Validity of recurrent neural networks to predict pedal forces and lower limb kinetics in cycling

Validity of recurrent neural networks to predict pedal forces and lower 1 limb kinetics in cycling 2 3 Juan Cordero-Sánchez1, Rodrigo Bini2, Gil Serrancolí3* 4 5 1Department of Physiotherapy, Faculty of Medicine and Health Science, University of 6 Alcalá, Alcalá de Henares, Spain. https://orcid.org/0000-0002-5890-2635 7 2La Trobe Rural Health School, La Trobe University, Bendigo, Australia. 8 https://orcid.org/0000-0002-2138-7350 9 3Simulation and Movement Analysis Lab (SIMMA Lab), Department of Mechanical 10 Engineering, Universitat Politècnica de Catalunya, Barcelona, Catalonia. 11 https://orcid.org/0000-0001-5034-2445 12 13 Word count: 3437 14 15 *Corresponding author: 16 Gil Serrancolí 17 Department of Mechanical Engineering, Universitat Politècnica de Catalunya 18 Av. Eduard Maristany 16, A8.40 19 08019 Barcelona 20 gil.serranc[email protected] 21 22 Abstract 23 Dynamic variables contribute to understand the mechanics of pedalling and can assist with injury 24 prevention. Measuring pedal forces and joint moments and powers has a high cost, which can 25 be mitigated by using trained artificial neural networks (ANN) to predict forces from kinematics. 26 Thus, this study aimed at training and validating recurrent ANN to predict 3D pedal forces, lower 27 limb joint moments and powers from lower limb kinematics. Ergometer pedalling data from 28 seventeen cyclists recorded in a single laboratory session were used to train the ANN, where 29 various ergometer power outputs and cadences were combined. A different dataset with ten 30 cyclists was utilized to test the ANN´s performance. Statistical Parametric Mapping (SPM) was 31 performed to explore significant correlations between measured and predicted kinetic variables 32 throughout the pedal cycle. Mean correlation values ranged from 0.79 to 0.96 and all variables 33 exhibited significant positive correlations at their peak absolute values (p<0.05), except for the 34 anteroposterior (p = 0.28) and mediolateral (p = 0.51) pedal forces and the knee flexion power 35 (p = 0.33). The maximum prediction errors of the ANN in the sagittal plane were 12.1% for the 36 pedal forces, 17.2% for the net joint moments and 9.4% for the joint powers, while for non37 sagittal plane were 13.0%, 28.9% and 24.0%, respectively. Thus, the ANN produces kinetic data 38 in cycling within the errors expected from the variability between assessment days. 39 Keywords: Machine learning, dynamics, pedalling, joint moments and powers 40 41 Introduction 42 The analysis of biomechanical variables during cycling can help identify abnormalities which, if 43 corrected in time, can prevent injuries as it is the case where cyclists with knee pain had much 44 larger knee moments (Bini et al., 2011; Callaghan, 2005; Priego Quesada et al., 2019). The effort 45 exerted by the cyclist at each joint can be quantified through an inverse dynamics analysis. The 46 resulting data on joint moments and joint power at individual joints can help prevent overuse 47 injuries and reduce the risk of joint pain (Murray, 2023). Lower limb joint moments and powers 48 are some of the most studied variables for analysing cycling technique (Bini and Hume, 2023; 49 Yamaguchi et al., 2023). Pedal forces are essential for optimizing training and rehabilitation 50 programs as they are correlated with lower limb muscle activity and joint reaction forces 51 (Ahmadi et al., 2024). However, accurate measurements of pedal forces are particularly 52 challenging, leading some studies to use custom-made instruments for research purposes (Bini 53 et al., 2014). Besides, although the required variables to perform inverse dynamics such as joint 54 angles and pedal forces can be collected both inside and outside laboratories using wearable 55 technology such as inertial sensors and instrumented pedals (Álvarez and Vinyolas, 1996; Bini 56 and Hume, 2013; Chen et al., 2005; Evans et al., 2022; Maruyama et al., 2019; Morbey et al., 57 2024; Wooles et al., 2005), their cost and availability pose limitations for both sports and 58 industrial applications (McDevitt et al., 2022). In addition, performing inverse dynamics analyses 59 using physics-based biomechanical models involves the personalization of skeletal models and 60 the computation of the equations of motion. Therefore, besides the high cost of pedal force 61 sensors, these processes are not quickly applicable in sports practice and are time-consuming 62 (Cecchini et al., 2014; Mayerhofer et al., 2024). 63 Artificial neural networks (ANN) offer an alternative method to obtain dynamics data. An ANN 64 can be trained to predict external forces, joint moments and powers using only kinematics data, 65 which are more accessible for sports scientists and coaches (Stetter et al., 2020; Seung et al., 66 2013; Komaris et al., 2019; Mundt et al., 2020a; Altai et al., 2023). ANNs are a subset of machine 67 learning techniques inspired by the networks of biological neurons in our brains, consisting of 68 trainable functions that estimate output variables from input variables without requiring specific 69 knowledge of their interactions. The use of ANNs requires identifying the input variables that 70 most significantly contribute to the outputs (Çolak, 2021) and providing a sufficient amount of 71 quality data (Klein and Rossin, 1999). One of the advantages of applying ANNs to cycling is that 72 they may not require the use of musculoskeletal models and their personalization (Mayerhofer 73 et al., 2024), or the use of sophisticated experimental techniques to record dynamics data (i.e. 74 instrumented pedals or cranks). This also facilitates assessment outside laboratory settings. 75 Despite these advantages, few studies have been published on the application of ANNs to cycling 76 biomechanics. Most studies predicting dynamics-related data were focused on single time77 independent parameters (i.e. zero-dimensional analysis), like the index of effectiveness (IE) or 78 positive impulse proportion (PIP) (Torres et al., 2024). The prediction of temporal patterns of 79 joint moments or joint contact forces, as performed in musculoskeletal-based studies 80 (Thompson et al., 2020) without the need to perform complex measurements, would facilitate 81 the analyses. Besides, as cycling is a widely practiced sport that enhances performance (Atkinson 82 et al., 2015) and health (Sommar et al., 2022), providing daily bicycle users with access to this 83 knowledge could make cycling safer and encourage its practise. 84 Thus, this study aimed to train and validate recurrent ANN to predict three-dimensional (3D) 85 pedal forces, lower limb joint moments and powers from lower limb kinematics. We 86 hypothesised that the trained model will accurately predict both pedal forces and joint kinetics. 87 88 Methods 89 Datasets 90 The dataset used to train the ANN came from the study of Bini and Hume (2023). It contains data 91 from seventeen cyclists aged 24 ± 6 years-old, with a body mass of 75 ± 8 kg and a stature of 181 92 ± 6 cm, pedalling in a cycle ergometer for one minute at nine randomised combinations of power 93 outputs (1.5, 2.5 and 3.5 W/kg of body mass) and cadences (60, 80 and 100 rpm). Data collection 94 from these participants was carried out with the approval of the ethics committee from La Trobe 95 University (HEC17-085). 