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J Appl Physiol 90: 2141-2150, 2001;
8750-7587/01 $5.00
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Vol. 90, Issue 6, 2141-2150, June 2001

Respiratory effects of transient axial acceleration

Stephen H. Loring, Hsueh-Tze Lee, and James P. Butler

Beth Israel Deaconess Medical Center and Harvard School of Public Health, Boston, Massachusetts 02115


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Whereas gravity has an inspiratory effect in upright subjects, transient upward acceleration is reported to have an expiratory effect. To explore the respiratory effects of transient axial accelerations, we measured axial acceleration at the head and transrespiratory pressure or airflow in five subjects as they were dropped or lifted on a platform. For the first 100 ms, upward acceleration caused a decrease in mouth pressure and inspiratory flow, and downward acceleration caused the opposite. We also simulated these experimental observations by using a computational model of a passive respiratory system based on anatomical data and normal respiratory characteristics. After 100 ms, respiratory airflow in our subjects became highly variable, no longer varying with acceleration. Electromyograms of thoracic and abdominal respiratory muscles showed bursts of activity beginning 40-125 ms after acceleration, suggesting reflex responses responsible for subsequent flow variability. We conclude that, in relaxed subjects, transient upward axial acceleration causes inspiratory airflow and downward acceleration causes expiratory airflow, but that after ~100 ms, reflex activation of respiratory musculature largely determines airflow.

respiratory mechanics; respiratory muscles; electromyogram; reflex


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

AS HUMANS PERFORM VARIOUS physical activities, the axial accelerations they experience can cause respiratory airflow. Axial accelerations are brief during running and walking (7) and more sustained during flight and in centrifuges. Gravity acts in upright humans like a constant upward axial acceleration and is traditionally thought to have an inspiratory effect (1). Support for the inspiratory effect of upward acceleration comes from studies involving a change in G forces during parabolic flight or in centrifuges (3, 4, 10). Thus in upright subjects, who normally experience a vertical acceleration (Gz) = 1 g, exposure to microgravity (Gz congruent  0 g) causes a decrease in lung volume, and exposure to hypergravity (e.g., Gz congruent  3 g) causes an increase in lung volume.

Recently, Wilson, Liu, and co-workers (8, 15) proposed that upward acceleration is expiratory, based on indirect, theoretical studies of gravitational effects on the chest wall and direct measurements of changes in mouth pressure during transient acceleration in an elevator. Because their conclusions were apparently inconsistent with those based on steady-state acceleration, we reexamined the respiratory system's response to transient axial acceleration. We also used a computational model of the respiratory system under acceleration to predict responses of a passive system. Our findings suggest that upward acceleration in the relaxed respiratory system, like gravity, is inspiratory, as is classically taught, but that muscle reflexes are important in determining the respiratory response to changing axial acceleration.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Subjects

We studied the respiratory responses to brief downward and upward axial accelerations (drop/lift experiments) in five subjects standing or sitting on a mobile platform. In three subjects, we also measured electromyographic (EMG) activity of the rib cage and abdominal wall during drops or lifts. Subjects were knowledgeable in respiratory physiology but varied in their experience as experimental subjects. Their physical characteristics are listed in Table 1.

                              
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  		Table 1.   Physical characteristics of subjects

Measurements

Acceleration. We measured the axial component of acceleration (Gz) at the top of the head with an accelerometer (Entran Devices, model EGC-240-5D, adequate to 110 Hz) taped to the underside of a baseball cap that was secured to the head with an elastic bandage. Gz was expressed in units of gravitational acceleration, g (e.g., a subject experiences 1 g while stationary on the earth's surface and 0 g during free fall). Accelerometers were calibrated by turning them over (Delta Gz = 2 g).

Pressure. To measure respiratory pressures at the mouth (Pm) during acceleration, subjects closed their mouth around a tube (0.4 cm ID, 50 cm length) connected to a stationary pressure transducer (Celesco model LCVR, 100 cmH2O diaphragm). The characteristic response time of the system was determined to be ~7 ms during a pressure transient created by popping a balloon inflated over the pressure tube.

