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Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions

Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 1971045, 10 pages https://doi.org/10.1155/2019/1971045 Research Article Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions 1 1 2 3 4 Chaofei Zhang , Wenjun Wang , Dennis Anderson, Sishu Guan, Guofa Li , 3 3 1 Hongyi Xiang, Hui Zhao , and Bo Cheng State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China Center for Advanced Orthopedic Studies, Beth Israel Deaconess Medical Center, Boston, MA 02215, USA Chongqing Key Laboratory of Vehicle/Biological Crash Security, Department 4th, Institute of Surgery Research, Daping Hospital, Third Military Medical University, Chongqing 400042, China Institute of Human Factors and Ergonomics, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China Correspondence should be addressed to Wenjun Wang; wangxiaowenjun@tsinghua.edu.cn and Guofa Li; hanshan198@gmail.com Received 3 April 2018; Revised 26 July 2018; Accepted 30 August 2018; Published 3 January 2019 Academic Editor: Li-Qun Zhang Copyright © 2019 Chaofei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Stretch reflex is an important factor that influences the biomechanical response of the human body under whole-body vibration. However, there is a lack of quantitative evaluation at lower frequencies. Thus, the aim of this study was to investigate the effects of vibration on the stretch reflex and, in particular, to explore the quantitative relationship between dynamic muscle responses and low-frequency vibrations. The gastrocnemius muscle of 45 Sprague-Dawley rats was dissected. Sinusoidal vibrations of five discrete frequencies (2~16 Hz) with peak-to-peak amplitudes of 1 mm were applied to the gastrocnemius muscles with 2 mm or 3 mm prelengthening. Variables including dynamic muscle force, vibration acceleration, and displacement were recorded in two conditions, with and without the stretch reflex. Results showed that the dynamic muscle forces decreased by 20% on average for the 2 mm prelengthening group after the stretch reflex was blocked and by 24% for the 3 mm prelengthening group. Statistical analysis indicated that the amplitude of dynamic muscle force in the “with stretch reflex” condition was significantly larger than that in the “without stretch reflex” condition (p <0 001). The tension-length curve was found to be a nonlinear hysteresis loop that changed with frequency. The phase difference between the dynamic muscle force and the length change was affected significantly by vibration frequency (p <0 01), and the minimum frequency was 4–8 Hz. Experimental results of this study could benefit musculoskeletal model by providing a theoretical support to build a stretch reflex model for low-frequency vibration. 1. Introduction Several studies have examined the effect of muscle contractions on whole-body vibration response. Huang Muscle fatigue caused by prolonged driving is an important and Griffin [5] and Nikooyan and Zadpoor [6] reported that the activation of muscles could have a significant factor affecting driving comfort and resulting in lower back pain [1]. Whole-body vibration exposure plays a key role in effect on human mechanical response under whole-body vibration. However, activation levels were set as constant producing muscle fatigue and accelerating the fatigue process values in their models, which is inconsistent with the actual [2, 3]. Shinohara [4] synthesized several findings about the effects of prolonged vibration on muscle activity and revealed situation. Kitazaki and Griffin [7] used a human finite ele- ment model with a muscle module to examine vibration that prolonged vibration modulated muscle activity, which led to reduced peak force during maximal contractions and comfort. Electromyography (EMG) data was used as activa- altered force fluctuations. tion inputs when predicting muscle response. However, 2 Applied Bionics and Biomechanics frequency oscillations and researched its mechanical charac- EMG must be measured before simulation, and the quan- titative relation between EMG and muscle activation is teristics by performing experiments on a piglet. more complex in actual conditions. Brown et al. [8] and To date, various studies have addressed the importance of the muscle stretch reflex on human vibration responses. Meng et al. [9] found that the response of drivers’ lumbar muscle forces reached a peak in the resonance frequency However, the quantitative effect of the stretch reflex induced by low-frequency (2~20 Hz) vibration on muscle bands of the human biomechanics system (2–25 Hz). These studies suggested that human biomechanical response, espe- response has not been sufficiently analyzed in previous studies, which is a common real-world condition and cially for the muscle activity, was significantly affected by important for the human musculoskeletal model. It is also frequency of whole-body vibration. suggested that the stretch reflex responses vary with differ- Vibration can cause muscle lengthening and shortening, potentially resulting in increased muscle tension due to a ent stretch frequencies, amplitudes [26], or muscle lengths. stretch reflex [10]. Souron et al. [11] reported that a training Thus, the hypothesis of this study was that the stretch period of local vibration was efficient in improving muscular reflex plays an important role in muscle vibration response performance. Stretch reflex was proposed as an important in the low-frequency range on driving condition, and the factor that influences the biomechanical response of the vibration frequency and initial muscle length will signifi- human body under whole-body vibration [12]. cantly affect the muscle response. This experimental study Human experiment had been conducted to examine the is aimed at (1) examining the stretch response differences effect of vibration frequency and amplitude on the stretch between muscles with/without stretch reflex arc at different reflex. Ritzmann et al. [10] reported that vibration-induced vibration frequencies and initial muscle length conditions stretch reflex increased EMG activity after the elimination and (2) exploring the quantitative relationship between of motion artifacts. Miles et al. [13] reported two different muscle responses and low-frequency vibrations. stretch reflex responses, which are short-latency reflex evoked by high-frequency stretches and long-latency reflex 2. Methods evoked by slower stretches. Wakeling et al. [14] found increasing EMG activity and damping when the vibration 2.1. Experiment Configuration. This study was approved by frequency was close to the natural frequency of the soft tissue. the Animal Welfare Committee, Third Military Medical Bosco et al. [15], Rittweger [16], and Cochrane [17] found University of China. Experiments were performed to exam- increased muscle activity and power after whole-body vibra- ine the reflex response to sinusoidal stretching of the gastroc- tion and suggested a potential benefit over traditional forms nemius muscles of the right hind limb of 45 male rats of resistive exercise. Zaidell et al. [18] also found increased (225 ± 20 g, 10 ± 1 week). Decerebration was conducted by muscle activation during whole-body vibration with a fre- cutting the spinal cord between T9 and T12 of each of quency of 25 Hz and 50 Hz and explained it with muscle the 45 rats before experimentation. Dynamic muscle modulation under tonic vibration reflex. response force, muscle length, and vibration acceleration However, most of the above studies focused on high- were recorded in two conditions: “with stretch reflex” frequency oscillations (over 25 Hz), while the vibration (WSR) condition (Figure 1(a)), meaning the stretch reflex frequency in driving situations is mostly below 20 Hz. And arc was intact for the lower-extremity muscles, and “with- biomechanical response such as spine loading and muscle out stretch reflex” (WOSR) condition (Figure 1(b)), mean- forces which are closely related to driving comfort and ing the stretch reflex arc was blocked by cutting off the fatigue had not been analyzed yet. Musculoskeletal model sciatic nerve after experimentation in the WSR condition. [19, 20] was an alternative way to calculate muscle force The animal experiment diagram is presented in and joint loading which used bunches of muscle fascicles to Figure 2(a). The gastrocnemius muscle was separated and model muscle groups. Thus, an assumption was made that tied to a vibrator. The lower part of the shin was fixed in a the human muscle response under whole-body vibration vise. Piezoelectric transducers were used to record the could be modelled using the combination of many muscle dynamic muscle force with the vibration stretching and fascicle responses under localized vibration. vibration