Journal of Orthopaedic Research 915C154 Raven Press, Ltd., New York 0 1991 Orthopaedic Research Society
Short Communication
The Impact Response of the Seated Subject Holger Broman, ?Malcolm H. Pope, "Michal Benda, Magnus Svensson, Charlotte Ottosson, and *Tommy Hansson Department of Applied Electronics, and Chalmers University of Technology and *Department of Orthopaedics, Sahlgren Hospital, Goteborg, Sweden and fMcClure Musculoskeletal Research Center, Department of Orthopaedic Surgery and the Vermont Rehabilitation Engineering Center, University of Vermont, Burlington, Vermont, U.S.A.
Summary: An impact method for establishing the dynamic response of the seated subject is introduced. The method employs a pendulum to apply the impact to the suspended seat. Pins are placed in the spinous process at L3. Highly reproducible results are obtained. The results were not affected by the amplitude of impact, implying a linear system. A marked peak of transmissibility is found in the 4-5 Hz range and an attenuation peak is found close to 8 Hz. Both muscle contraction and postural changes affect the dynamic response. A relaxed posture shows greater gain and attenuation peaks. A valsalva stiffens the system and reduces the effective damping. The vertical response of the body probably shows in the 5-6 Hz peak, while the rotational response is probably encompassed in the 8 Hz attenuation peak. Key Words: Impact-Vibration-Lumbar spine-Resonance.
The advent of the machine age has subjected many individuals to impact and vibration. Many investigators have established the response of the seated human subject to vibration. However, there are many differences in mechanical responses reported by different investigators. One problem is the variation in subjects and within subjects from day to day. In addition, we have shown (6) that errors occur when transducers are not rigidly mounted to the skeleton. In contrast, little work has been done on the response of the seated subject to impact. Hodgson et al. (3) subjected human cadavers to varying peak accelerations and acceleration rates (ierk) with different types of seat cushions. Jerk, in the case of a ramp function, is the slope of the leading edge of the ramp. The authors computed a dynamic load factor,
which they defined as the ratio of the peak to the mean response. This dynamic load factor increased with jerk at low jerk levels but then became independent of jerk. The main limitation of sinusoidal excitation as a means of determining the dynamic response of the seated subject is that this method is time consuming. In many test systems, it is not possible to sine sweep and considerable time is necessary to adjust the apparatus for different discrete frequencies (5). Even in those systems that permit sine sweeps, it is not possible to run multiple repetitions or multiple postural sequences without the test subject becoming fatigued or uncomfortable. This is of particular concern in those tests employing invasive techniques for the mounting of accelerometers. Thus, the purpose of this study was to examine the feasibility of an impact method, employing pin placement in the spinous process, to obtain the dynamic response of the lumbar spine. The eventual aim was to establish postural factors that could affect the dynamic response in the environment experienced by a driver. Several hypotheses were
Received February 15, 1989; accepted May 8, 1990. Address correspondence and reprint requests to Dr. M. H. Pope at McClure Musculoskeletal Research Center, Department of Orthopaedic Surgery and Vermont Rehabilitation Engineering Center, University of Vermont, Burlington, VT 05405, U.S.A.
150
IMPACT RESPONSE OF SEATED SUBJECT proposed: (a) The impact method will result in reproducible measures of the dynamic response within subjects. (b) The dynamic response will not be affected by small variations in the impact energy. (c) An erect posture will lead to a higher natural frequency and a lower peak transmissibility than that of a subject in a relaxed posture. (d) For a given posture, a Valsalva maneuver will tend to stiffen the system.
MATERIALS AND METHODS A whole body impactor described elsewhere was used (7). The major part of the apparatus was a platform that was suspended by eight rubber springs and guided by two linear bearings, as shown in Fig. 1. The rubber springs acted with a viscous component so they would tend to damp system oscillations after the device was activated. Adjustments were made to the spring platform after the subject was seated, so that the platform was always struck at the same point in the swing of the impact pendulum. The pendulum was released by means of disc brakes and a manual trigger started the data
FIG. 1. Drawing of whole-body impactor in which the position of the L3 accelerometer can be noted. From Pope et al. (7).
