature Selection Techniques.

The use of machine learning to estimate joint angles from inertial sensors is a promising approach to in-field motion analysis. In this context, the simplification of the measurements by using a small number of sensors is of great interest. Neural networks have the opportunity to estimate joint angles from a sparse dataset, which enables the reduction of sensors necessary for the determination of all three-dimensional lower limb joint angles. Additionally, the dimensions of the problem can be simplified using principal component analysis. Training a long short-term memory neural network on the prediction of 3D lower limb joint angles based on inertial data showed that three sensors placed on the pelvis and both shanks are sufficient. The application of principal component analysis to the data of five sensors did not reveal improved results. The use of longer motion sequences compared to time-normalised gait cycles seems to be advantageous for the prediction accuracy, which bridges the gap to real-time applications of long short-term memory neural networks in the future.

Estimation of Gait Mechanics Based on Simulated and Measured IMU Data Using an Artificial Neural Network.

Enhancement of activity is one major topic related to the aging society. Therefore, it is necessary to understand people's motion and identify possible risk factors during activity. Technology can be used to monitor motion patterns during daily life. Especially the use of artificial intelligence combined with wearable sensors can simplify measurement systems and might at some point replace the standard motion capturing using optical measurement technologies. Therefore, this study aims to analyze the estimation of 3D joint angles and joint moments of the lower limbs based on IMU data using a feedforward neural network. The dataset summarizes optical motion capture data of former studies and additional newly collected IMU data. Based on the optical data, the acceleration and angular rate of inertial sensors was simulated. The data was augmented by simulating different sensor positions and orientations. In this study, gait analysis was undertaken with 30 participants using a conventional motion capture set-up based on an optoelectronic system and force plates in parallel with a custom IMU system consisting of five sensors. A mean correlation coefficient of 0.85 for the joint angles and 0.95 for the joint moments was achieved. The RMSE for the joint angle prediction was smaller than 4.8° and the nRMSE for the joint moment prediction was below 13.0%. Especially in the sagittal motion plane good results could be achieved. As the measured dataset is rather small, data was synthesized to complement the measured data. The enlargement of the dataset improved the prediction of the joint angles. While size did not affect the joint moment prediction, the addition of noise to the dataset resulted in an improved prediction accuracy. This indicates that research on appropriate augmentation techniques for biomechanical data is useful to further improve machine learning applications.

Prediction of lower limb joint angles and moments during gait using artificial neural networks.

In recent years, gait analysis outside the laboratory attracts more and more attention in clinical applications as well as in life sciences. Wearable sensors such as inertial sensors show high potential in these applications. Unfortunately, they can only measure kinematic motions patterns indirectly and the outcome is currently jeopardized by measurement discrepancies compared with the gold standard of optical motion tracking. The aim of this study was to overcome the limitation of measurement discrepancies and the missing information on kinetic motion parameters using a machine learning application based on artificial neural networks. For this purpose, inertial sensor data-linear acceleration and angular rate-was simulated from a database of optical motion tracking data and used as input for a feedforward and long short-term memory neural network to predict the joint angles and moments of the lower limbs during gait. Both networks achieved mean correlation coefficients higher than 0.80 in the minor motion planes, and correlation coefficients higher than 0.98 in the sagittal plane. These results encourage further applications of artificial intelligence to support gait analysis. Graphical Abstract The graphical abstract displays the processing of the data: IMU data is used as input to a feedforward and a long short-term memory neural network to predict the joint kinematics and kinetics of the lower limbs during gait.

Intelligent prediction of kinetic parameters during cutting manoeuvres.

