In this study, in contrast with the simplified musculoskeletal plants (Hirashima and Nozaki, 2012; Hagio and Kouzaki, 2018; Song et al., 2022), we implemented a more realistic musculoskeletal plant for an isometric force production task by approximating the musculoskeletal dynamics calculation of OpenSim (Delp et al., 2007) so as not to miss the significant properties of musculotendon dynamics such as the passive force element and the force-length relationships of the muscles. In this study, we choose a realistic upper limb musculoskeletal model that we approximate and implement as an affine function of muscle activation (Saul et al., 2015).

The n-th muscle's force, F_n, is given by multiplication of its maximum isometric force, F_ison, normalized force function, f_n(a, l_n), and cosine of pennation angle, ψ_n(l_n) (Equation 1). Additionally, we can give the normalized force coefficient, f_n(a, l_n), as a summation of the active force element, f_ALn(l_n), that is scaled by muscle activation, a_n, and the passive force element, f_PLn(θ) (Equation 2). This is uniquely determined by the length of the muscle fiber, l_n, when enough time for muscle activation and muscle fiber speed convergence has passed.

In the musculoskeletal computation framework of OpenSim, the fiber length, l_n, is searched so that the tendon force and the fiber force, F_isonf_n(a_n, l_n)cos(α_n), are in equilibrium under a constraint that the total length of them is identical to the muscle-tendon length calculated from the musculoskeletal geometry, i.e., the posture of the model, θ. In this study, the posture is given as 2D vectors (θ ∈ ℝ²), with components representing the normalized values of shoulder horizontal flexion/extension angles and elbow flexion/extension angles. We normalized the posture value so that it falls within the interval of (0, 1). Furthermore, because the fiber force depends on muscle activation a_n(Equation 2), the fiber length, l_n, is affected by muscle activation. Therefore, the fiber length is determined by the model's posture and the activation at convergence, l_n : = l_n(θ, a_n), indicating that the muscle force is a function of the musculoskeletal posture and the activation of the muscle. However, it is difficult to find the analytical solution of fiber length directly, and active/passive force–length relationship computation requires large computation costs. Hence, we approximate the muscle force as a first-order form of the muscle activation determined by the model's posture (Equation 3).

Where F_ison denotes the maximum isometric force of n th muscle. We found the active force coefficient, k_ALn(θ), and the passive force coefficient, k_PLn(θ), by applying a least-square matching to the relation map of the muscle activation and the muscle force. We extracted 20 samples of the muscle force by intervals of Δa_n = 0.05 while fixing the posture of the musculoskeletal model. In this research, we approximated the mechanics of the musculoskeletal model at three postures that we refer to as “Base Posture,” “Fully Extended,” and “Mildly Extended” (see below and Section 2.4.1), and we conducted this sampling for each posture.

We choose a two-joint torque production system for the task: shoulder horizontal flexion/extension and elbow flexion/extension, denoted as “elv angle” and “elbow flexion”, respectively, in the model. In this research. we decide the task posture θ_task of the musculoskeletal model, which we refer to as “Base Posture” by horizontally and vertically flexing the shoulder by 30 degrees and 90 degrees, respectively, and flexing the elbow by 90 degrees (Figure 2). Similarly to the previous study (Hagio and Kouzaki, 2018), the target torque combination was randomly chosen from the 12 ideal torque targets. The 12 torque targets are evenly distributed along the circumference of the circle with a radius of 1[Nm] in the torque space (Figure 3A). The resultant torque, T, was calculated by multiplication of the moment arm matrix of N_mus simulated muscles, M(θ)∈ℝ2×Nmus, and muscle force vectors, F=[F1,F2,...,FNmus]⊤ (Equation 4).

Where K^AL and F_iso denote diagonal matrices whose diagonal components are the active force coefficients and the maximum isometric force, respectively, and K^PL denotes a ℝNmus vector of the passive force. a∈ℝNmus denotes the vector of the muscle activation. The mechanical function of the muscles or modules, which is defined as a mechanical pulling vector, is calculated as an active force component of Equation (4), M(θ)F_isoK_ALa. These torque calculation procedures are summarized as orange-colored flows in Figure 3E.

