Muscle shape changes in Parkinson's disease impair function during rapid contractions

Parkinson's disease (PD) is a progressive neurodegenerative disorder characterized, among the others, by muscle weakness. PD patients reach lower values of peak torque during maximal voluntary contractions but also slower rates of torque development (RTD) during explosive contractions. The aim of this study was to better understand how an impairment in structural/mechanical (peripheral) factors could explain the difficulty of PD patients to raise torque rapidly.


| INTRODUCTION
Parkinson's disease (PD) is a progressive neurodegenerative disorder of the basal ganglia characterized, among the others, by akinesia, bradykinesia, hypokinesia, muscle stiffness, and tremor. 1 Patients with PD have functional disability, 2 impaired work economy, and increased risk of falls. 3 In addition, PD patients are characterized by muscle weakness and present lower values of peak torque during maximal voluntary contractions (MVC) compared with their healthy peers, the severity of this torque reduction being strictly related to the severity of the disease. 4 The rate of torque development (RTD) is another useful parameter to describe muscle function: It reflects the capacity to exert force rapidly in response to different tasks, including daily situations such as avoiding an obstacle while walking 5 or recovering from an unexpected loss of balance. 3 RTD could be an important functional outcome for PD patients, due to their slowness in both initiating and performing a movement. 2 RTD has been shown to be more sensitive than peak torque in detecting chronic changes induced for example by aging, immobilization/ disuse, strength training, and rehabilitation, but also in detecting acute changes associated with exercise, muscle damage, and pain. 6,7 According to the literature, RTD is dependent on both neural/nervous (central: e.g., discharge rate, neural amplitude) and structural/mechanical (peripheral: e.g., muscle-tendon stiffness, fiber type, muscle geometry) factors. In healthy people, RTD is primarily determined by neural parameters (e.g., Ref. [8,9]), and neural parameters were also shown to affect RTD in PD patients: A reduction in RTD in this population was indeed explained by an impairment in voluntary muscle activation, an increased antagonist muscle co-activation, and an increased variability in motor unit discharge rates compared to healthy controls. [10][11][12] Structural/mechanical parameters (at the muscletendon level) were also shown to play a role in determining RTD. As an example, the stiffness of the muscle-tendon unit has been positively associated with an increase in RTD in healthy young subjects [13][14][15] : A stiffer MTU could transmit force from the muscle to the joint segment more rapidly than a compliant MTU. On the other hand, an impairment in dynamic shape changes during contraction has been associated with a decrease in RTD in healthy young subjects. 15,16 Dynamic shape changes depend on muscle tone, muscle architecture, and muscle mechanical properties 17 and can be investigated (in pennate muscles) by computing "belly gearing" (e.g., the architectural gear ratio). During contraction, skeletal muscles could change their thickness and/or width, their fibers can rotate and pennation angle can increase. 17 Fascicle rotation (i.e., the change in pennation angle relative to rest) contributes per se to the overall muscle length changes in addition to the changes in length attributed to fascicles shortening/ lengthening alone. The mismatch between muscle and fascicles velocity can be described in terms of belly gearing (G b : muscle velocity/fascicles velocity). High belly gearing, where fascicles undergo significant rotation, enables muscle shortening velocity to exceed fascicles shortening velocity. In young subjects, higher values of belly gearing have been correlated with higher values of RTD 15,16 and muscle power, 18 suggesting that this parameter could play a role in determining the rise of torque in humans.
To note, belly gearing is not dependent on nervous or neural factors; it is, rather, the result of an interaction between muscle fibers behavior and the characteristics of the connective tissues. As an example, Holt et al 19 reported that muscles from aging rats could not modulate gearing, due to high levels of muscle stiffness and an increased amount of intramuscular connective tissues. Moreover, Son and Rayman 20 showed that belly gearing is impaired in subjects after stroke, and this could partially explain muscle weakness in this population.
The rationale behind this investigation was, therefore, to investigate the structural/mechanical determinants of RTD in PD patients, to deepen our understanding on the functional capacities of the musculoskeletal system in this population. More specifically, we focused on MTU stiffness and dynamic muscle shape changes (belly gearing) because these parameters are likely affected by this pathology. Indeed, hypertonia and high muscle stiffness are typical of PD patients 1 and are expected to affect the muscle capability to exert force rapidly (RTD), contributing in explaining their loss of function.
Hence, in this study, we combined ultrasound measurements with EMG, torque, and kinematic data during maximal explosive contractions to investigate muscle-tendon mechanical behavior in PD patients and healthy matched controls with the aim to investigate how an impairment in structural/mechanical parameters (at the muscle-tendon level) could affect the capability to raise torque rapidly in this population.
We hypothesized that this impairment not only depends on neural/nervous factors but is also related to an impairment in muscle-tendon mechanical proprieties. Indeed, we expected that people with PD will show lower values of belly gearing and higher MTU stiffness compared to healthy controls, potentially affecting their explosive torque capacity. Furthermore, since in Parkinson's disease symptoms often begin on one side of the body and usually remain worse on that side, even after symptoms begin to affect the other, 21,22 we also investigated the differences between the affected and the less affected side in this population.