151
collection. The starting point of the pendulum was always at lo" above the horizontal. This represented a transfer of 3.9 J of energy to the platformspring-human system. In order to apply a known impulse vs. time impact to the platform, a striker plate composed of flexible, closed cell foam was placed between the pendulum and the platform. Its flat end was approximately 10 cm2 and its peak was about 9 cm in height. The base was attached to the bottom of the platform so the impact pendulum would strike its peak. This system tended to produce a relatively square force impulse in the time domain. The vertical natural frequency of the loaded platform was 1.8 Hz, below the frequencies of interest. The frame bending natural frequency was 60 Hz and the system was unaffected by cross talk in other directions. The system was calibrated by attaching known weights and masses, computing this natural frequency, and comparing this to the measured response. Three female subject were evaluated for their seated mechanical response. Anthropometric data were obtained from each subject at the time of testing. The subjects were ages 31, 34, and 37 years, weighed 65, 70, and 61 kg, and had heights of 1.73, 1.69, and 1.74 m, respectively, and were free of low back pain or other health problems. Several different postures were maintained by the seated subjects after careful instruction by a physical therapist. The first was the erect posture where the back of the head, the peak of the thoracic spine, and the midpoint between the posterior superior iliac spines were collinear and oriented normal to the seat. The second posture studied was relaxed, with the only constraint being that the subject's eyes looked forward at a local horizon. In both cases, the subjects were also asked to adopt a Valsalva. The subjects were instructed to pressurize voluntarily the abdomen with a closed glottis. Between 3 and 10 repetitions at each posture were accomplished. Under local anesthesia, a threaded K wire, 2.4 mm in diameter, was threaded about 10 mm into the L3 lumbar spinous process. A uniaxial accelerometer (Model 7265-10, Endevco, San Juan Capistrano, CA, U.S.A.) was attached to the L3 pin, and oriented to lie within the sagittal plane. Mechanical response was determined by recording acceleration vs. time at the seat, and at the pin accelerometer. Transfer functions could then be determined for each subject. Data were recorded on a 14 channel FM tape recorder (Model VT 3360, Bell and Howell Corp, %
J Orthop Res, Vol. 9, No. 1 , 1991
H . BROMAN ET AL.
152
Eiki International Inc., Camino Capistrano, Laguna Niguel, CA, U.S.A.) at 38 c d s . The accelerometer output was calibrated by orienting the accelerometer in the direction of the gravity vector and then turned upside down. Accelerometer data were amplified and low pass filtered at 50 Hz, with a fourth order filter (below the frame bending frequency), passed to an analog/ digital converter (Minc PDP 11/23-MNCllHA-RXOZMA, Digital Equipment Corp., Maynard, MA, U.S.A.), and digitized at 160 Hz for a duration of 3.2 s. The data were then displayed in both the time and frequency domains, and transfer function magnitude and phase relationships were determined by spectral analysis. RESULTS
