Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 3826503, 9 pages https://doi.org/10.1155/2020/3826503 Research Article Application of an Accelerometric System for Determination of Stiffness during a Hopping Task 1 2 1 2 Artur Struzik , Jerzy Zawadzki , Andrzej Rokita , and Bogdan Pietraszewski Department of Team Sport Games, University School of Physical Education, Wrocław 51-684, Poland Department of Biomechanics, University School of Physical Education, Wrocław 51-684, Poland Correspondence should be addressed to Artur Struzik; firstname.lastname@example.org Received 4 October 2019; Revised 30 January 2020; Accepted 17 February 2020; Published 26 May 2020 Guest Editor: Anton Kos Copyright © 2020 Artur Struzik 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. Currently, there are several computational methods for stiﬀness during a hopping task, but they do not necessarily yield the same values. Therefore, it is essential that the simplicity of the equipment used does not aﬀect the measurement validity. The aim of this study is to compare the stiﬀness values during a hopping task recorded in a laboratory environment and those acquired using the Myotest accelerometer. The measurements were performed on a group of 30 untrained female students (age: 23:0±1:7 years, body height: 1:72 ± 0:07 m, and body mass: 64:8±10:0kg). According to the manual for the Myotest accelerometric system, each study participant performed three sets of 5 hops. Vertical stiﬀness was determined based on two measurement methods, one using the Myotest accelerometer and the other using Kistler force plates. The mean value (±SD) of vertical stiﬀness was 19:0±9:3 kN/m in the countermovement phase and 15:1±5:9 kN/m in the take-oﬀ phase. Furthermore, the stiﬀness determined using the Myotest was 30:7±13:3 kN/m. However, signiﬁcant relationships between the vertical stiﬀness in the countermovement phase and the Myotest stiﬀness (r =0:79) and between the vertical stiﬀness in the take-oﬀ phase and the Myotest stiﬀness (r =0:89) were found. The relationships between the vertical stiﬀness (in the countermovement and take-oﬀ phases) and the stiﬀness estimated using the Myotest allow us to conclude that despite the signiﬁcantly overestimated stiﬀness value, the Myotest accelerometer can still be used for determination of the stiﬀness trends, e.g., following training. The overestimated stiﬀness values can result both from inaccuracy in the determination of ground contact time and ﬂight time by the Myotest accelerometer and from the use of an equation that assumes that the movement of the center of mass has a harmonic proﬁle. 1. Introduction surement of acceleration during motion and under training conditions is the Myotest performance measuring system (Myotest SA, Sion, Switzerland). Evaluation and monitoring of biomechanical variables have become an important element in the quantitative analysis The Myotest accelerometric system is a wireless handheld device weighing just a few ounces (59 g) and is attached to a spe- of athletic performance. Sports coaches will obtain valuable information from measurements carried out under condi- cially designed belt at the pelvic level. This 3-D accelerometer allows the estimation of variables such as jump height, time tions as close as possible to those during competitions. of contact, reactivity, and stiﬀness during a hopping task. Time Therefore, they are often skeptical of analyses performed under isolated laboratory conditions. However, recent tech- of contact refers to time when the feet (at least one) are in con- tact with the ground between the ﬂight phases. Reactivity nological innovations related to the miniaturization of wear- able sensors that do not inﬂuence the technical movements of should be understood as the reactive strength index (RSI), i.e., as the ratio of jump height to contact time . We can also athletes allow movement analysis to be performed during ﬁnd in the Myotest guide that “muscular rigidity, which is sporting activities. An example of a tool that allows the mea- 2 Applied Bionics and Biomechanics usually called stiﬀness, is an interesting indicator enabling you 2. Materials and Methods to ﬁnd the ideal muscular tension for bouncing in running events or team sports, for instance.” However, the problem of The measurements were performed on a group of 30 the “stiﬀness” estimated by the Myotest seems more complex untrained female students from the University School of than this deﬁnition. Physical Education. They