Computer simulation on the cueing movements in cue sports: a validation study

Participants

The current study was approved by the Nanyang Technological University Institutional Review Board (Protocol Number: IRB-2019-06-037). All participants provided written consent to participate. The back spin shot was analyzed for 10 male right-handed cue sports players (mean (standard deviation); age 26.7 (8.5) years; height 171.8 (4.7) cm; body mass 66.8 (6.2) kg; playing experience 7.6 (9.1) years). Among the 10 participants, four participants were recruited from the Singapore National Cue Sports team, one was from the university team, and five were recreational players who had roughly 2-year playing experience. The 9-ball break shot was performed by two male cue sports players, who were Participant A (recreational player, age 23 years; height 169 cm; body mass 58 kg; playing experience 5 years) and Participant B (national team player, age 29 years; height 170 cm; body mass 70 kg; playing experience 15 years), both right-handed.

Simulation model

The generic unimanual upper extremity musculoskeletal model adapted in this present study was previously customized and validated (Seth et al., 2016; Seth et al., 2019). This model included the torso and right arm, which had six degrees of freedom at the scapula, shoulder, elbow, and wrist. In addition, muscles were included in this model, including trapezius (scapula superior, scapula middle, scapula inferior, clavicle), serratus anterior (superior, middle, inferior), rhomboideus (superior, inferior), levator scapulae, coracobrachialis, deltoideus (anterior, middle, posterior), latissimus dorsi (superior, middle, inferior), pectoralis major (clavicle, thorax middle, thorax inferior), teres major, infraspinatus (superior, inferior), pectoralis minor, teres minor, subscapularis (superior, middle, inferior), supraspinatus (anterior, posterior), triceps (long), and biceps (long, brevis). This model has been applied in several studies on the upper limb movements when executing daily living activities (Seth et al., 2019; Gorkovenko et al., 2020; Karimi & Khademi, 2021; Fischer et al., 2021), and is expected to assist assessing functional roles of the muscles in the upper extremity (Seth et al., 2019).

Model customization

The generic model was updated to fit the cueing movements in cue sports. Specifically, the flexion/extension range of motion (ROM) of the elbow joint was set to 155° since full elbow flexion places the proximal forearm against the distal biceps and returns the joint to the outstretched anatomic position with the normal flexion ranging roughly from 150 to 160° (Lawry et al., 2010). This is also in line with a previous study on snooker which reported elbow flexion/extension ROM of approximately 145° while performing various cueing movements (Kong et al., 2021). Hence, changing from the original 130° to 150° would be more appropriate for the cueing movements. The wrist motions (i.e., flexion/extension and abduction/adduction) were not taken into consideration in the model for simplicity since the wrist joint ROM (Kong et al., 2021) and angular velocities (Haar, Van Assel & Faisal, 2020) were much smaller than those of the elbow. The mass of a cue stick, which is approximately 550 g, cannot be neglected in the model as it is similar to the mass of one hand (e.g., 70 kg × 0.66% = 462 g) based on the body segment mass reported by Cheng et al. (2000). For simplicity, hand movements were not included in the simulations. Lastly, the pronation/supination motion of the forearm was unlocked and customized for the cueing movements. All simulations of the cueing movements were performed using OpenSim (version 4.2, Stanford University, Stanford, CA, USA) (Delp et al., 2007) on a laptop computer with an Intel i7-10750H, 2.6 GHz processor, and 16 GB of RAM.

Experimental data (marker trajectories during the cueing movements of the back spin shots) were obtained from the experiment sessions. The back spin shot was executed by 10 male cue sports players, and three valid trials were used for analysis for each participant. The testing protocol was adopted from a previous study (Pan et al., 2022), whereby the participants were instructed to pot a ball into the middle pocket (Fig. 1A). The cue tip should impact the low part of the cue ball to generate back spin. The participants’ upper extremity kinematic data were collected with an eight-camera motion capture system (200 Hz, Vicon MX, Oxford Metrics Ltd., Oxford, UK). To facilitate data collection, 24 markers were fixed on the head, and trunk, upper extremity for each participant, including four markers on the head, four on the trunk, four on the pelvis, seven on the right arm, and five on the left arm. In one cueing movement stroke, the cue stick is first drawn back and then driven forward to hit the cue ball. As such, the stroke can be divided into several sub-phases according to the displacements of the cue stick. All kinematic results (joint angles) were analyzed for the period from the start of forward swing (the cue stick starts to move forward after being drawn back) to the end of the follow through (when the cue stick reaches the farthest point after hitting the cue ball) (Pan et al., 2022) using Visual3D (v2021.09.1, C-Motion, Germantown, MD, USA). During this period, the cue stick is driven forward rapidly. The raw marker trajectories were low-pass filtered with a fourth-order Butterworth filter at the cut-off frequency of 10 Hz. Joint angles for the shoulder, elbow, and wrist of the cue-wielding (right) arm were calculated in accordance with the recommendations of International Society of Biomechanics (ISB) (Wu et al., 2005; Gates et al., 2016). These joint angle data obtained experimentally would be used as reference to validate the subsequent simulation outputs.