There is excellent repeatability for the various trials within subjects as shown by the standard error of the mean (SEM) for 10 repetitions in Fig. 2. Only the Valsalva experiments showed slightly more differences within subjects. For frequency of peak transmissibility, the standard deviation within subjects ranged from 0 to 0.7 Hz. The seated individual in the relaxed posture exhibits a marked peak of transmissibility to the L3 vertebrae at 5-6.5 Hz, coupled with an attenuation peak-transmissibility valley at 6.5 to 8.5 Hz. The phase angle generally peaks at about 6.5 Hz. The data are fairly similar between subjects, as shown in Table 1. The response of the subject to impacts of two different energies was compared for the erect posture and it was found that there were no statistically significant differences in the curves. These results indicate that this low level of impact and over the frequency range examined, the system can be regarded as essentially linear. In comparison, between the relaxed and erect postures, it was found that the transmissibility curves have the same form except that the peaks are much more marked in the relaxed posture (Fig. 3). The transmissibility peak ranges from 4.5 to 6.5 Hz with a transmissibility valley at 6.5-8.0 Hz. Within subjects, the peak gain was less in the erect posture than the relaxed posture in two subjects (p < 0.025) but not in the third; the transmissibility peak was at a lower frequency in the relaxed posture (p < 0.025, p < 0.001, and NS) (ANOVA). The Valsalva maneuver, as shown in Fig. 3, was found to have a transmissibility peak ranging from 5-6.5 Hz. The Valsalva also increased the magnitude of the peak gain, as compared to the relaxed J Orthop Res, Vol. 9,
No. 1 , 1991
G a i n [dB]
l2I
1
frequency
[HL]
Phase [rad]
1.57
1 frequency [ H z ]
0.00
-'
2 -1.57
-3.14
1 J
FIG. 2. The upper graph shows gain (dB) against frequency while the lower graph shows phase angle against frequency. Figure 2 shows the response of subject II sitting erect to a high impact (15" of the pendulum). The mean 2 2 SEM are shown. The average curve represents discrete points averaged between 10 trials in the frequency domain.
and erect postures. The transmissibility curve has a markedly different shape beyond 6 Hz and demonstrates decreasing gain with frequency. The Valsalva gave an increased peak gain, compared to the relaxed posture in two cases (p < 0.05) but not in the third and an increased frequency of the transTABLE 1. Study results Transmissibility peak Posture Relaxed 1 2 3
Mean Erect 1 2 3
Mean Valsalva 1 2 3 Mean
Attenuation peak
Frequency
Gain
Frequency
Gain
4.5 4.5 6.0 5.0
5 2 4.5 3.8
8 6.5 8 1.5
- 10 -8 - 10
5.0 6.5 6.5 6.3
2 5 2 3
I
-1 - 10
5.5 5.5
6 3 3.5 4.2
-
1.5 6.2
8
I 1.3
-
-
-9.3
-5 -1.3
-
IMPACT RESPONSE OF SEATED SUBJECT Gain [dB]
Gain [dB]
A,B 12
12
1
8
153
0
-6
~
- 12 -
12
-ID
-18
-
Phase [rad]
1.57 3'14
0.00
-1.57
-3.14
1
-
%I' 1.57
f r e q u e n c y [Hz] 2
32
1
-1.57
1I
0 frequency [HI]
-J.14 -I
G a i n [dB]
C 12
1
6
0
-6
- 12 -18
FIG. 3. Response of subject I in a relaxed posture (A), an erect posture (B), and a voluntary Valsalva maneuver (C).
P h a s e [rad]
] f r e q u e n c y [Hz]
0.00
-1.57
-3.14
i
J Orthop Res, Vol. 9, No. 1, 1991
H . BROMAN ET AL.