were persons with no competitive- Stiﬀness is a quantitative measure of the elastic properties level sports training (within a period of at least 5 years before of the body and is expressed as a ratio of the deforming force the experiment) and with no injuries to the musculoskeletal to the deformation length (most commonly in relation to (motion) system. The study group was characterized by the longitudinal deformation) . Therefore, stiﬀness represents following mean parameters (±SD): body height: 1:72 ± 0:07 the measure of resistance to strain and is described as an m, body mass: 64:8±10:0kg, and age: 23:0±1:7 years. The essential factor in the optimization of human locomotion tests were carried out in the Biomechanical Analysis Labora- [3–5]. Dalleau et al.  argued that stiﬀness is also related tory (with PN-EN ISO 9001: 2009 certiﬁcation). Each subject to the maximal performance of single and cyclic movements. completed all trials in the same time period of test days (in the When hopping, the human body (movement of the center of morning) to eliminate any inﬂuence of circadian variation. mass) resembles a bouncing ball. Therefore, the term “bounc- Subjects refrained from physical activity for 24 hours before ing gait” has been used to describe the human body during testing, to avoid any interference in the experiment. Prior to hopping tasks where lower limbs perform the function of the measurements, the participants were familiarized with “springs” responsible for center of mass (COM) movements the purpose of the study and gave written consent for partici- [4, 5, 7]. Therefore, a hopping human body can be modeled pation in the experiment. Before the test, the subjects were by using a simple spring-mass model that contains a single informed of the activities they were supposed to perform (linear and massless) “leg spring” and a point that repre- and were motivated to properly perform the task. The sents the total body mass . Leg stiﬀness (deﬁned as the research project was approved by the Senate’s Research ratio of changes in the ground reaction force to the respec- Bioethics Commission, and the procedure complied with the tive changes in “spring length” representing both lower Declaration of Helsinki regarding human experimentation. limbs) and vertical stiﬀness (deﬁned as the ratio of changes We followed the methods of Struzik and Pietraszewski . in the ground reaction force to the respective vertical Each study participant performed three sets of 5 hops displacement of the COM) are commonly used to describe (hopping test). The measurement procedure was conducted the mechanical properties of a “spring” representing the in accordance with the Myotest performance measuring sys- lower limbs during a hopping task . tem: quick start guide (jump–plyometry test). The trials were The Myotest guide does not give an unambiguous answer simultaneously recorded by the Myotest accelerometric as to which of the above types of stiﬀness (leg or vertical) is system (Myotest SA, Sion, Switzerland) and by two force the value provided by the Myotest accelerometric system plates (9286A, Kistler Group, Winterthur, Switzerland). during the hopping test. Some authors equate the stiﬀness The sampling frequencies of the signal from the force plates value estimated by the Myotest with leg stiﬀness [9–12]. and the accelerometric system were set at 500 Hz. This However, the accelerometer is not capable of measuring the sampling frequency is the maximum common value for both change in “spring length.” Moreover, estimations of stiﬀness systems. The use of force plates is usually considered the gold using an accelerometer also do not provide insights about standard [13, 15]. the ratios of stiﬀness in individual joints. Therefore, it Prior to the measurements, a 10-minute-long warm-up, should be assumed that the stiﬀness value estimated by which included jogging (shuttle runs over a distance of the Myotest is vertical stiﬀness. The Myotest accelerometric 10 m, at a moderate pace of ca. 10 sections per minute), a system is recognized as a reliable and valid tool for the series of hops, and a familiarization test task, was adminis- estimation (despite signiﬁcant overestimation) of jump tered. Each study participant started performing a trial series height based on the ﬂight time method [13–17]. However, after becoming familiar with the test. After the trial series, the proper research procedure began. Next, the participant was it seems that the problem of the stiﬀness