| RESULTS
Demographical and physical characteristics of controls and PD patients are reported in Table 1. No significant differences (unpaired Student's t test) were observed regarding age, body mass, and stature between groups. No differences were also observed in terms of energy expenditure (IPAQ scores >2500 indicate physically active subjects) nor in terms of cognitive function (MMSE scores >24 indicate no cognitive dysfunction) between controls and patients. In patients, the UPDRS score ranged from 9 to 46 and the H&Y score from 0.5 to 3, indicating a mild to moderate stage of the pathology in our sample.
No significant differences were observed at rest in architectural parameters (PA, MT, and FL) between participants ( Table 2) whereas a main effect of group (p < 0.001) was observed for the changes in muscle thickness (ΔMT) and pennation angle (ΔPA) from rest to contraction: Dynamic muscle shape changes were reduced in PD patients compared to controls. Significant differences were observed between PDA and PDNA in ΔPA but not in ΔMT.
Control participants showed higher values of maximal torque (T max : about 170 Nm) and a better capacity to express force rapidly (RTD peak : about 500 Nm/s); a main effect of group (p < 0.001) was observed in both cases. T max and RTD peak were reduced in PD patients: about 130 Nm and 350 Nm/s, respectively (as an average between PDA and PDNA) ( Table 2) and RTD peak occurred earlier in PDA (about 50 ms after torque onset) than in PDNA and controls (about 60-70 ms) ( Table 2).
To better characterize the differences between controls and PD patients, torque, RTD, and EMG values were normalized and compared in the different time windows.
Torque and RTD values normalized to the maximal voluntary torque in the different time windows are reported in Figure 1 (nTorque: panel A; nRTD: panel B) for PD patients (affected and less affected leg) and controls (dominant leg only). A main effect of group and time was observed in both cases (nTorque: p = 0.043 and 0.001 for group and time, respectively; nRTD: p = 0.043 and 0.001 for group and time, respectively), but a significant interaction (group × time) was reported (p = 0.043) only for nRTD. Specifically, controls showed higher values of nTorque and nRTD compared to PDA and PDNA, but no significant differences were observed between PDA and PDNA in both variables. To note, control participants showed higher values of nRTD compared to the pathological population only in the first three time windows (where a significant interaction between group and time was observed).
EMG values (normalized to the maximal voluntary activity) in the different time windows are also reported in Figure 1 (nEMG: panel C). The EMG activity was affected by group (p = 0.002) and time (p = 0.027), with no significant interaction (group × time). Significant differences in nEMG were observed between controls and PDA as well as between PDA and PDNA (but no significant difference was observed between controls and PDNA) in all the investigated time windows.
Finally, in Figure 1 are also reported the values of belly gearing (G b : panel D) for all the investigated time windows. G b was affected by group (p = 0.041) and time (p < 0.001), and a significant interaction (group × time) was observed (p = 0.019). G b was higher in controls, and significant differences were also reported between PDA and PDNA. In all groups, G b decreased as a function of time, with significant differences in all time windows (p < 0.01); however, the differences between population (interaction) are significant only in the first three time windows (from 0 to 75 ms after torque onset).
Considering the peak values of the investigated variables, a main effect of group (p < 0.001) was observed for: nRTD peak (panel A), nEMG peak (panel B), muscle-tendon stiffness (k MTU , panel C), and the average belly gearing from torque onset to peak nRTD (G b 0-peak , panel D), see Figure 2. Comparison between groups revealed that controls had higher values of nRTD peak compared to PDA and PDNA (p < 0.001) and higher values of G b 0-peak compared to PDA and PDNA (p = 0.018 and 0.028, respectively) but lower values of k MTU compared to PDA and PDNA (p = 0.011 and 0.012, respectively). Furthermore, control participants had higher values of nEMG peak compared to PDA (p = 0.003). By comparing the affected and less affected limb, PDNA reached higher values of nRTD peak (p = 0.040), lower values of k MTU (p = 0.047), and higher values of G b 0-peak (p = 0.044) compared to PDA, whereas no significant differences were reported between PDA and PDNA in nEMG peak .
T A B L E 1 Participants' characteristics (data are means ± SD).

