Title: Motor variances in arm cranking as a function of the resistance

48 Background: Arm cycling on an ergometer is common in sports training and rehabilitation 49 protocols, but has not been widely studied from an aspect of neural control. The hand movement 50 is constrained along a circular path, and the user is working against a resistance, maintaining a 51 cadence. Even if the desired hand trajectory is given, there is the flexibility to choose patterns of 52 joint coordination and muscle activation, given the kinematic redundancy of the upper limb. 53 With changing external load, motor noise and changing joint stiffness may affect the pose of the 54 arm even though the endpoint trajectory is unchanged, unless a control mechanism maintains the 55 same arm configuration in corresponding time points of the cycles. However, the effect of crank 56 resistance on the variances of arm configuration and muscle activation has not been investigated, 57 yet. Methods: Fifteen healthy participants performed arm cranking on an arm-cycle ergometer 58 both unimanually and bimanually with a cadence of 60 rpm against three crank resistances. We 59 investigated arm configuration variances and muscle activation variances. Arm configuration 60 was given by inter-segmental joint angles, while muscle activation by surface EMGs of arm 61 muscles. Applying multifactorial ANOVA we evaluated the effects of resistance conditions. 62 Results: Arm configuration variance in the course of arm cranking was not affected by crank 63 resistance, while muscle activation variance was proportional to the square of electromyographic 64 muscle activity. Furthermore, the shape of the variance time profiles for both arm configuration 65 and muscle activation was not affected by crank resistance independently on cranking being 66 performed unimanually or bimanually. Conclusions: Contrary to the prevailing assumption that 67 an increased motor noise would affect the variance of auxiliary movements, the influence of 68 noise doesn’t appear at the arm configuration level even when the system is redundant. Our results suggest that neural control stabilizes arm configurations against altered external force in 70 arm cranking. This may reflect the separation of kinematic- and force-control, via mechanisms 71 that are compensating for dynamic non-linearities. Arm cranking may be suitable when the aim 72 is to perform training under different load conditions, preserving stable and secure control of 73 joint movements and muscle activations. 74


