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The Effect of Crank Length Changes from Cycling Rehabilitation on Muscle Behaviors

The Effect of Crank Length Changes from Cycling Rehabilitation on Muscle Behaviors Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 8873426, 8 pages https://doi.org/10.1155/2021/8873426 Research Article The Effect of Crank Length Changes from Cycling Rehabilitation on Muscle Behaviors Lu Zongxing , You Shengxian, Wei Xiangwen, Chen Xiaohui, and Jia Chao School of Mechanical Engineering and Automation, Fuzhou University, No. 2 Xueyuan Road, Fuzhou, 350116 Fujian, China Correspondence should be addressed to Jia Chao; jiachao8507@163.com Received 9 September 2020; Revised 6 April 2021; Accepted 17 April 2021; Published 27 April 2021 Academic Editor: Emanuele Luigi Carniel Copyright © 2021 Lu Zongxing et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background. Many sports and physical activities can result in lower limb injures. Pedaling is an effective exercise for lower extremity rehabilitation, but incorrect technique may cause further damage. To some extent, previous experiments have been susceptible to bias in the sample recruited for the study. Alternatively, methods used to simulation activities can enable parametric studies without the influence of noise. In addition, models can facilitate the study of all muscles in the absence of the effects of fatigue. This study investigated the effects of crank length on muscle behavior during pedaling. Methods. Six muscles (soleus, tibialis anterior, vastus medialis, vastus lateralis, gastrocnemius, and rectus femoris), divided into three groups (ankle muscle group, knee muscle group, and biarticular muscle group), were examined under three cycling crank lengths (100 mm, 125 mm, and 150 mm) in the present study. In addition, the relationship between crank length and muscle biological force was analyzed with the AnyBody Modeling System™, a human simulation modeling software based on the Hill-type model. Findings. Based on inverse kinematic analysis, the results indicate that muscle activity and muscle force decrease in varying degrees with increases in crank length. The maximum and minimum muscular forces were attained in the tibialis anterior and vastus lateralis, respectively. Interpretation. Studying the relationship between muscle and joint behavior with crank length can help rehabilitation and treating joint disorders. This study provides the pedal length distribution areas for patients in the early stages of rehabilitation. reason for these injuries. The third class of injuries encom- 1. Introduction passes ankle and foot problems. When riding long distances, Nowadays, cycling plays an important role in people’s daily it is very common to sustain a foot injury. Cycling in low life and rehabilitation. However, lower limb injuries often seating positions with a high pedaling frequency can cause occur during cycling. Injuries of the lower limb, including ankle and foot injuries, and an incorrect pedal position under the foot may cause metatarsalgia. the hip, knee, and ankle can occur if pedaling parameters (e.g., crank length) are not set appropriately or due to over- Pedaling exercise has been widely used in the rehabilita- use. There are three classifications for lower limb injuries, tion of lower limb injuries [4]. Rehabilitation with cycling under overuse and common cycling [1–3]. involves interactions between the nervous system, bones, First, cyclists may develop hip problems, such as trochan- and muscles. Understanding the relationship between body teric bursitis, which is due to the repetitive sliding of the fas- structures and cycling parameters (such as seat height and cia lata over the greater trochanter. This can result from a crank length) is not only important for patients to perform high seat position. Furthermore, high-seat can also cause tro- rehabilitative exercises but can also guide healthy people to chanteric synovitis and iliopsoas tendinitis. Second, knee perform physical activities safely. For example, setting an joint injuries are the most common injures from cycling. appropriate crank length [5–7], pedaling cadence [8], and Knee injuries account for 62% of all overuse injuries, and the pedal condition [9, 10] (pedal height and pedal position) many cyclists suffer from lateral, anterior, and medial knee affects the outcomes of rehabilitation. Martin and Spirduso pain. Of there, lateral knee pain is the most common knee [8] divided 710 feasible pedal places into 16 groups for joint injury. The overuse of bicycles is considered the main modeling and simulation and found that knee joint forces 2 Applied Bionics and Biomechanics abduction/adduction). In the AMS, all body segments are were smaller near saddle position (SP). Conversely, the ankle and hip joints in the far SP per saddle height (SH) were min- modeled as rigid bodies to eliminate the influence of soft tis- imal. Therefore, understanding changes in muscle strength sues and other uncertainties. and reaction forces when pedaling provides insights that In the process of establishing the model, the first step was can be used to guide rehabilitation. to determine the position of the world coordinate system, Many previous studies [11–13] have used electromyogra- which was set to [0, 0, 0] (the red coordinate system in phy (EMG) to examine the activation patterns of lower limb Figure 1). The center of the pedal