| Determinants of nRTD peak
To better understand the mechanisms that determine explosive torque capacity in PD patients, possible correlations among variables (peak values) were investigated (simple linear correlations are reported in Figure S2). A multiple stepwise linear regression analysis was utilized to assess the magnitude of the influence of the analyzed variables (G b 0-peak , nEMG, and k MTU ) on nRTD peak . Since we were interested in understanding the strength of the influence that each variable has on nRTD peak (and not in its prediction), the statistical effects of each parameter for all the investigated groups are reported in Table 3, whereas the resultant equations are not reported. In all groups, G b 0-peak played a significant role in determining nRTD peak ; nEMG was also a predictor of nRTD peak but only in control and PDNA. Only in PDA, k MTU was included in the model to predict nRTD peak .

| Determinants of belly gearing
Since belly gearing played a significant role in determining nRTD peak , we also investigated the possible determinants of this parameter (simple linear correlations are reported in Figure S2).
A multiple stepwise linear regression analysis was utilized to assess the magnitude of the influence of the analyzed variables on belly gearing. The parameters included in the model were ΔPA, ΔMT, and k MTU . Since we were interested in understanding the strength of the influence that each variable has on G b 0-peak (and not in its prediction), the statistical effects of each parameter for all the investigated groups are reported in Table 3, whereas the resultant equations are not reported. The changes in pennation angle played a significant role in determining G b 0-peak in all groups and the changes in muscle thickness played a significant role in determining G b 0-peak in PDA and PDNA.

| Relationships between clinical score and structural parameters
To better understand the effect of PD on muscle-tendon mechanical function, possible correlations between clinical score (UPDRS) and mechanical variables were investigated (see Figure 3). In PDA, a significant negative relationship between UDPRS score and belly gearing was observed (UPDRS = −300 × Gb 0-peack + 347, R 2 = 0.46, p = 0.0053), as well as a significant positive correlation between UDPRS score and MTU stiffness (UPDRS = 0.28 k MTU : 37.23, R 2 = 0.47, p = 0.0049). No relationships were observed between UPDRS and belly gearing or MTU stiffness in the less affected side (PDNA).

| DISCUSSION
Explosive torque capacity is an important functional parameter for daily life activities in PD patients, due to their slowness in both initiating and performing a movement. Muscle weakness and reduced muscle strength are symptoms that PD patients share with healthy aged individuals. For this reason, our groups were matched for age. In addition, these parameters are affected by the level of physical activities: Thus, our groups were also matched for IPAQ score. In young and healthy subjects, explosive torque capacity depends on both neural/nervous (central) and Abbreviations: FL, fascicle length at rest; MT, muscle thickness at rest; PDA, affected limb in PD patients; PDNA, less affected limb in PD patients; RTD peak , the highest RTD value; t RTD peak , the time at which RTD peak occurs; T max , maximal torque during the isometric contractions; ΔMT, changes in muscle thickness (from 0 to RTD peak ); ΔPA, changes in pennation angle (from 0 to RTD peak ); PA, pennation angle at rest.
T A B L E 2 Architectural parameters (vastus lateralis), (absolute) torque and RTD values (data are means ± SD).
structural/mechanical (peripheral) parameters. In this study, we investigated "central" parameters by assessing EMG activity, that was observed to differ between patients (PDA, affected limb) and controls but not between controls and PDNA (the less affected limb); this suggests a specific neural/nervous effect on the most affected side. We also investigated "peripheral" parameters by assessing MTU stiffness and dynamic muscle shape changes (in pennation angle, muscle thickness, and belly gearing): These parameters were found to differ between controls and patients and also between PDA and PDNA. Noteworthy, these alterations (in the more affected side) are correlated with the severity of the pathology, assessed by means of the UPDRS score (e.g., in PDA but not in PDNA). Thus, according to our hypotheses, the expected reduction in RTD (and nRTD peak ) in patients not only depends on neural/nervous factors (investigated by means of an EMG analysis) but is also related to peripheral factors (investigated by computing belly gearing and MTU stiffness). Thus, also these factors have a role in determining the impairment in force/torque output during rapid contractions in mild to moderate (and active) PD patients, potentially impacting their quality of life.

