*2.4. Statistical Analysis*

Descriptive statistics were performed. A normal distribution of MVC and MFCV values was confirmed by the Kolmogorov–Smirnov test. The independent t test was applied to compare the difference of MVC between the SCI and healthy control groups. A linear-mixed effects model was applied to analyze the main effects of group (SCI and Control), force (8 levels from 10% to 80% MVC) and the interaction of the two main effects on MFCV. The coefficient of determination of the quadratic fitting of the EMG–force relation was calculated for both control and SCI groups. Statistical analysis was conducted using SPSS (SPSS Inc., Chicago, IL, USA) with a significance level of *p* < 0.05. All values in the text are presented as mean ± SD.

#### **3. Results**

The SCI participants were significantly weaker compared to the controls (SCI MVC: 98.5 ± 69.9 N, range: 11.9–307.6 N; control MVC: 212.7 ± 111.3 N, range: 70.6–314.9 N, *p* = 0.005). Examination of differences of average MFCV value revealed a significantly slower value in the SCI group compared with the healthy control group (SCI: 3.97 ± 0.55 m/s, control: 4.62 ± 0.86 m/s, *p* = 0.025, Figure 2A). The results showed a significant main effect of group (presence of SCI) (*β* = −0.87, SE = 0.29, t = −2.97, *p* = 0.005), while the main effect of contraction level (*β* = −0.04, SE = 0.02, t = −1.67, *p* = 0.096) and interaction of the two main effects (*β* = 0.002, SE = −0.004, t = 1.79, *p* = 0.075) were not significant. Although a trend of increasing MFCV with muscle contraction level was observed in some subjects (Figure 2B), linear-mixed effects model analysis indicated that MFCV was not significantly related to the different target forces.

Normalized EMG–force relations in all the tested healthy control subjects and the averaged relation are shown in Figure 3A. For all 14 healthy control subjects, the EMG–force relation was well fit by a quadratic function (R<sup>2</sup> = 0.96, range: 0.89–0.99). All the control subjects had a positive quadratic coefficient (i.e., a > 0), suggesting that EMG tended to increase relatively more than force during the stronger target contractions. In contrast, a more diverse EMG–force relation was observed in the SCI subjects, although data for the group was also well fit by a quadratic function (R<sup>2</sup> = 0.87, range: 0.50–0.99). Two different quadratic patterns were observed after SCI. Among the 15 tested SCI subjects, seven had a positive quadratic coefficient (i.e., a > 0, Figure 3B), consistent with the responses in the controls. The other eight SCI subjects had a negative quadratic coefficient (i.e., a < 0, Figure 3C), suggesting that EMG tended to increase relatively less than force during the stronger target contractions. The two SCI sub-groups with negative and positive quadratic coefficients did not have significant differences in age, years post injury, ASIA scale, neurological level, and MVC force (*p* > 0.05).

**Figure 2.** Comparison of MFCV between SCI and control subjects. (**A**) Mean and individual MFCVs in each group (\* *p* < 0.05, error bar represents standard deviation); (**B**) MFCV at the different target forces in two subjects from SCI and control groups, respectively.

 **Figure 3.** (**A**) Normalized EMG–force relations from all healthy control subjects and the averaged relation (the thick line); (**B**,**C**) Two typical patterns of EMG–force relations from all the tested SCI subjects and the averaged relations (the thick lines).

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#### **4. Discussion**

A linear electrode array was applied in this study to examine the BB partially paralyzed by cervical SCI. The average MVC of the examined muscles was approximately 50% of healthy control subjects, and this weakness likely reflects both central neural (i.e., paralysis) and peripheral muscular changes. In the subacute or chronic stage after SCI, muscles innervated by spinal segments at and caudal to the SCI are prone to atrophy from both denervation and disuse [38]. A decrease in the number of motor units or axons following spinal motor neuron death could occur [9–15]. There were only a few motor units that remained under voluntary control since the injury interrupted many of the descending inputs to the motor neuron pool [39]. The disturbances of motor neuron control and contractile properties persist in chronic SCI survivors, and represent an important source of muscular weakness and increased fatigability [40]. These neurophysiological changes were also reflected in the current linear electrode array EMG analysis of the SCI subjects, focused on the MFCV and the EMG–force relation.