coincided with the world muscles during pedaling. coordinate system. At the same time, the angle of the knee In contrast, this study has used the AMS (AnyBody and ankle were adjusted to represent actual human cycling. Modeling System™) for simulation pedaling with different After these adjustments, the joint angles of both the knee crank lengths. The AMS software transforms parts of the and the hip were 90 degrees. In addition, to ensure the accu- human body, which is a very complex structure [14], into racy of the experiment, it was necessary to determine vari- rigid body systems for analysis [15]. In this study, a Hill- ables other than the crank length that should remain type [16] biomechanical model of cycling exercise (AnyBody unchanged. After a series of adjustments, the final parame- software version 6.0, AnyBody Technology, Aalborg, Den- ters were as follows: the seat position was [-0.7, 0.55, 0]; the mark) was used involving 84 muscles in the lower extremities contact point between the foot and the pedal was set to [L, based on the criteria for muscle recruitment [17, 18]. 0, 0.15] (right crank point), [-L,0, -0.15] (left crank point). There are several limitations of research on multibody “L” represents the crank length. In the model, there were five dynamics, such as the verification and validation of musculo- segments in total, each of which had six degrees of freedom. skeletal models and simulations. For studies on musculoskel- The human body model had a total of 30 degrees of freedom. etal modeling, Rasmussen and colleagues [19, 20] used Six constraints were added to the pelvis and seat through the dynamics and anatomical knowledge to continually modify stdjoint, while the hip, knee, and ankle had three, five, and and refine the model, so that the Hill-type musculoskeletal four constraints, respectively. There are one constraint of model better conformed to actual human movements. In the knee joint (lateral movement along the y-axis) and two the process of verifying the model, it was difficult to obtain constraints of the ankle joint (flexion/extension and abduc- EMG signals in vivo. Previous studies [21, 22] investigated tion/adduction). Three constraints were added between the muscle behavior during cycling, observing acceptable agree- foot and the pedal by using a spherical joint. Finally, the ment in the changes in muscle activation based on contrast- remaining degrees of freedom was determined by the driving ing analyses with other models. function of the pedal. In total, there were 29 constraints. If a The effect of cycling crank length on muscle behaviors mechanism is needed to perform a certain movement, the requires parametric further investigation. Both experimen- number of its original moving parts should be equal to the tal and simulation methods can be used to study the fac- number of degrees of freedom. In the model, the original tors that influence muscle behavior during cycling. While actuator was only a pedal rotation, and since there was one human experiments are susceptible to sample bias, simula- degrees of freedom in the mechanism, the model met the tion studies allow the examination of complex body sys- conditions for movement to occur. tems by changing only one parameter in the absence of In this study, 25 torque loads were added to the pedal. noise from other confounding variables [23]. In addition, Since the pedal driver had no motor, the torque had to be models can facilitate the study of all muscles in the balanced by the muscles in the system. After the model was established, the relevant biomechanical parameters absence of fatigue [24, 25]. As much, models provide valu- able insight into biomechanical variables that are difficult were analyzed by modifying crank length. A preliminary to measure directly (for example, muscle force and joint determination of three crank lengths was conducted at reaction force) and offer improvements upon many previ- 100 mm, 125 mm, and 150 mm. Every time the crank ous studies addressing joint kinetics [26] and cycling length changed, a kinematic analysis was performed again cadence [27] that can be directly measured. to verify the feasibility of the model. Then, an inverse The purpose of this study was to reveal the relationship kinematic analysis was conducted to obtain the data. between muscle activity and muscle force with different Figure 1 shows an overview of the model analysis process. crank lengths during the pedaling rehabilitation. The out- All whole lower limb muscles were divided into three comes may help to provide physicians with objective guid- groups: the knee muscle group (vastus medialis (VM) ance for programming bicycling for rehabilitation. and vastus lateralis (VL)), the ankle muscle group (soleus (SOL) and tibialis anterior (TA)), and the biarticular mus- cle group (gastrocnemius (GAS) and rectus femoris (RF)). 