| The effect of neural/nervous parameters on explosive torque development
To achieve maximal RTD, high motor unit discharge rates, rapid recruitment of the motor unit pool and effective summation of motor unit twitches are required. 9,43 The incapacity of people with PD in recruiting many single motor units simultaneously (with a high firing rate and within a relatively limited time) helps to explain their muscle weakness and their reduced capacity to produce rapid movements. 44,45 Accordingly, we observed lower RTD (both in absolute and relative terms) and EMG values in people with PD compared with healthy controls. When analyzing the different time windows, larger differences among groups (in nRTD and nEMG) were observed in the first three-time windows (from 0 to 75 ms from torque onset) where the neural/nervous factors play a more important role in determining the rise of torque (as previously observed, as an example, by Martignon et al 12 ). Furthermore, the maximum EMG activity reached during the explosive contractions was also impaired in people with PD. The mechanisms behind these alterations could be related to a malfunctioning of the basal ganglia, a F I G U R E 1 Normalized torque (A), normalized RTD (B), normalized EMG activity (C), and belly gearing (D) in all the investigated time windows. Columns and dots refer to mean and individual values, respectively; bars represent standard deviation. Red and green data refer to PD patients (more affected and less affected limb, respectively: PDA and PDNA); blue data refer to healthy controls. neural structure which is essential for inhibiting un-needed and inappropriate muscle activations. 46 Indeed, basal ganglia dysfunction may interfere with efficient cortical motor activation increasing the variability, while reducing the intensity and frequency, of corticospinal signaling thus leading to abnormal neuron discharge and recruitment of motor units in patients with PD. 47,48 Data reported in the literature suggest that a drop in neural activation may be an important mechanism driving PD motor signs, including strength loss. 47,48 In PD, symptoms often begin on one side of the body, as the disease progresses it eventually affects both sides even if the symptoms may remain more severe on one side. 21,22 In this study, we investigated both the affected and the less affected side (and this is a novelty in the literature), and we observed that the EMG activity of the more affected side (PDA) is reduced compared to that of the less affected side (PDNA). This asymmetry is related to the asymmetric degeneration of dopaminergic cells in the ventrolateral parts of the substantia nigra pars compacta and the subsequent asymmetric dysfunction of the dorsal striatal projection area, which includes the posterior putamen; the dorsal striatal area, in turn, projects to specific cortical areas involved in motor control. 48,49 Even if we did not investigate specifically the neurological alterations in PD, our results indicate that investigating EMG activity during rapid movements could be a useful tool to identify asymmetries in motor function in PD patients (at least in our cohort: active patients with mild to moderate PD).

| The effect of structural/mechanical parameters on explosive torque development
Despite the importance of neural/nervous factors in determining the torque rise, structural and mechanical parameters could also affect the force transfer along F I G U R E 2 Normalized RTD peak (A), normalized EMG peak (B), muscle-tendon stiffness (C: k MTU ), and belly gearing (D: G b 0-peak ). Red and green data refer to PD patients (more affected and less affected limb, respectively: PDA and PDNA), blue data refer to healthy controls. Dots represent individual values; mean values and standard deviation are also reported. the muscle-tendon unit leading to a further reduction in force/power output. Previous studies did not show any difference in architectural parameters at rest (e.g., Ref. [12]) between controls and (physically active) PD patients, and this was observed also in the present study. This suggests that an active lifestyle is a key factor to preserve muscle structure in this population.
A novel result of this study is the analysis of the dynamic shape changes (e.g., structural/mechanical factors) that were impaired in PD patients, who showed higher MTU stiffness (during the explosive contraction) and lower belly gearing compared to healthy individuals.
The higher MTU unit stiffness in PD patients is consistent with findings from previous studies that investigated the stiffness of the muscle belly 50 or the Achilles tendon stiffness 50 in this population. The higher MTU stiffness in PD patients could be explained by different mechanisms, such as (i) atrophy of the muscle fibers and replacement with connective tissue (i.e., sarcopenia) 51,52 ; and (ii) collagen disorganization and increase in tendon glycation. 53,54 These mechanisms could impede muscle shape changes 19 counteracting the positive association between MTU stiffness and RTD. Indeed, a stiffer MTU could better transmit force from the muscle to the joint segment and higher values of MTU stiffness were positively correlated with higher values of RTD in healthy young subjects. [13][14][15] However, in pathological situations (in PD, but also after a stroke), the increase in MTU stiffness is generally related to muscle and tendon deterioration, such as muscle connective tissue infiltration or higher muscle tone, resulting in tight muscles and stiff and inefficient movements.
We observed that the more affected side is stiffer than the less affected one and this asymmetry possibly exacerbates the mechanical dysfunction in these patients. Indeed, MTU stiffness in PDA was positively correlated with the UPDRS score (the subjects with the higher stiffness were those with the worst clinical score), but no correlation was observed between MTU stiffness and UPDRS k MTU ---Abbreviations: EMG peak , peak EMG activity; G b 0-peak , belly gearing (average value from 0 to the time at which RTD peak occurs); k MTU , stiffness of the VL muscle tendon unit; PDA, affected limb in PD patients; PDNA, less affected limb in PD patients; ΔMT, changes in muscle thickness (from 0 to RTD peak ); ΔPA, changes in pennation angle (from 0 to RTD peak ).