determined using an accelerometer is currently not properly investigated. To asked to perform a series of 5 bilateral hops (3 sets) from the standing position to the maximum height (performed our knowledge, only a few studies [9, 10] have raised the issue of stiﬀness estimated by the Myotest. as a bounce action on the fore foot) and with minimal time In the process of sports training control, it is necessary to of contact with the ground. The whole part of the hopping test took place on a rigid surface (force plates). As indicated quantify the eﬀects of the exercises and loads applied. There- fore, the use of a portable measuring device is a compromise by the guide, the participant wore a belt with the Myotest between measurements under laboratory conditions and accelerometer attached vertically on the left side of the body those under training conditions. However, there are cur- at the pelvic level (fastened around both greater trochanters rently several computational methods for (vertical) stiﬀness, of the femurs and the medium part of the gluteal region). Before each trial, the subjects were asked to stand over the but they do not necessarily yield the same values [8, 18–20]. Therefore, it is essential that the simplicity of the equipment force plates (each foot on a separate plate) while assuming a used does not aﬀect the measurement validity. The aim of vertical posture with arms akimbo, looking straight ahead this study is to compare the stiﬀness values during a hopping and standing still (Figure 1). The hopping test instructions task recorded in a laboratory environment and those given were as follows (according to Myotest guide): “at the short beep from accelerometer, perform a countermovement acquired using the Myotest accelerometer. Applied Bionics and Biomechanics 3 limbs were ﬂexed at the knee and/or hip joints during the ﬂight phase (incorrectly performed hopping task). Further analysis focused on the attempt with the highest mean height of hops obtained by each participant. From the hopping task, 5 hops were analyzed without taking into account the starting countermovement jump. The values of all presented variables were averaged for the ﬁve analyzed hops to obtain results analogous to those obtained from the Myotest. The hopping test was used with some simpliﬁca- tions that resulted from the use of the spring-mass model, which characterizes both running and hopping. The model assumes that the human body consists of a material point representing the total mass of the body; a massless “spring” representing both lower limbs, which performs the support- ing function; and a parallel source of force resulting from the active action of the muscles involved in the take-oﬀ . Based on the vertical ground reaction force (F) recorded by the force plates (the ground reaction forces registered by both force plates were added up), it was possible to determine the ﬂight time (t ) and ground contact time (t ) during the f c hopping task. The instantaneous pattern of changes in the height of the COM (y) was calculated by double integration of the COM vertical acceleration, as calculated from the vertical ground reaction force . The vertical (quasi-) stiﬀ- ness (K = ΔF/Δy) of the human body during the hopping task was determined as the ratio of the change in the ground reaction force (ΔF) to the corresponding change in the height of the COM (Δy) separately for the countermovement and take-oﬀ phases, similar to the method described by Struzik and Zawadzki . To reliably estimate vertical stiﬀness, it is necessary to determine the relationship FðΔyÞ shown in Figure 2. The slope coeﬃcient for part of the curve FðΔyÞ Figure 1: One of the participants standing on the force plates with equals the numerical value of stiﬀness in this range. Vertical the belt to which the Myotest accelerometer is attached vertically on stiﬀness was calculated for the parts of the countermovement the left side of the body at the pelvic level. and take-oﬀ phases where the slope of the F curve with respect to the Δy axis was relatively constant and the FðΔyÞ jump, then bounce back up ﬁve times as high as possible and proﬁle was nearly linear. For the countermovement phase with a ground contact time that is as short as possible, while (marked green in Figure 2), this range was the part between keeping your hands on your waist (jump oﬀ the soles of the the moment of landing on the plates and the lowest location foot with minimal bending of the knees, like on a trampo- of the