MFCV, which is directly related to membrane excitability, can reflect the dynamic changes and redistribution of ions during voluntary muscle contraction [41]. MFCVs calculated in the BB muscles were reported to range from 3.4 ± 0.2 to 5.0 ± 0.6 m/s in healthy subjects [28,42]. Our results from healthy control subjects (4.62 ± 0.86 m/s) are in similar range with the previous findings. Changes in MFCV have been reported after neuromuscular disorders. For example, BB MFCV during isometric contractions were found to be significantly slower in patients with Duchenne muscular dystrophy compared to healthy controls [43]. MFCV was also shown to be significantly slower in paretic muscles of stroke survivors [29]. In this study, BB MFCV was significantly slower after SCI compared to control subjects. This could be due to muscle fiber atrophy or degeneration of large motor units after SCI. Given that the BB has motor unit recruitment range up to 80% MVC, a clear correlation was expected between muscle force and MFCV to be revealed in current study. However, our results indicated no significant correlation between the averaged MFCV and muscle contraction level for both groups. For the SCI group, this is likely due to complex neuromuscular changes that may compromise the relationship between MFCV and muscle force. Admittedly, our results from healthy control subjects are somewhat different from most of the previous literatures [44–46], although a similar finding was also reported in a recent study that BB MFCV of healthy control subjects increased only slightly but non-significantly with force [47]. According to size principle, later recruited motor units are supposed to have larger muscle fiber diameters and thus higher MFCV. Although some of the healthy control subjects showed an increase trend of MFCV with muscle contraction level, group analysis did not reveal a significant relation. There might be multiple factors that likely compromise the MFCV of the healthy control subjects in this study, which were also suggested in previous studies. For example, Masuda et al. (1996) [48] examined MFCVs from vastus lateralis, tabialis anterior, and BB muscles of seven healthy subjects. Although increased MFCV was observed with increasing force of the vastus lateralis muscle, the results from BB muscle showed that the MFCV reduced rapidly with time before the muscle contraction force reached the designed target levels of 70% or 90% MVC. MFCV at these larger force levels was smaller than that at 50% MVC and then consequently MFCV in the BB showed no dependent on the contraction levels. These results suggest that although MFCV basically increases with muscle contraction force but this relation can become unclear when MFCV decreases rapidly with time. Other factors may also contribute to compromising the relation such as variability in interference surface EMG, variability between different sessions (especially at higher contraction force), muscle temperature variability (which may also affect MFCV) [49], and muscle fatigue. Although muscle fatigue was a controlled factor during experiment and subjects were allowed sufficient rest, it would be difficult to completely avoid its effect on MFCV, especially at high force levels when large and fast-fatigable motor units are recruited [50].

The EMG–force relation was also examined in this study, which can provide additional insights pertaining to neuromuscular changes in pathological conditions. Application of a linear electrode array can characterize the EMG–force relation unconfounded by muscle IZ effects on the EMG signal. This is important because surface EMG parameters can be significantly affected by IZs, and the uncertainty of electrode locations (with respect to the IZ) might compromise the signal interpretation [51,52]. Both linear and nonlinear EMG–force relations were reported in the literature [36,37]. For small muscles such as the first dorsal interosseous (FDI) whose force generation is dominated by motor unit rate coding, a linear EMG–force relation is often observed. For large muscles such as BB, motor unit recruitment takes an important role in muscle force generation, and the progressively recruited motor units have larger action potentials, increase EMG more than force despite the effect of action potential amplitude cancellation, thus resulting in a nonlinear EMG–force relation. In this study, we observed that for all healthy control subjects, the quadratic term coefficient of the EMG–force relation fitting was positive, suggesting that EMG increased faster than force, which is consistent with previous reports [36].

An interesting finding is that for the SCI group, diverse EMG–force relations were observed. In about half of the SCI subjects, a negative quadratic term coefficient of the EMG–force relation fitting was revealed, indicating that EMG tended to increase slower than force. There are various factors that may contribute to this EMG–force relation change after SCI. Previously, the effects of different motor unit property changes on the EMG–force relation were systematically investigated by simulating activities of motor neuron pool, surface EMG and force of the FDI muscle [53]. For example, it was found that reductions in motor unit firing rate would tend to increase the slope of EMG–force relation, which was experimentally confirmed in stroke subjects [21–23]. Jahanmiri-Nezhad et al. found a trend of decreased slope of the EMG–force relation in the FDI muscle of patients with amyotrophic lateral sclerosis compared with healthy control subjects, which could be related to selective degeneration of motor units with high threshold or a change in motor unit contractile properties [54]. In the current study of the SCI BB, the unusual negative quadratic term coefficients could be caused by motor unit property changes after SCI, such as the loss of large motor units, and altered motor unit recruitment as well as firing behavior. For example, Johanson et al. found two of the four SCI subjects had significantly reduced motor neuron recruitment and high firing rates, likely a compensatory effect of dramatic motor neuron loss after SCI, while the other two subjects with stronger elbow extension had relatively normal recruitment and firing rates [55]. It is worth noting that there are various interactive factors that can influence the EMG–force relation in different ways. Those positive quadratic term coefficients of the fitting in SCI subjects consistent with the healthy control group might be viewed as a collective effect of various factors, which can drive the EMG–force relation in opposite directions.