In this research, we extracted 22 task-relevant muscles (N_mus = 22, deltoid anterior [DeltAnt], deltoid middle [DeltMid], deltoid posterior [DeltPst], supraspinatus, infraspinatus, subscapularis, teres minor [TerMin], teres major [TerMaj], pectoralis major clavicular [PecMajClv], pectoralis major sternal [PecMajStr], pectoralis major ribs [PectMajRib], latissmus dorsi thoracic [LatDorTho], latissmus dorsi lumbar [LatDorLum], latissmus dorsi iliac [LatDorIil], coracobrachialis, triceps long [TRILong], triceps lateral [TRILat], triceps medial [TRIMed], biceps long [BICLong], biceps short [BICShort], brachialis, and brachioradialis), which are agonists or antagonists of the joints movement.

We are primarily focused on examining how the mechanical properties of a set of modules influence the performance of modularity in error-based learning. To this end, similarly to the related works, we modeled the motor learning system as a descending feed-forward neural network. Although a feed-forward neural network is a largely simplified motor control system which ignores some important complexities of actual neural networks, such as sensory feedback loop and recurrent connection, it provides powerful description capabilities against data of experimentally observed neural behavior (Rokni et al., 2007; Hirashima and Nozaki, 2012; Takiyama and Okada, 2012; Song et al., 2022). In this research, we modeled two types of neural network (Figures 3B, C): one is a non-synergy model that the CNS directly and individually control muscles, and the other is synergy model that the CNS indirectly controls muscles via a small number of modules. The performance of the network is defined as the learning error at the final learning trials and its learning speed. The function of the network and how it learns are summarized as blue-colored and green-colored flows in Figure 3E.

To assess how the mechanical properties of the modules affect the performance of the network, we proposed two criteria that quantify the mechanical properties of the modules in the task space.

To demonstrate the reproduction capability of our plant for the musculoskeletal model, the mean error and mean absolute deviation (MAD) of each muscle force at the base posture were calculated. Furthermore, R² value and p-value of linear hypothesis test based on F-test (Table 1). All the muscles are well reproduced by linear regression with high reliability (R² > 0.99, p < 0.05). Although most of the large approximation errors of the normalized muscle force concentrate around u = 0, 0.5, 1.0, its approximation error keeps within 2.5 × 10⁻³ (Figure 6B), and mean error of normalized muscle forces keep within 5% and MADs keeps within 6%. These results indicate that our musculoskeletal model reproduces characteristics of the musculoskeletal model, including a significant property, i.e., the passive force (Figure 6A) in the isometric force production.

The overall performance of the non-synergy model and synergy models with three NMF-derived synergies are shown in Figure 7, and the mechanical properties of each module and the performances were summarized in Figure 7D and DB and PB of those sets of modules and individual muscles are summarized in Table 2. Across the three synergy models, significant differences in performance in motor achievement and learning speed are found (Figure 7B; for motor achievement, p = 1.70 × 10⁻⁸⁰, for learning speed p = 4.39 × 10⁻⁶⁸, ANOVA). The synergy model with NMF-derived synergies at the base posture (BP mods) significantly degrades motor achievement compared with the non-synergy model (p = 3.02 × 10⁻¹¹, Wilcoxon). The synergy model with NMF-derived synergies of the elbow fully extended posture (FE mods) showed the worst motor achievement across the three module sets. Similarly, although the synergy model with the NMF-derived synergy of elbow mildly extended posture (ME mods) provides the best across the three modules, it significantly degraded the motor accuracy from the non-synergy model (p = 3.39 × 10⁻⁶, Wilcoxon).

On the other hand, the BP mods significantly promoted the learning speed compared with the non-synergy model (p = 4.98 × 10⁻¹¹, Wilcoxon). The synergy model with MD modules also promoted the motor learning (p = 5.07 × 10⁻¹⁰, Wilcoxon). However, the synergy model with FE modules significantly slowed down the motor learning compared with individual control (p = 3.02 × 10⁻¹¹, Wilcoxon). The results indicate that modularity may degrade motor achievement, and its learning promotion depends on the synergies used in a complex musculoskeletal model. Furthermore, the performance of modularity largely depends on the mechanical properties of the muscle synergies.

To qualitatively demonstrate how the performance of modularity correlates with DB and PB, we conducted extensive simulations of modularity with four modules at the base posture while changing their DB or PB. The scatter plot of the median of the learning performance of modularity and the criteria, i.e., DB and PB, was summarized in Figure 8. While DB showed a strong negative correlation with learning speed (Figure 8C; R² = 0.845, p = 6.97 × 10⁻⁴⁰, N = 90, F test), it shows an almost no correlation with motor achievement (Figure 8A R² = 0.0635, p = 1.13 × 10², N = 90, F test). In contrast, PB consistently and strongly correlated with both motor achievement and learning speed (for motor achievement R² = 0.7608, p = 4.32 × 10⁻³ and for learning speed R² = 0.7471, p = 1.05 × 10⁻⁷, N = 30, F test). These results indicate that PB and DB are effective criteria for evaluating the modules and predicting the performance of modularity with four modules at the base posture. Specifically, while motor achievement mainly depends only on PB, learning speed depends on both PB and DB.

