Energy Consumption during Going Down from a Step

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1 Bulletin of the Osaka Medical College 48 1, , Original Article Energy Consumption during Going Down from a Step Manabu MIYAMOTO 1, Jun YAMAGUCHI 2 and Masahiko SHINDO 1 1 First Department of Physiology, Osaka Medical College, 2 Department of Rehabilitation Medicine, Osaka Medical College, Takatsuki, Osaka, , Japan Key Words : motion analysis, acceleration, power curve, going down ABSTRACT How much energy is required during the motion of going down from a step? The power curves on the falling down movements were measured using an acceleration meter. There are two kinds of muscle works, one is positive work in which the moving direction is the same as that of the force provided by muscles, and the other is negative work in which the direction is opposite to that of the force taken by muscles. The experiments of going down from steps of altitudes of 17cm and 34cm were performed with 5 male volunteers. Then, the characters of these power and mechanical work curves of the supporting muscles were calculated and traced. Their amplitudes of the I (0.34 s) peak in the power curves were W and W for each step of 17cm and 34cm in height. Those of the II (0.5 s) peak were W and W. Their I phase of the mechanical work curves were J and J and their II phase were J and J. Their total mechanical works of the supporting muscles for a one-step motion were J and J. Their actual energy consumptions were estimated by multiplying the work efficiencies of muscle. They were J and J. As for the falling down motion, muscle power was not necessary during the fall. Only the negative power upon landing was necessary and it also included more energy for a rebound motion. INTRODUCTION On discussion of going down motion, it is very important to determine how much energy is required and expended by the anti-gravity muscles. Gravity acts on all organisms on the earth. Potential (position) energy must be taken into account in the vertical motion. We focus on the movement of falling down from a step, in which potential energy is used as a driving force. Is any other energy necessary in this motion? From this point of view, analysis of the falling down motion was attempted by accelerometry using two different stairs of altitudes of 17cm or 34cm. That is, acceleration in the vertical direction during falling down from a step was measured, and the velocity, displacement, power and energy were estimated, after which the balance of energy as mechanical energy was examined. An acceleration meter was attached to about the center of gravity of a volunteer. Motion measurement using an acceleration meter is simple and easy in anywhere. Moreover, direct measurement of acceleration becomes energy analysis easy. There are two kinds of power for the support muscles, one is positive power in which the moving direction is the same as that of the force provided by muscles, and the other is negative power in which the direction is opposite to that of the 7

2 8 M. MIYAMOTO, J. YAMAGUCHI, M. SHINDO force taken by muscles. The power analysis takes into consideration all input and output energies through a unit of power (BARGER et al., 1973; WINTER, 1979). Such an analysis of falling down movement was performed. We attempted to study the characteristics of these power curves. THEORETICAL If x coordinate is taken upward in perpendicular direction and F is defined as the force which come from the support to the body, Equation (1) can be deduced from the equation of motion. (1) Therefore, the power P done by the support force is (2) The total work done by the support force through such a motion is calculated as follows. (3) This becomes equal to the change of potential energy. T is the time at which step down finished here. In equation (3), we use the kinetic energy becomes 0 before and after falling down stairs. The power done for the support muscles is obtained by changing its code of equation (2). The acceleration meter shows the value of and the support force F from the floor can be obtained if we multiply it by the body weight. The work done for the support muscles can be estimated by integration of this power curve as described in equation (3). Physical and physiological significance of this power curve becomes clear. METHODS 1. Measurement of acceleration (1) Determination of the center of gravity. The distance between the center of gravity and the heels was calculated to be 52% of a subject, s height (KALEPS et al., 1984) in the midline of the back. However, a deviation from the center of gravity among each segment was ignored, and every segment was supposed to be located on the same plane of the frontal section. (2) Installation of acceleration meter and measurement of acceleration in the vertical direction. Acceleration in the vertical direction was measured using the acceleration measurement system consisting of the voltage recorder VR-71 and the G (acceleration) sensor VR-00S1 (T AND D Company). The acceleration sensor was fixed on a MAXBELT regular type II belt (SIGMAX Incorporated Company) and set on the appropriate median line of a subject, s back at the same height of his determined center of gravity (KALEPS et al., 1984; Human Life Engineering Industry Technological Laboratory, 2001; Life Engineering Research Center, 1997; NAKAMURA et al., 2000). After the set up, calibration of the sensor was performed. Data were inputted in a data recorder at a sampling rate of 20 ms, and also in a computer (Dell Dimension XPST450 (Dell Company)), via RS232C, equipped with a voltage recorder for Windows Ver Data outputted individually were changed to a text form with Microsoft Excel (Microsoft Company). Kaleida Graph Vers 3.5 (Hulinks Company) and Math Cad (SMI Company) were used for data processing (MIYAMOTO, 2001; MIYAMOTO, 2002). 2. The acceleration of the center of gravity during falling down motion. These experiments were performed with 5 male volunteers (age 31-55, height cm, weight kg) with no disturbance of gait. The two different stairs were used, one was 30cm in depth and 17cm in height and the other was 30cm in depth and 34cm in height. The slide stop of the rubber was settled at each end of step. Their falling processes began by lowering the tips of feet from the position of both heels supporting the 8 Bulletin of the Osaka Medical College 48 1, , 2002