T A B L E 3
Results of the multiple linear regression analyses. Data refer to standardized β coefficients and adjusted p values (between brackets) for the significant predictive variables in determining rate of torque development and belly gearing.

F I G U R E 3
Correlations between UPDRS score, belly gearing (G b 0-peak , left panel), and MTU stiffness (k MTU , right panel). Red and green data refer to PD patients (more affected and less affected limb, respectively: PDA and PDNA). Red-shaded areas represent the confidence interval for PDA data, where the correlations reached a significant level (with p < 0.05). score in PDNA, and this suggests a specific effect of PD on the mechanical properties of the MTUs. A stiffer MTU is also associated with an impairment in muscle fascicle behavior (asymmetrical in this case too). We indeed observed lower changes in muscle thickness, pennation angle, and belly gearing during contraction in Parkinson's disease patients, indicating that their muscles are not as capable of changing shape as those of healthy controls.
A decrease in belly gearing could represent an important disadvantage for patients. In healthy subjects, belly gearing was found to play an important role during rapid movements since it is positively correlated with mechanical power production 18 as well as with the capability to increase force rapidly. 15 More recently, it was observed that belly gearing could play a role in determining the metabolic energy demands during walking at increasing speed 39 and this could partially explain the increase in the metabolic demands during walking in PD patients compared to controls.
To note, belly gearing was reported to be independent of EMG activity both in animals 19,55 and in humans. 38 These mechanical alterations of muscle behavior in PD patients, which are unrelated to the EMG activity of the recruited muscle, suggest that this pathology affects the intrinsic mechanical characteristics of the muscles, and this provides new insight into the functional effects of Parkinson's disease. In this regard, the loss of variable gearing on the more affected side observed in the present study appears somewhat analogous to the loss of variable gearing in aging rat muscles 19 or in the paretic side in people after stroke. 20 In these studies, the changes in gearing were, indeed, explained by a stiffer MTU, supporting the hypothesis that variable gearing is the outcome of an interaction between contractile and connective tissues. 55 We observed a negative correlation between belly gearing and MTU stiffness in PD patients, (the subjects with the stiffer MTU were those with the lower values of belly gearing) and a negative correlation between belly gearing and UPDRS score (in PDA only); this reinforces the idea of a specific effect of this pathology on peripheral structures and represents an important functional outcome to better understand the effects of Parkinson's disease on structural/mechanical parameters.
These considerations are reinforced by the results of our multiple linear regression model. The main determinants of RTD peak in PDA are, indeed, structural/peripheric (e.g., belly gearing and MTU stiffness), whereas the neural/nervous parameters (e.g., EMG activity) play a more important role in control participants (and in the less affected limb in patients). Therefore, our data suggest that PD patients had compromised structural/mechanical parameters, and this impairment helps in explaining their reduced muscle mechanical output (e.g., explosive torque production).