154
missibility peak (p < 0.001,' p < 0.001, and p < 0.025) (ANOVA). DISCUSSION ,
The experimental method showed excellent reproductibility within subjects. The data were remarkably similar between subjects. The small differences that existed were probably due to anthropometric differences between subjects. Other factors of possible importance are differences in muscle guarding due to discomfort, differences of static postural stability, and different abilities of given subjects to produce a Valsalva. There were substantial differences between the response measured on a bite bar and those measurements made directly on a pin mounted to the L3 vertebra. The response, as measured at the bite bar, which was reported in a separate publication, is different (7). This is probably due to the effect of the head-neck system. The bite bar gain in the frequency domain shows a resonant frequency lower than that measured by the L3 accelerometer. The bite bar transducer exhibits a gain at approximately 7 Hz, rather than an attenuation peak. In addition, the bite bar measurements are diminished in magnitude as a result of the increased damping of the upper body systems. This demonstrates the importance of making such measurements at the point of interest and not at some remote location. Unfortunately, the measurements much be made with rigid fixation to the skeleton and thus invasively, since we have demonstrated elsewhere that measurements made by skin-mounted transducers lead to artifacts. We believe that the technique described herein avoids the postural artifacts, especially head movement, of the bite bar method. The use of the spectral analysis method assumes a linear system. The response of a subject to impulses of two different amplitudes demonstrates that there are only very minor differences in the range of 0-32 Hz. This suggests that only minor nonlinearities exist in the system and thus this should be considered a minor limitation of our methodology since we have assumed a linear system. It should be noted that Panjabi et al. (9,using accelerometers mounted to an L3 pin and a discrete sinusoidal input, found no effect on the transfer function of input signal amplitude over the range of 0-12 Hz. Several of the experiments suggest the important role of the musculature in affecting the dynamic response. The Valsalva increases the resonant frequency and the amplitude of this resonant freJ Orthop Res, Vol. 9, No. I , 1991
quency. This implies a stiffening and reduced damping of the system. However, it has been shown that the Valsalva does not lead to a decrease in disc loads (4). In fact, as the subject voluntarily contracts the anterior trunk muscles, there is a concomitant increase in dorsal muscle activity. Thus, all of the spinal muscles, both anterior and posterior, are contracted, causing marked stiffening of the trunk. It is probable that the resonant frequency is due to the biological subsystems between the L3 level and the seat, as suggested by Hagena et al. (2), rather than the spine bending or compression such as has been suggested by others. However, pelvic motion will change the lordosis and lead to some spine bending. Sandover and Dupuis (8), in a reanalysis of Christ and Dupuis' (1) original data, report bending of the lumbar spine, rather than compression, and suggest that this may be due to pelvic rocking. Unfortunately, these data are of only one subject in a nondefined posture. The experiments discussed herein suggest that the pelvis acts as a rotational system at higher frequencies. Thus, it is likely that the 4-6 Hz resonant frequency is due to compression of the buttocks tissue and to the interaction of this vertical response with the rotational subsystem. Acknowledgment:The authors wish to acknowledge the support of the Swedish Work Environment Fund, the Volvo Educational Foundation, and the U.S. Department of Education, National Institute of Disability and Rehabilitation Research (Vermont Rehabilitation Engineering Center).
REFERENCES 1 . Christ W, Dupuis H: Uber die Beanspruchung die Wirbelsaule unter dem Einfluss sinusformiger und stochastischer Schwingungen. Int Z Angew Phys Arbeitsphys 22:25&278, 1966 2. Hagena FW, Wirth CJ, Piehler J, Plitz W, Hofmann GO, Zwingers Th: In vivo experiments on the response of the human spine to sinusoidal Gz vibration. AGARD Conference Proceedings N o . 578, Springfield, VA, NTIS, 1985 3. Hodgson VR, Lissner HR, Patrick LM: The effect of jerk on the human spine. ASME Paper No. 63-WA-316, 1963 4. Krag MH, Byrne K, Gilbertson L, Haugh LD: Intraabdominal pressurization: failure to reduce erector spinae loads during lifting tasks. International Society for the Study Lumbar Spine, Dallas, 1986 5. Panjabi MM, Andersson GBJ, Jorneus L, Hult E, Mattson L: In vivo measurement of spinal column vibrations. J Bone Joint Surg [Am] 68:695-703, 1986 6. Pope MH, Svensson M, Broman H, Andersson GBJ: Mounting of the transducer in measurements of sequential motion of the spine. J Biomech 19:675477, 1986 7. Pope MH, Wilder DG, Jorneus L, Broman H, Svensson M, Andersson GBJ: The response of the seated human to sinusoidal vibration and impact. J Biomech Eng 109:27%284, 1987 8. Sandover J, Dupuis H: A reanalysis of spinal motion during vibration. Ergonomics 30:975-985, 1987
Short Communication
The Impact Response of the Seated Subject Holger Broman, ?Malcolm H. Pope, "Michal Benda, Magnus Svensson, Charlotte Ottosson, and *Tommy Hansson Department of Applied Electronics, and Chalmers University of Technology and *Department of Orthopaedics, Sahlgren Hospital, Goteborg, Sweden and fMcClure Musculoskeletal Research Center, Department of Orthopaedic Surgery and the Vermont Rehabilitation Engineering Center, University of Vermont, Burlington, Vermont, U.S.A.