Flow. To measure flow at the mouth, subjects breathed through a cardboard mouthpiece, flexible respiratory tubing (3.0 cm ID, 30 cm length), and pneumotachometer (Fleisch no. 2) connected to a differential pressure transducer (Validyne MP 45; 12 cmH2O diaphragm). The pneumotachometer and pressure transducer were stationary. We calibrated the flow signal by setting the integral of flow to a known volume delivered from a syringe. The half-response time of the flow- measuring system was 7 ms, determined by connecting the mouthpiece to a high-flow vacuum pump, occluding the other end of the pneumotachometer, and observing the rise in the flow signal after removing the occlusion.

EMG signals. We measured EMG signals from two pairs of surface electrodes, one placed on the rib cage, over the second right intercostal space overlying the inspiratory parasternal intercostal muscles, and the other placed on the abdomen, over the external abdominal oblique muscles at the level of the umbilicus. Signals were band-pass filtered (100-300 Hz) and amplified (Grass Instrument, model P511K).

Signal processing. Signals were digitized, stored, and analyzed on a personal computer using DI-220 hardware and Windaq software (Dataq Instruments, Akron, OH). Sampling rates were 500 Hz for acceleration, flow, and pressure signals, 1 kHz for EMG signals, and 10-20 kHz for determinations of response characteristics of our instruments.

Procedure

Subjects stood near one end of a platform that moved vertically about a hinge at its other end (Fig. 1). Bungee cords between the ceiling and the mobile end of the platform provided variable upward force. A crank and shaft connected to the mobile end constrained vertical motion and increased effective inertia. Downward accelerations (drops) and upward accelerations (lifts) were initiated by removing a hinged strut under the crank or platform. Transient initial accelerations had maximum amplitudes of less than 1.0 g for drops and 1.1 g for lifts during vertical displacements of ~10 cm.


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  		Fig. 1.   Apparatus for drop/lift studies. Axial acceleration (Gz) and flow at the mouth (V) were recorded in subjects who stood or sat on a mobile platform while relaxed at functional residual capacity (FRC). On release, the platform either lifted or dropped, depending on the tension of bungee cords attached to the ceiling. See text.

We recorded flow or pressure while subjects on the platform either sat on a cushioned box or stood. They wore a nose clip and held their heads straight to keep the accelerometer level. After panting for 1-2 s to enlarge the glottal opening (5), subjects relaxed to functional residual capacity (FRC), closed their mouths completely around the flow or pressure tube, and signaled readiness, and then the platform was released. For each subject, five drops and five lifts were recorded for each set of conditions (measuring either flow or pressure, standing or seated). Because even experienced subjects find it difficult to keep the glottis open during apnea, we were concerned that subjects awaiting the drop/lift might inadvertently allow the glottis to close, isolating the oropharynx from the rest of the respiratory system. To help us recognize and eliminate measurements so affected, we had subjects close the glottis voluntarily for two additional measurements of each type. Although the subjects were expectant and knew in advance the direction of movement (up or down), they could not anticipate the exact moment of drop or lift.

In separate drop/lift experiments in three standing subjects, rib cage and abdominal EMG signals were recorded with acceleration and flow signals. Before each drop or lift, subjects listened to rib cage or abdominal muscle EMG activity to help them relax.