3 Power during Going down stairs 9 body at the edge of the stair and ended by the landing in both legs. The accelerations were measured using one step of each stairs. 3. Estimation of velocity and displacement based on the movement of the center of gravity. The value of the acceleration meter at rest in the vertical direction is gravitational acceleration of 1.0 G. In these experiments, the upward acceleration and displacement are indicated as positive deflection on all the records. Then the acceleration to calculate velocity and distance during motion of the actual center of gravity was corrected by deducting the value at rest from the measurement value. The time courses of the acceleration in the vertical direction were traced. Smoothing by a cubic spline function was adopted in the analysis of raw data with respect to time and acceleration (WOOD et al., 1979). Then, numerical integration was performed with respect to time. The initial velocity at rest was 0. The velocity of the center of gravity in the vertical direction can be obtained. When numerical integration was performed again, the change in the position (displacement) of the center of gravity was also calculated. The time courses of velocity, displacement and power for each session of falling downstairs were traced and analyzed. The above relations with power were utilized for the analysis of the motion process. actual velocity and body weight. The mechanical work was calculated by numerical integration of the power curve, if the initial displacement at rest was 0. The time courses of power and work with respect to the support muscles were represented in Figure 3,4. Three major peaks could be distinguished in the power curves. They were named I- III peak as described in Results 1(2). Their amplitudes and durations were measured in Table 1. The mechanical works of muscles in correspondence with each I- III and the remainder ( ) peak of the power curves were also calculated in Figure 4 and Table 2. The values of power and work shown here were normalized to a body weight of 60kg. RESULTS 1. Measurement of acceleration during falling from a step (1) Velocity and displacement of the center of gravity Figure 1 showed the relationship between the 4. Interpretation of the acceleration data based on the muscles supporting the body. The value of 1.0 G in the vertical direction of the acceleration meter at rest is equivalent to the force of the muscles supporting a body in this case. The actual velocity and displacement of the center of gravity during falling down stairs were calculated in Method 3. Subsequently, when acceleration was multiplied by velocity and body weight, power (work per unit time) was obtained. The absorbed power of the anti-gravity muscles can be consequently obtained from the product of Fig. 1 Time course of the displacement with relation to the acceleration in the falling from a step. the value of acceleration sensor ( ) and Fig. 2 Time course of the velocity with relation to the acceleration in the falling from a step. Bulletin of the Osaka Medical College 48 1, ,