The raw trajectories of 11 out of the 24 markers on the upper extremity were exported as the inputs for the simulation model. These 11 markers included RSHO (right acromion process), STRN (suprasternal notch), XIPH (xiphoid process), C7 (7th cervical vertebra), T8 (8th thoracic vertebra), RELM (medial epicondyle of the right elbow), RELL (lateral epicondyle of the right elbow), RWRU (most caudal-medial point on ulnar styloid of the right wrist), RWRR (most caudal-lateral point on radial styloid of the right wrist), R5MC (5th metacarpal head of the right hand), and R3MC (3rd metacarpal head of the right hand). These marker trajectories were low-pass filtered with a fourth-order Butterworth filter at the cut-off frequency of 10 Hz, and then applied to scale the generic model to determine the marker positions on the model (Fig. 2A). Several scale factors were used for scaling the generic model, including ‘Humerus’ (from RSHO to RELL, from RSHO to RELM; for the scapula and humerus), ‘Forearm’ (from RELM to RWRU, from RELL to RWRR; for ulna and radius), and ‘Hand’ (from R3MC to RWRR, from R5MC to RWRU; for hand). The segment masses for the OpenSim model were set according to the results reported by Cheng et al. (2000) who applied magnetic resonance imaging (MRI) to provide accurate parameters of Chinese males for simulation modeling. Their results were largely similar to those in the literature (Dempster, 1955; Clauser, McConville & Young, 1969) with slight differences in the upper arm, thigh, and foot compared with the Caucasian participants (Cheng et al., 2000). Since this present study also recruited male Chinese participants, the results provided by Cheng et al. (2000) could be appropriate for scaling the mass of body segment for the participants.

A participant-specific model, fitting each participant’s anthropometric dimensions and muscular insertion points, was saved (Fig. 2B). After that, three valid back spin shots were used for simulation, whereby the marker trajectories of each back spin shot were used to drive the model to perform the cueing movements for Inverse Kinematics (Fig. 2C) (Seth et al., 2019). In this step, upper extremity joint angles were generated based on the simulation model. The marker trajectories of the simulation model and actual trajectories obtained during experiments were first visually checked. Subsequently, the model-generated joint angles were compared against those derived from the experiment, using statistical procedures (details are described under the ‘Model validation’ section below) (Mei et al., 2019).

For the break shot, three valid trials were used for simulation for each of Participants A and B. Besides the marker trajectories during the cueing movements, electromyography (EMG) data were utilized as the simulation model inputs. In each trial, the participants were required to break the racked 9 balls with best effort, in order to make the balls well separated on the pool table (Figs. 1B–1D). The upper extremity kinematic data generated by the simulation model were obtained using the same methods stipulated above for the back spin shot. For Participants A and B, EMG data were collected for five muscles located in the upper extremity of the right side, including trapezius descendens (upper), deltoideus (anterior), deltoideus (posterior), triceps brachii (long head), and biceps brachii (long head). The EMG sensor placement in the present study followed the recommendations of the SENIAM project (Hermens et al., 1999). After the experiment, the participants were required to conduct maximal voluntary contraction (MVC) trials for the specific muscles, following the recommendations of the SENIAM project (Hermens et al., 1999), in order to normalize the EMG results (Ertan et al., 2003; Oliver, Plummer & Gascon, 2016; Yang & Côté, 2021). The MVC trials were intentionally conducted after the experiment to avoid possible fatigue effects on the shot performance. The raw EMG data for both MVC and break shot trials were processed with a bandpass filter of 20–450 Hz (Balshaw et al., 2017). Then root mean square (RMS) amplitude analysis for EMG signals was conducted using Visual3D for the same movement period as the kinematic data. At the same time, peak MVC-RMS of each specific muscle was identified, and the break shot EMG-RMS was normalized to peak MVC-RMS.