96 In order to assess the validity of the trained model, a separate dataset of ten recreational cyclists 97 (four females and six males: 24.4 ± 5.9 years, 175 ±8 cm, 72.5 ± 12.8 kg) pedalling on a cycle 98 ergometer at 2.5 W/kg and 90 rpm was used in this study, which was approved by the University 99 Ethics Committee (HEC19-001). Data from these participants was previously utilised in a 100 publication (Bini, 2021). This sample size was calculated based on the inter-session variability 101 reported in a prior study for pedal force outputs (i.e. left pedal index of effectiveness (Bini and 102 Hume, 2020)). The statistical model involved a correlation aiming for an effect size of 0.78, based 103 on the inter-sessions ICC from Bini and Hume (2020). The resulting model indicated that eight 104 cyclists would be required, and we opted to expand to ten participants to avoid any missing data 105 points in the validation component. Sample size calculation was conducted using GPower 106 statistical package (Faul et al., 2007). 107 108 Data analysis 109 Joint moments used to train the ANNs were obtained using a musculoskeletal model (Lai et al. 110 2017) scaled for each participant from static poses. This model was composed of 22 body 111 segments and 37 degrees of freedom (DoF) including the main lower body DoF in cycling. This 112 model is suitable for movements involving high hip and knee flexion as is the case of pedalling. 113 Kinematics (i.e. joint coordinates and their derivatives) and external forces (i.e. pedal forces) 114 were used to perform inverse kinematics and inverse dynamics in OpenSim (Delp et al., 2007). 115 Pedal forces were filtered using a zero-lag four-order lowpass Butterworth digital filter at a cutoff 116 frequency of 10 Hz. Motion data were lowpass filtered at 10 Hz using the OpenSim Inverse 117 Dynamics tool. Joint mechanical powers were computed for the right lower limb at each degree 118 of freedom as the scalar product of the joint moment by its angular velocity. The degrees of 119 freedom analysed were hip flexion-extension, adduction-abduction, internal-external rotation, 120 knee flexion-extension and ankle dorsi-plantarflexion. Data were time normalized to 101 data 121 points for each pedal cycle. 122 123 Neural networks 124 Recurrent neural networks (RNN) were trained to predict pedal forces and net joint moments. 125 The implemented RNN were a sequential model composed of one layer with 64 long short-term 126 memory (LSTM) cells followed by a dense layer with 8 neurons. The rectified linear unit (ReLU) 127 activation function was used due to its fast computation and because it does not saturate for 128 positive values. Finally, a one-neuron dense layer with a linear activation function was added to 129 produce a single output per time step. The adaptive moment estimation (Adam) algorithm 130 (Kingma and Ba, 2015) was used as optimizer (with a learning rate of 1x10-4) due to its good 131 convergence quality and speed, while early stopping was implemented to regularize the learning 132 process. The RNN’s structure and the learning rate were selected according to the GridSearch 133 algorithm using cross-validation to evaluate all the possible combinations among the number of 134 layers (1, 2 or 3) and LSTM cells (32, 64 or 128) and the learning rate (1x10-2, 1x10-3 or 1x10-4). 