| Further considerations
In the present study, all participants were tested during the medication "on" condition of the dopaminergic treatment. Levodopa medication is the most efficient treatment for motor symptoms of Parkinson's disease: It alleviates rigidity, rest tremor, and bradykinesia. As reported by Ruonola et al, 56 levodopa medication could affect EMG activity and force production in PD patients. As an example, these authors showed (i) that the amplitude of the EMG activity during elbow flexion exercises is reduced during the "on" phase of the treatment and (ii) that levodopa reduces passive force during a flexionextension task, suggesting an effect on involuntary muscle tone in PD patients. The "increase" in muscle tone during the "off" phase of the pharmacological treatment is thus expected to exacerbate the impairment in muscle shape changes and belly gearing observed in this study (during levodopa treatment) further reducing the patient's capability to exert torque rapidly. These hypotheses should be investigated in future studies.
Finally, PD patients could be classified into two main phenotypes: postural instability gait difficulty (PIGD) or tremor-dominant subtype. 57 Our PD patients were all classified as PIGD and, therefore, the results obtained in the present study are valid only for this specific phenotype. Further studies are needed to investigate whether similar findings would be observed in the tremor dominant subtype. Moreover, since we recruited physically active patients with mild to moderate PD (stages I-III of the H&Y scale), further studies are needed to investigate whether similar findings would be observed in less active PD patients at more severe stages of the pathology.

| CONCLUSION
As a neurodegenerative disease, PD affects the neural/nervous parameters involved in explosive torque production. Our findings indicate that also mechanical/structural parameters (MTU stiffness and muscle shape changes), which are peripheral and not related to changes in neural/nervous variables, are affected by the disease further compromising the ability of these patients to rise torque rapidly in response to different tasks (such as avoiding an obstacle while walking or recovering from an unexpected loss of balance). The higher MTU stiffness exhibited by PD patients is likely responsible for the impaired capability of the muscle to change in shape, reducing belly gearing which, in turn, negatively affects the torque rise.
These findings provide new insight into the effects of this pathology on the locomotor system and open new questions for interventional studies. As an example, training programs able to reduce MTU stiffness could be useful to reduce the mechanical disadvantage (belly gearing) imposed by the pathology.

| MATERIALS AND METHODS
The methods utilized in this study conform to good publishing practice in physiology. 23 Based on previous studies, 20 the desired sample size, calculated using a statistical software (G*Power), was enclosed from 9 (for the stiffness calculation) to 11 (for the belly gearing calculation) participants. To obtain this sample size, we adopted an alpha level of 0.05 and a statistical power of 0.8. The participants were recruited to obtain two groups with similar characteristics, especially in terms of physical activity, that was assessed by means of the IPAQ questionnaire (www.ipaq.ki.se).
Inclusion criteria for PD patients were a diagnosis of idiopathic PD, carried out by a neurologist in accordance with the guidelines established by the London Brain Bank. 24 All subjects belonged to a postural instability and gait disorders phenotype (PIDG). The disease severity was classified according to the modified Hoehn and Yahr scale 25 and the assessment of the degree of motor and functional impairment was obtained using part III of the Unified Parkinson's Disease Rating Scale (UPDRS 26 ). Finally, cognitive function was assessed by using the Mini Mental State Examination (MMS 27 ).
Exclusion criteria were any type of dementia and inability to walk. All procedures were conducted during the medication "on" condition of the dopaminergic treatment.
The study agreed with the Declaration of Helsinki for the study on human participants. The local ethical committee approved the experimental protocol (2021-UNVRCLE-0450152), and all participants gave their written informed consent.

| Experimental design
A preliminary screening included a health history, a familiarization with the study procedures, and the questionnaires assessment.
Each subject participated in one single session. After preparation, warm-up, and familiarization with the equipment, the subjects were asked to perform a series of maximal voluntary isometric contractions at different knee angles. After 15 min rest, they were asked to perform a series of explosive contractions. PD patients were tested twice, in the same session, to investigate both the affected (PDA) and less affected (PDNA) side (as ranked by their neurologist); the affected limb was the right in 10 out of 15 patients. For the controls, since no differences are expected in maximal voluntary force (MVF) and rate of force development (RFD) between dominant and nondominant knee extensors in healthy subjects (e.g., Ref. [28]), only the dominant leg was investigated (10 out of 12 subjects were right dominant). The maximal voluntary contractions were performed at different knee angles to obtain the torque-angle (T-A) relationship (two repetitions per angle), whereas the explosive contractions (five repetitions) were performed at the optimal knee angle only (as obtained from the T-A relationship, see data analysis).
During each contraction, the torque generated by the knee extensors was recorded by means of a dynamometer (Cybex NORM). The raw EMG activity of vastus lateralis (VL) and biceps femoris (BF) was recorded using an electromyographic equipment (ZeroWire, Aurion); the VL fascicle and aponeuroses behavior were recorded by means of an ultrasound apparatus (Mycrus Ext-1, Telemed).