COM (Δy ). The boundaries of the part for the take- max line).” After 5 hops, the participant reassumed a vertical oﬀ phase (marked blue in Figure 2) were represented by the standing posture, and the double beep from the accelerome- local maximum of the ground reaction forces (point F max ter signals the end of the test. During the experiment, the from which ground reaction forces decreased only) and the participant was asked to rest her palms on her hips to exclude moment of take-oﬀ from the plates . This observation the eﬀect of arm swing on hopping performance. Landings holds true only if the value of the coeﬃcient of determination were performed on the same plates as take-oﬀs. According R that expresses the quality of adjustment of the trend line to to the Myotest guide, a one-minute rest took place between the relevant part of the FðΔyÞ curve is suﬃciently high (over test repetitions. Errors in hopping task execution are signaled 0.6) . If the points Δy and F occur at exactly the max max by a deep beep from the accelerometer. The Myotest accel- same time, then the whole FðΔyÞ curve is analyzed. If not, erometric system tolerates two errors before automatically then the part of the FðΔyÞ curve between the Δy and max stopping the test. An error message is generated if the follow- F points (marked in black in Figure 2) is omitted to main- max ing points are not observed (according to Myotest guide): tain the maximum possible linearity of the studied parts of “(1) execute the movements energetically so that the Myotest the countermovement and take-oﬀ phases. It is possible that can clearly detect them, (2) stand still before the starting beep, the FðΔyÞ curve intersects , for example, in the upper part, (3) ground contact time must be short and clearly below the as shown by Choukou et al. , which causes the F point max time of ﬂight, and (4) perform a total of 5 bounces.” During to appear before the Δy point. Then, the proﬁle of the F max performance of the hopping test, the participant should ðΔyÞ curve should be considered individually, and the take-oﬀ with the knees and ankles extended and land in a boundary of the analyzed parts of the countermovement and take-oﬀ phases should be modiﬁed. For example, the similarly extended position. The test was repeated if the lower 4 Applied Bionics and Biomechanics 3500 analyses. Pearson’s r correlation coeﬃcient was used to eval- uate the concurrent validity of the Myotest accelerometric system and force plate. The signiﬁcance of the correlation coeﬃcient value was veriﬁed with the t-test. To demonstrate possible diﬀerences between the values of the variables obtained from diﬀerent measuring devices, Student’s t-test y = –15647x + 1778.7 2 of signiﬁcance of diﬀerences for dependent variables was R = 0.98 used. In all tests performed, the level of signiﬁcance was set y = –17373x + 1146.1 at α =0:05. Statistical calculations were made by means of R = 0.93 0 the Statistica 13.3 software package (TIBCO Software Inc., –0.1 –0.05 0 0.05 0.1 0.15 Palo Alto, CA). Furthermore, the remaining calculations 𝛥y (m) were made using a Microsoft Excel 2016 spreadsheet (Micro- soft Corporation, Redmond, WA). Additionally, concurrent Figure 2: Ground reaction force depending on the COM vertical validity was analyzed through a Hopkins  spreadsheet displacement for one of the study participants during the hopping to quantify the relationship between the practical (Myotest) test (for one of the hops), along with trend lines and equations that and criterion (force plate) measures. The validity spreadsheet describe these dependences for the parts of the countermovement (marked green) and take-oﬀ phases (marked blue) and the values is based on simple linear regression to derive a calibration of coeﬃcients of determination R . equation, a typical error of the estimate, and Pearson’s r cor- relation coeﬃcient. The criterion was the dependent variable, analyzed countermovement phase part will end at the point and the practical was the predictor in a consecutive pairwise F , and the analyzed part of the take-oﬀ phase will begin manner. The typical error of the estimate was standardized max at the point Δy . (SEE) by dividing by the SD of the criterion. SEE was evalu- max The Myotest accelerometer was used to record the ated using half the thresholds of the modiﬁed Cohen scale: following variables during the hopping test: jump height <0.1, trivial; 0.1–0.3, small; 0.3–0.6, moderate; 0.6-1.0, large; (h ), ground contact time (t ), and stiﬀness (K ). 