acceleration. A laser displacement transducer was Animal experiment is an effective method used in previ- used to measure the change in muscle length. ous studies to analyze the mechanism of stretch reflex of a single muscle [8]. Matthews [21–23] studied the relationship 2.2. Surgical Procedure. The surgical procedures were between muscle tension and muscle length in different performed under general anesthesia (ether, inhalational stretching velocities on decerebrate cats. Factors that could anesthesia). The nerves and muscles of the hind limbs were influence the stretch reflex, such as muscle length, stimulat- prepared, and a laminectomy was performed between T9 ing style, and motor nerve inhibition, were analyzed. Roberts and T12 in preparation for later spinalization; see [24] studied the hysteresis loop of tension against length Figure 2(b). A few trails were conducted to explore the loca- plots when sinusoidal fluctuating tensions were applied to tion of spinalization. Results indicated that the best location the soleus muscle of decerebrate cats, suggesting that there was between T9 and T12. If the location was too high, a was damping in the process of stretching. However, the serious spinal injury would occur, and if the location was period in his study is from 0.7 to 16.5 seconds; the highest too low, the stretch reflex arc would be cut off. After spinali- frequency is 1.4 Hz that is not a common real-world driving zation, the ether was removed, and the rat would regain condition. Günther et al. [25] noticed the damping in high- consciousness. The effectiveness of the operation was proven Applied Bionics and Biomechanics 3 Spinal cord Spinal cord Sciatic nerve Sciatic nerve Gastrocnemius Gastrocnemius Cut off (a) With stretch reflex (b) Without stretch reflex Figure 1: Two experimental conditions. (1) Vibrator (2) Force & acceleration Laser displacement transducer transducer Data acquisition (3) Mini vise Vibrator 4 (4) Shin Gastrocnemius (5) Gastrocnemius muscle 3 muscle Force & acceleration Mini vise transducer (6) Laser Tendon displacement transducer (a) Experiment diagram (b) Experimental apparatus Figure 2: Experiment configuration. gastrocnemius lengthened 7 mm corresponding to an ankle by the free movement of the front legs and paralysis of the hind legs. The nerve connection between the brain and the dorsiflexion of approximately 135 . Therefore, we ensured lower extremities was cut off, and the rat was ensured to that the length of the gastrocnemius would not exceed the be alive. physical limitation during the vibration test with a peak-to- Then the rat was anesthetized again, and its right peak amplitude of 1 mm. hind limb was extensively dissected (Figure 2(b)). All Sinusoidal vibrations were applied along the longitudinal the other nerves (femoral nerve, distal branches of the axis of the muscle. Five discrete frequencies (2, 4, 8, 12, and sciatic, obturator nerve, and hamstring nerve), except 16 Hz) were employed. The peak-to-peak amplitude in for those to the gastrocnemius muscles, were denervated. stretching was 1 mm for all frequencies. Each frequency was The ipsilateral gastrocnemius muscles were freed from tested twice in both the WSR and WOSR conditions. In total, their surrounding tissue. The end of the hind calcaneus each rat experienced 22 tests (5×2+1 for trial 1 and 5×2 bone was cut to keep a piece of bone to leave the ten- +1 for trial 2). To make sure the quality of measurement, don of the gastrocnemius muscle intact. The muscle we kept recording until 10 stable periods signals have been slack length after surgery was measured. measured and then we stopped recording the data for a test. The rat was then mounted in a stereotaxic frame According to our recording, the duration for the test is (Figure 2(b)). The other three legs besides the right hind 35~40 s. limb were fixed with adhesive tape. The shin bone of the Because the gastrocnemius muscle was repeatedly right hind limb was held in a bench vise. The distal ten- stretched using different frequencies vibration, it may cause don of the gastrocnemius muscle was tied to a vibrator muscle fatigue which would affect the result of muscle using an alligator clip. response. To exclude the effect of repeated stretching, a 15 s break was added between each adjacent test for recovery. 2.3. Experimental Procedure. To investigate the effect of ini- Moreover, an additional test with the same frequency as the tial muscle length on the response, the decerebrate rats were first test in the trial was performed to examine whether the divided into two prelengthening groups, which are 2 mm or muscle was tired. No significant decline of muscle response 3 mm longer than the slack length of the muscle. Measure- force was observed in this additional test as compared to the first test in the same trial. This strategy ensured the ment results before the surgical procedure showed that the 4 Applied Bionics and Biomechanics 0.2 exclusion of the fatigue effect on muscle response. Since we have already excluded the fatigue effect, the experiment did not use a random order. Another important influencing factor was spinal shock in −0.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 which all neurological activity was lost. Nesmeyanova [27] t (s) found a normal electrical response of the soleus muscle in spinal patients with clonus compared with absence of clonus after spinal cord injury. However, it was difficult to measure the spinal shock level quantitatively. To ensure normal −2 response after spinal injury, we proposed the following −4 method to avoid or mitigate the influence of spinal shock. −6 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 After spinalization, the anesthesia was removed and a piece t (s) of gauze was used to stanch bleeding. After the rat regained consciousness, if the rat climbed forward or in a circle with −1.5 the two front legs and the two hind legs seemed powerless because of a loss of brain control, this meant that the rat −2 had recovered partially or totally from the spinal shock. −2.5 −3 2.4. Data Progress. In total, 45 rats were involved in the 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 experiment, 15 in the 2 mm prelengthening group and 14 t (s) in the 3 mm prelengthening group. The other 16 rats either Raw data died in surgery or failed to yield useful results, typically Fitting result because of the vagaries of the decerebrate preparation rather than the occasional failure of the recording operation. A Figure 3: Typical example of raw data and fitting result at 8 Hz with zero-phase 8th-order Butterworth low-pass filter with a cut- stretch reflex under 2 mm prelengthening condition. off frequency of 25 Hz was used for data filtering. The system inertial mass was identified prior to the tests The phase difference between the dynamic muscle force without muscle connection. The inertial mass included the and the muscle length change was calculated as follows: mass of an alligator clip, a laser reflection plate for length recording, and the connection bolt to the acceleration trans- Δφ = φ − φ 3 f l ducer. Sinusoidal signals of 5 Hz and 10 Hz were provided by the vibrator. The force F and the acceleration a were inertial Here, Δφ is the phase difference, and φ and φ are, f l recorded. The system inertial mass m can be computed system respectively, the phase of dynamic muscle force and muscle according to length identified with the least squares method according to equation 2. F To exclude the effect of the individual difference, a nor- inertial m = 1 system malization method was proposed to further analyze the force data for each rat as follows: It was found that the system inertia mass was about WOSR F = , 4 34.8 g. Therefore, the system inertial force can be calculated WOSR WSR if the vibration acceleration is known. The inertial force was subtracted from the measured forces to obtain the dynamic where F and F are the identified amplitude of WOSR WSR muscle force. dynamic muscle force measured in the WOSR and WSR con- Ignoring the nonlinear factors, a three-parameter model ditions, respectively, and F is the normalized amplitude WOSR was used to fit the time history curve of the experimental data for the WOSR condition. with the least squares method; see equation (2). In addition, to quantify the biomechanical properties of the hysteresis loops of tension length, the stiffness and visco- elasticity were estimated as follows: gt = A · sin 2πft + φ + C, 2 F = k · l + c · l, 5 where g t is the time-dependent experimental data, f is the corresponding vibration frequency, A is the identification where F is the muscle force, k is the stiffness, c is the damping amplitude, φ is the identification phase, and C is the identifi- coefficient, and l is the muscle length. cation shift. An example of fitting results is shown in Figure 3. The muscle force presented here was the dynamic 2.5. Statistical Analysis. Three-way analysis of variance muscle force with the change in the muscle length. A negative (ANOVA, 2×2 × 5) was conducted to analyze the signifi- value represents a decrease in the muscle force. cance of stretch reflex, muscle initial length, and vibration Displacement (mm) Force (N) Acceleration (m/s ) Applied Bionics and Biomechanics 5 0.30 and no significant difference was found for both the WSR and the WOSR conditions (F (1,14) = 2.02, p =0 1561). 