Model

We used a mathematical model to test the hypothesis that a mechanical system with geometrical and mechanical characteristics of the relaxed respiratory system could, indeed, respond passively to acceleration as our subjects did. To accomplish this, we assigned parameter values based on typical physiological values from the literature and estimates of geometrical and kinematic properties of a typical chest wall. We simulated the effects of steady-state changes in body position, transient accelerations similar to those in our experiments, and oscillatory acceleration, and compared the simulations with experimental results from our study and the literature.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Pressure Studies

Mouth pressure decreased for the first 50 ms of upward acceleration (lift studies, Fig. 2), and increased for the first 50 ms of downward acceleration (drop studies) in all subjects, whether the glottis was open or closed (Fig. 3). With the glottis closed, pressure amplitudes at peak Gz (at ~40 ms) were often larger than with the glottis open (Fig. 3), and pressure fluctuations reflected changes in acceleration (Fig. 2). (These pressure fluctuations with the glottis closed apparently resulted from motion-induced compression of gas within the oral cavity, due to movement of the cheeks, tongue, palate, or jaw. No pressure fluctuations were seen when the tube was occluded with the tongue.) Because it was often impossible to discern from pressure signals whether the glottis was open or closed, we abandoned the use of pressure to study respiratory system responses to acceleration.


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  		Fig. 2.   Mouth pressure (Pm) during a drop (subject TH, standing). Arrows point to start of a drop (t = 0). Gz decreased smoothly to its first maximum deviation (peak Gz) within 38-56 ms, then reversed sign and fluctuated unsteadily as the platform was restrained by the rotating crank. Over the first 50 ms, Pm increased with initial downward acceleration (Gz < 1 g). A: open glottis. After ~100 ms, pressure fluctuations did not vary consistently with acceleration. B: closed glottis. At peak Gz, Pm magnitude was larger with the glottis closed than open, and pressure continued to reflect acceleration for ~1 s after the drop.



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  		Fig. 3.   Pm at peak Gz during drops and lifts (subject TH, standing and seated). At peak Gz, pressure was positive with downward acceleration (Gz < 1 g) and negative with upward acceleration. Pressure changes with the glottis closed were usually larger than with the glottis open.

Flow Studies

Unlike pressure signals, flow signals were much smaller with the glottis closed than open; flow at peak Gz with the glottis closed was <15% of that with the glottis open (Figs. 4 and 5). With the glottis open, flow in the first 40-100 ms of upward acceleration was inspiratory, and in the corresponding period of downward acceleration was expiratory (Figs. 5 and 6A). During this period, flow changed smoothly with acceleration (Fig. 4A and 6), but flow amplitudes at peak Gz were quite variable (Fig. 5). For example, in subject JK seated, flow varied almost threefold (0.32-0.83 l/s) whereas acceleration varied by only 20% (0.50-0.59 g).


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  		Fig. 4.   V during a drop (subject TH, standing). Arrows point to start of a drop (t = 0). Inspiratory flow is positive. Over the first 60 ms, flow was expiratory with downward acceleration to the first peak Gz, then inspiratory with upward acceleration. A: open glottis. After 100 ms, changes in flow did not closely follow changes in acceleration, although larger subsequent fluctuations generally followed those in Gz. B: closed glottis. Flow magnitudes were smaller than those with the glottis open.



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  		Fig. 5.   V at peak Gz during drops and lifts. Inspiratory flow is positive. For all subjects, upward acceleration (Gz > 1 g) was inspiratory, downward acceleration was expiratory. With the glottis closed, flow was less than with the glottis open. Initials in top left of each plot represent individual subjects.



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  		Fig. 6.   Gz and V during a drop (subject BB, standing). Drop begins at t = 0 s (arrow). A: over the first 0.1 s, flow was expiratory with downward acceleration to first peak Gz, then inspiratory with upward acceleration. After 0.1 s (arrow), flow no longer followed acceleration. B: flow vs. acceleration. Before 0.1 s, the curve was smooth. An abrupt divergence occurred at 0.1 s (arrow), at which time the curve changed direction and became crooked.

After ~100 ms, flow no longer changed smoothly with acceleration (e.g., Fig. 6A). When flow was plotted against acceleration, two parts of the curve could be distinguished (Fig. 6B). In the first 50-100 ms, the trajectory of flow vs. acceleration was smoothly curved, but then it diverged unpredictably from its former smooth path. In subject BB, abrupt divergence occurred at ~100 ms in all five trials (Fig. 7). The abruptness of the divergence and its timing (starting at 60-160 ms) varied within and among subjects.