1.0-2.0, very large; and >2.0, extremely large. Uncertainty in Myo c‐Myo Myo the estimates was expressed as 90% conﬁdence limits. To In the Myotest guide, the manufacturer did not explain how complement the correlation analysis, Bland-Altman plots the values of individual variables are estimated. However, were used to visualize the mean of the diﬀerence (bias) and based on the accelerometer capabilities, one can guess that the limits of agreement (95% conﬁdence intervals). the values of jumping height (h ) and ground contact time Myo (t ) were determined based on the duration of the ﬂight c‐Myo 3. Results and ground contact phases . Based on the jump height (h ) recorded by the Myotest accelerometer, the ﬂight time Myo The mean value (±SD) of vertical stiﬀness was 19:0±9:3 (t ) could be determined using the following formula: f ‐Myo kN/m in the countermovement phase and 15:1±5:9 kN/m in the take-oﬀ phase during the hopping test. Furthermore, sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ the stiﬀness determined using the Myotest accelerometric 2 ⋅ h Myo t =2 ⋅ , ð1Þ system was 30:7±13:3 kN/m. Therefore, the stiﬀness values f ‐Myo determined using the Myotest were signiﬁcantly higher than the stiﬀness values determined using the force plate in both where g is the acceleration due to gravity . Furthermore, the countermovement (Δ =11:7±8:2 kN/m) and take-oﬀ (vertical quasi-) stiﬀness (K ) can be evaluated using the phases (Δ =15:6±8:5 kN/m). However, signiﬁcant relation- v‐Myo equation described by Dalleau et al. , which assumes that ships between the vertical stiﬀness in the countermovement the curve reﬂecting the ground reaction force versus time is phase and the Myotest stiﬀness (r =0:79, SEE = 0:77, a part of the sine wave: Figure 3) and between the vertical stiﬀness in the take-oﬀ phase and the Myotest stiﬀness (r =0:89, SEE = 0:50, Figure 4) were found. A signiﬁcant diﬀerence between the m ⋅ π · t + t f ‐Myo c‐Myo K = , ð2Þ v‐Myo vertical stiﬀness values in the countermovement phase and t · t + t /π − t /4 c‐Myo f ‐Myo c‐Myo c‐Myo those in the take-oﬀ phase (Δ =4:0±5:7 kN/m, p <0:001) was also found. where K is the vertical stiﬀness, m is the body mass, t v‐Myo f ‐Myo Bland-Altman plots are presented in Figures 5 and 6. is the ﬂight time, and t is the ground contact time. There- For any measurement system to be valid, most of the paired c‐Myo fore, it may be accepted that the stiﬀness value estimated by diﬀerences should lie within the 95% limits of agreement, the Myotest is the vertical (quasi-) stiﬀness. whereas their mean can help identify whether any system The sample size was determined based on the power underestimates or overestimates measurements relative to analysis. For n =30, the power of applied statistical tests the criterion (bias). The results indicate that the Myotest (1 − β) is close or equal 1. The Shapiro-Wilk (W) and Lillie- accelerometric system overestimated measurements of stiﬀ- fors tests were used to examine the distribution of individual ness during the hopping test. In Figures 5 and 6, 28 of the variables. All the studied variables had a distribution close to 30 analyzed measurements are within the limits of agree- normal. Therefore, parametric tests were used for further ment. However, signiﬁcant relationships between the paired F (N) Applied Bionics and Biomechanics 5 50 5 +1.96 SD 1.0 –5 –10 Mean –15 –15.6 –20 y = 0.5546x + 2.0199 –25 R = 0.63 –30 –1.96 SD –35 –32.2 0 10203040506070 –40 Myotest stiffness (kN/m) 0 102030405060 Mean of vertical stiffness in the take-off phase Figure 3: Vertical stiﬀness in the countermovement phase versus and Myotest stiffness (kN/m) stiﬀness determined using the Myotest accelerometric system during the hopping test with an equation describing the trend line Figure 6: Bland-Altman plot of the force plate (in the take-oﬀ and the value of the determination coeﬃcient R . phase) and Myotest stiﬀness (95% limit of agreement is 16.6 kN/m). Table 1 contains the mean values (±SD) of ground contact time and ﬂight time obtained with the Myotest accel- erometric system and force plate. The ground contact time estimated by the Myotest was signiﬁcantly shorter than that 15 obtained from the force plate measurements. In turn, the ﬂight time estimated by the Myotest was signiﬁcantly longer than that obtained from the force plate measurements. y = 0.3952x + 2.9444 Moreover, the value of stiﬀness determined using the R = 0.80 force plate time measurements (t and t ) and the equation c f described by Dalleau et al.  was K =15:6±5:7 kN/m. 0 10203040506070 K was signiﬁcantly lower than the vertical stiﬀness in the Myotest stiffness (kN/m) D countermovement phase (Δ =3:4±5:2 kN/m, p <0:01) and Figure 4: Vertical stiﬀness in the take-oﬀ phase versus stiﬀness the Myotest stiﬀness (Δ =15:1±8:4kN/m) and was at a determined using the Myotest accelerometric system during the similar level as the vertical stiﬀness in the take-oﬀ phase. hopping test with an equation describing the trend line and the value of the determination coeﬃcient R . 