0.25 3.3. Effect of Vibration Frequency. As can be seen from 0.20 Figure 4, the dynamic muscle force increased with increas- 0.15 ing vibration frequency in both prelengthening groups. Note that the muscle force of the WOSR condition also 0.10 had an increasing trend with increasing frequency. Three- way ANOVA analysis showed that the vibration frequency 0.05 had a significant effect on the amplitude of dynamic muscle 0.00 force (Table 2, F (1,14) = 25.21, p =0 000). The post hoc 2 Hz 4 Hz 8 Hz 12 Hz 16 Hz Tukey-Kramer test showed that the lower frequency 2 mm WSR condition 2 mm WOSR condition (2 Hz) and higher frequency (16 Hz) had a significant effect 3 mm WSR condition 3 mm WOSR condition on the dynamic muscle force, while the middle frequency (8 Hz) did not show any significance. However, the fre- Figure 4: Comparison of muscle response force with/without quency had no significant effect on the normalized muscle stretch reflex for 2 mm and 3 mm prelengthening group. force F (F (4,52) = 0.95, p =0 4377). WOSR Phase differences between the dynamic muscle force and frequency for muscle response force. Then a post hoc Tukey- the length change were also analyzed (see Figure 6). The force Kramer test was used to compare the significance between had a phase lead compared with the length change. The each level. Two-way ANOVA (2×5) was further conducted phase difference decreased sharply at first and then increased for the normalized muscle force F . In addition, the sig- slowly with increasing frequency for the 2 mm and 3 mm pre- WOSR lengthening groups. It reached the lowest value at approxi- nificance of the phase difference was also explored using three-way ANOVA (2×2×5). The values p <0 05 were con- mately 8 Hz at approximately 20 . Surprisingly, the variance of the phase at 2 Hz was extremely large among the tested sidered statistically significant. Statistical analysis was done using the MATLAB R2017a Statistics Toolbox (The Math- rats. As the frequency increased, the variance reduced rapidly Works Inc., Natick, Massachusetts, United States). and almost disappeared at 8 Hz. Significance was observed from three-way ANOVA analysis (F (4,56) = 73.73, p = 0 000). The post hoc Tukey-Kramer test showed that 2 Hz 3. Results and 16 Hz significantly differed with the other three groups at p <0 05; the middle frequencies (4~12 Hz) were not signif- 3.1. Effect of Stretch Reflex. The amplitudes of dynamic mus- icantly different with each other. cle force in the 2 mm and 3 mm prelengthening groups are summarized in Figure 4. It is clearly shown that the muscle 3.4. Tension-Length Curves. The relationship between mus- response force with stretch reflex was larger than that with- cle force and muscle length for the 2 mm prelengthening out stretch reflex at every frequency for both 2 mm and group is shown in Figure 7. The blue and red lines repre- 3 mm prelengthening groups. sent the dynamic muscle force of the WSR and WOSR Data analysis results (Table 1) indicated that the muscle conditions, respectively. The force-length curve shows a response force decreased by 20% on average after the stretch clockwise loop, and its shape is substantially an ellipse. It reflex arc was blocked for the 2 mm prelengthening group indicates that both damping and stiffness factors were and by 24% for the 3 mm prelengthening group. The statisti- included in the muscle biomechanical system. The distri- cal analysis result of three-way ANOVA for the muscle force bution of the stiffness and damp forces calculated accord- is presented in Table 2. As we can see from Table 2, com- ing to equation 5 is presented in Figure 8. It was shown pared with WSR condition, the muscle force had a significant that the damp force was highest at 2 Hz and then had a reduction (F (1,14) = 25.21, p =0 000) at WOSR condition. linear increase from 4 to 16 Hz. Nonlinear increase of Three-way ANOVA was also applied to phase difference, the stiffness was observed with frequency. Consistent with and result showed that there is no significance between the dynamic muscle force, the stiffness was also decreased WSR and WOSR conditions (F (1,14) = 0.86, 0 = 0.3357). after the stretch reflex arc was blocked. 3.2. Effect of Initial Length. The average dynamic muscle 4. Discussion force in the 3 mm prelengthening group was larger than that of the 2 mm prelengthening group for all frequencies This study investigated the gastrocnemius muscle force (Figure 4). However, there was no significant difference response to vibration stretching of 2–16 Hz using decere- between 2 mm and 3 mm prelengthening group (Table 2, F brate rats. Significant reductions in dynamic muscle force (1,14) = 2.06, p =0 1522). Normalized muscle force F response were observed with the elimination of stretch WOSR was also analyzed (Figure 5), and two-way ANOVA showed reflex (p <0 001). This is consistent with the findings of a significant difference between 2 mm and 3 mm prelength- previous studies using nerve inhibition methods, such as ening group (F (1,13) = 9.1, p =0 003). In addition, the effect sectioning of the reflex arc nerve and nerve anesthesia. of the initial length on the phase difference was investigated, Roberts [24] observed an increase of tension with the Muscle force (N) 6 Applied Bionics and Biomechanics Table 1: Percent decrease of dynamic muscle force from WSR to WOSR condition. 1 − F /F × 100% 2Hz 4Hz 8Hz 12Hz 16Hz WOSR WSR 2 mm prelengthening condition 20.1% 20.3% 18.9% 18.9% 17.7% 3 mm prelengthening condition 27.2% 25.5% 22.7% 21.1% 22.6% Table 2: Three-way ANOVA analysis result of dynamic muscle force. Source df Fp L (muscle length, 2 levels) 1 2.06 0.1522 F (frequency, 5 levels) 4 17.74 0.000 S (stretch reflex, 2 levels) 1 25.21 0.000 L × F 4 0.06 0.9931 L × S 1 0.61 0.4358 F × S 4 0.11 0.9782 2 Hz 4 Hz 8 Hz 12 Hz 16 Hz 2 mm WSR conditioin 3 mm WSR condition 2 mm WOSR condition 3 mm WOSR condition Figure 6: Phase difference between dynamic muscle force and length change for 2 mm and 3 mm prelengthening group. 0.8 0.6 prelengthening condition tested in our study. However, 0.4 there is no significance between the two prelengthening conditions for muscle force (F (1,14) = 2.06, p =0 1522), 0.2 while a significant difference was observed for normalized muscle force F (F (1,13) = 9.1, p =0 003). WOSR 2 Hz 4 Hz 8 Hz 12 Hz 16 Hz The obtained results showed that the tension-length 3 mm prelengthening group curve was a clockwise loop and its shape was substantially 2 mm prelengthening group an ellipse. Roberts [24] researched rhythmic excitation of the stretch reflex using the soleus muscle of decerebrate Figure 5: Comparison of normalized muscle response force F WOSR cats. Rhythmic excitation of several frequencies and ampli- between 2 and 3 mm prelengthening group. tudes was used to stretch the muscle. It was found that plots of tension against length showed a clockwise hyster- stretch reflex and redefined stretch reflex as an increase of esis loop consistent with the results found in this study. muscle stiffness. Serres et al. [28] published similar results Jansen and Rack [29] also studied the stretch reflex with using the triceps surae muscles of decerebrate cats. After the soleus muscle of cerebrate cats by sinusoidal stretching sectioning the L5 to S2 dorsal roots, muscle response force of the soleus muscle at various frequencies and ampli- decreased significantly for low and high levels of back- tudes. Similarly, clockwise elliptical hysteresis loops were ground force. observed at some frequencies with a 1 mm peak-to-peak Although these studies reached a similar conclusion amplitude. It was also reported that when the stretch that muscle response to vibration is significantly reduced amplitude was increased to 3.8 mm (peak-to-peak), the after the stretch reflex arc is disrupted, few studies have tension-length ran clockwise. The effect of stretch ampli- quantified the difference between the WSR and WOSR tude on the tension-length hysteresis loop needs to be conditions. This study found an over 20% reduction after studied in future work. the stretch reflex arc was blocked, which mainly depended Further analysis for hysteresis loop indicated that the on the stretching magnitude and frequency. It also showed stiffness had a nearly linear increase from 