We verified the robustness of the explanation capabilities of the criteria to the number of modules. The results are summarized in the Figure 9. Figures 9A–D illustrates the correlation between the performance of the modularity and PB or DB when N_mod = 22. Similar to the case of N_mod = 4, learning speed strongly correlates with both DB and PB (Figures 9C, D; for DB R² = 0.5647, p = 9.98 × 10⁻¹⁹ and for PB R² = 0.5133, p = 8.46 × 10⁻⁶, F test), and we also found strong correlation of PB and motor achievement (Figure 9A). However, in contrast, DB correlates with motor achievement (Figure 9A). In other cases with different modules (N_mod = 8 and 15), we also found similar tendencies (Figures 9E, H) except for the correlation of DB and motor achievement N_mod = 4 (Figure 9E).

Furthermore, we tested the performance of modularity with different numbers of modules with zero PB and DB. The result is summarized in Figure 10. As for motor achievement, we found significant difference of motor achievement performance across groups (p = 4.66 × 10⁻18, ANOVA), and varies across the case of N_mod = 4, 8 and 15 (Figure 10A; comparison of N_mod = 4 and N_mod = 8, p = 3.39 × 10 − 6, and comparison of N_mod = 8 and N_mod = 15, p = 4.94 × 10 − 4, Wilcoxon). Motor achievement performance of N_mod = 15 and N_mod = 22 did not show significant difference (p = 5.61 × 10⁻¹, Wilcoxon). On the other hand, as for learning speed, there is no significant difference across the groups (p = 4.45 × 10⁻¹, ANOVA). These results suggest that maximum learning speed does not depend on the number of modules, while motor achievement does.

In all cases, PB and DB are independent and there is no multicollinearity (VIF = 1.0008 for N_mod = 4, 1.0005 for N_mod = 8, 1.0677 for N_mod = 15 and 1.0436 for N_mod = 22). Figure 11 illustrates example of the spatial distribution of the performance of modularity in the PB-DB space and comparison of explanation power among the different number of modules. The planes in each figure represent the approximated 3D planes of predicted performances of modularity against PB and DB that assume PB and DB independently affect the performance of modularity. While the independent description of motor achievement by PB and DB was not so successful (Figure 11B; R² = 0.15699, p = 7.7 × 10⁻³. F test, N = 60), it successfully explained the major variance of learning speed (Figure 11A; R² = 0.7220, p = 1.43 × 10⁻¹⁶, F test, N = 60). On the other hand, the explanation power of criteria decreased when the synergy model controls more modules (Figures 11C, F). The independent model of PB and DB exhibit a limited explanation power for a limited part of the variance of both learning speed (R² = 0.254, p = 2.37 × 10⁻⁴ for N_mod = 8, R² = 0.217, p = 9.44 × 10⁻⁴ for N_mod = 15, and R² = 0.280, p = 8.60 × 10⁻⁵ for N_mod = 22) and learning error (R² = 0.1803, p = 3.46 × 10⁻³ for N_mod = 8, R² = 0.2169, p = 9.41 × 10⁻⁴ for N_mod = 15, and R² = 0.294, p = 4.93 × 10⁻⁵ for N_mod = 22).

We verified the robustness of the criteria to the scale of the passive force. Figure 12 illustrates how the explanation capabilities of the criteria change with the scale of the passive force. DB successfully explained the major variance of the learning speed data (Figure 12A; R² = 0.6931 for T_PL = 0.3[Nm], R² = 0.6768 for T_PL = 0.7[Nm]). However, it failed to explain the data on motor achievement except for T_PL = 0.7 [Nm] (Figure 12B; R² = 0.0392 for T_PL = 0.3[Nm], R² = 0.5557 for T_PL = 0.7[Nm]). On the other hand, PB relatively succeeded in explaining the variance of the data. For motor achievement, PB explained a large part of the data when T_PL = 0.3[Nm] (Figure 12C; R² = 0.7252), while it only explained some parts of the data when T_PL = 0.7[Nm] (R² = 0.2411). For learning speed (Figure 12D), similar to motor achievement, the explanation capability of the criteria is strong when T_PL = 0.3[Nm] (R² = 0.9330), while it gets weak when T_PL = 0.7[Nm] (R² = 0.4254).