48
Background: Arm cycling on an ergometer is common in sports training and rehabilitation 49 protocols, but has not been widely studied from an aspect of neural control. The hand movement 50 is constrained along a circular path, and the user is working against a resistance, maintaining a 51 cadence. Even if the desired hand trajectory is given, there is the flexibility to choose patterns of 52 joint coordination and muscle activation, given the kinematic redundancy of the upper limb. 53 With changing external load, motor noise and changing joint stiffness may affect the pose of the 54 arm even though the endpoint trajectory is unchanged, unless a control mechanism maintains the 55 same arm configuration in corresponding time points of the cycles. However, the effect of crank 56 resistance on the variances of arm configuration and muscle activation has not been investigated, 57 yet. Methods: Fifteen healthy participants performed arm cranking on an arm-cycle ergometer 58 both unimanually and bimanually with a cadence of 60 rpm against three crank resistances. We 59 investigated arm configuration variances and muscle activation variances. Arm configuration 60 was given by inter-segmental joint angles, while muscle activation by surface EMGs of arm 61 muscles. Applying multifactorial ANOVA we evaluated the effects of resistance conditions. 62 Results: Arm configuration variance in the course of arm cranking was not affected by crank 63 resistance, while muscle activation variance was proportional to the square of electromyographic 64 muscle activity. Furthermore, the shape of the variance time profiles for both arm configuration 65 and muscle activation was not affected by crank resistance independently on cranking being 66 performed unimanually or bimanually. Conclusions: Contrary to the prevailing assumption that 67 an increased motor noise would affect the variance of auxiliary movements, the influence of 68 noise doesn't appear at the arm configuration level even when the system is redundant. Our 69 cycling movements is limited relative to that on lower limb cycling. However, the importance of 87 arm cycling has recently been supported by several investigations. Arm cycling in males and 88 females has been compared [8], and sex-related differences in peak and mean power were more 89 pronounced in arm cycling than in leg cycling [2]. Other noteworthy studies include the 90 physiological characteristics of eccentric arm cycling [9]; the influence of differences in arm 91 cycling at various cadences on the modulation of supraspinal and spinal excitability, and the 92 (soleus H reflex) [10]. No significant differences were seen in the level of suppression of the H 94 reflex at different crank loads. It was proposed, and supported by data, that neural coupling 95 between the arms helps to increase movement symmetry and to ensure stable arm cycling [11]. It 96 has been shown that arm cycling training improves strength, coordination of muscle activity 97 during other types of motor tasks, such as walking, and neurological connectivity between the 98 arms and the legs [12]. 99 We investigate arm cranking from the aspect of motor variance. We asked the following 100 question: "How are the variances of arm cycling (cranking) movements affected if the resistance 101 of the crank is changed?" There is literature in robotics about control of manipulators where the 102 movement of the end-effector is constrained, but the load on it is changed [13,14]. This 103 literature offers models for accomplishing the task. Our particular purpose was to analyze the 104 physiological parameters of human subjects during a constrained motion (arm cranking) when an 105 increasing load is applied (effect of crank resistance). The metrics we analyzed are the arm 106 configuration variance (in joint space) and the muscle activation variance (in muscle space). 107 These parameters can indirectly validate the type of control utilized for this complex task. The 108 maintenance of the same arm configuration is not guaranteed as the resistance of the crank increases. It 109 has been demonstrated that joint stiffness increases as the load at the end-effector increases [15]. Changes 110 in joint stiffness at each joint can substantially change the pose of the arm even though the endpoint 111 trajectory is unchanged. If the arm configuration variance is not affected by crank resistance, it 112 ensures the separation of kinematic-and force-control [16,17] where the kinematic task can be 113 maintained safely when crank resistance is altered. Knowing the type of control strategy is 114 important in training and rehabilitation protocols. It is not the aim of this paper to evaluate 115 rehabilitation protocols, but to experimentally examine this potentially useful feature of arm 116 rehabilitation [18][19][20]. 118 The research on motor variance of multi-joint and multi-muscle systems covers several motor 119 tasks but regarding arm movements, most of them are unconstrained, reaching or pointing 120 movements [21][22][23]. It has been reported that for object transporting arm movements, the joint 121 configuration variance depends on the weight of the object held in the hand [24]. It is a 122 remaining question and it is investigated to a smaller extent that how motor variances in joint 123 space and muscle space are affected by external loads, in the case of constrained arm 124 movements, when the end effector (hand) path in the workspace is constrained [25]. Here we 125 extend these studies. When arm cycling on an ergometer, the hand path is constrained, and the 126 variance in the endpoint trajectory is assumed to be very small if the hand moves on a fixed 127 circle with constant angular velocity. 128 However, if the external load does not have an effect on the endpoint trajectory, it still may have 129 an effect on the arm configuration variance. During arm cycling, when the endpoint trajectory is 130 fixed, there is still the possibility for an infinity of change of the arm configuration that would 131 result in the same endpoint trajectory. It is not trivial that the effect of the load does not appear at 132 joint rotations. The underlining notion of motor variances famously reported by Bernstein [26], 133 who observed that when the blacksmith wields the hammer, the hammer's trajectory is more 134 reproducible than the arm configurations used to perform that movement. In our case, the 135 endpoint variance is very small by definition, but it does not imply automatically that the joint 136 configuration is reproducible during consecutive cycles. 137 In the present study, we investigate unimanual and bimanual arm cycling, focusing on motor 138 variance at the joint and muscle levels. 139 that variances in joint angular displacement are impervious to crank resistance but that variances 141 in muscle activities (EMG) increases quadratically as the crank resistance increases. This 142 behavior would underline that 1) there exists a mechanism for the concurrent control of motion 143 and force where the two can be controlled separately, 2) the controller of the motion is linear, 3) 144 there exists a predictive mechanism capable of compensating the dynamic non-linearities. as the torque with which the crank resists rotation. In unimanual cycling, the low, moderate and 196 high resistances were 1.16 Nm, 2.08 Nm, and 3.09 Nm, respectively. In bimanual cycling, they 197 were 1.16 Nm, 3.09 Nm, and 6.14 Nm, respectively.

275
Neither the factors nor their interaction with each other creates a significant difference for 276 the arm configuration variance. On the other hand, we can observe a significant effect of both the 277 the EMG. Furthermore, there is a significant interaction between the subject and side (F=4.52, 279 p=0.0282) and subject and mode, indicating that subjects perform the task with a statistically 280 significant difference between the two sides, and between double-hand and single-hand cycling 281 when compared to each other. This suggests that the subject is a confounding factor and must be 282 considered as a random factor. 283 284