2. Methods Several of the most representative muscles were selected The AMS is a human simulation software that provides for further analysis. The musculotendon parameters were set using constant values from the patient-specific muscu- human musculoskeletal models. The model used in this study had 84 muscles in the lower limb, incorporating three degrees loskeletal model (Table 1). In the AMS, careful consideration must be given to mus- of freedom at the hip (flexion/extension, abduction/adduc- tion, and internal/external rotation), one degree of freedom cle recruitment. Muscle recruitment refers to the overall effi- at the knee (lateral movement along the y-axis), and two ciency of muscle use. The solution for muscle recruitment in inverse dynamics is usually expressed as a mathematical degrees of freedom at the ankle (flexion/extension and Applied Bionics and Biomechanics 3 Model validation Evaluation Model Kinematic analysis Divided into three parts: ankle, knee, biarticular. Inverse kinematic analysis Compare the related parameters of each part Modify the crank Conclusion length parameter Figure 1: Analysis process of the influence of crank length on muscle behavior during cycling. can be expressed by equilibrium Equation (2), where C is the Table 1: Musculotendon parameters, based on and adapted from Ward et al. [28] and Millard et al. [29]. coefficient matrix, and d is the vector used to represent all known forces. Equation (3) indicates the nonnegativity con- Optimal Optimal Tendon straint on muscle forces. This means that within a certain Muscle Pennation force fiber length slack length segment angle ( ) strength range (0-N ), the muscle can only be pulled but (N) (cm) (cm) not pushed. Moreover, in the AMS, all muscles have a preset Soleus (SOL) 6195 4.4 27.7 21.9 strength; exceeding this muscle strength will cause further Tibialis injury, and the system will also report errors, which must 1227 6.8 24.1 11.2 anterior (TA) be avoided in modeling. Vastus medialis In the AMS, the position of the ith body is described by 2748 9.7 20.0 24.2 (VM) Equation (4), where r is the global position vector of the cen- Vastus lateralis ter of mass and p is the vector of four Euler parameters. 5149 9.9 22.1 14.5 (VL) T T Gastrocnemius q = r q : ð4Þ 1575 5.9 37.6 12.0 i i i (GAS) Rectus femoris When modeling, taking the right leg as an example, the 2192 7.6 44.9 12.4 (RF) crank angle changes as shown in Figure 2, and the angle changes can be plotted as shown in the figure. The crank drive equation determines the movement of optimization problem. The goal is to minimize the value by the foot pedal and is described as follows: ðMÞ the objective function Gðf Þ. ðÞ M n ðÞ ð5Þ φ = 〠½ A cosðÞ w t + B sinðÞ w t , i i i i M i ðÞ Gf = 〠 : ð1Þ i=1 i=1 w =ðÞ i − 1 2πf , Subject to ð6Þ A =½ A , A , A , 1 2 3 ðÞ ð2Þ Cf = d, B = B , B , B , ð7Þ 1 2 3 ðÞ ð3Þ 0 ≤ f ≤ N , i ∈ðÞ 1, 2 ⋯ n , where φ is the pedal angle. A and B are the Fourier coeffi- i i cients, and ƒ is the natural frequency; w is the angular fre- where G is the objective function of the mathematical quency (w is equivalent to the angular velocity of the optimization problem, and its solution depends on the max- 2 crank). The components of A and B control foot motion dur- imum of the unknown force in the problem. In Equation (1), ing cycling. F and N represent muscle force and muscle strength, i i The crank torque pattern by means of a sine function was respectively. The i is the ith muscle, and the power of the described as follows: polynomial criterion (p) in the AMS shows the synergy between the muscles. To ensure the minimum value of M = M +ðÞ M − M sinðÞ 4πf + α : ð8Þ offset offset TDC M fatigue strength, p =3 [30]. Redundancy in the muscle system 4 Applied Bionics and Biomechanics Figure 2: Variation in crank angles during movement. Figure 4. The trend in muscle activity was roughly the same under different crank lengths. The time points at which the peak occurs and activity begins are roughly the same, and this also shows the accuracy of the established model to some extent. As crank length increases, muscle activity decreases. Figure 5 shows the variation in the muscular force of six muscles under three different crank lengths. As the crank length increased, muscle force decreased. The peak muscle force of the TA was the smallest, being only 166 N. The change in muscle force was not accompanied by a measur- able change in crank length. Peak muscle force was reduced from 166 N in the 100 mm condition to 110 N in the 0 150 mm condition. While the peak force of the VL was the 0 90 180 270 360 largest of all muscles, up to 1321 N, the decrease in muscle force was also the greatest, as peak force decreased from 1321 N in the 100 mm condition to 859 N in the 150 mm con- SOL VM dition, a reduction of 462 N. The SOL and VM muscles only ° ° ° ° TA GAS participated in the motion between 0 –45 and 225 –360 . VL RF Variation in SOL muscle force at different crank lengths was relatively weak, while variation in the VM force at differ- Figure 3: The activity of each muscle when the crank length was ent crank lengths was larger than that of the SOL. The force 100 mm. of the TA was very small throughout the whole pedaling cycle, only generating force in the middle and early stages In Equation (8), the crank torque M at the top of the TDC of the cycle. The force of the GAS was only active in the 0 – ° ° pedal cycle and the phase angle α at the top of the pedal M 225 range, peaking at 50 with 689 N. The force of the RF cycle are independent variables and were determined during changed in the initial and final stages, but in the second half, the optimization process. M represents the input data. offset the trend was more obvious. The angular frequency of the torque function was twice the In Figure 6, the maximum muscle force of each muscle at frequency of the circular pedal frequency, due to the inclu- different crank lengths is shown. The change in the maxi- sion of two legs in the model [21]. mum muscle force of each muscle can