135 The inputs of the RNN were the hip, knee and ankle flexion-extension and hip rotation joint 136 angles. The hip abduction joint angle was removed from the inputs, as including it increased the 137 ANN prediction errors by approximately 20% overall. Additionally, power output, cadence and 138 participants’ body mass were included in the inputs, as these factors affect pedal forces, joint 139 moments and powers (Bini et al., 2010b; Ettema et al., 2009; Mornieux et al., 2007). Each 140 variable was normalized by their maximum absolute value to ensure that all variables have a 141 similar magnitude, thereby facilitating the learning process of the RNN. Data analysis and RNN 142 training were carried out in Python (v3.11.5) with TensorFlow and Keras using an Intel i9-9880H 143 CPU computer with 32GB RAM and a Nvidia GeForce RTX 2080 with Max-Q Desing GPU. 144 145 Statistical analysis 146 Pearson’s correlation and the root mean squared error (RMSE) were calculated to evaluate the 147 agreement between the measured (i.e. data from ten recreational cyclists) and the predicted 148 pedal force and joint moment and power variables. We computed the mean and standard 149 deviation of the correlation and RMSE between curves across all participants. Additionally, error 150 percentages were computed as the mean RMSE normalized to the value range of the test dataset 151 for each variable (Equation 1). 152 𝑒𝑟𝑟𝑜𝑟 (%)= 𝑚𝑒𝑎𝑛 𝑅𝑀𝑆𝐸 𝑟𝑎𝑛𝑔𝑒 𝑥 100 ( 1) 153 Correlation was ranked as poor (0–0.5), moderate (0.5–0.75), good (0.75–0.90) and excellent 154 (> 0.9) (Dancey and Reidy, 2004). A regression analysis using Statistical Parametric Mapping 155 (SPM) (Pataky et al., 2015) was performed in Python to compare the measured and predicted 156 time-dependent variables. A regression test (using spm1d.stats.regress) was performed to assess 157 whether the correlation coefficients were significantly different from zero (p-value <.05) at each 158 instant of the pedal cycle. 159 160 Results 161 Good to excellent agreement was found for pedal forces, net joint moments and joint powers. 162 Excellent agreement was observed for ankle flexion power (Table 1). Mean RMSE ranged 163 between 9.90-13.0 % for pedal forces, 12.10-28.90 % for net joint moments and 5.50-24.0 %, for 164 joint powers (Table 1). 165 166 167 Table 1. Mean and standard deviation of the correlations and RMSE between measured and predicted variables. The 168 error percentage is the RMSE normalized to the range of the underlying data for each variable. 169 Correlation RMSE Anteroposterior Pedal Force 0.77 ± 0.12 25.5 ± 14.8 N (9.9 ± 5.7 %) Vertical Pedal Force 0.89 ± 0.13 58.9 ± 21.8 N (12.1± 4.5 %) Mediolateral Pedal Force 0.82 ± 0.14 9.1 ± 3.1 N (13.0 ± 4.3 %) Hip Flexion Moment 0.79 ± 0.12 29.7 ± 10.0 Nm (17.2 ± 5.8 %) Hip Abduction Moment 0.77 ± 0.11 31.4 ± 26.4 Nm (28.9 ± 24.5 %) Hip Rotation Moment 0.79 ± 0.12 15.9 ± 14.1 Nm (28.4 ± 25.5 %) Knee Flexion Moment 0.88 ± 0.11 13.3 ± 4.7 Nm (15.4 ± 5.4 %) Ankle Flexion Moment 0.88 ± 0.08 7.9 ± 2.7 Nm (12.1 ± 4.1 %) Hip Flexion Power 0.89 ± 0.1 87.4 ± 37.9 W (9.4 ± 4.0 %) Hip Abduction Power 0.75 ± 0.14 18.5 ± 14.1 W (24.0 ± 18.5 %) Hip Rotation Power 0.80 ± 0.17 10.8 ± 7.44 W (13.9 ± 9.6 %) Knee Flexion Power 0.86 ± 0.11 51.9 ± 22.4 W (9.1 ± 3.9 %) Ankle Flexion Power 0.96 ± 0.06 8.7 ± 4.1 W (5.5 ± 2.7 %) 170 171 Figure 1 and Figure 2 show the mean measured and predicted pedal forces and net joint 172 moments and joint powers, respectively. There was good agreement between them in terms of 173 correlation and RMSE. According to the regression SPM results (Figure 1), the percentage of the 174 cycle with significant correlations varied for each variable. The anteroposterior pedal force 175 showed significant positive correlation around 30% of the pedal cycle with a mean error below 176 5.0 N (Figure A1, Appendix A). However