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  		Fig. 7.   V vs. Gz during drops (subject BB, standing). All 5 plots during drops show an initially smooth curve followed by an abrupt divergence of flow from acceleration at ~0.1 s. The subsequent trajectory was inconsistent among trials.

EMG Studies

To explore the possibility that reflex muscle activity caused flow to diverge from its smooth trajectory with acceleration, we measured EMG activity of rib cage and abdomen during drops and lifts to address the following questions: 1) Does reflex activity of respiratory muscles occur soon enough to affect flow before maximum acceleration, which occurs at 38-56 ms? 2) Could reflex activity account for the abrupt divergence at ~100 ms?

We retrospectively determined the latencies between the start of acceleration and the first apparent change in EMG signals. The time of change in the EMG signals was determined without reference to acceleration or flow records. Changes in rib cage and abdominal muscle activity were easy to discern in most trials (e.g., Fig. 8A). When the onset of a change in muscle activity was less clear (e.g., RC-EMG in Fig. 8B), records were read several times, and the reported latency was the one most consistently determined. Most rib cage and abdominal muscle latencies were clustered between 40 and 125 ms (Fig. 9). Latencies associated with the less distinct changes in EMG were often longer than 125 ms, and occasional sporadic EMG bursts were observed at times clearly unrelated to acceleration (e.g., 5 ms before a lift).


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  		Fig. 8.   Rib cage (RC) and abdominal (Ab) electromyographic (EMG; RC-EMG and Ab-EMG, respectively) activity with acceleration. Onset of change in EMG activity (arrows) was determined without seeing acceleration and flow records. A: drop in subject SL. Latencies of RC-EMG and Ab-EMG activity were 92 and 79 ms, respectively. B: lift in subject MC. EMG latency was more difficult to determine: 347 ms for RC-EMG and 71 ms for Ab-EMG. (Note: different time scales.)



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  		Fig. 9.   RC-EMG and Ab-EMG latencies. Latencies during drops and lifts for 3 subjects were mostly between 40 and 125 ms.

Model Simulations

The mathematical model of a passive respiratory system, with parameters based on typical physiological values from the literature and typical anatomical measurements, simulated a passive response to various accelerations similar to those in the literature and the present study.

Transient acceleration. Model simulations with initial parameter values predicted prominent expiratory flow with downward acceleration and inspiratory flow with upward acceleration. This behavior was similar to that observed in our subjects during the first 40 ms of drops and lifts. We improved the model's ability to fit the data by adjusting its least certain parameter values: the masses of the rib cage (mrc) and abdomen (mab), and the angles of their respective motions (alpha  and beta ). Using the optimizer feature of a spreadsheet (Quattro Pro), we minimized deviations between model simulations and the measured flow and acceleration during the initial 104 ms in each of the 5 drops in Fig. 7. We constrained alpha  to lie between 0 and 90 degrees and beta  between 90 and 180 degrees (see APPENDIX). After parameter optimization, the fit to the data was excellent (e.g., Fig. 10). However, we could not use our model and data to determine the parameter values with any certainty. For example, the first trace in Fig. 7 could be equally well simulated with mrc of 1,402 or 2,773 g, and the third trace could be fit with mrc values of 523, 925 or 1,333 g and alpha  values of 0 and 82 degrees. In many of the runs from all subjects, parameters could not be optimized without driving alpha  or beta  to their limits. Thus the values of parameters above should be taken as adequate for simulation, but not unique. On the basis of these optimizations, we made small changes to the standard values of alpha  and mab, and all simulations below were done with these standard values (Table A1).


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  		Fig. 10.   Predicted and measured V during a drop. During the first 40 ms, including time at peak acceleration, experimental and simulated flows were similar. Optimization of the parameters resulted in a close fit (predicted curve). See text.

Oscillatory acceleration. For sinusoidal oscillations of 0.5 g amplitude at 8 Hz, the model predicted a sinusoidal flow with an amplitude of 318 ml/s. Inspiratory flow lagged upward acceleration by 73 degrees.