Kinematic variances 285
Crank resistance (CR) did not have a significant effect on angular variances (F=1.43, 286 p=0.2573). Furthermore, the interaction between load and cycling mode was also not significant 287 (F=0.28, p=0.7574) (Fig. 2 A1 and A2). Side (F=0.15, p=0.7062) and cycling mode (F=0.5, 288 p=0.4894) did not have a significant effect on angular variances ( Fig. 2B and 2C).  CRs (Fig. 3). 302 303 Insert Figure 3 here 304 Higher crank resistance was associated with higher muscle activity variances (Fig. 4 A1  316 and A2) in all examined cycling conditions for both arms. This difference was significant when 317 low and high crank resistance conditions were compared in either bimanual (p<0.0001) or 318 unimanual cycling (p<0.0001) according to a post-hoc multicompare analysis based on 319 Tukey's honestly significant difference criterion. This was also true when moderate and high 320 RCs were compared in either bimanual (p<0.00025) or unimanual cycling (p<0.0001). 321 Comparing bimanual and unimanual cranking, the muscle activity variance was higher for 322 cranking by the left and right arm did not show significant difference (Fig. 4 C). 324 325 Figure 4 here 326 In addition to comparing average muscle activity variances, muscle activity variance 335 profiles were also compared among various cycling conditions. It was found that the shape of the 336 variance profiles did not change for the specific arm, only its magnitude changed according to 337 crank resistance. This finding is presented in Fig. 5. 338 339 Insert Figure 5 here 340  (Table 1). 352 Correlation coefficients between 0.40 and 0.59 were defined as 'moderate positive correlation', 357 between 0.60 and 0.79 were defined as 'strong positive correlation', and between 0.80 and 1.00 358 were defined as 'very strong positive correlation'. 359 360 Naturally, if muscles are working against higher external resistance, the EMG amplitudes 361 increase. On the other hand, the profile of the muscle activites does not necessarily need to 362 remain the same, but we can reveal that it does within the same arm/condition. If the amplitude 363 increases in such a manner that the signal with lower values is simply multiplied by a constant 364 the control variable needs to be linear [13], and the system to be controlled is highly nonlinear. 366 Indeed, the force of each muscle (and the activation signal that mediates it) is required to 367 accomplish 3 distinct tasks. These tasks are 1) providing the operational command for the hand 368 to follow the prescribed trajectory, 2) compensating non-inertial forces such as centrifugal and 369 Coriolis forces that are generated by the nonlinear dynamics as a result of the movement and, 3) 370 generating additional forces for matching the resistance. Thus, for the variance to change 371 quadratically between load conditions the controller must be able to decouple these components 372 to guarantee that the operational task remains the same and that the resistance force is matched. 373 We investigated how EMG amplitudes and muscle activity variances increased when crank 374 resistance increased. We found that the variances changed almost quadratically with respect to 375 the change in average muscle activities (EMG values). Fig. 6. presents that the average variance 376 of muscle activities (EMG signals) increases approximately at the same rate as the mean squared 377 EMG values when the crank resistance is increased. 378 For each participant, the average EMG values across time was computed for moderate and low 379 crank resistances separately. The average obtained for moderate resistance was divided by the 380 average that was obtained for low resistance. Thus, we get one ratio for each participant. The 381 squares of this ratios were averaged across partcipants and this average values are presented at 382 variances of EMG magnitudes in high respect to low CR were also computed and presented. We 387 compared the ratio of variances and the square of ratio of muscle activities applying paired 388 sample t-test, (p=0.05). There were no significant differences in any cycling conditions (Fig. 6. resistance, what changes is the additional effort necessary to execute the movement. This 431 aspect suggests that when a mapping is chosen between operational space and joint space, it is 432 maintained as the resistance at the crank increases. Furthermore, it provides evidence for the 433 existence of an independent control of force and position [16]. The central nervous system 434 trajectory and velocity is executed. On the other hand, it is able to regulate the force the hand 436 needs to apply without changing the kinematics, even though the kinematics and force generation 437 are highly coupled through the non-linear dynamics of the neuro-mechanical system. The CNS 438 thus parses muscular force for specific tasks, separately controlling the force necessary for the 439 kinematics and the additional force required for the increasing crank resistance. 440 Studies on bimanual circle drawing tasks found that movements of the non-dominant arm 441 was more variable than the movement of the dominant arm [34]. We did not find variance related 442 differences between the arms in our experiments on constrained arm cranking movements. This 443 may be explained by the fact that the hand path was fixed and the execution of the task did not 444 require high dexterity. Future work will require to study variability of movements of the two 445 arms in other constrained motor tasks and the relation of such variabilities to the dynamic-446 dominance hypothesis that was developed and applied for targeted reaching movements [35]. 447 448