be clearly seen. Among these muscles, the maximum muscle force was in the VL and the lowest was from the TA. With increases in crank length, 3. Results all maximum muscle forces were decreased. The changes in muscle activity during pedaling with a 100 mm crank length can be seen in Figure 3. Activation of 4. Discussion the ankle muscle group (SOL and TA) was sensitive from 0 to 135 , showing an initial increase followed by a decrease Pedaling is enabled by a coordinated sequence of leg muscle in the activity. The SOL reached its maximum activity at contractions, of which the SOL, TA, VL, VM, GAS, and RF ° ° 45 , but the TA reached its maximum at 90 . Moreover, the muscles all make an important contribution. A wide variety knee muscle group (VL and VM) was active at the beginning of methods have been used to study the biomechanics of ped- and end of the motion, with the activity of the VL and VM aling. In one study, the inertial load on the crank was set to muscles first increasing and then decreasing. The activity of 150 W and 250 W [31], and a different range of cycling (such 2 2 2 2 the VL and VM reached peak muscle at 265 . The peak mus- as 9 kg/m to 36 kg/m and 56 kg/m to 182 kg/m ) was used cle activity of the VL was the largest of all muscles. The GAS to study pedaling modeling. Some studies have used different ° ° muscle was active from 0 to 225 . The activity of the GAS saddle positions with 182 feasible pedaling places [4]. Setting ° ° was relatively weak in the 225 to 360 range. The RF muscle an appropriate crank length is an important issue. In some was active throughout the cycle, reaching peak muscle activ- studies [32–34], kinematic and inverse kinematic analyses ity at 200 . have been used to investigate the behaviors of cycling power The activity of the TA, VL, and RF muscles when pedal- output and cadence with different crank lengths. However, ing under three different crank lengths have is shown in all these previous studies have focused on t external forces, Muscle activity (%) Applied Bionics and Biomechanics 5 100 100 80 80 60 60 40 40 20 20 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) (a) (b) 0 90 180 270 360 100mm 125mm 150mm (c) ° ° Figure 4: The activity of the TA, VL, and RF muscles during a cycle (0 -360 ) with different crank lengths (100 mm, 125 mm, and 150 mm). (a) TA, (b) VL, and (c) RF. not biological forces. In this study, the effect of three crank The maximum activity of the VL muscle was higher than lengths (100 mm, 125 mm, and 150 mm) on muscle kinetics all other muscles. The maximum activity of the TA muscle (muscle activity) and muscular force was investigated. was the lowest of all the muscles. This study showed that The previous studies investigated the relationship the SOL muscle was active from the top to the bottom of between crank length and muscle behavior. For example, the pedal cycle and that the VL muscle was inactive during Macdermid and Edwards [7] investigated seven female the middle stage of pedaling. In the ankle muscle group, the active phases of the SOL cross-country mountain bike athletes to examine the effect of different crank lengths (170 mm, 172.5 mm, and and TA muscles were staggered, such that the SOL muscle ° ° ° ° 175 mm) on power output during cycle ergometry at a was active during the 0 –45 and 230 –360 sections of the constant cadence (50 rpm). In this paper, only the rela- pedaling cycle, while the TA muscle was active between 45 tionship between crank length and power output was and 225 of the cycle. Comparing the force curves of the studied. two muscles, the TA produced a smaller force than the According to Hicks’ research [35], the validation of a SOL. In the ankle muscle group, the SOL provided the most model requires multiple steps. One important limitation is muscle force during the pedaling cycle. In the knee muscle the lack of verification of in vivo EMG signals on the premise group, the activity of the VL and VM muscles was basically of missing comparative data. Alternatively, validation can be the same through the whole cycle, but the muscle force of achieved by comparing the model and simulation data to the VL was larger than that of the VM. The active stages of independent experiments and other models. In order to pre- the GAS and RF muscles were also different, as the GAS ° ° vent secondary injury during rehabilitation, it is necessary to was active during 0 –225 , while the RF was active during ° ° avoid muscle activation greater than its maximum capacity. 180 –360 of the cycle. Muscle activity (%) Muscle activity (%) Muscle activity (%) 6 Applied Bionics and Biomechanics 1400 1400 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) (a) (b) 1400 1400 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) Angle (°) (c) (d) 1400 1400 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) Angle (°) 100mm 125mm 150mm (e) (f) Figure 5: The muscle force of six muscles during a cycle (0-360 ) in the different crank lengths: (a) SOL, (b) TA, (c) VL, (d) VM, (e) GAS, and (f) RF. Muscle force (N) Muscle force (N) Muscle force (N) Muscle force (N) Muscle force (N) Muscle force (N) Applied Bionics and Biomechanics 7 References [1] M. R. Silberman, “Bicycling injuries,” Current Sports Medicine 1200 Reports, vol. 12, no. 5, pp. 337–345, 2013. [2] T. Wanich, C. Hodgkins, J. A. Columbier, E. Muraski, and J. G. 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The Effect of Crank Length Changes from Cycling Rehabilitation on Muscle Behaviors