Summary: An impact method for establishing the dynamic response of the seated subject is introduced. The method employs a pendulum to apply the impact to the suspended seat. Pins are placed in the spinous process at L3. Highly reproducible results are obtained. The results were not affected by the amplitude of impact, implying a linear system. A marked peak of transmissibility is found in the 4-5 Hz range and an attenuation peak is found close to 8 Hz. Both muscle contraction and postural changes affect the dynamic response. A relaxed posture shows greater gain and attenuation peaks. A valsalva stiffens the system and reduces the effective damping. The vertical response of the body probably shows in the 5-6 Hz peak, while the rotational response is probably encompassed in the 8 Hz attenuation peak. Key Words: Impact-Vibration-Lumbar spine-Resonance.
The advent of the machine age has subjected many individuals to impact and vibration. Many investigators have established the response of the seated human subject to vibration. However, there are many differences in mechanical responses reported by different investigators. One problem is the variation in subjects and within subjects from day to day. In addition, we have shown (6) that errors occur when transducers are not rigidly mounted to the skeleton. In contrast, little work has been done on the response of the seated subject to impact. Hodgson et al. (3) subjected human cadavers to varying peak accelerations and acceleration rates (ierk) with different types of seat cushions. Jerk, in the case of a ramp function, is the slope of the leading edge of the ramp. The authors computed a dynamic load factor,
which they defined as the ratio of the peak to the mean response. This dynamic load factor increased with jerk at low jerk levels but then became independent of jerk. The main limitation of sinusoidal excitation as a means of determining the dynamic response of the seated subject is that this method is time consuming. In many test systems, it is not possible to sine sweep and considerable time is necessary to adjust the apparatus for different discrete frequencies (5). Even in those systems that permit sine sweeps, it is not possible to run multiple repetitions or multiple postural sequences without the test subject becoming fatigued or uncomfortable. This is of particular concern in those tests employing invasive techniques for the mounting of accelerometers. Thus, the purpose of this study was to examine the feasibility of an impact method, employing pin placement in the spinous process, to obtain the dynamic response of the lumbar spine. The eventual aim was to establish postural factors that could affect the dynamic response in the environment experienced by a driver. Several hypotheses were
Received February 15, 1989; accepted May 8, 1990. Address correspondence and reprint requests to Dr. M. H. Pope at McClure Musculoskeletal Research Center, Department of Orthopaedic Surgery and Vermont Rehabilitation Engineering Center, University of Vermont, Burlington, VT 05405, U.S.A.
150
IMPACT RESPONSE OF SEATED SUBJECT proposed: (a) The impact method will result in reproducible measures of the dynamic response within subjects. (b) The dynamic response will not be affected by small variations in the impact energy. (c) An erect posture will lead to a higher natural frequency and a lower peak transmissibility than that of a subject in a relaxed posture. (d) For a given posture, a Valsalva maneuver will tend to stiffen the system.
MATERIALS AND METHODS A whole body impactor described elsewhere was used (7). The major part of the apparatus was a platform that was suspended by eight rubber springs and guided by two linear bearings, as shown in Fig. 1. The rubber springs acted with a viscous component so they would tend to damp system oscillations after the device was activated. Adjustments were made to the spring platform after the subject was seated, so that the platform was always struck at the same point in the swing of the impact pendulum. The pendulum was released by means of disc brakes and a manual trigger started the data
FIG. 1. Drawing of whole-body impactor in which the position of the L3 accelerometer can be noted. From Pope et al. (7).