4 10 M. MIYAMOTO, J. YAMAGUCHI, M. SHINDO acceleration and the displacement (distance) calculated by integration of the velocity. In Figure 2, the acceleration and the time course of the velocity were traced. When the volunteer fell, the acceleration changed first from 0 to -1.0G, then changed to a little more than 1G upon landing. The negative value of the velocity reached maximum at 0.3 s, when the acceleration returned from -1.0G to 0. The positive peak of the velocity at 0.5 s reflected the rebound motion. There were also some vibrations before a complete standstill. The displacement also reached more than 17cm or 34cm distance temporally and terminates at 17cm or 34cm length followed by some vibrations. (2) Results based on the muscle supporting the body The time courses of power calculated in the motion of falling down from a step of 17cm in height with respect to the support muscles were represented in Figure 3. There were three major peaks in the power curves. The first large peak named I (0.34 s) peak, was negative and had a maximum value at 0.34 s from the beginning of the motion. The next peak was positive and reached a maximum at 0.5 s and was called II (0.5 s) peak. The third peak was defined a III (0.72 s) peak, which was negative and had its maximum peak at 0.72 s. The amplitudes and durations of the above-mentioned I-III peak were shown in Table 1 in the experiments of falling down from both steps of altitudes of 17cm and 34cm. The absorption of the power by the muscles upon landing was complete. The subsequent vibration required more excessive positive power as shown by the small peak due to the muscular over-response as the reflection and kinetic energy was provided. The time courses of work calculated in the motion of falling down from a step of 17cm in height were also represented in Figure 4. We can decide four phases from 1 to 3 and the remainder Fig. 3 Time course of the power for support muscles with relation to the acceleration in the falling from a step. Fig. 4 Time course of the mechanical work for support muscles with relation to the acceleration in the falling from a step. Table 1 Characteristics of power curves step height 17cm(n=5) 34cm(n=5) peak (positive) peak (positive) peak amplitude (W) duration (S) Bulletin of the Osaka Medical College 48 1, , 2002

5 Power during Going down stairs 11 Table 2 Characteristics of work curves step height 17cm(n=5) work (positive) work total ( work muscular work (J) cm(n=5) (positive) work total ( ) work ( ) in correspondence with each peak (I-III) of the power curve. Not only the positive but also negative powers indicated output of energy by interpretation based on the support muscles. Figure 4 showed the time courses of the total work with respect to the support muscles. The total mechanical works of muscles in each I- III and the remainder ( ) phase were calculated using the equation of A value of each work in the I- III and remainder ( ) phase was shown in Table 2. The amplitudes of the I (0.34 s) peak in the power curves for the different steps of the heights of 17cm and 34cm were W and W each. Those of the II (0.5 s) peak in the power curves were W and W. Those of the III (0.72 s) peak in the power curves were W and W. Their durations were s and s for the I (0.34 s) peak and s and s for the II (0.5 s) power curve and s and s for the III (0.72 s) peak. The mechanical work was small during the fall, but increased due to the negative power upon landing (Figure 3). The total amount of work expressed by the muscles can be calculated when each absolute value of the power curves was integrated with respect to time. The work provided by the muscles increased against any change in the power curve. The mechanical works of muscles were calculated in each I- III and the remainder ( ) peak in Table 2. The I (0.34 s) peak of the work in falling down steps of 17cm in height were J and those of 34cm were J. These energies were absorbed by the muscular negative power upon landing and caused their II (0.5 s) peak of J and J. The II (0.5 s) peak of the work curves were powered by upward force on landing and resulted in the rebound motion. The III (0.72 s) peak of the work in falling down steps of 17cm in height was J and those of 34cm were J. Then, there were also some vibrations before a complete standstill. The total (I+II+III+ ) mechanical work of the muscles for falling down one step of 17cm and 34cm in height were J and J each as the areas surrounded by the power curves and the base lines or the maximum value of the work curves. DISCUSSION The gravity always acts on a human body on the earth. The muscles supporting a body spend energy even during standing up without motion. However, mechanical work is not being performed. Mechanical work arises for the first time from the beginning of a motion. Fenn had proposed that heat production was in proportion to the displacement of the muscular contraction (FENN, 1926). Hill also found an importance of the muscular shortening on the heart production based on his experiments (HILL, 1938). However, they had not distinguished the negative work from the positive work and had not taken the difference of their energy efficiency into account. In this paper, we estimated the increment of the energy consumption from that in resting state using the concept of the power. We measured accelerations in the vertical direction and estimated the energy consumed during muscular work against gravity and the other support works by muscles. We assumed the center Bulletin of the Osaka Medical College 48 1, ,