One of the key contributions of our research is the consideration of the passive force element in muscle mechanics within the criteria and our musculoskeletal model. This element is a significant component of typical Hill-type musculoskeletal mechanics, although it has been underappreciated and neglected in some previous literature (Rokni et al., 2007; Hirashima and Nozaki, 2012; Hirashima and Oya, 2016; Hagio and Kouzaki, 2018; Song et al., 2022). In a static condition, specifically isometric torque production, the upper limb musculoskeletal mechanics (Saul et al., 2015) is simplified into an affine-like system for muscle activation. Despite this simplification, its reproducibility is high (Table 1) due to the negligible second-order or higher-order behavior in this context. As shown in Figure 6, some muscles produce non-zero force even when no control signals are provided (a = 0), and these forces act as constant passive joint torque based on their joint moment arms depending on the posture of the musculoskeletal model.

The passive characteristics of muscles play a crucial role in controlling musculoskeletal mechanics by influencing impedance modification in musculoskeletal systems (Winters et al., 1988) or storing elastic energy (Roberts, 2016). Although it has recently gained renewed attention for its significant role in modeling musculoskeletal mechanics (Herbert and Gandevia, 2019; Herzog, 2019) and is gradually being considered in the context of computational control of realistic musculoskeletal models (Al Borno et al., 2020; Fischer et al., 2021), how it interacts with musculoskeletal control has not been well elucidated.

However, except for a weak correlation case found in lower-dimensional modularity (i.e., N_mod = 4; Figures 8A, 9A), certain correlations between DB and learning error or the speed of the network directly demonstrate the necessity of efficiently occupying task space considering elastic components by utilized modules for higher control performance. This tendency is preserved across different scales of passive-derived torque for learning speed (Figure 12B), while it fails to explain the data variance for learning accuracy (Figure 12A). This failure may stem from the limitation of the network's dimensionality because the explanatory capability of DB for learning error is extremely low only when N_mod = 4, compared with higher-dimensional modularity (Figure 9A). It is considered that this limitation does not cast doubt on the effectiveness of DB.

The other criterion we proposed, i.e., PB, which quantifies the evenness in torque amplitude of the utilized modules, generally succeeds in explaining the data tendencies of learning performances. In contrast to DB, its validity is relatively preserved across the number of network dimensionalities (Figures 9C, D). However, it tends to decline as the amplitude of the passive force increases (Figures 12C, D). This is possible because the definition of PB disregards the passive force element of the muscles, as the results show. Overall, the passive element of muscle significantly affects the selection of the direction of the module torque for the improvement of learning performance, whereas it does not strongly affect the selection of the amplitude of the module torque, at least in the region where the action of passive force is weak. It seems that the direction regularity and power evenness of the torque of the modules serve as a good guideline for modularity in the given task setting.

The previous study (Hagio and Kouzaki, 2018) suggested that the more sparsely the modules exert the forces in the task space, the more accurate and faster motor learning the network obtains. This is the basis of the concept of DB, and it derives from learning characteristics of a neural network. For instance, in a shallow linear neural network, the forces of the modules, F_isoK_ALW_syn, largely affect the eigenvalues of the system matrix of the network, M(θ)F_isoK_ALW_synZ_synW_inp, which dominantly determines the learning speed and largely affects the accuracy of the network. If the forces of the modules are biased in a specific direction, the motor targets in the module-concentrated direction should be achieved more accurately and faster than the other quadrants because the eigenvalue of the system matrix corresponding to the module-concentrated gets high while the other gets low under the Z_syn normalization.