Muscle activity variances 449
Cycling against a higher crank resistance requires increased muscle activity. It is a 450 general assumption that activation signals with higher amplitudes produce higher motor 451 variances due to signal-dependent noise. In the present study, we found that measured EMG 452 signals have higher variances in higher CRs. It is unknown whether larger variances, observed 453 when cranking was performed against higher CR, are a consequence only of higher signal 454 amplitudes or if other motor control factors also contribute. The magnitude of muscle activity 455 variances was significantly affected by crank resistance. However, the shape of the variance 456 curve did not depend on crank resistance (Fig. 5, Table 1). 457 hand, the resulting kinematic (angular) variances were unchanged. Our results support the idea 459 that arm configuration variances while cycling on an ergometer are not affected by crank 460 resistance and that during this motor task, neural control stabilizes arm configurations against 461 altered external force. This conclusion held true for both arms. This suggests that the CNS is able 462 to modulate separately a kinematic task and a force task. Impedance control has been proposed 463 as a strategy for the execution of such combined tasks [16]. Considering the significant standard deviation of the variance in our measurements of the 472 joints' angles, we can analyze different sources for this phenomenon. Errors could come from the 473 instrumental setup; on the other hand, we have placed particular care on these aspects. 474 Specifically, we have used a system that is able to measure the position of the limbs without 475 direct contact and with submillimeter precision. Thus, we have avoided errors that can come 476 from using systems like an encoder, where plays in the kinematic chain between hand and 477 transducer via a transmission can affect the measurements. In our setup, measurements strictly 478 depend on what the subject has performed and not from additional errors in the measurement 479 chain. The precision of the ultrasound system we utilized is actually very high. Considering an 480 segment equal to 1 millimeter, the average angular error due to the measurement system is about 482 0.2 degrees. It can be seen that the standard deviation of the angular variance is much larger than 483 that. Therefore, we can see that the variance of the joint angular displacement does not depend 484 on the measurement errors but is strictly depending on the task. Considering the Uncontrolled 485 Manifold Theory, we can speculate that there are infinite poses that can guarantee proper 486 tracking of the handle along the circular trajectory. Thus, the subject is free to choose among 487 every possible solution without compromising the kinematics of the endpoint. 488 489

Useful insights for rehabilitation 490
An aspect for rehabilitation practice that the present study provides is to help to plan 491 proper upper body exercises for people with paraplegia, whose lower limbs are paralyzed. It is 492 essential to prevent further health problems, which would be the consequence of a physically 493 inactive lifestyle of people with paraplegia. Arm-cycling on arm-cycle ergometer offers them an 494 excellent exercise which helps to enhance physical capacity and maintain stable movement 495 execution when employing increased crank resistances during the series of training sessions. As 496 the arm configuration variance is not affected by crank resistance, this motor task may involve a 497 stable movement execution and may be well used in rehabilitation and training protocols. 498 Another example of a potential application is functional electrical stimulation (FES) driven arm 499 cycling for people with tetraplegia, who are unable to move the arm crank voluntarily (Zhou et 500 al. 2018). When spinal cord injured individuals are not able to generate active muscle forces 501 voluntarily, FES controlled arm cycling is a useful exercise. The aforementioned practice helps 502 to strengthen muscles by increasing crank resistance during the series of training sessions. If 503 individuals, then when resistance is increased during FES driven cranking, the amplitude of the 505 stimulation has to be increased, and the stability of the control can be conserved. This may make 506 the FES control easily adaptable to increased crank resistance. In spite of the limitation that in 507 this study we investigated unimpaired participants, we feel that the results provide a starting 508 point and further studies may evaluate related training protocols for motor impaired individuals. 509 510

Conclusions 511
In summary, we investigated arm cranking movements performed by able-bodied 512 individuals on a cycle ergometer and addressed the question of how external load (crank 513 resistance) affects the variances of arm configuration and muscle activation. The arm 514 configuration variance was not affected by the crank resistance either in unimanual or bimanual 515 cranking. This aspect was surprising because even though the hand path and cadence were 516 constrained, a variability could be expected given that an increased resistance is associated to an 517 increased motor noise that could have affected the time profile of the arm configuration variance. 518 Muscle activation variances increased quadratically with respect to the change in average muscle 519 activities as the crank resistance increased, underlining a linear control system. This observed 520 kinematic, and muscle activity variances may reflect the separation of kinematic-and force-521 control. While a single controller based on the equilibrium point hypothesis was proposed in 522 [20], more recent literature put forth the need for two separate controllers to compensate for 523 dynamical forces [18]. Our investigation suggests that the control scheme appears to allow a 524 freedom, must all increase -fold. These terms represent the product of the transmission ratios 592 for the generic degree of freedom and its derivative with respect to . It is obvious that if the 593 transmission ratios do not change, we have that = 0 and thus the result is absurd. 594 To allow for constant transmission ratio, and therefore to maintain the variance constant, there 595 needs to be an additional term in the equation that is able to control the torque without changing 596 the kinematic. 597  Mean muscle activity variances A1) in low, moderate, and high resistance conditions for 718 bimanual cycling (across participants and sides); A2 ) in low, moderate, and high resistance 719 conditions for unimanual cycling (across participants and sides); B) in bimanual and unimanual 720 arm cycling (mean across participants, resistances, and sides F=20.11, p=0.0005); C) in left and 721 right arms (mean across partcipants, resistances and modes F=0.15, p=0.7062); 722

Figure Captions
Lines above bars denote standard errors of the mean. 723