2 Hz to 12 Hz that a greater prelengthening might lead to a higher mus- and then stayed stable from 12 Hz to 16 Hz (Figure 8). cle force at lower frequencies such as at 2–8 Hz, but not at The damp force was highest at 2 Hz and then had a linear 12–16 Hz. Though both higher frequency and greater increase from 4 to 16 Hz. But when considering damp prelengthening could lead to a higher muscle force, pre- coefficient, that is the division of damp force and stretch lengthening was the dominant factor at low frequency, so velocity, a downtrend was observed from low to high fre- the muscle force was greater at higher prelengthening con- quencies. The result of the hysteresis loop indicated a non- dition. While frequency was the dominant factor at high linear relation of dynamic muscle force and frequency, frequency, the muscle force seemed the same for the two while Hasan [30] built a spindle afferent model to research Normalized muscle force Phase difference (deg) Applied Bionics and Biomechanics 7 2 Hz 4 Hz 0.2 0.2 0 0 −0.2 −0.2 −0.5 0 0.5 −0.5 0 0.5 Length change (mm) Length change (mm) 8 Hz 12 Hz 0.2 0.2 0 0 −0.2 −0.2 −0.5 0 0.5 −0.5 0 0.5 Length change (mm) Length change (mm) Measured F WSR Measured F WOSR 16 Hz 0.2 −0.2 −0.5 0 0.5 Length change (mm) Figure 7: Representative muscle force vs. length curve (2 mm prelengthening group). 0.25 response force under muscle stretch, whose parameters were the same for different stretch velocities. 0.2 In this study, the phase difference between the dynamic muscle force and the length change was calculated (see 0.15 Figure 6). The large variance of phase difference at low fre- quencies may be related to the fact that the phase was mainly 0.1 influenced by the damping force and was relatively small at low frequencies. Therefore, the phase of the muscle force 0.05 would be heavily influenced by random error. The overall 0 phase difference trend showed that the minimum value was 2 Hz 4 Hz 8 Hz 12 Hz 1 6Hz 4~8 Hz. Furthermore, the phase difference between the 2 mm WSR 3 mm WOSR WSR and WOSR conditions was negligible (p >0 5), which 2 mm WOSR suggested the stretch reflex had little influence on the damp- 3 mm WSR Damp force ing factor of the muscle spindle. The phase difference between the muscle force and length Figure 8: Identification of average stiffness force and damp force of was compared with that of previous studies. Roberts [24] the hysteresis loops. reported that length change lagged behind tension change Muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) 8 Applied Bionics and Biomechanics Stretch reflex PE Activation SE External Muscle force force AC Body posture Muscle model Figure 9: Diagram of current muscle model in solid line and potential stretch reflex module in dash line. by 15–20 , which is consistent with our findings. However, However, even though we have researched the effect of the phase difference was independent of the imposed fre- different low-frequency vibrations on the muscle response at different neurointact conditions and provided theoretical quency reported by Roberts (0.6–1.4 Hz), while the phase advance of muscle force varied with frequency (2–16 Hz) in support for muscle model, there are still some limitations of our result. Lippold et al. [31] found an approximate 90 phase this study: (1) although the effects of vibrational frequency difference between the sensory discharge and the displace- and muscle length were examined in detail, the amplitude ment record at frequencies between 4 and 15 Hz. He sug- of the stretching was not considered; (2) as fatigue is a com- mon but challenging problem in driving, the effect of differ- gested that the muscle spindle response was greatest when velocity, rather than displacement, was maximal. Another ent fatigue levels on muscle response needs to be result worth noting was the nonlinearity of the phase differ- considered in future studies; (3) the result of this study is ence of the WOSR and WSR conditions. This phenomenon based on the rat, even many studies suggest it is similar for indicated that the tension-length diagram could not be human muscle, more validations should be done for the mus- cle model based on this result; (4) the relation between attributed to frequency-dependent damping. A mathematical model based on identification method should be proposed in response under the whole-body vibration and localized further study. vibration is very complex, further research should be con- The results of this study could benefit musculoskeletal ducted. We will build a new muscle model incorporating modeling by providing a theoretical support to build a stretch the stretch reflex module (Figure 9) based on this experimen- tal result. More experiments considering the effect of fatigue reflex model for low-frequency vibration. Frequently used muscle models include Hill muscle model [32–35], Thelen will be conducted in the future. muscle model [36], and Millard muscle model [37]. The structures of the above models are similar as shown in 5. Conclusion Figure 9. External force (caused by vibration), activation (measured via EMG), and body posture or motion were This study explored the biomechanical response of decere- model inputs, and muscle force was the model output brate rats with/without stretch reflex to low-frequency vibra- (marked as solid lines in Figure 9). However, these muscle tion and described the quantitative relationship between models could not conduct simulations when the activation muscle force and muscle length. Results indicated that the was missing, because the amount of activation was difficult amplitude of muscle response force decreased by over 20% to measure. when the stretch reflex arc was blocked (p <0 001). The rela- There are several studies that had built linearly stretch tionship between muscle response force and muscle length reflex models to research the neural control and human loco- was found to be a nonlinear hysteresis loop that changed with motion. Geyer and Herr [38] built a reflex model to research frequency (Figure 7). The phase difference between the walking using a proportional coefficient for muscle length dynamic muscle force and the change in muscle length was combined with upper and lower constrains. Similarly, two affected significantly by the vibration frequency (p <0 05), proportional coefficients for angle and angle velocity were and the minimum frequency was 4–8 Hz. Experimental used in Eilenberg’s stretch reflex model [39]. However, non- results of this study demonstrated that the stretch reflex linearity relation of phase difference is observed in this study had a tremendous effect on muscle vibration response (over which is consistent with Miles et al.’s [13] findings. Zhang 20%) and could benefit musculoskeletal modeling by provid- et al. [40] and Mirbagheri et al. [41] used system identifica- ing a theoretical support to build a stretch reflex model for tion methods to model the intrinsic properties of human low-frequency vibration. arm and ankle system separately. The nonlinearity suggests that simple frequency-dependent damping (proportional method) does not really match the reality. Therefore, a more Data Availability realistic muscle model incorporating stretch reflex module is needed to perform human vibration simulation based on our The data used to support the findings of this study are avail- current work. able from the corresponding author upon request. Applied Bionics and Biomechanics 9 Journal of Muscle Research & Cell Motility, vol. 17, no. 2, Additional Points pp. 221–233, 1996. [9] X. Meng, X. Tao, W. Wang et al., “Effects of sinusoidal whole New and Noteworthy. Stretch reflex is an important factor body vibration frequency on drivers’ muscle responses,” in that influences the biomechanical response of the human SAE Technical Paper, Detroit, Michigan, USA, April 2015. whole-body vibration, which has not been sufficiently ana- [10] R. Ritzmann, A. Kramer, M. Gruber, A. Gollhofer, and lyzed for low-frequency condition in previous studies. Exper- W. Taube, “EMG activity during whole body vibration: motion iment has been conducted to explore the quantitative effect of artifacts or stretch reflexes?,” European Journal of Applied the stretch reflex induced by low-frequency vibration on Physiology, vol. 110, no. 1, pp. 143–151, 2010. muscle response, which is common in real-world condition [11] R. Souron, T. Besson, G. Y. Millet, and T. Lapole, “Acute and and important for the human musculoskeletal model. Results chronic neuromuscular adaptations to local vibration train- of this study demonstrated that the stretch reflex had a tre- ing,” European Journal of Applied Physiology, vol. 117, mendous effect on muscle vibration response (over 20%) at no. 10, pp. 1939–1964, 2017. low frequencies and could benefit musculoskeletal modeling [12] A. F. J. Abercromby, W. E. Amonette, C. S. Layne, B. K. by providing a theoretical support to build a stretch reflex Mcfarlin, M. R. Hinman, and W. H. Paloski, “Variation in model for low-frequency vibration. neuromuscular responses during acute whole-body vibration exercise,” Medicine & Science in Sports & Exercise, vol. 39, no. 9, pp. 1642–1650, 2007. Conflicts of Interest [13] T. S. Miles, S. C. Flavel, and M. A. Nordstrom, “Stretch reflexes in the human masticatory muscles: a brief review and a new We declare that we have no conflict of interest in this study. functional role,” Human Movement Science, vol. 23, no. 3-4, pp. 337–349, 2004. Acknowledgments [14] J. M. Wakeling, B. M. Nigg, and A. I. Rozitis, “Muscle activity damps the soft tissue resonance that occurs in response to This research is supported by the National Natural Science pulsed and continuous vibrations,” Journal of Applied Physiol- Foundation of China (grant nos. 51575303 and U1664263). ogy, vol. 93, no. 3, pp. 1093–1103, 2002. This research is also supported by the Natural Science Foun- [15] C. Bosco, R. Colli, E. Introini et al., “Adaptive responses of dation of SZU (grant no. 2017033). human skeletal muscle to vibration exposure,” Clinical Physi- ology, vol. 19, no. 2, pp. 183–187, 1999. [16] J. 