Due to its capabilities in analysing injury risk, the ability to analyse an athlete's ground reaction force and joint moments is of high interest in sports biomechanics. However, using force plates for the kinetic measurements influences the athlete's performance. Therefore, this study aims to use a feed-forward neural network to predict hip, knee and ankle joint moments as well as the ground reaction force from kinematic data during the execution and depart contact of a maximum effort 90° cutting manoeuvre. A total number of 525 cutting manoeuvres performed by 55 athletes were used to train and test neural networks. Either marker trajectories or joint angles were used as input data. The correlation coefficient between the measured and predicted data indicated strong correlations. By using joint angles as the input parameters, slightly but not significantly higher accuracy was found in joint moments predictions. The prediction of the ground reaction force showed significantly higher accuracy when using marker trajectories. Hence, the proposed feed-forward neural network method can be used to predict motion kinetics during a fast change of direction. This may allow for the simplification of cutting manoeuvres experimental set-ups for and through the use of inertial sensors. Graphical abstract The left part of the graphical abstract displays the angle progression of the hip, knee and ankle joint as an example of the kinematic input data and is supported by a stick figure of the motion task, a 90° cutting manoeuvre. This data is used to train a feed-forward neural network, which is displayed in the middle. The neural network's output is displayed on the right. As an example of the kinetic data, the joint moments of hip, knee and ankle joint are displayed and supported by a stick figure.

Does hamstrings co-contraction constrain knee internal rotation in patients with knee endoprosthesis during decline slope walking?

BACKGROUND: Medial and lateral hamstrings are known for their capacity to promote internal or external rotation of the knee. Apart from implant geometry, increased co-contraction to a larger share of either the medial or lateral hamstrings has the potential to contribute to the restricted knee internal rotation especially under consideration of cruciate ligament substituting compared to cruciate ligament retaining knee endoprosthesis designs. Hence, the purpose of the study was to evaluate, whether increased co-contraction of the hamstrings contribute to the impaired knee internal rotation in total and unicondylar knee arthroplasty patients during level and decline walking. METHODS: Knee joint angles were calculated using an inverse kinematics model in Anybody. Muscle activity was examined of the semitendinosus and biceps femoris. FINDINGS: Knee internal rotation was constraint in the operated compared to the non-operated limb only in the total knee arthroplasty group during decline slope walking. Co-contraction values revealed no statistically significant differences between the operated and non-operated limb during the limited knee internal rotation period of time (59-94% of stance). Biceps femoris activity was significantly reduced (69-71% of stance) in the operated limb in the total knee arthroplasty group during decline slope walking. INTERPRETATION: Contrary to the proposed mechanism, aspects other than co-contraction between semitendinosus and biceps femoris are involved in the impaired transverse plane knee motion. These include implant congruency and probably friction. Unexpectedly, the biceps femoris did not compensate the absence of the anterior cruciate ligament with increased muscular activity in the operated limb of the total knee arthroplasty group.

Agreement of measured and calculated muscle activity during highly dynamic movements modelled with a spherical knee joint.

The inclusion of muscle forces into the analysis of joint contact forces has improved their accuracy. But it has not been validated if such force and activity calculations are valid during highly dynamic multidirectional movements. The purpose of this study was to validate calculated muscle activation of a lower extremity model with a spherical knee joint for running, sprinting and 90°-cutting. Kinematics, kinetics and lower limb muscle activation of ten participants were investigated in a 3D motion capture setup including EMG. A lower extremity rigid body model was used to calculate the activation of these muscles with an inverse dynamics approach and a cubic cost function. Correlation coefficients were calculated to compare measured and calculated activation. The results showed good correlation of the modelled and calculated data with a few exceptions. The highest average correlations were found during walking (r = 0.81) and the lowest during cutting (r = 0.57). Tibialis anterior had the lowest average correlation (r = 0.33) over all movements while gastrocnemius medius had the highest correlation (r = 0.9). The implementation of a spherical knee joint increased the agreement between measured and modelled activation compared to studies using a hinge joint knee. Although some stabilizing muscles showed low correlations during dynamic movements, the investigated model calculates muscle activity sufficiently.

Assessment of the measurement accuracy of inertial sensors during different tasks of daily living.