Steady-state acceleration. In simulations of steady-state changes in gravitational acceleration and body position, the model predicted changes in lung volume and chest wall configuration qualitatively consistent with data from the literature (Table 2). When Gz increased from 1 to 2 g, the model predicted a net increase in lung volume (VL) of 0.16 liter [rib cage volume (Vrc) decreased by 0.25 liter and abdominal volume (Vab) increased by 0.40 liter]. This linear model predicted symmetrically opposite changes from 1 to 0 g. The transition from upright to supine caused a decrease in lung volume of 0.55 liter (Vrc increased 0.19 liter and Vab decreased 0.75 liter).

                              
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  		Table 2.   Model predictions and literature values for changes in volumes caused by steady-state changes in gravitational acceleration


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

We found that during the first 40-100 ms of a drop or lift, upward acceleration caused inspiratory flow and downward acceleration caused expiratory flow. After the initial 100 ms, flows were highly variable, apparently because of respiratory muscle activity initiated by the drop/lift. Our model of a passive respiratory system undergoing transient axial acceleration predicted transient flows that were similar to those measured in our experiments before 100 ms, and it simulated steady-state changes in lung volume consistent with published effects of steady-state changes in acceleration, gravity, and position.

Flow Studies

As acceleration increased to peak amplitude, respiratory flows were consistently inspiratory for upward acceleration and expiratory for downward accelerations for all subjects, standing and seated. Flow amplitude increased smoothly with acceleration until acceleration reached a maximum at ~40 ms. Because bursts of EMG activity were rarely seen before this time, muscle reflexes are unlikely to have affected flows at peak acceleration. However, flows at peak acceleration varied by a factor of three within some individuals, possibly because of variations in glottal opening or the level of tonic activation of trunk, postural, or other muscles. Although subjects panted to keep the glottis open (5), glottal opening at maximum acceleration probably varied. Even in those subjects who were most experienced in respiratory maneuvers (SL and BB), complete inadvertent glottal closure occasionally occurred, as evidenced by markedly reduced flows. Differences in tonic activation of various muscles may also have affected the amplitude of respiratory airflow by changing the effective compliances of the abdomen, diaphragm, and rib cage.

Changes in transrespiratory pressure during the first 100 ms of acceleration were consistent with flow data; upward acceleration caused a decrease in mouth pressure and consequential inspiratory flow, whereas downward acceleration caused an increase in mouth pressure and expiratory flow. Although we could not easily identify pressure records affected by inadvertent glottal closure, the consistency of these results supports the hypothesis that upward acceleration is inspiratory.

Reflexes

After 60-100 ms, respiratory muscle reflexes (reviewed in Ref. 13) could have caused the abrupt and variable changes in flow we observed. Spinal reflexes have sufficiently short latencies, with a typical time from stimulus to muscle EMG response on the order of 50 ms. The time from activation of respiratory muscle to the onset of flow at the mouth also appears to be on the order of 50 ms, as inferred from electrical stimulation of abdominal muscles and magnetoelectric stimulation of the phrenic nerve (unpublished observations). Thus 100 ms is a reasonable time for the first appearance of flow caused by reflexes.

The variation of flow amplitude and pattern of response to acceleration (see Fig. 7) is consistent with reflexive action. Unlike the stereotypical response seen with simple reflexes under tightly controlled conditions, the reflexive response in our experiments was modulated by the background state of neural and muscular activity at the time of drop or lift (posture, degree of respiratory muscle activation, joint position, etc.; e.g., see Ref. 2). Thus variability in the response was to be expected.