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Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 8873426, 8 pages https://doi.org/10.1155/2021/8873426 Research Article The Effect of Crank Length Changes from Cycling Rehabilitation on Muscle Behaviors Lu Zongxing , You Shengxian, Wei Xiangwen, Chen Xiaohui, and Jia Chao School of Mechanical Engineering and Automation, Fuzhou University, No. 2 Xueyuan Road, Fuzhou, 350116 Fujian, China Correspondence should be addressed to Jia Chao; jiachao8507@163.com Received 9 September 2020; Revised 6 April 2021; Accepted 17 April 2021; Published 27 April 2021 Academic Editor: Emanuele Luigi Carniel Copyright © 2021 Lu Zongxing et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background. Many sports and physical activities can result in lower limb injures. Pedaling is an effective exercise for lower extremity rehabilitation, but incorrect technique may cause further damage. To some extent, previous experiments have been susceptible to bias in the sample recruited for the study. Alternatively, methods used to simulation activities can enable parametric studies without the influence of noise. In addition, models can facilitate the study of all muscles in the absence of the effects of fatigue. This study investigated the effects of crank length on muscle behavior during pedaling. Methods. Six muscles (soleus, tibialis anterior, vastus medialis, vastus lateralis, gastrocnemius, and rectus femoris), divided into three groups (ankle muscle group, knee muscle group, and biarticular muscle group), were examined under three cycling crank lengths (100 mm, 125 mm, and 150 mm) in the present study. In addition, the relationship between crank length and muscle biological force was analyzed with the AnyBody Modeling System™, a human simulation modeling software based on the Hill-type model. Findings. Based on inverse kinematic analysis, the results indicate that muscle activity and muscle force decrease in varying degrees with increases in crank length. The maximum and minimum muscular forces were attained in the tibialis anterior and vastus lateralis, respectively. Interpretation. Studying the relationship between muscle and joint behavior with crank length can help rehabilitation and treating joint disorders. This study provides the pedal length distribution areas for patients in the early stages of rehabilitation. reason for these injuries. The third class of injuries encom- 1. Introduction passes ankle and foot problems. When riding long distances, Nowadays, cycling plays an important role in people’s daily it is very common to sustain a foot injury. Cycling in low life and rehabilitation. However, lower limb injuries often seating positions with a high pedaling frequency can cause occur during cycling. Injuries of the lower limb, including ankle and foot injuries, and an incorrect pedal position under the foot may cause metatarsalgia. the hip, knee, and ankle can occur if pedaling parameters (e.g., crank length) are not set appropriately or due to over- Pedaling exercise has been widely used in the rehabilita- use. There are three classifications for lower limb injuries, tion of lower limb injuries [4]. Rehabilitation with cycling under overuse and common cycling [1–3]. involves interactions between the nervous system, bones, First, cyclists may develop hip problems, such as trochan- and muscles. Understanding the relationship between body teric bursitis, which is due to the repetitive sliding of the fas- structures and cycling parameters (such as seat height and cia lata over the greater trochanter. This can result from a crank length) is not only important for patients to perform high seat position. Furthermore, high-seat can also cause tro- rehabilitative exercises but can also guide healthy people to chanteric synovitis and iliopsoas tendinitis. Second, knee perform physical activities safely. For example, setting an joint injuries are the most common injures from cycling. appropriate crank length [5–7], pedaling cadence [8], and Knee injuries account for 62% of all overuse injuries, and the pedal condition [9, 10] (pedal height and pedal position) many cyclists suffer from lateral, anterior, and medial knee affects the outcomes of rehabilitation. Martin and Spirduso pain. Of there, lateral knee pain is the most common knee [8] divided 710 feasible pedal places into 16 groups for joint injury. The overuse of bicycles is considered the main modeling and simulation and found that knee joint forces 2 Applied Bionics and Biomechanics abduction/adduction). In the AMS, all body segments are were smaller near saddle position (SP). Conversely, the ankle and hip joints in the far SP per saddle height (SH) were min- modeled as rigid bodies to eliminate the influence of soft tis- imal. Therefore, understanding changes in muscle strength sues and other uncertainties. and reaction forces when pedaling provides insights that In the process of establishing the model, the first step was can be used to guide rehabilitation. to determine the position of the world coordinate system, Many previous studies [11–13] have used electromyogra- which was set to [0, 0, 0] (the red coordinate system in phy (EMG) to examine the activation patterns of lower limb Figure 1). The center of the pedal coincided with the world muscles during pedaling. coordinate system. At the same time, the angle of the knee In contrast, this