This description is illustrated in Figure 13. In this case, the module set is biased toward the direction of a normal basis (Figure 13A, left). This module set provides a large eigenvalue in the direction while it provides a small eigenvalue in the vertical direction. These biased eigenvalues provide the learning path with fast learning in the force-concentrated direction and slow learning in the vertical direction (Figures 13B, C, green arrows), requiring many steps for overall convergence. On the other hand, the module set unbiased in a specific direction (Figure 13A, right) provides even eigenvalues in the whole direction in the task space. These even eigenvalues provide the learning path with fast convergence for all directions, requiring fewer steps for overall convergence (Figures 13B, C, blue arrows). Importantly, the more learning proceeds, the less update the network has, resulting in a learning equilibrium that derives from forgetting and learning (Figures 13B, C, shaded circle). Weight update of the biased modules soon gets equilibrium with the forgetting compared with unbiased modules because its effective update is smaller. Therefore, biased modules provide less accurate motor achievement and slower learning speed. Such a learning speed-motor achievement relationship is preserved even in a non-linear neural network where the passive force contribution is zero or weak enough (Figure 13D), also seen in the previous study (Hagio and Kouzaki, 2018). In the same context, PB also affects the eigenvalue distribution of the system matrix of the network. Even if the torque of the modules regularly distribute on the task space in direction, unless their gains are not even, the eigenvalues are biased and affect the performance of the modularity. This system characteristic description for learning performance is very similar to and experimentally supported by a very recent work (Barradas et al., 2024). Therefore, DB and PB can be said to have the same mathematical origin as parameters affecting eigenvalues of the system matrix.

However, we should note that the above learning speed-motor achievement description is true only to linear networks or non-linear neural networks where the passive force is zero, negligible, or compensated. If the plant is non-linear, and the passive force is significant, its plausibility can be limited due to the contributions of biomechanical complexities such as changes in moment arm, passive force, and active force coefficient or the non-linearity of the muscles. These components function computationally as an affine transformation (Bebis et al., 1999) and typical rectifying units, such as ReLU layers (Dittmer et al., 2019). These characteristics would interact to affect the learning path of the network and make it difficult to predict what kind of system property is necessary for a better control performance.

To address this question, this study extend the idea of the eigenvalues of the system matrix to the non-linear neural network by dividing the property of the system matrix into two factors; regularity in direction of torque of modules and their power evenness. Through the experiment, as discussed above, although in some cases, they failed to explain the major variance of the data possibly due to the data contamination caused by feasibility cutoff in generating feasible synergies (=0.1[Nm]), the proposed criteria actually clarified the necessary property for improving the performance. Moreover, in terms of the learning behavior of an actual network, the interaction between DB and PB is not collinear; it seems they act almost independently (Figure 11; VIF = 1.0008). Therefore, while originally inspired by linear theory and heuristics, both PB and DB can be considered as independent explanatory variables that demonstrate a certain efficacy in explaining the behavior of non-linear networks and systems. Then, can we further apply the criteria to other situation such as leaning a task that is more dynamic and have multiple optimality such as walking or more dynamic reaching task? We speculate that even in the situation of more dynamic movements, it may be possible to partly expand the discussion of PB and DB when the movement optimization is done by an gradient-based learning algorithm. For example, with a proper expansion, our metrics may be applicable in a gradient-based learning of feedforward arm reaching where an ideal trajectory is already given, and they may inform us what kind of synergies are better regarding converging the error-term. However, even in this simple case, it is still unclear whether expanded metrics are easily measurable or not, and we should investigate the point in future study. In addition, while metrics are relevant only with an error-term, it will not directly explain the other optimality such as energy consumption or cost of transport, which is often used in locomotion studies. Therefore, direct use and expansion of our metrics may have a potential limitation or technological difficulties in application to such complex optimization process. Moreover, for a physiological evidence, it is necessary to see whether the criteria actually correlates with the learning curve data of primate isometric force reaching task in future.

In Experiment 1, we compared the synergy network models and non-synergy models for addressing why muscle synergies extracted from a specific biomechanical contexts sometimes fail to perform well in other contexts. Overall, the synergy model, which utilizes synergies from the non-synergy model optimized for the Base Posture, i.e., BP mods, expedited the learning at the expense of motor accuracy. On the other hand, FE and ME mods showed high DB and PB (Table 2, Figure 7), and their performance significantly degraded despite the postural changes in the experiment are relatively small. It suggests that minor difference in biomechanical contexts can easily make modularity using context-specific synergies less effective. Consistent with the results of the previous study (Kutsuzawa and Hayashibe, 2022), the modularity performance largely depends on the biomechanical context from which the synergies are extracted.

However, it is important to acknowledge the limitations in our experimental protocols that may have influenced the results. We used NMF to extract each set of synergies from the non-synergy model optimized for each BP, FE, or ME. It is worth noting that NMF does not guarantee solution uniqueness or convexity of the objective function, i.e., square error of data reproduction, and determining the number of synergies is somewhat arbitrary (Barradas et al., 2020). Therefore, the extraction of synergies using NMF can miss significant components for control, and variability of synergy organization in each extraction can provide synergies with different PB and DB. These experimental limitations may have influenced the performance of each synergy model.