4. Discussion 10 Although popular motor ability tests can be performed in a +1.96 SD simple manner and under any conditions (for example, the 4.5 Sargent vertical jump test), modern measurement equipment provides more accurate information about a particular ability –5 or variable. The development of technology also allows a –10 Mean more objective and precise evaluation. It is also becoming –11.7 –15 easier to collect more data than was previously possible using conventional methods and tools. Therefore, it is fundamental –20 that coaches should utilize available methods for applying –25 –1.96 SD scientiﬁc output in sports training. Utilizing these methods –30 –27.8 is likely to provide them with feedback on the current skill –35 level of an athlete and the eﬃciency of the particular practice 0 102030405060 stimuli used and will help them plan future training Mean of vertical stiffness in the countermovement programs. Modern measurement tools also oﬀer possibilities phase and Myotest stiffness (kN/m) for the detection of irregularities in an athlete’s body that Figure 5: Bland-Altman plot of the force plate (in the might lead to injuries. countermovement phase) and Myotest stiﬀness (95% limit of Reliability can be deﬁned as the consistency of measure- agreement is 16.1 kN/m). ments (test-retest) . Choukou et al.  and Ruggiero et al.  stated that the stiﬀness values estimated using the Myotest accelerometer showed a high level of reliability. On diﬀerences and means were found, indicating that the bias the other hand, validity refers to the ability of a measurement is not constant over the entire range. Therefore, as the tool to reﬂect what it is designed to measure . However, Myotest stiﬀness value increases, the vertical stiﬀness the problem of validity of stiﬀness measurements using estimation error in the countermovement (r = −0:51) and take-oﬀ phases (r = −0:90) also increases. Myotest is much more complex and not yet fully explained. Vertical stiffness in the Vertical stiffness in the countermovement Vertical stiffness in the phase minus Myotest stiffness (kN/m) take-off phase (kN/m) countermovement phase (kN/m) Vertical stiffness in the take-off phase minus Myotest stiffness (kN/m) 6 Applied Bionics and Biomechanics Table 1: Mean values (±SD) of ground contact time (t ) and ﬂight vertical stiﬀness values in the take-oﬀ phase. The overesti- time (t ) obtained with the Myotest accelerometric system and mated stiﬀness value by the Myotest accelerometer during force plates. the hopping test can therefore result from inaccuracy in the determination of ground contact time and ﬂight time. These t (s) t (s) t + t (s) c f c f two variables are mainly responsible for the stiﬀness value 0:18 ± 0:06 0:51 ± 0:03 0:68 ± 0:07 Myotest estimated using the equation presented by Dalleau et al. . 0:25 ± 0:07 0:44 ± 0:04 0:69 ± 0:07 In this study, the ground contact time estimated by the Myot- Force plate ∗ ∗ est was signiﬁcantly shorter than that obtained from the force Δ −0:08 ± 0:01 0:07 ± 0:02 −0:01 ± 0:01 plate measurements. In turn, the ﬂight time estimated by the Δ represents diﬀerences between the values of times obtained with the Myotest was signiﬁcantly longer than that obtained from the Myotest accelerometric system and force plates. Statistically signiﬁcant at force plate measurements. The trends in the mentioned p <0:05. diﬀerences coincide with those presented by other authors [9, 13]. Choukou et al.  stated that the measurement of Both the laboratory and ﬁeld tests must be valid and reliable in ground contact time by the Myotest during the hopping test order to properly use information obtained on their basis. is nonvalid. The most accurate devices for recording vertical Therefore, laboratory measuring systems [26–28], portable jump ﬂight time and ground contact time are force plates, measuring tools [29–31], calculation methods, and measuring which allow precise identiﬁcation