151
collection. The starting point of the pendulum was always at lo" above the horizontal. This represented a transfer of 3.9 J of energy to the platformspring-human system. In order to apply a known impulse vs. time impact to the platform, a striker plate composed of flexible, closed cell foam was placed between the pendulum and the platform. Its flat end was approximately 10 cm2 and its peak was about 9 cm in height. The base was attached to the bottom of the platform so the impact pendulum would strike its peak. This system tended to produce a relatively square force impulse in the time domain. The vertical natural frequency of the loaded platform was 1.8 Hz, below the frequencies of interest. The frame bending natural frequency was 60 Hz and the system was unaffected by cross talk in other directions. The system was calibrated by attaching known weights and masses, computing this natural frequency, and comparing this to the measured response. Three female subject were evaluated for their seated mechanical response. Anthropometric data were obtained from each subject at the time of testing. The subjects were ages 31, 34, and 37 years, weighed 65, 70, and 61 kg, and had heights of 1.73, 1.69, and 1.74 m, respectively, and were free of low back pain or other health problems. Several different postures were maintained by the seated subjects after careful instruction by a physical therapist. The first was the erect posture where the back of the head, the peak of the thoracic spine, and the midpoint between the posterior superior iliac spines were collinear and oriented normal to the seat. The second posture studied was relaxed, with the only constraint being that the subject's eyes looked forward at a local horizon. In both cases, the subjects were also asked to adopt a Valsalva. The subjects were instructed to pressurize voluntarily the abdomen with a closed glottis. Between 3 and 10 repetitions at each posture were accomplished. Under local anesthesia, a threaded K wire, 2.4 mm in diameter, was threaded about 10 mm into the L3 lumbar spinous process. A uniaxial accelerometer (Model 7265-10, Endevco, San Juan Capistrano, CA, U.S.A.) was attached to the L3 pin, and oriented to lie within the sagittal plane. Mechanical response was determined by recording acceleration vs. time at the seat, and at the pin accelerometer. Transfer functions could then be determined for each subject. Data were recorded on a 14 channel FM tape recorder (Model VT 3360, Bell and Howell Corp, %
J Orthop Res, Vol. 9, No. 1 , 1991
H . BROMAN ET AL.
152
Eiki International Inc., Camino Capistrano, Laguna Niguel, CA, U.S.A.) at 38 c d s . The accelerometer output was calibrated by orienting the accelerometer in the direction of the gravity vector and then turned upside down. Accelerometer data were amplified and low pass filtered at 50 Hz, with a fourth order filter (below the frame bending frequency), passed to an analog/ digital converter (Minc PDP 11/23-MNCllHA-RXOZMA, Digital Equipment Corp., Maynard, MA, U.S.A.), and digitized at 160 Hz for a duration of 3.2 s. The data were then displayed in both the time and frequency domains, and transfer function magnitude and phase relationships were determined by spectral analysis. RESULTS