Comparison With Previous Studies

Our experimental results contradict the conclusions of Wilson, Liu, and co-workers (8, 15) that upward acceleration is expiratory. Liu et al. (8) used the vertical force exerted by subjects performing respiratory maneuvers to calculate the gravitational potential energy of the rib cage and abdominal masses, and they inferred that the expiratory gravitational pressure acting on the rib cage and the inspiratory pressure acting on the abdomen were of similar magnitude, ~8 cmH2O. Later, Wilson and Liu (15) reasoned that, because the rib cage is more compliant than the abdomen, gravity would cause a greater decrease in rib cage volume than increase in abdominal volume, thus producing a net expiratory effect. They found support for this prediction by measuring changes in airway pressure in subjects riding in an elevator. They suggested that their findings could have differed from previous results because of an alinear response of the respiratory system to acceleration (their elevator accelerated at only ±0.16 g, unlike parabolic flight and centrifuges, which change Gz by ~1 g) and because their measurements had been in a closed respiratory system instead of in breathing subjects. Our data suggest that their measurements, made after 1 s of steady acceleration, could have been affected by reflexes, and their use of pressure as a measure of respiratory response could have been affected by glottal closure during apnea.

Zechman et al. (16) applied periodic, quasi-square-wave and sinusoidal vertical displacements to subjects seated on a platform and measured the resonant frequency and damping coefficient of the respiratory system. Like previous investigators, they analyzed the respiratory system as a passive mechanical system, and the resonance and damping they observed may have been affected by reflexive muscular activity, which they did not discuss. Furthermore, because they did not explicitly deal with the question of whether upward acceleration is inspiratory or expiratory, their work does not directly address the central point of the present study, nor do their published data give a clear answer to this question.

Model Predictions

Transient acceleration. With parameters optimized, the simulations fit data from our experiments (Fig. 10), supporting the hypothesis that transient upward acceleration is inspiratory.

Oscillatory acceleration. For oscillatory acceleration of 0.5-g amplitude at 8 Hz, the model predicted an oscillatory flow amplitude of 318 ml/s, approximately half the average value reported in eight normal subjects by Zechman et al. (16).

Steady-state changes in acceleration. Our model predicted changes in lung volume with changes in Gz similar to those described in humans at relaxed FRC undergoing postural change from upright to supine (1) and changes in G force during parabolic flight and in centrifuges (3, 4, 10). It is likely that subjects in those studies were relatively relaxed and that changes in lung volume during those steady-state changes reflect the characteristics of the relaxed chest wall. For changes of Gz from 1 to 0 g, the decrease in FRC was ~200 ml in all studies except for the study by Paiva et al. (10). Edyvean et al. (3) suggested that the greater decrease (~400 ml) in Paiva's subjects was probably caused by taping their shoulders to a back support, limiting rib cage expansion. In the absence of these shoulder straps, subjects, including some who had participated in the earlier study, experienced a smaller decrease in FRC of 240 ml on average (3), closer to the 210 ml in the study by Prisk et al. (11) and the 160 ml predicted by our model.

For change from upright to supine posture, our model predicted a net decrease in lung volume of 0.55 liter, about half Agostoni and Mead's (1) finding of ~1.0 liter. Our model also predicted an increase in rib cage volume, i.e., opposite to the effects of gravity on an isolated rib cage, a result also inferred by Agostoni and Mead. In the model simulation, the mechanism of this increase is an inward movement of abdominal mass, which causes a decrease in lung volume, an increase in pleural pressure of 2.8 cmH2O, and an outward displacement of the rib cage.

In 1948, USAF Lieutenant Shaw studied the effects of downward (negative Gz) acceleration in seated humans and proposed that the forceful exhalation caused by such acceleration was mediated by a cephalad displacement of abdominal viscera and diaphragm (14), a phenomenon since referred to as displacement of the "visceral piston." The net inspiratory effect of transient upward acceleration in our experiments is consistent with such a model in which the inspiratory effect of downward gravitational force on the abdominal viscera dominates over its expiratory effect on the rib cage. Our model parameters provide rough estimates of the magnitudes of the gravitational forces on the rib cage. In particular, the value of g · mrc · cos(alpha )/Arc is the gravitational force on the rib cage (Pgrc), and g · mab · cos(beta )/Aab is the gravitational force on the abdomen (Pgab). From the fits to the data, we obtain the following estimates for these forces: Pgrc approx  1 cmH2O and Pgab approx  -9 cmH2O. The value of Pgab is near the value of -8 cmH2O reported by Liu et al. (8), but the value of Pgrc is considerably smaller than their value of 8 cmH2O. Thus, taking into account the fact that the compliance of the rib cage is three times that of the abdomen, we conclude, contrary to Liu et al., that the expiratory effect of the force on the rib cage balances ~30% of the inspiratory effect of the force on the abdomen and that the net effect of gravity on the chest wall is inspiratory. This conclusion is consistent with data on the shift in FRC during brief periods of weightlessness and hypergravity in parabolic flights (Table 2).