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Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions

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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 1971045, 10 pages https://doi.org/10.1155/2019/1971045 Research Article Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions 1 1 2 3 4 Chaofei Zhang , Wenjun Wang , Dennis Anderson, Sishu Guan, Guofa Li , 3 3 1 Hongyi Xiang, Hui Zhao , and Bo Cheng State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China Center for Advanced Orthopedic Studies, Beth Israel Deaconess Medical Center, Boston, MA 02215, USA Chongqing Key Laboratory of Vehicle/Biological Crash Security, Department 4th, Institute of Surgery Research, Daping Hospital, Third Military Medical University, Chongqing 400042, China Institute of Human Factors and Ergonomics, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China Correspondence should be addressed to Wenjun Wang; wangxiaowenjun@tsinghua.edu.cn and Guofa Li; hanshan198@gmail.com Received 3 April 2018; Revised 26 July 2018; Accepted 30 August 2018; Published 3 January 2019 Academic Editor: Li-Qun Zhang Copyright © 2019 Chaofei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Stretch reflex is an important factor that influences the biomechanical response of the human body under whole-body vibration. However, there is a lack of quantitative evaluation at lower frequencies. Thus, the aim of this study was to investigate the effects of vibration on the stretch reflex and, in particular, to explore the quantitative relationship between dynamic muscle responses and low-frequency vibrations. The gastrocnemius muscle of 45 Sprague-Dawley rats was dissected. Sinusoidal vibrations of five discrete frequencies (2~16 Hz) with peak-to-peak amplitudes of 1 mm were applied to the gastrocnemius muscles with 2 mm or 3 mm prelengthening. Variables including dynamic muscle force, vibration acceleration, and displacement were recorded in two conditions, with and without the stretch reflex. Results showed that the dynamic muscle forces decreased by 20% on average for the 2 mm prelengthening group after the stretch reflex was blocked and by 24% for the 3 mm prelengthening group. Statistical analysis indicated that the amplitude of dynamic muscle force in the “with stretch reflex” condition was significantly larger than that in the “without stretch reflex” condition (p <0 001). The tension-length curve was found to be a nonlinear hysteresis loop that changed with frequency. The phase difference between the dynamic muscle force and the length change was affected significantly by vibration frequency (p <0 01), and the minimum frequency was 4–8 Hz. Experimental results of this study could benefit musculoskeletal model by providing a theoretical support to build a stretch reflex model for low-frequency vibration. 1. Introduction Several studies have examined the effect of muscle contractions on whole-body vibration response. Huang Muscle fatigue caused by prolonged driving is an important and Griffin [5] and Nikooyan and Zadpoor [6] reported that the activation of muscles could have a significant factor affecting driving comfort and resulting in lower back pain [1]. Whole-body vibration exposure plays a key role in effect on human mechanical response under whole-body vibration. However, activation levels were set as constant producing muscle fatigue and accelerating the fatigue process values in their models, which is inconsistent with the actual [2, 3]. Shinohara [4] synthesized several findings about the effects of prolonged vibration on muscle activity and revealed situation. Kitazaki and Griffin [7] used a human finite ele- ment model with a muscle module to examine vibration that prolonged vibration modulated muscle activity, which led to reduced peak force during maximal contractions and comfort. Electromyography (EMG) data was used as activa- altered force fluctuations. tion inputs when predicting muscle response. However, 2 Applied Bionics and Biomechanics frequency oscillations and researched its mechanical charac- EMG must be measured before simulation, and the quan- titative relation between EMG and muscle activation is teristics by performing experiments on a piglet. more complex in actual conditions. Brown et al. [8] and To date, various studies have addressed the importance of the muscle stretch reflex on human vibration responses. Meng et al. [9] found that the response of drivers’ lumbar muscle forces reached a peak in the resonance frequency However, the quantitative effect of the stretch reflex induced by low-frequency (2~20 Hz) vibration on muscle bands of the human biomechanics system (2–25 Hz). These studies suggested that human biomechanical response, espe- response has not been sufficiently analyzed in previous studies, which is a common real-world condition and cially for the muscle activity, was significantly affected by important for the human musculoskeletal model. It is also frequency of whole-body vibration. suggested that the stretch reflex responses vary with differ- Vibration can cause muscle lengthening and shortening, potentially resulting in increased muscle tension due to a ent stretch frequencies, amplitudes [26], or muscle lengths. stretch reflex [10]. Souron et al. [11] reported that a training Thus, the hypothesis of this study was that the stretch period of local vibration was efficient in improving muscular reflex plays an important role in muscle vibration response performance. Stretch reflex was proposed as an important in the low-frequency range on driving condition, and the factor that influences the biomechanical response of the vibration frequency and initial muscle length will signifi- human body under whole-body vibration [12]. cantly affect the muscle response. This experimental study Human experiment had been conducted to examine the is aimed at (1) examining the stretch response differences effect of vibration frequency and amplitude on the stretch between muscles with/without stretch reflex arc at different reflex. Ritzmann et al. [10] reported that vibration-induced vibration frequencies and initial muscle length conditions stretch reflex increased EMG activity after the elimination and (2) exploring the quantitative relationship between of motion artifacts. Miles et al. [13] reported two different muscle responses and low-frequency vibrations. stretch reflex responses, which are short-latency reflex evoked by high-frequency stretches and long-latency reflex 2. Methods evoked by slower stretches. Wakeling et al. [14] found increasing EMG activity and damping when the vibration 2.1. Experiment Configuration. This study was approved by frequency was close to the natural frequency of the soft tissue. the Animal Welfare Committee, Third Military Medical Bosco et al. [15], Rittweger [16], and Cochrane [17] found University of China. Experiments were performed to exam- increased muscle activity and power after whole-body vibra- ine the reflex response to sinusoidal stretching of the gastroc- tion and suggested a potential benefit over traditional forms nemius muscles of the right hind limb of 45 male rats of resistive exercise. Zaidell et al. [18] also found increased (225 ± 20 g, 10 ± 1 week). Decerebration was conducted by muscle activation during whole-body vibration with a fre- cutting the spinal cord between T9 and T12 of each of quency of 25 Hz and 50 Hz and explained it with muscle the 45 rats before experimentation. Dynamic muscle modulation under tonic vibration reflex. response