there was significant negative correlation between the 177 40% and 95% with a maximum mean error of 15.0 N. From the 10 to 65% of the pedal cycle there 178 were significant positive correlation for the vertical pedal forces with a maximum mean error of 179 50.0 N. The mediolateral pedal force showed, from the beginning to the 22% and from the 75% 180 to the end, significant positive correlations with mean errors below 3.0 N. Between 25% and 52% 181 of the pedal cycle the significant correlation was negative showing a mean error smaller than 6.0 182 N. Hip flexion and abduction moments as well as ankle flexion moment displayed significant 183 positive correlation for the most of pedalling cycle. Their maximum mean errors were 30.0 Nm, 184 15.0 Nm and 8.0 Nm, respectively. On the contrary, hip rotation moment and knee flexion 185 moment only reported significant positive correlations between 21-32% and 25-53% of the pedal 186 cycle, respectively. However, their mean errors were below 10.0 Nm. In a similar way, except for 187 the knee flexion power, there were significant positive correlations for most of the pedalling 188 cycle (Figure 2) with maximum mean errors of 100.0 W, 25.0 W, 14.0 W and 13.0 W for the hip 189 flexion, abduction and rotation powers and ankle flexion power, respectively. Only hip flexion 190 (about 60%) and rotation (about 15% and 95%) powers reported significant negative differences 191 with maximum mean errors of 50.0 W and 14.0 W, respectively. Knee flexion power showed 192 significant positive correlation between 35% and 55 % with mean error smaller than 20.0 W. On 193 the other hand, significant negative correlations were found from 0% to 15% and from 58% to 194 the end of the pedal cycle reporting a maximum mean error of 45.0 W. 195 In addition, all variables exhibited significant positive correlations at their peak absolute values 196 (i.e. within the power phase), except for the anteroposterior and mediolateral pedal forces and 197 the knee flexion power. Depending on the phase of the pedal cycle, the RNN predictions either 198 overestimated or underestimated the measured data (Figure A1, Appendix A). At the maximum 199 peaks of the curves, the predictions tended to underestimate. The hip, knee and ankle flexion 200 moments were underestimated at the start and end of the pedal cycle, while from approximately 201 between 20% to 60% of the cycle, they were overestimated. The opposite pattern was observed 202 for the vertical pedal force. The rest of the variables did not show such as clear pattern. 203 204 205 Figure 1. Mean (thick lines) and standard deviation (shadowed areas) for the measured (blue) and predicted (red) 206 pedal forces and net joint moments. Percentage of cycle stand for the position of the pedal in the pedal cycle. The 207 instants of 0 and 100% correspond to the top position and the 50 % correspond to the bottom one. The SPM plots 208 display the t statistic outputs (solid lines) whilst the dashed red lines show the critical t value for significant 209 correlations. 210 211 212 213 214 number of data on the error rates of artificial neural networks. Int. J. Energy Res. 45, 478– 391 500. doi: https://doi.org/10.1002/er.5680 392 Costes, A., Turpin, N.A., Villeger, D., Moretto, P., Watier, B. 2018. Spontaneous change from 393 seated to standing cycling position with increasing power is associated with a 394 minimization of cost functions. J. Sports Sci. 36, 907–913. doi: 395 https://doi.org/10.1080/02640414.2017.1346272 396 Dancey, C., Reidy J. 2004. Statistics without maths for psychology with psychology dictionary. 397 Pearson Education, Limited, London. 