6 12 M. MIYAMOTO, J. YAMAGUCHI, M. SHINDO of gravity as the center of the body. We could not determine all parameters for all parts attached to the human body, but the energy balance of the center of gravity was the most useful point to represent the entire body. The relationship of directions between force and velocity for the support muscles are complex to be understood. However, it is a positive work (power) when both force and displacement are in the same direction and it becomes a negative work (power) when directions are opposite to each other. Winter reported that the energy efficiency of the negative work was 0.6 and that of the positive work in intrinsic muscle contraction was 0.3 (WINTER, 1979). The total energy for mechanical work of the muscles can be calculated using this relationship. The amplitudes of the I (0.34 s) peak in the power curves were W and W for steps of 17cm and 34cm in height and their ratio was The I (0.34 s) peak were larger than those of both the II (0.5 s) peak and the III (0.72 s) peak. The amplitudes of the I (0.34 s) peak also increased in relation to the distances for fall, but their duration did not be so prolonged. The durations of the I (0.34 s) peak for the steps of 17cm height were slightly shorter than those for the steps of 34cm height and their ratio was However, there was only a little difference between their durations of the I (0.34 s) peak and their ratio was near 1. The I (0.34 s) peak became so larger for a long down step and became able to absorb the increased kinetic energy within such a short time. The amplitudes of the II (0.5 s) peak in the power curves for steps of 17cm and 34cm in height were W and W (their ratio: 0.54). The amplitudes of the II (0.5 s) peak were also related with the heights of the steps or the distances for fall. The amplitudes of the III (0.72 s) peak in the power curves for steps of 17cm and 34cm in height were 44.4 W and W (their ratio: 0.25). The amplitudes of the III (0.72 s) peak were less related with the heights of the steps or the distances for fall. Their durations of peaks increased in order of I, II and III peak gradually. The potential energy acquired by falling down for h cm was calculated by mgh, where m was weight and g was the gravitational acceleration. On falling down motion, the same amount of energy as potential energy was absorbed by muscles upon landing. Their first peaks of the muscular work curves were J and J and their ratio was These calculated potential energies were equal to the mechanical works of the supporting muscles. The center of gravity took gravitational acceleration almost fully at the beginning of stepping down motion, and this gravitational acceleration was weakened by the support muscles, power and changed to negative. The integrated negative power due to the support muscles or the energy absorption overcame each corresponding amount of kinetic energy, and the negative work exceeded the positive work. The excess energy accounted the second upward vibration. Their second peaks of the work curves were 16.2 J and 25.8 J. Vibrations were caused by contractions due to reflexes of the muscles and the absorption process. The center of gravity always took a gravitational acceleration of 1G under the stationary condition. From the standpoint of the muscles, gravitational acceleration was always accumulated on them. As for the falling down motion, muscle power was not necessary during a fall. Kinetic energy was transformed from potential energy during a fall. Only the negative power upon landing was necessary. By interpretation of energy consumption based on the support muscles, not only positive (intrinsic) but also negative (eccentric) work consumed energy of the muscles. We used the equation of in Figure 4 to take the energy consumption of the support muscles into consideration. If these calculations were performed using the equation of, the work curve fell from 0 and increased with a curve to wave, finally became -100J, which is equal to the value of mgh. However we used instead of in Figure 4 and Table 2. Then the total (I+II+III+ ) muscular mechanical work in the falling down motion was J for the steps of 17cm height and J for the steps of 34cm height. Winter reported that the energy efficiency of the negative work was 0.6 and that of the positive work was 0.3 (WINTER, 1979). Energy consumption for each mechanical work was calculated by multiplying it by these coefficients. They became J for the steps of 17cm height and J for the steps of 34cm height, when these coeffi- 12 Bulletin of the Osaka Medical College 48 1, , 2002