force, muscle length, and vibration acceleration However, most of the above studies focused on high- were recorded in two conditions: “with stretch reflex” frequency oscillations (over 25 Hz), while the vibration (WSR) condition (Figure 1(a)), meaning the stretch reflex frequency in driving situations is mostly below 20 Hz. And arc was intact for the lower-extremity muscles, and “with- biomechanical response such as spine loading and muscle out stretch reflex” (WOSR) condition (Figure 1(b)), mean- forces which are closely related to driving comfort and ing the stretch reflex arc was blocked by cutting off the fatigue had not been analyzed yet. Musculoskeletal model sciatic nerve after experimentation in the WSR condition. [19, 20] was an alternative way to calculate muscle force The animal experiment diagram is presented in and joint loading which used bunches of muscle fascicles to Figure 2(a). The gastrocnemius muscle was separated and model muscle groups. Thus, an assumption was made that tied to a vibrator. The lower part of the shin was fixed in a the human muscle response under whole-body vibration vise. Piezoelectric transducers were used to record the could be modelled using the combination of many muscle dynamic muscle force with the vibration stretching and fascicle responses under localized vibration. vibration acceleration. A laser displacement transducer was Animal experiment is an effective method used in previ- used to measure the change in muscle length. ous studies to analyze the mechanism of stretch reflex of a single muscle [8]. Matthews [21–23] studied the relationship 2.2. Surgical Procedure. The surgical procedures were between muscle tension and muscle length in different performed under general anesthesia (ether, inhalational stretching velocities on decerebrate cats. Factors that could anesthesia). The nerves and muscles of the hind limbs were influence the stretch reflex, such as muscle length, stimulat- prepared, and a laminectomy was performed between T9 ing style, and motor nerve inhibition, were analyzed. Roberts and T12 in preparation for later spinalization; see [24] studied the hysteresis loop of tension against length Figure 2(b). A few trails were conducted to explore the loca- plots when sinusoidal fluctuating tensions were applied to tion of spinalization. Results indicated that the best location the soleus muscle of decerebrate cats, suggesting that there was between T9 and T12. If the location was too high, a was damping in the process of stretching. However, the serious spinal injury would occur, and if the location was period in his study is from 0.7 to 16.5 seconds; the highest too low, the stretch reflex arc would be cut off. After spinali- frequency is 1.4 Hz that is not a common real-world driving zation, the ether was removed, and the rat would regain condition. Günther et al. [25] noticed the damping in high- consciousness. The effectiveness of the operation was proven Applied Bionics and Biomechanics 3 Spinal cord Spinal cord Sciatic nerve Sciatic nerve Gastrocnemius Gastrocnemius Cut off (a) With stretch reflex (b) Without stretch reflex Figure 1: Two experimental conditions. (1) Vibrator (2) Force & acceleration Laser displacement transducer transducer Data acquisition (3) Mini vise Vibrator 4 (4) Shin Gastrocnemius (5) Gastrocnemius muscle 3 muscle Force & acceleration Mini vise transducer (6) Laser Tendon displacement transducer (a) Experiment diagram (b) Experimental apparatus Figure 2: Experiment configuration. gastrocnemius lengthened 7 mm corresponding to an ankle by the free movement of the front legs and paralysis of the hind legs. The nerve connection between the brain and the dorsiflexion of approximately 135 . Therefore, we ensured lower extremities was cut off, and the rat was ensured to that the length of the gastrocnemius would not exceed the be alive. physical limitation during the vibration test with a peak-to- Then the rat was anesthetized again, and its right peak amplitude of 1 mm. hind limb was extensively dissected (Figure 2(b)). All Sinusoidal vibrations were applied along the longitudinal the other nerves (femoral nerve, distal branches of the axis of the muscle. Five discrete frequencies (2, 4, 8, 12, and sciatic, obturator nerve, and hamstring nerve), except 16 Hz) were employed. The peak-to-peak amplitude in for those to the gastrocnemius muscles, were denervated. stretching was 1 mm for all frequencies. Each frequency was The ipsilateral gastrocnemius muscles were freed from tested twice in both the WSR and WOSR conditions. In total, their surrounding tissue. The end of the hind calcaneus each rat experienced 22 tests (5×2+1 for trial 1 and 5×2 bone was cut to keep a piece of bone to leave the ten- +1 for trial 2). To make sure the quality of measurement, don of the gastrocnemius muscle intact. The muscle we kept recording until 10 stable periods signals have been slack length after surgery was measured. measured and then we stopped recording the data for a test. The rat was then mounted in a stereotaxic frame According to our recording, the duration for the test is (Figure 2(b)). The other three legs besides the right hind 35~40 s. limb were fixed with adhesive tape. The shin bone of the Because the gastrocnemius muscle was repeatedly right hind limb was held in a bench vise. The distal ten- stretched using different frequencies vibration, it may cause don of the gastrocnemius muscle was tied to a vibrator muscle fatigue which would affect the result of muscle using an alligator clip. response. To exclude the effect of repeated stretching, a 15 s break was added between each adjacent test for recovery. 2.3. Experimental Procedure. To investigate the effect of ini- Moreover, an additional test with the same frequency as the tial muscle length on the response, the decerebrate rats were first test in the trial was performed to examine whether the divided into two prelengthening groups, which are 2 mm or muscle was tired. No significant decline of muscle response 3 mm longer than the slack length of the muscle. Measure- force was observed in this additional test as compared to the first test in the same trial. This strategy ensured the ment results before the surgical procedure showed that the 4 Applied Bionics and Biomechanics 0.2 exclusion of the fatigue effect on muscle response. Since we have already excluded the fatigue effect, the experiment did not use a random order. Another important influencing factor was spinal shock in −0.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 which all neurological activity was lost. Nesmeyanova [27] t (s) found a normal electrical response of the soleus muscle in spinal patients with clonus compared with absence of clonus after spinal cord injury. However, it was difficult to measure the spinal shock level quantitatively. To ensure normal −2 response after spinal injury, we proposed the following −4 method to avoid or mitigate the influence of spinal shock. −6 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 After spinalization, the anesthesia was removed and a piece t (s) of gauze was used to stanch bleeding. After the rat regained consciousness, if the rat climbed forward or in a circle with −1.5 the two front legs and the two hind legs seemed powerless because of a loss of brain control, this meant that the rat −2 had recovered partially or totally from the spinal shock. −2.5 −3 2.4. Data Progress. In total, 45 rats were involved in the 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 experiment, 15 in the 2 mm prelengthening group and 14 t (s) in the 3 mm prelengthening group. The other 16 rats either Raw data died in surgery or failed to yield useful results, typically Fitting result because of the vagaries of the decerebrate preparation rather than the occasional failure of the recording operation. A Figure 3: Typical example of raw data and fitting result at 8 Hz with zero-phase 8th-order Butterworth low-pass filter with a cut- stretch reflex under 2 mm prelengthening condition. off frequency of 25 Hz was used for data filtering. The system inertial mass was identified prior to the tests The phase difference between the dynamic muscle force without muscle connection. The inertial mass included the and the muscle length change was calculated as follows: mass of an alligator clip, a laser reflection plate for length recording, and the connection bolt to the acceleration trans- Δφ = φ − φ 3 f l ducer. Sinusoidal signals of 5 Hz and 10 Hz were provided by the vibrator. The force F and the acceleration a were inertial Here, Δφ is the phase difference, and φ and φ are, f l recorded. The system inertial mass m can be computed system respectively, the phase of dynamic muscle force and muscle according to length identified with the least squares method according to equation 2. F To exclude the