There are several limitations in the present study. We solely applied global surface EMG parameters and it might be difficult to differentiate or quantify various motor unit properties that may contribute to the changes in surface EMG. Surface EMG decomposition is required to perform analysis at the motor unit level. Given that it is more ideal to perform surface EMG decomposition using 2-dimensional electrode arrays which provide EMG recordings not only parallel to but also perpendicular to muscle fibers, surface EMG decomposition was not attempted in this study. Motor unit number, size, and control property changes after SCI can readily be examined through 2-dimensional high density surface EMG recording and decomposition in future studies [56,57]. Considering that surface electrode only records superficial regions of a muscle, intramuscular recording with needle or fine wire electrodes is necessary in order to capture activity of deeper motor units in the muscle. As computational modeling provides a useful approach in neuromuscular performance investigations [53,58], a delicate simulation analysis incorporating experimental motor unit behaviors can help understand the global surface EMG parameter alterations after SCI. The current study focused on MFCV and the relation of EMG amplitude and muscle force for a relatively steady segment of signals, while there are more advanced or complex signal processing methods which can be applied in data analysis. For example, wavelet transform is promising to explore time and frequency dependence of the examined

parameters [59]. In this study, EMG was not recorded from synergistic and antagonistic muscles, although a previous SCI study found that BB coactivation did not have a major effect on the triceps brachii EMG–force relation [25]. Simultaneous recording from synergistic and antagonistic muscles is suggested in the future study, which can assess the potential effects of the "sharing load" strategy, especially during strong contractions. In addition, the shoulder and trunk position may influence EMG signal measurement [60], and this should be considered in data analysis and interpretation. Finally, this study is limited by a relatively small subject number for performing meaningful sub-group analysis.

In summary, this study presents findings from a linear electrode array surface EMG examination of the BB in chronic cervical SCI subjects. The results demonstrated significantly slower MFCV in SCI subjects compared with healthy controls. The EMG–force relation was also altered in a subset of the SCI participants. Using quadratic fitting of the EMG–force relation, approximately half of the SCI participants demonstrated a negative quadratic term coefficient, possibly reflecting impaired motor unit control at high forces. In contrast, positive quadratic coefficients were observed for all healthy control subjects. These findings suggest both central neural and peripheral muscular changes in the BB after SCI.

**Author Contributions:** Conceptualization, C.S.K. and P.Z.; methodology, L.L., H.H. and P.Z.; software, B.Y., C.H. and Z.L.; validation, B.Y., C.H. and Z.L.; formal analysis, L.L. and H.H; investigation, L.L., H.H., B.Y., C.H. and Z.L.; resources, P.Z.; data curation, L.L., H.H. and B.Y.; writing—original draft preparation, L.L. and H.H; writing—revision, review and editing, C.S.K. and P.Z.; visualization, L.L., H.H. and C.S.K.; supervision, P.Z.; project administration, L.L. and P.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by Shandong Provincial Natural Science Foundation (ZR2020KF012), National Natural Science Foundation of China (32071316, 32211530049, 82102179), the Fundamental Research Funds for the Central Universities (G2021KY05101, W016204, G2022WD01006), the Key Research and Development Project of Shaanxi province (2022SF-117), and the Natural Science Foundation of Shaanxi province (2022-JM482).

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki, and approved by the Committee of Protection of Human Subjects of University of Texas Health Science Center at Houston and TIRR Memorial Hermann Hospital (Approval Code: HSC-MS-14-1031, Approval Date: 18 August 2015).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Acknowledgments:** We acknowledge the help of Henry Shin, Xiaoyan Li, Argyrios Stampas, and Zichong Luo during performance of this study.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **References**


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