398 Delp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, 399 D.G. 2007. OpenSim: Open-source software to create and analyze dynamic simulations of 400 movement. IEEE Trans. Biomed. Eng. 54, 1940–1950. doi: 401 https://doi.org/10.1109/TBME.2007.901024 402 Dunst, A.K., Grüneberger, R. 2021. A novel approach of modelling and predicting track cycling 403 sprint performance. Appl. Sci. 11. doi: https://doi.org/10.3390/app112412098 404 Ebbecke, J., Viellehner, J., Potthast, W., 2023. Improving cycling force sensor accuracy using 405 multilayer perceptrons. In Program & Abstract Book: 29th Congress of the International 406 Society of Biomechanics; July 30 - August 3, 2023, Fukuoka (pp. 354). 407 Ettema, G., Lorås, H., Leirdal, S. 2009. The effects of cycling cadence on the phases of joint 408 power, crank power, force and force effectiveness. J. Electromyogr. Kinesiol. Off. J. Int. 409 Soc. Electrophysiol. Kinesiol. 19, e94-101. doi: 410 https://doi.org/10.1016/j.jelekin.2007.11.009 411 Evans, S.A., Ballhause, K., James, D.A., Rowlands, D., Lee, J.B. 2022. The development and 412 validation of an inertial sensor for measuring cycling kinematics: a preliminary study. J. 413 Sci. Cycl. 10(3), 34-44. doi: https://doi.org/10.28985/1221.jsc.08 414 Fábio J. Lanferdini, Rodrigo R. Bini, Pedro Figueiredo, Fernando Diefenthaeler, Carlos B. Mota, 415 Anton Arndt, M.A.V. 2016. Differences in pedalling technique in cycling: a cluster analysis. 416 Int. J. Sports Physiol Perform. 11(7):959-964. doi: 10.1123/ijspp.2015-0142 417 Farahani, S.D., Bertucci, W., Andersen, M.S., Zee, M. de, Rasmussen, J. 2015. Prediction of 418 crank torque and pedal angle profiles during pedaling movements by biomechanical 419 optimization. Struct. Multidiscip. Optim. 51, 251–266. doi: 420 https://doi.org/10.1007/s00158-014-1135-6 421 Faul F., Erdfelder E., Lang A.G. 2007. G*Power 3: A flexible statistical power analysis program 422 for the social, behavioral, and biomedical sciences. Behav. Res. Methods 39(2):175-191. 423 doi: https://doi.org/10.3758/BF03193146 424 Geron, A., 2019. End-to-End Machine Learning Project, Hands-on Machine Learning with Scikit425 Learn, Keras & TensorFlow. Second Edi. O´Reilly Media Inc. 426 Gonzalez, H., Hull, M.L., 1989. Mulitvariate optimization of cycling biomechanics. J. Biomech. 427 22, 1151–1161. doi: doi: 10.1016/0021-9290(89)90217-0 428 Hull, M.L., Jorge M. 1985. A Method for Biomechaniccal Analysis of Bicycle Pedalling. J. 429 Biomech. 18, 631–644. doi: https://doi.org/10.1016/0021-9290(85)90019-3 430 Kingma, D.P., Ba, J.L. 2015. Adam: A method for stochastic optimization. 3rd Int. Conf. Learn. 431 Represent. ICLR 2015 - Conf. Track Proc. 1–15. doi: 432 https://doi.org/10.48550/arXiv.1412.6980 433 Klein, B.D., Rossin, D.F. 1999. Data quality in neural network models: Effect of error rate and 434 magnitude of error on predictive accuracy. Omega 27, 569–582. doi: 435 https://doi.org/10.1016/S0305-0483(99)00019-5 436 Komaris, D-S., Pérez-Valero, E., Jordan, L., Barton, J., Hennessy, L., O’Flynn, B., and Tedesco, S. 437 2019. Predicting Three-Dimensional Ground Reaction Forces in Running by Using Artificial 438 Neural Networks and Lower Body Kinematics. IEEE Access, vol. 7, pp. 156779-156786. 439 doi: 10.1109/ACCESS.2019.2949699 440 Komnik, I., Weiss, S., Fantini Pagani, C.H., Potthast, W. 2015. Motion analysis of patients after 441 knee arthroplasty during activities of daily living - A systematic review. Gait Posture. 