of the instant of take-oﬀ movements [8, 20, 24, 32–34] are subject to veriﬁcation. Com- (the point at which the feet lose contact with the ground pared to other devices for ﬁeld-based jumping evaluation, the and the value of vertical ground reaction force drops to zero) Myotest has the advantages of being small and portable, easy and instant of landing (the feet land in the same position as to handle, relatively cheap, able to provide immediate results, take-oﬀ). It is assumed that the COM height at take-oﬀ is and usable on particular surfaces (e.g., on the sand), which relatively the same as that at landing . The Myotest allows measurements under any conditions without limita- estimates ﬂight time using the time diﬀerence between the tions on the measurement space [13, 14]. However, it cannot positive (during take-oﬀ phase) and negative (during landing be used during a game or competition . phase) peaks of vertical velocity. However, the maximal The stiﬀness determined using the Myotest accelero- positive vertical velocity is reached shortly before the instant metric system during the hopping test was signiﬁcantly of take-oﬀ, and the maximal negative vertical velocity is higher than the vertical stiﬀness determined using the force reached shortly after the instant of landing. Therefore, the plate measurements in the countermovement and take-oﬀ ﬂight time recorded by the Myotest accelerometer is overes- phases. Therefore, the Myotest overestimated measurements timated, and the ground contact time is underestimated [9, of stiﬀness, as in other studies [9, 10]. Choukou et al.  13, 24]. The ground contact time and ﬂight time values noted signiﬁcantly higher values of stiﬀness estimated by presented in Table 1 conﬁrm the above assumptions, which the Myotest (by 7.8 kN/m) during the hopping test than the can signiﬁcantly distort the stiﬀness values estimated by the vertical stiﬀness values determined using a force plate. The Myotest during hopping. stiﬀness estimation method during hopping presented by A signiﬁcant relationship between the vertical stiﬀness in Dalleau et al.  assumed that the curve that describes the the countermovement phase and the Myotest stiﬀness dependence of the ground reaction force on time is a part obtained during hopping was found. This relationship was of the sine wave and therefore that the COM motion is very high but also had a large SEE. A signiﬁcant relationship harmonic. However, this method is only the ﬁrst half of oscil- between the vertical stiﬀness in the take-oﬀ phase and the lations, as a result of which it does not strictly meet the Myotest stiﬀness was also found. This relationship was very assumptions of harmonic motion. The description (equa- high and had a moderate SEE. When the SEE is large, the tion) is appropriate for the steady course of such oscillations. predicted y values are scattered widely above and below the Notably, the method presented by Dalleau et al.  can cause regression line (Figures 3 and 4). However, based on the the values of vertical stiﬀness to be signiﬁcantly overesti- Bland-Altman plots (Figures 5 and 6), most of the paired mated, especially at relatively low hopping frequencies. Based diﬀerences are within the 95% limits of agreement. There- on the given hopping test instruction and the obtained t and fore, it can be concluded that the Myotest accelerometric t values, it can be concluded that the hopping frequency system is valid but overestimates the vertical stiﬀness values chosen by the participants in this study was low. during hopping. Moreover, greater overestimation is On the other hand, Hobara et al.  reported that the observed with an increase in the criterion value. Therefore, stiﬀness estimation method presented by Dalleau et al.  the Myotest stiﬀness is not interchangeable with respect to signiﬁcantly underestimates vertical stiﬀness values during the values obtained from other measurement devices and hopping compared to those obtained from other calculation methods. The Myotest accelerometric system determines an methods. However, Hobara et al.  took all measurements approximate value that can provide information about only on a force plate without using the accelerometer. In this changes in vertical stiﬀness during the hopping test. study, the values of stiﬀness determined using the force plate Determination of the vertical stiﬀness during the hop- measurements (t and t ) and the equation described by ping task requires several assumptions that sometimes seem c f