effect of the individual difference, a nor- inertial m = 1 system malization method was proposed to further analyze the force data for each rat as follows: It was found that the system inertia mass was about WOSR F = , 4 34.8 g. Therefore, the system inertial force can be calculated WOSR WSR if the vibration acceleration is known. The inertial force was subtracted from the measured forces to obtain the dynamic where F and F are the identified amplitude of WOSR WSR muscle force. dynamic muscle force measured in the WOSR and WSR con- Ignoring the nonlinear factors, a three-parameter model ditions, respectively, and F is the normalized amplitude WOSR was used to fit the time history curve of the experimental data for the WOSR condition. with the least squares method; see equation (2). In addition, to quantify the biomechanical properties of the hysteresis loops of tension length, the stiffness and visco- elasticity were estimated as follows: gt = A · sin 2πft + φ + C, 2 F = k · l + c · l, 5 where g t is the time-dependent experimental data, f is the corresponding vibration frequency, A is the identification where F is the muscle force, k is the stiffness, c is the damping amplitude, φ is the identification phase, and C is the identifi- coefficient, and l is the muscle length. cation shift. An example of fitting results is shown in Figure 3. The muscle force presented here was the dynamic 2.5. Statistical Analysis. Three-way analysis of variance muscle force with the change in the muscle length. A negative (ANOVA, 2×2 × 5) was conducted to analyze the signifi- value represents a decrease in the muscle force. cance of stretch reflex, muscle initial length, and vibration Displacement (mm) Force (N) Acceleration (m/s ) Applied Bionics and Biomechanics 5 0.30 and no significant difference was found for both the WSR and the WOSR conditions (F (1,14) = 2.02, p =0 1561). 0.25 3.3. Effect of Vibration Frequency. As can be seen from 0.20 Figure 4, the dynamic muscle force increased with increas- 0.15 ing vibration frequency in both prelengthening groups. Note that the muscle force of the WOSR condition also 0.10 had an increasing trend with increasing frequency. Three- way ANOVA analysis showed that the vibration frequency 0.05 had a significant effect on the amplitude of dynamic muscle 0.00 force (Table 2, F (1,14) = 25.21, p =0 000). The post hoc 2 Hz 4 Hz 8 Hz 12 Hz 16 Hz Tukey-Kramer test showed that the lower frequency 2 mm WSR condition 2 mm WOSR condition (2 Hz) and higher frequency (16 Hz) had a significant effect 3 mm WSR condition 3 mm WOSR condition on the dynamic muscle force, while the middle frequency (8 Hz) did not show any significance. However, the fre- Figure 4: Comparison of muscle response force with/without quency had no significant effect on the normalized muscle stretch reflex for 2 mm and 3 mm prelengthening group. force F (F (4,52) = 0.95, p =0 4377). WOSR Phase differences between the dynamic muscle force and frequency for muscle response force. Then a post hoc Tukey- the length change were also analyzed (see Figure 6). The force Kramer test was used to compare the significance between had a phase lead compared with the length change. The each level. Two-way ANOVA (2×5) was further conducted phase difference decreased sharply at first and then increased for the normalized muscle force F . In addition, the sig- slowly with increasing frequency for the 2 mm and 3 mm pre- WOSR lengthening groups. It reached the lowest value at approxi- nificance of the phase difference was also explored using three-way ANOVA (2×2×5). The values p <0 05 were con- mately 8 Hz at approximately 20 . Surprisingly, the variance of the phase at 2 Hz was extremely large among the tested sidered statistically significant. Statistical analysis was done using the MATLAB R2017a Statistics Toolbox (The Math- rats. As the frequency increased, the variance reduced rapidly Works Inc., Natick, Massachusetts, United States). and almost disappeared at 8 Hz. Significance was observed from three-way ANOVA analysis (F (4,56) = 73.73, p = 0 000). The post hoc Tukey-Kramer test showed that 2 Hz 3. Results and 16 Hz significantly differed with the other three groups at p <0 05; the middle frequencies (4~12 Hz) were not signif- 3.1. Effect of Stretch Reflex. The amplitudes of dynamic mus- icantly different with each other. cle force in the 2 mm and 3 mm prelengthening groups are summarized in Figure 4. It is clearly shown that the muscle 3.4. Tension-Length Curves. The relationship between mus- response force with stretch reflex was larger than that with- cle force and muscle length for the 2 mm prelengthening out stretch reflex at every frequency for both 2 mm and group is shown in Figure 7. The blue and red lines repre- 3 mm prelengthening groups. sent the dynamic muscle force of the WSR and WOSR Data analysis results (Table 1) indicated that the muscle conditions, respectively. The force-length curve shows a response force decreased by 20% on average after the stretch clockwise loop, and its shape is substantially an ellipse. It reflex arc was blocked for the 2 mm prelengthening group indicates that both damping and stiffness factors were and by 24% for the 3 mm prelengthening group. The statisti- included in the muscle biomechanical system. The distri- cal analysis result of three-way ANOVA for the muscle force bution of the stiffness and damp forces calculated accord- is presented in Table 2. As we can see from Table 2, com- ing to equation 5 is presented in Figure 8. It was shown pared with WSR condition, the muscle force had a significant that the damp force was highest at 2 Hz and then had a reduction (F (1,14) = 25.21, p =0 000) at WOSR condition. linear increase from 4 to 16 Hz. Nonlinear increase of Three-way ANOVA was also applied to phase difference, the stiffness was observed with frequency. Consistent with and result showed that there is no significance between the dynamic muscle force, the stiffness was also decreased WSR and WOSR conditions (F (1,14) = 0.86, 0 = 0.3357). after the stretch reflex arc was blocked. 3.2. Effect of Initial Length. The average dynamic muscle 4. Discussion force in the 3 mm prelengthening group was larger than that of the 2 mm prelengthening group for all frequencies This study investigated the gastrocnemius muscle force (Figure 4). However, there was no significant difference response to vibration stretching of 2–16 Hz using decere- between 2 mm and 3 mm prelengthening group (Table 2, F brate rats. Significant reductions in dynamic muscle force (1,14) = 2.06, p =0 1522). Normalized muscle force F response were observed with the elimination of stretch WOSR was also analyzed (Figure 5), and two-way ANOVA showed reflex (p <0 001). This is consistent with the findings of a significant difference between 2 mm and 3 mm prelength- previous studies using nerve inhibition methods, such as ening group (F (1,13) = 9.1, p =0 003). In addition, the effect sectioning of the reflex arc nerve and nerve anesthesia. of the initial length on the phase difference was investigated, Roberts [24] observed an increase of tension with the Muscle force (N) 6 Applied Bionics and Biomechanics Table 1: Percent decrease of dynamic muscle force from WSR to WOSR condition. 1 − F /F × 100% 2Hz 4Hz 8Hz 12Hz 16Hz WOSR WSR 2 mm prelengthening condition 20.1% 20.3% 18.9% 18.9% 17.7% 3 mm prelengthening condition 27.2% 25.5% 22.7% 21.1% 22.6% Table 2: Three-way ANOVA analysis result of dynamic muscle force. Source df Fp L (muscle length, 2 levels) 1 2.06 0.1522 F (frequency, 5 levels) 4 17.74 0.000 S (stretch reflex, 2 levels) 1 25.21 0.000 L × F 4 0.06 0.9931 L × S 1 0.61 0.4358 F × S 4 0.11 0.9782 2 Hz 4 Hz 8 Hz 12 Hz 16 Hz 2 mm WSR conditioin 3 mm WSR condition 2 mm WOSR condition 3 mm WOSR condition Figure 6: Phase difference between dynamic muscle force and length change for 2 mm and 3 mm prelengthening group. 