    APPENDIX
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

We modeled the respiratory system with two moving masses [rib cage and abdomen (rc and ab, respectively)] that slide as pistons in cylinders oriented at angles to the body axis (Fig. A1). Muscles, which are passive viscoelastic elements characterized by a stiffness and a viscous damping coefficient, constrain each mass. (Parts of the diaphragm are incorporated in both rib cage and abdominal muscle groups.) An elastic lung, bounded by the two masses, contains compressible gas that is vented to the atmosphere through an airway, which is characterized by an inertance and resistance. Movements of the pistons cause compression or decompression of gas, which causes flow through the airway. The structure is anchored to an axially accelerating spine.


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  		Fig. A1.   Model of a respiratory system under axial acceleration. Rib cage and abdominal masses (hatched) slide in cylinders that are angled with respect to the spin at angles alpha  and beta , respectively. A passive muscle restrains each mass. An elastic lung surrounds gas that is compressed by movements of the masses to flow through the airway. Positive directions for displacements are shown.

The net force (F) on each mass (m), which determines its acceleration, is the sum of the forces due to the gas, lung elastance, elastic and resistive components of the muscles of the rib cage (rcm) and abdomen (abm), and axial acceleration. Thus for the rib cage mass
F<IT>=</IT>m<A><AC>x</AC><AC>¨</AC></A>rc<IT>=</IT>(P<SC>g</SC>Arc)<IT>−</IT>(Pel,<SC>l</SC><IT> A</IT>rc)<IT>−</IT>(Krcm xrc)<IT>−</IT>(Rrcm <A><AC>x</AC><AC>˙</AC></A>rc)<IT>−</IT>m<A><AC>x</AC><AC>¨</AC></A><SUB>s</SUB> cos <IT>&agr;−</IT>mG<SUB>z0</SUB> cos <IT>&agr;−</IT>mG<SUB>y0</SUB> sin <IT>&agr;,</IT>
and for the abdominal mass
F<IT>=</IT>m<A><AC>x</AC><AC>¨</AC></A>ab<IT>=</IT>(P<SC>g</SC><IT> A</IT>ab)<IT>−</IT>(Pel, <SC>l</SC><IT> A</IT>ab)<IT>−</IT>(Krcm xab)<IT>−</IT>(Rabm <A><AC>x</AC><AC>˙</AC></A>ab)<IT>−</IT>m<A><AC>x</AC><AC>¨</AC></A><SUB>s</SUB> cos<IT> &bgr;−</IT>mG<SUB>z0</SUB> cos<IT> &bgr;−</IT>mG<SUB>y0</SUB> sin<IT> &bgr;.</IT>
In the above equations, x, &xdot;, and &xuml; refer to displacements, velocities, and accelerations of rib cage (rc) and abdominal (ab) masses and of the spine (s), measured along the axes of the constraining cylinders and the axis of the spine, respectively. PG is pressure of the gas relative to atmospheric, and Pel,L is the elastic recoil pressure of the lung. Arc and Aab are projected areas of the masses perpendicular to the cylinder axes, and K and R are stiffness and viscous damping (resistance) coefficients of muscles. Krc and Kab are determined from known compliances (C), e.g., Krcm = Arc2/Crc. R is determined by assuming a ratio of R/K that gives damping characteristics of the respiratory system approximating experimental data. Gz0 and Gy0 are components of gravitational acceleration in the axial (cephalad) and dorsoventral (ventrad) directions, and alpha  and beta  are the angles of the rib cage and abdominal cylinders with respect to the spinal axis (Fig. A1).