| Torque-angle relationship
The participants were secured on a dynamometer (Cybex NORM) with a trunk and pelvic strap, the arms crossed in front of the chest. Due to the knee joint rotation that occurs during knee extension contractions from rest to MVC, 29 the knee and the dynamometer axis of rotation were aligned during MVC at 60° of knee flexion. 30 After a warm-up based on submaximal isometric contractions, the T-A relationship was obtained based on maximum isometric contractions (MVCs) at six different joint angles (from 90 to 15°; 0°= knee fully extended) with 15° intervals. During the MVCs, the subjects were instructed to push "as hard as possible" for 4-5 s. Two maximal isometric contractions were performed for each angle, with 2 min of recovery in between. 18 The raw EMG activity of both VL and BF was recorded during each contraction by means of two bipolar Ag-AgCl electrodes. The electrodes were attached over the muscle belly according to the SENIAM recommendations.
Cybex data (torque, velocity, and position) and raw EMG data were acquired at 1000 Hz with a PowerLab System (PowerLab, ADInstruments), using the related software (LabChart v.6 ADInstruments). A trigger signal (with an amplitude of 5 V) initiated ultrasound acquisition while producing a square-wave visual marker on the LabChart video, where all data were recorded, thus allowing for subsequent synchronization of all data.

| Explosive contractions
For the explosive contractions, each participant was positioned on the dynamometer as described in the previous section (see Torque-angle relationship). The contractions were performed at a single knee joint angle (equal to the optimal one, as calculated based on the T-A relationship). During these contractions, the participants were instructed to extend their knee "as fast and as hard" as possible with an emphasis on "fast". 6 Each participant performed a series of explosive contractions until a total of five "good contractions" were obtained for each participant. 31,32 Participants were instructed to start from a resting state (i.e., zero active torque) and to avoid any countermovement (negative/flexor torque). The quality of the contraction was controlled in real time by an operator using the PowerLab software. To do that, the raw EMG and the torque signal were analyzed in real time with the PowerLab tools box. The contractions were repeated if baseline torque in the 100 ms preceding active-torque onset changed by >1 Nm. 18,31,32 During all contractions, the raw EMG of both VL and BF was recorded as described in the previous section (see Torque-Angle relationship). Moreover, fascicle length and aponeuroses changes were recorded by means of an ultrasound device with a 6-cm linear array probe operating at 110 Hz (Mycrus Ext-1, Telemed). The probe was attached to the skin approximately at 50% of the femoral length, aligned on the muscle belly, and corrected with respect to the superficial and deep aponeurosis, to have a clear image of the perimysial connective intramuscular tissue (e.g., indicative of the muscle fascicle structure). The probe was never removed during the entire experimental session.
A trigger signal was used to synchronize all data in post-processing, as described above.

| Torque-angle relationship
The total moment generated by the knee extensors was corrected for the gravitational torque effects (determined during a passive joint rotation driven by the dynamometer) and for the EMG-moment relationships of the antagonist muscles (BF). 33,34 The greatest value of knee extensor torque recorded during each isometric contraction was defined as the maximum voluntary torque (MVT). MVTs at all angles (and from both contractions) were used to establish the T-A relationship. Experimental data were fitted with a polynomial function: The maximum value of torque (T max ) was calculated as the vertex of the parabola, whereas the optimal angle (A 0 ) was identified as the position of the vertex in respect to the abscissa (see Figure S1). 18,35 The individual data of T max and A 0 are reported in Table S1.
Raw EMG signals during the isometric contractions were filtered with a fourth-order band-pass (20-400 Hz) Butterworth filter. The root mean square (RMS) of the raw EMG signal was calculated over a 10-ms epoch at each knee angle. 31 The maximum value was then utilized for further analysis (and termed EMG max ).