The low cost and ease of use of inertial measurement units (IMUs) make them an attractive option for motion analysis tasks that cannot be easily measured in a laboratory. To date, only a limited amount of research has been conducted comparing commercial IMU systems to optoelectronic systems, the gold standard, for everyday tasks like stair climbing and inclined walking. In this paper, the 3D joint angles of the lower limbs are determined using both an IMU system and an optoelectronic system for twelve participants during stair ascent and descent, and inclined, declined and level walking. Three different datasets based on different hardware and anatomical models were collected for the same movement in an effort to determine the cause and quantify the errors involved with the analysis. Firstly, to calculate software errors, two different anatomical models were compared for one hardware system. Secondly, to calculate hardware errors, results were compared between two different measurement systems using the same anatomical model. Finally, the overall error between both systems with their native anatomical models was calculated. Statistical analysis was performed using statistical parametric mapping. When both systems were evaluated based on the same anatomical model, the number of trials with significant differences decreased markedly. Thus, the differences in joint angle measurement can mainly be attributed to the variability in the anatomical models used for calculations and not to the IMU hardware.

Understanding cutting maneuvers - The mechanical consequence of preparatory strategies and foot strike pattern.

OBJECTIVES: This study investigated the relation of different previously reported preparatory strategies and musculo-skeletal loading during fast preplanned 90° cutting maneuvers (CM). The aim was to increase the understanding of the connection between whole body orientation, preparatory actions and the solution strategy to fulfil the requirements of a CM. METHODS: Three consecutive steps of anticipated 90° CMs were investigated in a 3D movement analysis setup. Pelvis orientation clustered the subjects in two groups, with minor and major pre-orientation. To understand the impact of body orientation on the specific movement strategy, joint angles, moments and energy as well as spatio-temporal parameters of the movement were analysed. RESULTS: Early rotation of the body was initiated by a small step width during braking resulting in a more constant path velocity of the centre of mass and less demands on the hip- and knee surrounding muscles. Minor pre-orientation required increased work of the hip muscles to decelerate, reaccelerate and in particular to rotate the body. This resulted in an increase of contact time. While pre-orientation in combination with fore-foot striking led to a strategy where energy absorption and generation is mainly generated by the ankle plantar flexors, less pre-orientation and rear-foot striking resulted in a knee- and hip dominant strategy. CONCLUSION: Step width before transition strongly determined pre-orientation and overall body position. Both strategies fulfil the requirements of a CM but induce different demands regarding muscular capacities. Pelvis orientation and step width are easy-to-use assessment parameters in the practical field.

Compromised knee internal rotation in total knee arthroplasty patients during stair climbing.

Due to the significant role of rotational properties for normal knee function, this study aimed to investigate transverse plane kinematics and kinetics in total knee arthroplasty and unicondylar knee arthroplasty patients during activities of daily living compared to a healthy control group, including stair ascent and descent. The study participants consisted of a total knee arthroplasty group including posterior cruciate retaining and posterior stabilized designs as well as a unicondylar knee arthroplasty group and a healthy control group. Three-dimensional kinematics and kinetics were captured using a Vicon system and two Kistler force plates embedded in the floor and another two in a staircase. Inverse dynamics of the lower limbs was computed in Anybody™ Modeling System. Transverse plane joint angles and joint moments were analyzed utilizing the statistical non-parametric mapping approach, considering the entire curve shape for statistical analysis. The patients with total knee arthroplasty exhibited significantly reduced knee internal rotation of the operated knee compared to the control group and the patients' unimpaired limb, especially during the stair climbing tasks. Both unicondylar and total knee arthroplasty patients were found to have similar reduced internal rotation motion time series in stair descent. In conclusion, potential kinematic and kinetic benefits of unicondylar knee arthroplasty over total knee arthroplasty could not be proven in the current study. Aside from the usually mentioned reasons inducing constrained knee internal rotation in total knee arthroplasty patients, future studies should investigate to what extent co-contraction may contribute to this functional impairment in patients after knee arthroplasty surgery.