Furthermore, synergies extracted from the non-synergy model are features of the control and implicitly encode prior knowledge of a particular biomechanical context in which they are extracted. This means that the performance of each synergy model can partly depend on the similarity of musculoskeletal mechanics in a position of interest. This qualitative premise on simulated muscle synergies, i.e., assuming only context-specific synergies, can be distinct from the essential purpose or function of actual muscle synergies. In any case, the limitations of experimental procedures and synergy dependency in control performance obscure the contribution of muscle synergies in control. Then, what is the plausible role of muscle synergies in motor learning?

From the perspective of optimality, our results highlight the necessity of the CNS to store specific synergies for every different context, i.e., posture, as previous studies suggested (de Rugy et al., 2013; Sharif Razavian et al., 2015). If the CNS were provided with enough modules (e.g., N_mod > 4) that minimize both DB and PB corresponding to the posture-dependent limb mechanics, they achieved much more accurate and faster control than individually muscle-optimized control (see Figures 7C, D, 10A, B). However, strategy of storing every context-dependent control and synergy poses the problem of having to store an unlimited number of motor programs (Loeb, 1983). One possible solution to this memory storage and optimality problem is approximating a wide range of movements through generalizable synergies and subsequent optimization through context specification of the synergies as necessary.

Similar to the good-enough control strategy (Loeb, 2021), generalizable muscle synergies can be utilized across various motor contexts with reasonably good performance. While there is room for debate on such synergies, it can be potentially relevant to the shared muscle synergies observed in various static (Ting and Macpherson, 2005; Torres-Oviedo et al., 2006; Roh et al., 2012; Leonardis et al., 2020; Pham et al., 2023) and dynamic motor tasks or contexts (d'Avella and Bizzi, 2005; Chvatal and Ting, 2013; Barroso et al., 2014). Interestingly, in the lower limb static task of the cat (Torres-Oviedo et al., 2006), the experimental study reported that the rotation of the force direction exerted by shared muscle synergies is similar to limb axis rotation angles (McKay and Ting, 2008). Sohn et al. demonstrated that spatial organization of these synergies can be formed in pursuit of generalization rather than optimization for each biomechanical context (Sohn and Ting, 2016). We can relate the formation of such generalizable synergies to the minimization of DB. Suppose spatial organization of generalizable synergies is formed to minimize the average DB across similar biomechanical contexts. In that case, the CNS can efficiently generalize them for learning arbitrary similar biomechanical contexts quickly and with good enough generalization performance on average. Such DB-minimizing generalizable synergies may be represented at the medulla or spinal cord (Giszter et al., 1993; Roh et al., 2011), and robustly preserved through the subsequent development (Yang et al., 2019).

On the other hand, the specification of synergies for the optimization may be done at the higher level of motor planning, such as cortical regions where more complicated information of dynamics is encoded as synergies (Overduin et al., 2012, 2015; Amundsen Huffmaster et al., 2017). In these areas, minimization of both DB and PB is likely associated with movement optimization. However, modulation of PB may be a separate process from DB. Our experiment demonstrated that PB and DB affected learning independently to some extent. It may suggest that modulation of DB and PB of muscle synergies do not necessarily share the exact neural mechanisms. One recent study (Yaron et al., 2020) reported that, unlike the force direction of modules, the force amplitude were adjusted in supralinear form. Moreover, several suggest that sensory feedback, essential for motor planning and online control, affects the amplitude and timing of muscle synergies control while never affecting synergies' spatial organization (Inglis et al., 1994; Stapley et al., 2002; Cheung et al., 2005). PB modulation may occur in areas related to online control planning and feedback control. Meanwhile, DB modulation may take place in areas related to offline motor planning schemes, such as the selection or combination of synergies expressed in cortical areas and the coordination of the extent to which non-synergetic control elements are intervened through a cortico-motoneuronal pathway (Isa et al., 2007) or reticulospinal and vestibulospinal pathways (Cruce, 1974).

To summarize, our research has shown that the performance of fixed muscle synergy control through learning can vary significantly depending on the synergy utilized. This highlights the need to consider the role of synergy in motor control beyond a simple comparative approach to optimality. Instead, we should focus on how to exploit or overcome the dependence of synergy on control performance, such as the pursuit of generalizability or the modulation of synergy with learning. These insights have important implications for our understanding of muscle synergies and their role in motor control.