There is excellent repeatability for the various trials within subjects as shown by the standard error of the mean (SEM) for 10 repetitions in Fig. 2. Only the Valsalva experiments showed slightly more differences within subjects. For frequency of peak transmissibility, the standard deviation within subjects ranged from 0 to 0.7 Hz. The seated individual in the relaxed posture exhibits a marked peak of transmissibility to the L3 vertebrae at 5-6.5 Hz, coupled with an attenuation peak-transmissibility valley at 6.5 to 8.5 Hz. The phase angle generally peaks at about 6.5 Hz. The data are fairly similar between subjects, as shown in Table 1. The response of the subject to impacts of two different energies was compared for the erect posture and it was found that there were no statistically significant differences in the curves. These results indicate that this low level of impact and over the frequency range examined, the system can be regarded as essentially linear. In comparison, between the relaxed and erect postures, it was found that the transmissibility curves have the same form except that the peaks are much more marked in the relaxed posture (Fig. 3). The transmissibility peak ranges from 4.5 to 6.5 Hz with a transmissibility valley at 6.5-8.0 Hz. Within subjects, the peak gain was less in the erect posture than the relaxed posture in two subjects (p < 0.025) but not in the third; the transmissibility peak was at a lower frequency in the relaxed posture (p < 0.025, p < 0.001, and NS) (ANOVA). The Valsalva maneuver, as shown in Fig. 3, was found to have a transmissibility peak ranging from 5-6.5 Hz. The Valsalva also increased the magnitude of the peak gain, as compared to the relaxed J Orthop Res, Vol. 9,
No. 1 , 1991
G a i n [dB]
l2I
1
frequency
[HL]
Phase [rad]
1.57
1 frequency [ H z ]
0.00
-'
2 -1.57
-3.14
1 J
FIG. 2. The upper graph shows gain (dB) against frequency while the lower graph shows phase angle against frequency. Figure 2 shows the response of subject II sitting erect to a high impact (15" of the pendulum). The mean 2 2 SEM are shown. The average curve represents discrete points averaged between 10 trials in the frequency domain.
and erect postures. The transmissibility curve has a markedly different shape beyond 6 Hz and demonstrates decreasing gain with frequency. The Valsalva gave an increased peak gain, compared to the relaxed posture in two cases (p < 0.05) but not in the third and an increased frequency of the transTABLE 1. Study results Transmissibility peak Posture Relaxed 1 2 3
Mean Erect 1 2 3
Mean Valsalva 1 2 3 Mean
Attenuation peak
Frequency
Gain
Frequency
Gain
4.5 4.5 6.0 5.0
5 2 4.5 3.8
8 6.5 8 1.5
- 10 -8 - 10
5.0 6.5 6.5 6.3
2 5 2 3
I
-1 - 10
5.5 5.5
6 3 3.5 4.2
-
1.5 6.2
8
I 1.3
-
-
-9.3
-5 -1.3
-
IMPACT RESPONSE OF SEATED SUBJECT Gain [dB]
Gain [dB]
A,B 12
12
1
8
153
0
-6
~
- 12 -
12
-ID
-18
-
Phase [rad]
1.57 3'14
0.00
-1.57
-3.14
1
-
%I' 1.57
f r e q u e n c y [Hz] 2
32
1
-1.57
1I
0 frequency [HI]
-J.14 -I
G a i n [dB]
C 12
1
6
0
-6
- 12 -18
FIG. 3. Response of subject I in a relaxed posture (A), an erect posture (B), and a voluntary Valsalva maneuver (C).
P h a s e [rad]
] f r e q u e n c y [Hz]
0.00
-1.57
-3.14
i
J Orthop Res, Vol. 9, No. 1, 1991
H . BROMAN ET AL.