The volume of gas in the lung (VL) is
V<SC>l</SC><IT>=</IT>V<SUB>0</SUB><IT>+A</IT>rc xrc<IT>+A</IT>ab xab<IT>,</IT>
the sum of an initial lung volume (V0) and the change in volume resulting from the displacement of the rib cage and abdominal masses.

The change in lung elastic recoil pressure (Pel,L) is
Pel,<SC>l</SC><IT>=</IT>(V<SC>l</SC><IT>−</IT>V<SUB>0</SUB>)<IT>/</IT>C<SC>l</SC><IT>,</IT>
i.e., the change in gas volume in the lung divided by lung compliance (CL).

Resistive and inertial characteristics of the airway (aw) determine flow caused by a pressure difference (PG) between gas in the lung and atmosphere
P<SC>g</SC><IT>=</IT>Raw <A><AC>V</AC><AC>˙</AC></A><IT>+</IT>Iaw <A><AC>V</AC><AC>¨</AC></A>
where V and V are flow and volume acceleration and I is inertance. Pressure difference (PG) between lung gas and atmosphere is determined by the difference between the quantity of gas, expressed as its volume at standard pressure (VG0), and its actual volume (VL)
P<SC>g</SC><IT>=</IT>(<IT>1−</IT>V<SC>l</SC><IT>/</IT>V<SC>g</SC><SUB>0</SUB>)<IT>/</IT>C<SC>g</SC>
where CG is gas-specific compliance, which is equal to the inverse of the ambient pressure (CG = 1/Patm). Values for the parameters of the model were taken from the literature, where possible; some were chosen on the basis of anatomical observation and physiological inference (Table A1).

                              
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  		Table A1.   Standard input parameters of the model

The change in position and velocity of the rib cage and the abdominal pistons and the change in quantity of gas were determined by continuous integration. We simulated transient acceleration by applying the accelerations (Gz0) observed in one of the drops (Fig. 10). We simulated steady-state changes from upright to supine positions by applying step changes in gravitational vectors (Gz0 and Gy0), and we simulated whole body axial vibration with 0.5 g oscillations in &xuml;s at 8 Hz.

We analyzed the sensitivity of the model to its parameters by varying each parameter individually and determining how the simulations changed. For transient and steady-state changes in acceleration, a variation of +25% or -20% in most parameters caused only minor changes in the outcome variables, which were generally within 20% of the standard values, and did not qualitatively affect the simulations. The exception was a change in the angle of abdominal displacement beta , which changed the direction of flow during transient acceleration, and the sign of the change of rib cage volume (Delta Vrc) during transition from upright to supine. For sinusoidal oscillations at 8 Hz, a variation of +25% or -20% in all parameters produced small to moderate changes in flow amplitude (<50%) and variations of phase within a narrow range (within 30°). As with transient and steady-state accelerations, the model was most sensitive to the angle of abdominal displacement (beta ). In all simulations, peak inspiratory flow lagged peak upward acceleration.


    ACKNOWLEDGEMENTS

We thank Prof. Theodore A. Wilson for suggestions concerning interpretation of the model simulations.


    FOOTNOTES

This work was supported in part by Grant HL-07118 from the National Heart, Lung, and Blood Institute and by Beth Israel Anesthesia Foundation.

Address for reprint requests and other correspondence: S. H. Loring, Anesthesia & Critical Care, DANA-717, Beth Israel Deaconess Medical Center, 330 Brookline Ave., Boston, MA 02215-5491 (slor{at}chest.bidmc.harvard.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 26 April 2000; accepted in final form 3 January 2001.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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J APPL PHYSIOL 90(6):2141-2150
8750-7587/01 $5.00 Copyright © 2001 the American Physiological Society


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