study has used the AMS (AnyBody and ankle were adjusted to represent actual human cycling. Modeling System™) for simulation pedaling with different After these adjustments, the joint angles of both the knee crank lengths. The AMS software transforms parts of the and the hip were 90 degrees. In addition, to ensure the accu- human body, which is a very complex structure [14], into racy of the experiment, it was necessary to determine vari- rigid body systems for analysis [15]. In this study, a Hill- ables other than the crank length that should remain type [16] biomechanical model of cycling exercise (AnyBody unchanged. After a series of adjustments, the final parame- software version 6.0, AnyBody Technology, Aalborg, Den- ters were as follows: the seat position was [-0.7, 0.55, 0]; the mark) was used involving 84 muscles in the lower extremities contact point between the foot and the pedal was set to [L, based on the criteria for muscle recruitment [17, 18]. 0, 0.15] (right crank point), [-L,0, -0.15] (left crank point). There are several limitations of research on multibody “L” represents the crank length. In the model, there were five dynamics, such as the verification and validation of musculo- segments in total, each of which had six degrees of freedom. skeletal models and simulations. For studies on musculoskel- The human body model had a total of 30 degrees of freedom. etal modeling, Rasmussen and colleagues [19, 20] used Six constraints were added to the pelvis and seat through the dynamics and anatomical knowledge to continually modify stdjoint, while the hip, knee, and ankle had three, five, and and refine the model, so that the Hill-type musculoskeletal four constraints, respectively. There are one constraint of model better conformed to actual human movements. In the knee joint (lateral movement along the y-axis) and two the process of verifying the model, it was difficult to obtain constraints of the ankle joint (flexion/extension and abduc- EMG signals in vivo. Previous studies [21, 22] investigated tion/adduction). Three constraints were added between the muscle behavior during cycling, observing acceptable agree- foot and the pedal by using a spherical joint. Finally, the ment in the changes in muscle activation based on contrast- remaining degrees of freedom was determined by the driving ing analyses with other models. function of the pedal. In total, there were 29 constraints. If a The effect of cycling crank length on muscle behaviors mechanism is needed to perform a certain movement, the requires parametric further investigation. Both experimen- number of its original moving parts should be equal to the tal and simulation methods can be used to study the fac- number of degrees of freedom. In the model, the original tors that influence muscle behavior during cycling. While actuator was only a pedal rotation, and since there was one human experiments are susceptible to sample bias, simula- degrees of freedom in the mechanism, the model met the tion studies allow the examination of complex body sys- conditions for movement to occur. tems by changing only one parameter in the absence of In this study, 25 torque loads were added to the pedal. noise from other confounding variables [23]. In addition, Since the pedal driver had no motor, the torque had to be models can facilitate the study of all muscles in the balanced by the muscles in the system. After the model was established, the relevant biomechanical parameters absence of fatigue [24, 25]. As much, models provide valu- able insight into biomechanical variables that are difficult were analyzed by modifying crank length. A preliminary to measure directly (for example, muscle force and joint determination of three crank lengths was conducted at reaction force) and offer improvements upon many previ- 100 mm, 125 mm, and 150 mm. Every time the crank ous studies addressing joint kinetics [26] and cycling length changed, a kinematic analysis was performed again cadence [27] that can be directly measured. to verify the feasibility of the model. Then, an inverse The purpose of this study was to reveal the relationship kinematic analysis was conducted to obtain the data. between muscle activity and muscle force with different Figure 1 shows an overview of the model analysis process. crank lengths during the pedaling rehabilitation. The out- All whole lower limb muscles were divided into three comes may help to provide physicians with objective guid- groups: the knee muscle group (vastus medialis (VM) ance for programming bicycling for rehabilitation. and vastus lateralis (VL)), the ankle muscle group (soleus (SOL) and tibialis anterior (TA)), and the biarticular mus- cle group (gastrocnemius (GAS) and rectus femoris (RF)). 