154
missibility peak (p < 0.001,' p < 0.001, and p < 0.025) (ANOVA). DISCUSSION ,
The experimental method showed excellent reproductibility within subjects. The data were remarkably similar between subjects. The small differences that existed were probably due to anthropometric differences between subjects. Other factors of possible importance are differences in muscle guarding due to discomfort, differences of static postural stability, and different abilities of given subjects to produce a Valsalva. There were substantial differences between the response measured on a bite bar and those measurements made directly on a pin mounted to the L3 vertebra. The response, as measured at the bite bar, which was reported in a separate publication, is different (7). This is probably due to the effect of the head-neck system. The bite bar gain in the frequency domain shows a resonant frequency lower than that measured by the L3 accelerometer. The bite bar transducer exhibits a gain at approximately 7 Hz, rather than an attenuation peak. In addition, the bite bar measurements are diminished in magnitude as a result of the increased damping of the upper body systems. This demonstrates the importance of making such measurements at the point of interest and not at some remote location. Unfortunately, the measurements much be made with rigid fixation to the skeleton and thus invasively, since we have demonstrated elsewhere that measurements made by skin-mounted transducers lead to artifacts. We believe that the technique described herein avoids the postural artifacts, especially head movement, of the bite bar method. The use of the spectral analysis method assumes a linear system. The response of a subject to impulses of two different amplitudes demonstrates that there are only very minor differences in the range of 0-32 Hz. This suggests that only minor nonlinearities exist in the system and thus this should be considered a minor limitation of our methodology since we have assumed a linear system. It should be noted that Panjabi et al. (9,using accelerometers mounted to an L3 pin and a discrete sinusoidal input, found no effect on the transfer function of input signal amplitude over the range of 0-12 Hz. Several of the experiments suggest the important role of the musculature in affecting the dynamic response. The Valsalva increases the resonant frequency and the amplitude of this resonant freJ Orthop Res, Vol. 9, No. I , 1991
quency. This implies a stiffening and reduced damping of the system. However, it has been shown that the Valsalva does not lead to a decrease in disc loads (4). In fact, as the subject voluntarily contracts the anterior trunk muscles, there is a concomitant increase in dorsal muscle activity. Thus, all of the spinal muscles, both anterior and posterior, are contracted, causing marked stiffening of the trunk. It is probable that the resonant frequency is due to the biological subsystems between the L3 level and the seat, as suggested by Hagena et al. (2), rather than the spine bending or compression such as has been suggested by others. However, pelvic motion will change the lordosis and lead to some spine bending. Sandover and Dupuis (8), in a reanalysis of Christ and Dupuis' (1) original data, report bending of the lumbar spine, rather than compression, and suggest that this may be due to pelvic rocking. Unfortunately, these data are of only one subject in a nondefined posture. The experiments discussed herein suggest that the pelvis acts as a rotational system at higher frequencies. Thus, it is likely that the 4-6 Hz resonant frequency is due to compression of the buttocks tissue and to the interaction of this vertical response with the rotational subsystem. Acknowledgment:The authors wish to acknowledge the support of the Swedish Work Environment Fund, the Volvo Educational Foundation, and the U.S. Department of Education, National Institute of Disability and Rehabilitation Research (Vermont Rehabilitation Engineering Center).
REFERENCES 1 . Christ W, Dupuis H: Uber die Beanspruchung die Wirbelsaule unter dem Einfluss sinusformiger und stochastischer Schwingungen. Int Z Angew Phys Arbeitsphys 22:25&278, 1966 2. Hagena FW, Wirth CJ, Piehler J, Plitz W, Hofmann GO, Zwingers Th: In vivo experiments on the response of the human spine to sinusoidal Gz vibration. AGARD Conference Proceedings N o . 578, Springfield, VA, NTIS, 1985 3. Hodgson VR, Lissner HR, Patrick LM: The effect of jerk on the human spine. ASME Paper No. 63-WA-316, 1963 4. Krag MH, Byrne K, Gilbertson L, Haugh LD: Intraabdominal pressurization: failure to reduce erector spinae loads during lifting tasks. International Society for the Study Lumbar Spine, Dallas, 1986 5. Panjabi MM, Andersson GBJ, Jorneus L, Hult E, Mattson L: In vivo measurement of spinal column vibrations. J Bone Joint Surg [Am] 68:695-703, 1986 6. Pope MH, Svensson M, Broman H, Andersson GBJ: Mounting of the transducer in measurements of sequential motion of the spine. J Biomech 19:675477, 1986 7. Pope MH, Wilder DG, Jorneus L, Broman H, Svensson M, Andersson GBJ: The response of the seated human to sinusoidal vibration and impact. J Biomech Eng 109:27%284, 1987 8. Sandover J, Dupuis H: A reanalysis of spinal motion during vibration. Ergonomics 30:975-985, 1987