7 Power during Going down stairs 13 cients were applied in the mechanical work of the support muscles. On the other hand, the energy consumption to the motion direction for a step of 30-40cm was 24 Joules based on our report (MIYAMOTO et al., 2002; MIYAMOTO et al., 2002) and was 80 Joules if the energy efficiency in intrinsic muscle contraction was assumed to be 0.3. The total energy consumption in the both vertical and motion directions was 280 J (WINTER, 1979; NAKAMURA et al., 2000). Our volunteer, s basal metabolic rates were supposed to be about 70 W by Inoue, s calculation (INOUE et al., 1969). Because the EMR for a level-ground walk was 3, the energy consumption increase was calculated to be 210 W, and 278 J per step when the body weight was 60kg. It corresponded to oxygen consumption increase per step of this stairs, being about the same as that for a level-ground walk reported by INOUE et al. Inoue also estimated that EMR in a standing posture was only 0.2 and suspected that energy consumption of the support muscles materially increased in work with movement (INOUE et al., 1969). We did not think that the coefficients used for the energy conversion were complete. The study of muscle structure suggests that its thickness is related to force. The produced force by muscles depends on the muscle thickness. On the other hand, their length is related to the contractile velocity. The velocity produced by muscles depends on the muscle length. The dynamical work (the power) is calculated as the product of force and velocity. The muscle structure itself is related to the concept of power. However, the energy consumption with respect to the relationship between the muscles forces and their positive and negative work cannot be understood well as yet (HOF et al., 1987; WINNER, 1979; INMANN, 1981), and needs further examination in future studies. REFERENCES BARGER VD. OLSSEN MG.: CLASSICAL MECHAN- ICS A MODERN PERSPECTIVE McGraw-Hill, Inc. New York, 1973 FENN WO.: A quantitative comparison between the energy liberated and the work performed by the isolated sartorius muscle of the frog. J. Physiol. 58, ,1923 HILL AV.: The heat of shortening and the dynamic constants of muscle. Soc. Lond. B126, ,1938 HOF AL, PRONK CNA, VAN BEST JA: Comparison between EMG to force processing and kinetic analysis for the calf muscle moment in walking and stepping. J. Biomech. 20(2), ,1987 Human Life Engineering Research Center: Japanese human body measuring data Human Life Engineering Research Center, Tokyo, 1997 (in Japanese) INMANN VT: Human Walking. Williams & Wilkins, Baltimore, 86, 1981 INOUE A, SHINAGAWA Y: Introduction of exercise physiology. Nannkodo, Tokyo1969 (in Japanese) KALEPS, I., CLAUSER, C.E.: Investigation into the mass distribution properties of the human body and its segments. : ERGONOMICS 27, , 1984 Life Engineering Industry Technological Laboratory: A human body dimension data for design. Japanese Publishing Service, Tokyo, 2001 (in Japanese) MIYAMOTO M, IMAI Y, YAMAGUCHI J, KONISHI M, NISHIMURA Y, SHIMADA M: Kinematic analysis of a fall. J. Osaka Med. Coll. 60, 83-92, 2001 (in Japanese) MIYAMOTO M, IMAI Y: Estimation of Dynamical Properties of Human Lower Limbs on squatting down motion by Acceleration Measurement.. J. Osaka Med. Coll. 61, 33-37, 2002 (in Japanese) MIYAMOTO M, SHINDO M: Measuring acceleration of the human gait by motion analysis and the power concept.. J. Osaka Med. Coll. (in press), 2002 (in Japanese) MIYAMOTO M, SHINDO M: Use of accerlerometry to estimate power changes at the individual, s center of gravity while descending stairs by stepping and jumping.. J. Osaka Med. Coll. (in press), 2002 (in Japanese) NAKAMURA R, SAITO H: Fundamental Kinematics. Ishiyakusyuppann, Tokyo, 2000 (in Japanese) WINTER DA, ROBERTSON DGE: Joint torque and energy pattern in normal gait. Biol. Cybernetics, 29, , 1978 WINTER DA: A new definition of mechanical work done in human movement. J.appl.Physiol.46, 79-83, 1979 WINNER DA: Biomechanics of human movement. John Wiley & Sons, New York, 140, 1979 WOOD GA, JENNINGS LS: On the use of spline function for data smoothing. J. Biomechanics. 12, , 1979 Bulletin of the Osaka Medical College 48 1, ,

CHAPTER 12: THE CONDITIONS OF LINEAR MOTION

CHAPTER 12: THE CONDITIONS OF LINEAR MOTION KINESIOLOGY Scientific Basis of Human Motion, 12 th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University