2. Methods Several of the most representative muscles were selected The AMS is a human simulation software that provides for further analysis. The musculotendon parameters were set using constant values from the patient-specific muscu- human musculoskeletal models. The model used in this study had 84 muscles in the lower limb, incorporating three degrees loskeletal model (Table 1). In the AMS, careful consideration must be given to mus- of freedom at the hip (flexion/extension, abduction/adduc- tion, and internal/external rotation), one degree of freedom cle recruitment. Muscle recruitment refers to the overall effi- at the knee (lateral movement along the y-axis), and two ciency of muscle use. The solution for muscle recruitment in inverse dynamics is usually expressed as a mathematical degrees of freedom at the ankle (flexion/extension and Applied Bionics and Biomechanics 3 Model validation Evaluation Model Kinematic analysis Divided into three parts: ankle, knee, biarticular. Inverse kinematic analysis Compare the related parameters of each part Modify the crank Conclusion length parameter Figure 1: Analysis process of the influence of crank length on muscle behavior during cycling. can be expressed by equilibrium Equation (2), where C is the Table 1: Musculotendon parameters, based on and adapted from Ward et al. [28] and Millard et al. [29]. coefficient matrix, and d is the vector used to represent all known forces. Equation (3) indicates the nonnegativity con- Optimal Optimal Tendon straint on muscle forces. This means that within a certain Muscle Pennation force fiber length slack length segment angle ( ) strength range (0-N ), the muscle can only be pulled but (N) (cm) (cm) not pushed. Moreover, in the AMS, all muscles have a preset Soleus (SOL) 6195 4.4 27.7 21.9 strength; exceeding this muscle strength will cause further Tibialis injury, and the system will also report errors, which must 1227 6.8 24.1 11.2 anterior (TA) be avoided in modeling. Vastus medialis In the AMS, the position of the ith body is described by 2748 9.7 20.0 24.2 (VM) Equation (4), where r is the global position vector of the cen- Vastus lateralis ter of mass and p is the vector of four Euler parameters. 5149 9.9 22.1 14.5 (VL) T T Gastrocnemius q = r q : ð4Þ 1575 5.9 37.6 12.0 i i i (GAS) Rectus femoris When modeling, taking the right leg as an example, the 2192 7.6 44.9 12.4 (RF) crank angle changes as shown in Figure 2, and the angle changes can be plotted as shown in the figure. The crank drive equation determines the movement of optimization problem. The goal is to minimize the value by the foot pedal and is described as follows: ðMÞ the objective function Gðf Þ. ðÞ M n ðÞ ð5Þ φ = 〠½ A cosðÞ w t + B sinðÞ w t , i i i i M i ðÞ Gf = 〠 : ð1Þ i=1 i=1 w =ðÞ i − 1 2πf , Subject to ð6Þ A =½ A , A , A , 1 2 3 ðÞ ð2Þ Cf = d, B = B , B , B , ð7Þ 1 2 3 ðÞ ð3Þ 0 ≤ f ≤ N , i ∈ðÞ 1, 2 ⋯ n , where φ is the pedal angle. A and B are the Fourier coeffi- i i cients, and ƒ is the natural frequency; w is the angular fre- where G is the objective function of the mathematical quency (w is equivalent to the angular velocity of the optimization problem, and its solution depends on the max- 2 crank). The components of A and B control foot motion dur- imum of the unknown force in the problem. In Equation (1), ing cycling. F and N represent muscle force and muscle strength, i i The crank torque pattern by means of a sine function was respectively. The i is the ith muscle, and the power of the described as follows: polynomial criterion (p) in the AMS shows the synergy between the muscles. To ensure the minimum value of M = M +ðÞ M − M sinðÞ 4πf + α : ð8Þ offset offset TDC M fatigue strength, p =3 [30]. Redundancy in the muscle system 4 Applied Bionics and Biomechanics Figure 2: Variation in crank angles during movement. Figure 4. The trend in muscle activity was roughly the same under different crank lengths. The time points at which the peak occurs and activity begins are roughly the same, and this also shows the accuracy of the established model to some extent. As crank length increases, muscle activity decreases. Figure 5 shows the variation in the muscular force of six muscles under three different crank lengths. As the crank length increased, muscle force decreased. The peak muscle force of the TA was the smallest, being only 166 N. The change in muscle force was not accompanied by a measur- able change in crank length. Peak muscle force was reduced from 166 N in the 100 mm condition to 110 N in the 0 150 mm condition. While the peak force of the VL was the 0 90 180 270 360 largest of all muscles, up to 1321 N, the decrease in muscle force was also the greatest, as peak force decreased from 1321 N in the 100 mm condition to 859 N in the 150 mm con- SOL VM dition, a reduction of 462 N. The SOL and VM muscles only ° ° ° ° TA GAS participated in the motion between 0 –45 and 225 –360 . VL RF Variation in SOL muscle force at different crank lengths was relatively weak, while variation in the VM force at differ- Figure 3: The activity of each muscle when the crank length was ent crank lengths was larger than that of the SOL. The force 100 mm. of the TA was very small throughout the whole pedaling cycle, only generating force in the middle and early stages In Equation (8), the crank torque M at the top of the TDC of the cycle. The force of the GAS was only active in the 0 – ° ° pedal cycle and the phase angle α at the top of the pedal M 225 range, peaking at 50 with 689 N. The force of the RF cycle are independent variables and were determined during changed in the initial and final stages, but in the second half, the optimization process. M represents the input data. offset the trend was more obvious. The angular frequency of the torque function was twice the In Figure 6, the maximum muscle force of each muscle at frequency of the circular pedal frequency, due to the inclu- different crank lengths is shown. The change in the maxi- sion of two legs in the model [21]. mum muscle force of each muscle can be clearly seen. Among these muscles, the maximum muscle force was in the VL and the lowest was from the TA. With increases