Model scaling and Inverse Kinematics were performed following the same procedures as those of the back spin shot. After that, Computed Muscle Control (CMC) was executed to obtain EMG-driven simulations with both kinematic and EMG inputs (Thelen, Anderson & Delp, 2003; Seth et al., 2019). For this simulation, kinematic inputs were joint angles generated in the Inverse Kinematics step and the EMG inputs were the processed experimental data. In this step, muscle excitations (e.g., muscle activation level, muscle force, muscle fiber length) were computed as model outputs. For the EMG inputs, 0% was considered not activated for the particular muscle, and 100% as fully activated (Mei et al., 2019; Lu et al., 2020). A model-estimated muscle activation was performed accordingly (Lu et al., 2020). The muscle activation timing ranged from 0 to 100% of the cueing movement in a break shot. Muscle forces were normalized to the individual body weight (BW) (Demers, Pal & Delp, 2014; Hall et al., 2019), and expressed as BW%.

Model validation

To validate the model for the back spin shot, two types of comparisons were made between the upper extremity joint angles calculated using visual3D (experimental data) and those generated using the OpenSim model. Firstly, statistical parametric mapping (SPM1D) (Nichols & Holmes, 2002; Pataky, 2012) was applied to compare the entire waveforms of the angle-time waveforms of shoulder elevation, elbow flexion/extension, and elbow pronation/supination between the two sets of data using MATLAB (version 2021b, MathWorks, Natick, MA, USA) (Mei et al., 2019), whereby all experimental and OpenSim data were normalized to 101 data points using a liner interpolation method. Secondly, to examine the discrete variables which have been commonly used in biomechanics studies, joint ROM were compared between the two sets of data. Specifically, shoulder elevation, elbow flexion/extension, and elbow pronation/supination obtained using OpenSim and experiments were compared with paired-samples t test using the JASP statistical software (version 0.17.1; JASP Team, 2023), whereby the data normal distribution was confirmed by the Shapiro–Wilk test. All statistical significance was set at the 0.05 level.

Since only two participants were selected for the simulation of the break shot, no inferential statistical analysis was conducted. Instead, the muscle activation data (EMG) obtained from the experiment and simulation model were plotted to facilitate model validation.

Back spin shot

To visually check the quality of the simulation, marker trajectories during the cueing movements were compared between the experimental data (blue markers) and model-generated data (pink markers) (Fig. 3). To facilitate this comparison, after Inverse Kinematics, the marker trajectories of the cueing movement were associated with the OpenSim model to show both experimental and model-generated markers. As shown in Fig. 3, the OpenSim markers and experiment markers corresponded well on the cue-wielding (right) arm, while visible discrepancies were found for the trunk markers.

In terms of the kinematic comparisons, the results of SPM1D showed that the entire angle-time waveforms of the shoulder elevation angles significantly differed between the OpenSim-generated and experimental data (Fig. 4D, from 0 to 100%, p < 0.001), although the two waveforms showed similar tendency (Fig. 4A). No significant difference was found throughout the entire waveforms of the elbow flexion/extension angles (Fig. 4E, p > 0.05) between the two sets of data. For the elbow pronation/supination angles, there was a significant difference in the first half of the cueing movement (Fig. 4F, from 0 to 50%, p = 0.005).

The results of t test showed no significant difference in the elbow flexion/extension ROM between the OpenSim-generated and experimental data (Table 1, p = 0.827). For the shoulder elevation ROM, the OpenSim-generated data were significantly greater than the experimental results (p = 0.042, medium effect size). The elbow pronation/supination ROM was significantly smaller in the OpenSim-generated data than the experimental results (p = 0.004, large effect size).

Break shot

The OpenSim-generated muscle activations were visually compared against the experimental EMG data (Fig. 5) for Participants A and B. The model outputs did not show a good agreement in the shoulder muscle activations between the two sets of data, in particular for the trapezius of Participant B and deltoideus (anterior) of Participant A. For the deltoideus (posterior), triceps brachii, and biceps brachii, the time-varying waveforms corresponded well between the two sets of data. Muscle forces (Fig. 6) were extracted for the deltoideus (anterior), deltoideus (posterior), triceps brachii (long head), biceps brachii (long head), and biceps brachii (short head). The force of the trapezius was not included due to the relatively poor simulations of this specific muscle found in the previous steps.