Dalleau et al.  were also signiﬁcantly lower than the verti- to have been omitted, whereas measurement validity would cal stiﬀness values in the countermovement phase and the require veriﬁcation of these assumptions. The simplest case Myotest stiﬀness values and were at a similar level as the is when F occurs exactly at the same time as Δy . max max Applied Bionics and Biomechanics 7 presented in this paper (between the paired diﬀerences and Without this synchronization, it would be necessary to deter- means), even larger bias values (larger overestimation of mine which of these events occur ﬁrst and, consequently, to modify the equation to reproduce the proﬁle of the FðΔlÞ vertical stiﬀness values by the Myotest) can be expected in groups of males and athletes. curve as accurately as possible. The increase in the ground reaction force with respect to the COM displacement should be linear or close to linear over the whole duration of the con- 5. Conclusions tact with the ground phase. If the moment of occurrence of The relationships between vertical stiﬀness (in the counter- F divided t into two halves (harmonic movement), it max c movement and take-oﬀ phases) and the stiﬀness estimated would theoretically mean the same values of vertical stiﬀness using the Myotest accelerometric system allow us to conclude during the countermovement and take-oﬀ phases. Meeting that, despite the signiﬁcantly overestimated value of stiﬀness, the above conditions would justify using one value as vertical the Myotest accelerometer can be used for determination of stiﬀness for a speciﬁc movement while neglecting the calcula- the stiﬀness trend. Therefore, this measurement device oﬀers tions for the take-oﬀ phase . Ferris and Farley  empha- only an approximate stiﬀness value that can provide infor- sized that during hopping, F and Δy do not necessarily max max mation about changes, e.g., following training. Therefore, occur at the same time. It is assumed that for a hopping the Myotest stiﬀness is not interchangeable with respect to frequency lower than 2 Hz, lower limbs stop behaving as lin- the values obtained from other measurement devices and ear springs, thereby distorting the FðΔlÞ proﬁle [7, 37]. In methods because of systematic overestimation. The overesti- this work, the vertical stiﬀness values in the countermove- mated stiﬀness value can result both from inaccuracy in the ment phase were signiﬁcantly higher than those in the take- determination of ground contact time and ﬂight time by oﬀ phase. Therefore, to fully understand the phenomena the Myotest accelerometer and from the use of an equation occurring during human motion, it seems necessary to deter- that assumes that the movement of the center of mass has a mine the vertical stiﬀness for both phases of motion sepa- harmonic proﬁle. rately. The assumption that the value of vertical stiﬀness in the countermovement phase is always the same as that in the take-oﬀ phase may be too much of a simpliﬁcation. Data Availability Luhtanen and Komi  estimated vertical stiﬀness during The data used to support the ﬁndings of this study are running and long jump with a division into the eccentric available from the corresponding author upon request. and concentric phases. Furthermore, the stiﬀness determined based on observation during motion should be viewed as Disclosure quasi-stiﬀness, i.e., the ability of the human body to resist external displacements while ignoring the temporal proﬁle Part of this manuscript was presented at the 21st Annual of the displacement. Vertical stiﬀness is not stiﬀness viewed Congress of the European College of Sport Science 2016 in in strict terms due to the substantial contribution of other Vienna, Austria. factors (such as damping and inertia) that aﬀect the FðΔyÞ relationship, especially during transient states . Conflicts of Interest Despite the clearly established procedures for hopping test performance and Myotest accelerometer ﬁxation, The authors declare that there is no conﬂict of interest between-subject diﬀerences in hopping technique (diﬀer- regarding the publication of this paper. ences in jumping technique due to gender [23, 36, 37, 39] and sports training [36, 40–42]), elastic belt fastening and References positioning around the hips, and, consequently, Myotest orientation may cause unexpected device displacements  D. Mcclymont and A. Hore, Use of the reactive strength index during hopping. 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Published: May 26, 2020