442 41(2):370–7. doi: https://doi.org/10.1016/j.gaitpost.2015.01.019 443 Koo, T.K., Li, M.Y. 2016. A Guideline of Selecting and Reporting Intraclass Correlation 444 Coefficients for Reliability Research. J. Chiropr. Med. 15, 155–163. doi: 445 https://doi.org/10.1016/j.jcm.2016.02.012 446 Lai, A.K.M., Arnold, A.S., Wakeling, J.M. 2017. Why are Antagonist Muscles Co-activated in My 447 Simulation? A Musculoskeletal Model for Analysing Human Locomotor Tasks. Ann 448 Biomed Eng. 45(12):2762-2774. doi: 10.1007/s10439-017-1920-7 449 Li, P.F., Hou, Z.G., Zhang, F., Chen, Y.X., Xie, X.L., Tan, M., Wang, H.B. 2010. Adaptive neural 450 network control of FES cycling. 2010 4th Int. Conf. Bioinforma. Biomed. Eng. iCBBE 2010. 451 doi: https://doi.org/10.1109/ICBBE.2010.5515015 452 Marsh, A.P., Martin, P.E., Sanderson, D.J. 2000. Is a joint moment-based cost function 453 associated with preferred cycling cadence? J. Biomech. 33, 173–180. doi: 454 https://doi.org/10.1016/s0021-9290(99)00155-4 455 Martín-Sosa, E., Chaves, V., Soler-Vizán, E., Mayo, J., Ojeda, J. 2023. Methodology to Analyse 456 Three-Dimensional Asymmetries in the Forces Applied to the Pedals in Cycling. Ann. 457 Biomed. Eng. 51, 618–631. doi: https://doi.org/10.1007/s10439-022-03076-y 458 Martin, J., Milliken, D. 1998. Validation of a Mathematical Model for Road Cycling Power 459 Noncircular Chainrings Do Not Influence Maximum Cycling Power View project 460 Nondimensional Tire Model View project. Artic. J. Appl. Biomech. 14(3):276–291. doi: 461 10.1123/jab.14.3.276 462 Maruyama, T., Tada, M., Toda, H. 2019. Riding motion capture system using inertial 463 measurement units with contact constraints. Int. J. Autom. Technol. 13, 506–516. doi: 464 https://doi.org/10.20965/ijat.2019.p0506 465 Mayerhofer, P., Bajić, I., Maxwell Donelan, J. 2024. Comparing the advantages and 466 disadvantages of physics-based and neural network-based modelling for predicting 467 cycling power. J. Biomech. 169, 1–7. doi: 468 https://doi.org/10.1016/j.jbiomech.2024.112121 469 McDevitt, S., Hernandez, H., Hicks, J., Lowell, R., Bentahaikt, H., Burch, R., Ball, J., Chander, H., 470 Freeman, C., Taylor, C., Anderson, B. 2022. Wearables for Biomechanical Performance 471 Optimization and Risk Assessment in Industrial and Sports Applications. Bioengineering 472 9(1) 33. doi: https://doi.org/10.3390/bioengineering9010033 473 Morbey, S., Tronslien, M., Kong, K., Chapman, D.W., Netto, K. 2024. Using Inertial 474 Measurement Units to Examine Selected Joint Kinematics in a Road Cycling Sprint: A 475 Series of Single Cases. Sensors 24(11):3453 . doi: https://doi.org/10.3390/s24113453 476 Mornieux, G., Guenette, J.A., Sheel, A.W., Sanderson, D.J. 2007. Influence of cadence, power 477 output and hypoxia on the joint moment distribution during cycling. Eur. J. Appl. Physiol. 478 102, 11–18. doi: https://doi.org/10.1007/s00421-007-0555-z 479 Mundt, M., Koeppe, A., Bamer, F., Potthast, W., Pforzheim, A.C. 2018. Prediction of joint 480 kinetics based on joint kinematics using neural networks. Institute of Biomechanics and 481 Orthopaedics , German Sport University. 36th Conf Int Soc Biomech Sport. 9:794–7 482 Mundt, M., Koeppe, A., David, S., Bamer, F., Potthast, W., Markert, B. 2020a. Prediction of 483 ground reaction force and joint moments based on optical motion capture data during 484 gait. Med. Eng. Phys. 86, 29–34. doi: https://doi.org/10.1016/j.medengphy.2020.10.001 485 Mundt, M., Thomsen, W., Witter, T., Koeppe, A., David, S., Bamer, F., Potthast, W., Markert, B. 486 2020b. Prediction of lower limb joint angles and moments during gait using artificial 487 neural networks. Med. Biol. Eng. Comput. 58, 211–225. doi: 488 https://doi.org/10.1007/s11517-019-02061-3 489 Pataky, T.C., Robinson, M.A., Vanrenterghem, J. 2013. Vector field statistical analysis of 490 kinematic and force trajectories. J. Biomech. 