| Explosive contractions
All the analyzed variables (ultrasound, torque, and EMG parameters) were averaged over the five analyzed trials. The offline analysis was conducted using customdeveloped programs in MATLAB.
As in the case of the MVCs, the joint moment generated by the knee extensors was calculated by taking into account the gravitational torque and the antagonist contribution. 18,31,32 The torque generated by the knee extensor muscles was normalized for T max and expressed in percentage (nTorque).
The rate of torque development (RTD) was calculated as the first derivative of the torque-time signal over five different time windows starting from torque onset: 0-25, 25-50, 50-75, 75-100, and 100-125 ms (see Appendix S1). Torque onset was defined as the point at which the first derivative of the active torque-time curve crossed zero for the last time. 31,32 RTD was then normalized for T max (nRTD) and expressed in T max /s. Moreover, the peak nRTD value (nRTD peak ), which typically occurs from 75 to 100 ms, was selected as an indicator of the maximum explosive torque capacity.
Raw EMG signals were filtered with a fourth-order band-pass (20-400 Hz) Butterworth filter. To assess neuromuscular activation of the VL during each condition, the root mean square (RMS) was calculated with a time window of 10 ms, from EMG onset up to 150 ms and normalized for EMG max (and termed nEMG). As in the case of nRTD , the nEMG values were calculated over five-time windows after torque onset (0-25, 25-50, 50-75, 75-100, and 100-125 ms); the nEMG value at nRTD peak was termed nEMG peak .
For the ultrasound measurements, a validated automatic tracking algorithm was used to quantify muscle thickness (MT) and pennation angle (PA) frame by frame. 36 Muscle thickness was defined as the distance between the deep and superficial aponeuroses, whereas pennation angle was defined as the angle between the collagenous tissue and the deep aponeurosis. At the end of the auto-tracking, every frame of the tracked parameters was visually examined to check the algorithm accuracy. Whenever MT or PA was deemed inaccurate, the two points defining the muscle fascicles were manually repositioned. Fascicle length (FL) was then calculated using a classical trigonometric function: FL = MT/(sen PA). Fascicle velocity (V f ) was calculated as the first derivative of the fascicle length-time curve, whereas the muscle belly velocity (V b ) was calculated as the first derivative of the belly length obtained as: FL ⋅ (cos PA). Note that this gives not the length of the entire VL muscle belly but the projection of the instant fascicle length to the plane of the MTU, which can be used to calculate the changes of the belly length. [37][38][39] Finally, to take into account the possible mismatch among fascicle and muscle belly, the belly gearing (G b ) was calculated as the ratio between belly velocity (V b ) and fascicle velocity (V f ). As in the case of RTD and EMG data, belly gearing was calculated over the five-time windows (0-25, 25-50, 50-75, 75-100, and 100-125 ms); the mean value of G b from 0 to RTD peak was also calculated to better characterize the gearing necessary to reach this peak (G b 0-peak ).
To investigate the muscle shape changes during contraction, the changes in pennation angle (ΔPA) and muscle thickness (ΔMT) from 0 to RTD peak were calculated.
The stiffness of the VL MTU (k MTU ) was calculated during the explosive contractions as the slope of the torque versus muscle belly elongation curve in the first 150 ms after torque onset. 14,15 The longitudinal displacement of the muscle belly was considered to represent the combined elongation of the distal aponeurosis, muscle, and free tendon. 13,14 The torque versus muscle belly displacement curve was then obtained for each participant, and fitted to a second-order polynomial forced through zero. 40 To represent the value of MTU stiffness that better characterize the explosive torque capacity for each subject, the mean value from 0 to nRTD peak was calculated and utilized for further analysis (k MTU ).

| Statistical analysis
Data are reported as means ± SD. All data points were included in data analysis (no outliers excluded). For the variables measured in the five-time windows (RTD, EMG, and G b ), the influence of time and "group" (controls, PDA and PDNA) was analyzed by means of a two-way repeated measure ancova (group × time). A Bonferroni post hoc test was used to determine the possible differences among groups in the specific time period. Additionally, a oneway ancova was used to assess the possible interactions between populations. Covariates were age, mass, stature, and physical activity (IPAQ score). To determine the relationships between variables, the Pearson's correlation coefficient was used. Equality of correlation coefficients was used to check the statistical differences between correlations in the investigated populations (e.g., Hotelling's statistics 41 ). Since the possibility of false-positive correlations increases with the number of correlations performed, Pearson's product moment correlation p values were corrected for multiple tests using the Benjamini-Hochberg 42 procedure with a false detection rate of 5% (significance was defined as adjusted p < 0.05).
We further conducted a series of multiple stepwise linear regression analyses to assess the magnitude of the effect of the analyzed variables on RTD peak and to investigate the main determinants of belly gearing (G b 0-peak ). The predictive variables were checked for collinearity: When the variance inflation factors (VIF) were larger than 5 for any predictor variable, the variables were standardized (e.g., by subtracting the mean) before they were used in the model. Statistical analyses were conducted using R (v.31.1).