0.8 0.6 prelengthening condition tested in our study. However, 0.4 there is no significance between the two prelengthening conditions for muscle force (F (1,14) = 2.06, p =0 1522), 0.2 while a significant difference was observed for normalized muscle force F (F (1,13) = 9.1, p =0 003). WOSR 2 Hz 4 Hz 8 Hz 12 Hz 16 Hz The obtained results showed that the tension-length 3 mm prelengthening group curve was a clockwise loop and its shape was substantially 2 mm prelengthening group an ellipse. Roberts [24] researched rhythmic excitation of the stretch reflex using the soleus muscle of decerebrate Figure 5: Comparison of normalized muscle response force F WOSR cats. Rhythmic excitation of several frequencies and ampli- between 2 and 3 mm prelengthening group. tudes was used to stretch the muscle. It was found that plots of tension against length showed a clockwise hyster- stretch reflex and redefined stretch reflex as an increase of esis loop consistent with the results found in this study. muscle stiffness. Serres et al. [28] published similar results Jansen and Rack [29] also studied the stretch reflex with using the triceps surae muscles of decerebrate cats. After the soleus muscle of cerebrate cats by sinusoidal stretching sectioning the L5 to S2 dorsal roots, muscle response force of the soleus muscle at various frequencies and ampli- decreased significantly for low and high levels of back- tudes. Similarly, clockwise elliptical hysteresis loops were ground force. observed at some frequencies with a 1 mm peak-to-peak Although these studies reached a similar conclusion amplitude. It was also reported that when the stretch that muscle response to vibration is significantly reduced amplitude was increased to 3.8 mm (peak-to-peak), the after the stretch reflex arc is disrupted, few studies have tension-length ran clockwise. The effect of stretch ampli- quantified the difference between the WSR and WOSR tude on the tension-length hysteresis loop needs to be conditions. This study found an over 20% reduction after studied in future work. the stretch reflex arc was blocked, which mainly depended Further analysis for hysteresis loop indicated that the on the stretching magnitude and frequency. It also showed stiffness had a nearly linear increase from 2 Hz to 12 Hz that a greater prelengthening might lead to a higher mus- and then stayed stable from 12 Hz to 16 Hz (Figure 8). cle force at lower frequencies such as at 2–8 Hz, but not at The damp force was highest at 2 Hz and then had a linear 12–16 Hz. Though both higher frequency and greater increase from 4 to 16 Hz. But when considering damp prelengthening could lead to a higher muscle force, pre- coefficient, that is the division of damp force and stretch lengthening was the dominant factor at low frequency, so velocity, a downtrend was observed from low to high fre- the muscle force was greater at higher prelengthening con- quencies. The result of the hysteresis loop indicated a non- dition. While frequency was the dominant factor at high linear relation of dynamic muscle force and frequency, frequency, the muscle force seemed the same for the two while Hasan [30] built a spindle afferent model to research Normalized muscle force Phase difference (deg) Applied Bionics and Biomechanics 7 2 Hz 4 Hz 0.2 0.2 0 0 −0.2 −0.2 −0.5 0 0.5 −0.5 0 0.5 Length change (mm) Length change (mm) 8 Hz 12 Hz 0.2 0.2 0 0 −0.2 −0.2 −0.5 0 0.5 −0.5 0 0.5 Length change (mm) Length change (mm) Measured F WSR Measured F WOSR 16 Hz 0.2 −0.2 −0.5 0 0.5 Length change (mm) Figure 7: Representative muscle force vs. length curve (2 mm prelengthening group). 0.25 response force under muscle stretch, whose parameters were the same for different stretch velocities. 0.2 In this study, the phase difference between the dynamic muscle force and the length change was calculated (see 0.15 Figure 6). The large variance of phase difference at low fre- quencies may be related to the fact that the phase was mainly 0.1 influenced by the damping force and was relatively small at low frequencies. Therefore, the phase of the muscle force 0.05 would be heavily influenced by random error. The overall 0 phase difference trend showed that the minimum value was 2 Hz 4 Hz 8 Hz 12 Hz 1 6Hz 4~8 Hz. Furthermore, the phase difference between the 2 mm WSR 3 mm WOSR WSR and WOSR conditions was negligible (p >0 5), which 2 mm WOSR suggested the stretch reflex had little influence on the damp- 3 mm WSR Damp force ing factor of the muscle spindle. The phase difference between the muscle force and length Figure 8: Identification of average stiffness force and damp force of was compared with that of previous studies. Roberts [24] the hysteresis loops. reported that length change lagged behind tension change Muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) Dynamic muscle force (N) 8 Applied Bionics and Biomechanics Stretch reflex PE Activation SE External Muscle force force AC Body posture Muscle model Figure 9: Diagram of current muscle model in solid line and potential stretch reflex module in dash line. by 15–20 , which is consistent with our findings. However, However, even though we have researched the effect of the phase difference was independent of the imposed fre- different low-frequency vibrations on the muscle response at different neurointact conditions and provided theoretical quency reported by Roberts (0.6–1.4 Hz), while the phase advance of muscle force varied with frequency (2–16 Hz) in support for muscle model, there are still some limitations of our result. Lippold et al. [31] found an approximate 90 phase this study: (1) although the effects of vibrational frequency difference between the sensory discharge and the displace- and muscle length were examined in detail, the amplitude ment record at frequencies between 4 and 15 Hz. He sug- of the stretching was not considered; (2) as fatigue is a com- mon but challenging problem in driving, the effect of differ- gested that the muscle spindle response was greatest when velocity, rather than displacement, was maximal. Another ent fatigue levels on muscle response needs to be result worth noting was the nonlinearity of the phase differ- considered in future studies; (3) the result of this study is ence of the WOSR and WSR conditions. This phenomenon based on the rat, even many studies suggest it is similar for indicated that the tension-length diagram could not be human muscle, more validations should be done for the mus- cle model based on this result; (4) the relation between attributed to frequency-dependent damping. A mathematical model based on identification method should be proposed in response under the whole-body vibration and localized further study. vibration is very complex, further research should be con- The results of this study could benefit musculoskeletal ducted. We will build a new muscle model incorporating modeling by providing a theoretical support to build a stretch the stretch reflex module (Figure 9) based on this experimen- tal result. More experiments considering the effect of fatigue reflex model for low-frequency vibration. Frequently used muscle models include Hill muscle model [32–35], Thelen will be conducted in the future. muscle model [36], and Millard muscle model [37]. The structures of the above models are similar as shown in 5. Conclusion Figure 9. External force (caused by vibration), activation (measured via EMG), and body posture or motion were This study explored the biomechanical response of decere- model inputs, and muscle force was the model output brate rats with/without stretch reflex to low-frequency vibra- (marked as solid lines in Figure 9). However, these muscle tion and described the quantitative relationship between models could not conduct simulations when the activation muscle force and muscle length. Results indicated that the was missing, because the amount of activation was difficult amplitude of muscle response force decreased by over 20% to measure. when the stretch reflex arc was blocked (p <0 001). The rela- There are several studies that had built linearly stretch tionship between muscle response force and muscle length reflex models to research the neural control and human loco- was found to be a nonlinear hysteresis loop that changed with motion. Geyer and Herr [38] built a reflex model to research frequency (Figure 7). The phase difference between the walking using a proportional coefficient for muscle length dynamic muscle force and the change in muscle length was combined with upper and lower constrains. Similarly, two affected significantly by the vibration frequency (p <0 05), proportional coefficients for angle and angle velocity were and the minimum frequency was 4–8 Hz. Experimental used in Eilenberg’s stretch reflex model [39]. However, non- results of this study demonstrated that the stretch reflex linearity relation of phase difference is observed in this study had a tremendous effect on muscle vibration response (over which is consistent with Miles et al.’s [13] findings. Zhang 20%) and could benefit musculoskeletal modeling by provid- et al. [40] and Mirbagheri et al. [41] used system identifica- ing a theoretical support to build a stretch reflex model for tion methods to model the intrinsic properties of human low-frequency vibration. arm and ankle system separately. The nonlinearity suggests that simple frequency-dependent damping (proportional method) does not really match the reality. Therefore, a more Data Availability realistic muscle model incorporating stretch reflex module is needed to perform human vibration simulation based on our The data used to support the findings of this study are avail- current work. able from the corresponding author upon request. 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