in crank length, 3. Results all maximum muscle forces were decreased. The changes in muscle activity during pedaling with a 100 mm crank length can be seen in Figure 3. Activation of 4. Discussion the ankle muscle group (SOL and TA) was sensitive from 0 to 135 , showing an initial increase followed by a decrease Pedaling is enabled by a coordinated sequence of leg muscle in the activity. The SOL reached its maximum activity at contractions, of which the SOL, TA, VL, VM, GAS, and RF ° ° 45 , but the TA reached its maximum at 90 . Moreover, the muscles all make an important contribution. A wide variety knee muscle group (VL and VM) was active at the beginning of methods have been used to study the biomechanics of ped- and end of the motion, with the activity of the VL and VM aling. In one study, the inertial load on the crank was set to muscles first increasing and then decreasing. The activity of 150 W and 250 W [31], and a different range of cycling (such 2 2 2 2 the VL and VM reached peak muscle at 265 . The peak mus- as 9 kg/m to 36 kg/m and 56 kg/m to 182 kg/m ) was used cle activity of the VL was the largest of all muscles. The GAS to study pedaling modeling. Some studies have used different ° ° muscle was active from 0 to 225 . The activity of the GAS saddle positions with 182 feasible pedaling places [4]. Setting ° ° was relatively weak in the 225 to 360 range. The RF muscle an appropriate crank length is an important issue. In some was active throughout the cycle, reaching peak muscle activ- studies [32–34], kinematic and inverse kinematic analyses ity at 200 . have been used to investigate the behaviors of cycling power The activity of the TA, VL, and RF muscles when pedal- output and cadence with different crank lengths. However, ing under three different crank lengths have is shown in all these previous studies have focused on t external forces, Muscle activity (%) Applied Bionics and Biomechanics 5 100 100 80 80 60 60 40 40 20 20 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) (a) (b) 0 90 180 270 360 100mm 125mm 150mm (c) ° ° Figure 4: The activity of the TA, VL, and RF muscles during a cycle (0 -360 ) with different crank lengths (100 mm, 125 mm, and 150 mm). (a) TA, (b) VL, and (c) RF. not biological forces. In this study, the effect of three crank The maximum activity of the VL muscle was higher than lengths (100 mm, 125 mm, and 150 mm) on muscle kinetics all other muscles. The maximum activity of the TA muscle (muscle activity) and muscular force was investigated. was the lowest of all the muscles. This study showed that The previous studies investigated the relationship the SOL muscle was active from the top to the bottom of between crank length and muscle behavior. For example, the pedal cycle and that the VL muscle was inactive during Macdermid and Edwards [7] investigated seven female the middle stage of pedaling. In the ankle muscle group, the active phases of the SOL cross-country mountain bike athletes to examine the effect of different crank lengths (170 mm, 172.5 mm, and and TA muscles were staggered, such that the SOL muscle ° ° ° ° 175 mm) on power output during cycle ergometry at a was active during the 0 –45 and 230 –360 sections of the constant cadence (50 rpm). In this paper, only the rela- pedaling cycle, while the TA muscle was active between 45 tionship between crank length and power output was and 225 of the cycle. Comparing the force curves of the studied. two muscles, the TA produced a smaller force than the According to Hicks’ research [35], the validation of a SOL. In the ankle muscle group, the SOL provided the most model requires multiple steps. One important limitation is muscle force during the pedaling cycle. In the knee muscle the lack of verification of in vivo EMG signals on the premise group, the activity of the VL and VM muscles was basically of missing comparative data. Alternatively, validation can be the same through the whole cycle, but the muscle force of achieved by comparing the model and simulation data to the VL was larger than that of the VM. The active stages of independent experiments and other models. In order to pre- the GAS and RF muscles were also different, as the GAS ° ° vent secondary injury during rehabilitation, it is necessary to was active during 0 –225 , while the RF was active during ° ° avoid muscle activation greater than its maximum capacity. 180 –360 of the cycle. Muscle activity (%) Muscle activity (%) Muscle activity (%) 6 Applied Bionics and Biomechanics 1400 1400 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) (a) (b) 1400 1400 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) Angle (°) (c) (d) 1400 1400 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 0 0 90 180 270 360 0 90 180 270 360 Angle (°) Angle (°) 100mm 125mm 150mm (e) (f) Figure 5: The muscle force of six muscles during a cycle (0-360 ) in the different crank lengths: (a) SOL, (b) TA, (c) VL, (d) VM, (e) GAS, and (f) RF. Muscle force (N) Muscle force (N) Muscle force (N) Muscle force (N) Muscle force (N) Muscle force (N) Applied Bionics and Biomechanics 7 References [1] M. R. Silberman, “Bicycling injuries,” Current Sports Medicine 1200 Reports, vol. 12, no. 5, pp. 337–345, 2013. [2] T. Wanich, C. Hodgkins, J. A. Columbier, E. Muraski, and J. G. 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Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Apr 27, 2021

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