Identification and risk estimation of movement strategies during cutting maneuvers.

OBJECTIVES: Approximately 70% of anterior cruciate ligament (ACL) injuries occur in non-contact situations during cutting and landing maneuvers. Parameters such as footstrike patterns and trunk orientation were found to influence ACL relevant knee loading, however, the relationship between the whole body movement and injury risk is debated. This study identifies whole body movement strategies that increase injury risk, and provides training recommendations to reduce this risk or enable a save return to sports after injury. DESIGN: Experimental cross-sectional study design. METHODS: Three dimensional movement analysis was carried out to investigate 50 participants performing anticipated 90° cutting maneuvers. To identify and characterize movement strategies, footstrike pattern, knee valgus moment, knee internal rotation moment, angle of attack, shoulder and pelvis axis were analyzed using statistical parametric mapping. RESULTS: Three different movement strategies were identified. One strategy included rearfoot striking in combination with a relatively upright body position which generated higher knee joint loads than the second strategy, forefoot striking in combination with more backwards leaning and pre-rotation of the trunk towards the new movement direction. A third strategy combined forefoot striking with less preorientation which increased the ACL relevant knee joint load compared to the second strategy. CONCLUSIONS: The identified movement strategies clearly pre-determine the injury risk during non-contact situations with the third strategy as the most unfavorable one. Compared to the study of isolated parameters, the analysis of the whole body movement allowed for detailed separation of more risky from less risky cutting strategies. These results give practical recommendations for the prevention of ACL injury.

Non-Sagittal Knee Joint Kinematics and Kinetics during Gait on Level and Sloped Grounds with Unicompartmental and Total Knee Arthroplasty Patients.

After knee arthroplasty (KA) surgery, patients experience abnormal kinematics and kinetics during numerous activities of daily living. Biomechanical investigations have focused primarily on level walking, whereas walking on sloped surfaces, which is stated to affect knee kinematics and kinetics considerably, has been neglected to this day. This study aimed to analyze over-ground walking on level and sloped surfaces with a special focus on transverse and frontal plane knee kinematics and kinetics in patients with KA. A three-dimensional (3D) motion analysis was performed by means of optoelectronic stereophogrammetry 1.8 ± 0.4 years following total knee arthroplasty (TKA) and unicompartmental arthroplasty surgery (UKA). AnyBody™ Modeling System was used to conduct inverse dynamics. The TKA group negotiated the decline walking task with reduced peak knee internal rotation angles compared with a healthy control group (CG). First-peak knee adduction moments were diminished by 27% (TKA group) and 22% (UKA group) compared with the CG during decline walking. No significant differences were detected between the TKA and UKA groups, regardless of the locomotion task. Decline walking exposed apparently more abnormal knee frontal and transverse plane adjustments in KA patients than level walking compared with the CG. Hence, walking on sloped surfaces should be included in further motion analysis studies investigating KA patients in order to detect potential deficits that might be not obvious during level walking.

Musculoskeletal modelling under an evolutionary perspective: deciphering the role of single muscle regions in closely related insects.

Insects show a remarkable diversity of muscle configurations, yet the factors leading to this functional diversity are poorly understood. Here, we use musculoskeletal modelling to understand the spatio-temporal activity of an insect muscle in several dragonfly species and to reveal potential mechanical factors leading to a particular muscle configuration. Bite characteristics potentially show systematic signal, but absolute bite force is not correlated with size. Muscle configuration and inverse dynamics show that the wider relative area of muscle attachment and the higher activity of subapical muscle groups are responsible for this high bite force. This wider attachment area is, however, not an evolutionary trend within dragonflies. Our inverse dynamic data, furthermore, show that maximum bite forces most probably do not reflect maximal muscle force production capability in all studied species. The thin head capsule and the attachment areas of muscles most probably limit the maximum force output of the mandibular muscles.