46, 2394–2401. doi: 491 https://doi.org/10.1016/j.jbiomech.2013.07.031 492 Pataky, T.C., Vanrenterghem, J., Robinson, M.A. 2015. Zerovs. one-dimensional, parametric 493 vs. non-parametric, and confidence interval vs. hypothesis testing procedures in one494 dimensional biomechanical trajectory analysis. J. Biomech. 48, 1277–1285. doi: 495 https://doi.org/10.1016/j.jbiomech.2015.02.051 496 Pigatto, A.V., Balbinot, A. 2018. An automatic cycling performance measurement system based 497 on ANFIS. Studies in Computational Intelligence. Computational Intelligence for Pattern 498 Recognition (pp.227-252). doi: https://doi.org/10.1007/978-3-319-89629-8_8 499 Priego Quesada, J.I., Kerr, Z.Y., Bertucci, W.M., Carpes, F.P. 2019. A retrospective international 500 study on factors associated with injury, discomfort and pain perception among cyclists. 501 PLoS One 14, 1–16. doi: https://doi.org/10.1371/journal.pone.0211197 502 Redfield R., Hull M.L. 1981. Prediction of pedal forces in bicycling optimization methods. 503 Biomechanics 19, 523–540. doi: https://doi.org/10.1016/0021-9290(86)90126-0 504 Seung, E.O., Ahnryul, C., Joung H.M. 2013. Prediction of ground reaction forces during gait 505 based on kinematics and a neural network model. J. Biomech. 46:14, 2372-2380. doi: 506 https://doi.org/10.1016/j.jbiomech.2013.07.036 507 Sommar, J.N., Johansson, C., Lövenheim, B., Schantz, P., Markstedt, A., Strömgren, M., Stigson, 508 H., Forsberg, B. 2022. Overall health impacts of a potential increase in cycle commuting in 509 Stockholm, Sweden. Scand. J. Public Health 50, 552–564. doi: 510 https://doi.org/10.1177/14034948211010024 511 Stetter, B.J., Krafft, F.C., Ringhof, S., Stein, T., Sell, S. 2020. A Machine Learning and Wearable 512 Sensor Based Approach to Estimate External Knee Flexion and Adduction Moments 513 During Various Locomotion Tasks. Front. Bioeng. Biotechnol. 8:9. doi: 514 10.3389/fbioe.2020.00009 515 Thompson, R.L., Gardner, J.K., Zhang, S., Reinbolt, J.A. 2020. Lower-limb joint reaction forces 516 and moments during modified cycling in healthy controls and individuals with knee 517 osteoarthritis. Clin. Biomech. 71, 167–175. doi: 518 https://doi.org/10.1016/j.clinbiomech.2019.11.004 519 Torres, A., Nougarou, F., & Domingue, F. 2024. Predicting pedalling metrics based on lower 520 limb joint kinematics. Comput. Methods Biomech. Biomed. Engin. 1–15. doi: 521 https://doi.org/https://doi.org/10.1080/10255842.2024.2371044 522 Turpin, N.A., Watier, B. 2020. Cycling biomechanics and its relationship to performance. Appl. 523 Sci. 10, 1–15. doi: https://doi.org/10.3390/APP10124112 524 Wannawas, N., Faisal, A.A. 2023. Towards AI-controlled FES-restoration of movements: 525 Learning cycling stimulation pattern with reinforcement learning. Computer Science 526 Robotics. doi: https://doi.org/10.48550/arXiv.2303.09986 527 Winter, D.A. 2009. Biomechanics and Motor Control of Human Movement, Fourth Edi. ed. 528 University of Waterloo, Waterloo, Ontario, Canada. 529 Wooles, A.L., Robinson, A.J., Keen, P.S. 2005. A static method for obtaining a calibration factor 530 for SRM bicycle power cranks. Sport. Eng. 8, 137–144. doi: 531 https://doi.org/10.1007/bf02844014 532 Yamaguchi, Y., Otsuka, M., Wada, N., Nishiyama, T. 2023. Power production strategy during 533 steady-state cycling is cadence dependent. J. Biomech. 158, 111772. doi: 534 https://doi.org/10.1016/j.jbiomech.2023.111772 535 Zignoli, A., Biral, F., Pellegrini, B., Jinha, A., Herzog, W., Schena, F. 2017. An optimal control 536 solution to the predictive dynamics of cycling. Sport Sci. Health 13, 381–393. doi: 537 https://doi.org/10.1007/s11332-017-0370-9 538 539