Back spin shot (model validation)

This present study selected three joint angles for analysis, including shoulder elevation, elbow flexion/extension, and elbow pronation/supination angles, all of which are greatly engaged in the cueing movements. The results showed a significant difference in the shoulder elevation angles (Fig. 4, from 0 to 100%, p < 0.001) between the OpenSim-generated and experimental data although these two waveforms showed a similar tendency. Several factors likely contributed to the discrepancy in the shoulder elevation angles between the two sets of data. Firstly, in the work by Seth et al. (2019), a few sensors were placed on the thorax, scapula, and humerus to obtain the kinematics of the upper extremity joints, in particular for the shoulder. However, in the current study on the cueing movements, no markers or sensors were fixed on the scapula, while markers were only put on the acromion (RSHO) and spine (C7, T8). The scapula motions could deviate from the experimental results and led to incorrect shoulder elevation angles in the simulations. In addition, the model scaling in OpenSim may not be anatomically accurate by simply scaling the bone length according to the marker data while neglecting the possibly varied bone shapes. A statistical shape modeling could be plausible to address this issue (Zhang et al., 2016). Hence, future studies should include more detailed shoulder data (e.g., scapula motion) and better scaling methods to improve the simulations, aiming to reduce the discrepancy between experimental and OpenSim-generated biomechanics results.

For the elbow, the OpenSim-generated joint angles corresponded well with the experimental data. For the elbow flexion/extension angles, no significant difference was found in the entire angle-time waveforms between the two sets of data. However, for the elbow pronation/supination angles, a significant difference was observed for the entire waveforms from 0 to 50%. In addition, greater elbow pronation/supination ROM was found in the OpenSim-generated results than the experimental data according to the results of the t test (Table 1, p = 0.042). The elbow pronation/supination angles represent the rotations of the forearm during the cueing movements. While the makers fixed on the anatomical landmarks (e.g., RSHO, RELM, RELL, RWRU, RWRR) were sufficient for the joint angle calculation on Visual3D, the lack of tracking markers on the forearm during the cueing movements may lead to the relatively poor kinematic data generated using the OpenSim simulation models. Future studies should consider adding a few tracking markers (e.g., marker cluster) on the forearm to obtain better kinematic data for simulating the elbow pronation/supination motions.

Collectively, the generic unimanual upper extremity musculoskeletal model (Seth et al., 2019) together with the experimental kinematic data could run good simulations of the elbow motion but not yet shoulder motion. Hence, it is feasible to customize the generic unimanual upper extremity musculoskeletal model (Seth et al., 2019) to cater for biomechanical investigations of the upper extremity movements in cue sports. Further studies are needed to refine the model with more detailed data (e.g., scapula motion, forearm motion) as model inputs to improve the simulation of shoulder motion.

Break shot (model validation and muscle force calculation)

The CMC step utilizes the marker trajectories as well as the EMG data as the model inputs, and estimates the muscle force variables that are difficult to measure directly from experimental methods alone (Seth et al., 2019). After executing the CMC step, muscle activations were extracted for the upper extremity muscles by the simulation model to validate against the experimental EMG data. The results of the break shot simulation showed that OpenSim-generated shoulder muscle activations deviated substantially from the experimental data in the two participants (Fig. 5). The mismatch could also be attributed to the relatively poor simulation for the shoulder joint owing to the lack of sufficient scapula motions. For triceps brachii and biceps brachii, the time-varying waveforms were similar between the two sets of data. This suggests good simulations for the upper arm muscles.

After validating the simulation model, muscle forces were calculated for the two participants. As the cueing movement was analyzed for the period from the start of forward swing to the end of follow through, the early phase in the entire waveform should be the forward swing phase, and the latter should be the follow through phase. For both participants, according to the preliminary results, the biceps brachaii did not contribute much to the forward swing (early phase) while the deltoideus forces were great during the forward swing phase (Fig. 6). Great triceps brachii force may contribute to the shoulder movement and stabilize the shoulder joint during forward swing. The current results indicated that the cueing movement may primarily rely on the shoulder muscles instead of the biceps brachii. Players are hence recommended to focus on training the triceps brachii and shoulder muscles, which could generate a high cue tip speed. The deltoideus anterior force of Participant A (>100% BW, Fig. 6) was much greater than that of Participant B. This great discrepancy could be due to the different muscle activation patterns between the two participants. More simulations on different participants are needed to evaluate the muscle activations across individuals to confirm the current preliminary results. Additionally, since some players may have overuse injuries in their neck or shoulder, it is of importance to investigate the impacts on these parts and/or inappropriate muscle activations. Using experimental methods alone, it is difficult to directly measure the upper extremity kinetics and muscle forces during cueing movements. Using simulation models can help obtain these important kinetic variables. Therefore, simulation models are promising tools to help better understand the biomechanics and injury risks associated with cue sports.