Video and ciné films of mammals running at the trot-gallop transition were analysed to measure breathing frequencies. Breathing frequency at the trotgallop transition (fb, in Hz) was shown to decrease with increasing body mass (M, in kg) and was described by the equation fb=5.08M-0 14. The stiffness of the thorax and diaphragm of mice, rats, rabbits and wallabies was calculated and this, together with the mass of the viscera, was used to calculate the natural frequency of the system (nft, in Hz). The relationship between nft and body mass can be described by the equation nft=5.02Mf-0.18. The significance of these results is discussed in relation to models of mechanical linkage between respiratory and locomotory movements.
A linkage between breathing and locomotory movements has not been systematically investigated in terrestrial mammals, and small mammals have been neglected completely. There is thus no published evidence for a relationship between breathing frequency during galloping and body mass that would allow us to test the above hypothesis. The aim of the present study was to measure breathing frequencies in mammals of widely different sizes and to look for evidence of coupling between respiratory and locomotory movements in small mammals.
Bramble and Carrier (1983), Baudinette et al. (1987) and Alexander (1989) have described a visceral piston mechanism in which locomotory accelerations cause oscillations of the abdominal viscera that, in turn, cause displacements of the diaphragm and so drive breathing. The frequency and the magnitude of these displacements will be determined by the mass of the viscera and the viscoelastic properties of the respiratory system. Crawford (1962) found that dogs pant at very constant frequencies, which he suggested might be the natural frequency of the respiratory system. He found that the panting frequency was the same as the ‘natural frequency of the respiratory system’ measured by mechanically ventilating anaesthetised dogs. He also estimated the stiffness of the diaphragm, and hence the natural frequency of the system, by measuring the displacement of the diaphragm produced by the weight of the viscera, from X-rays of dog cadavers taken in the head-down position. This produced quite different estimates and suggested at least a second mode of vibration of the respiratory system. The present study estimates the natural frequency of a ‘mass/spring’ system, where the viscera act as the mass and the elastic properties of the thorax and the diaphragm constitute the spring. This is related to body size, breathing frequency and stride frequency at the trot-gallop transition.
Recent studies have shown that phylogenetic and ecological effects may be important in determining many allometric relationships (e.g. Gompper and Gittleman, 1991; Nee et al. 1991; Promislow, 1991). We have not entered this controversy. Since we can draw apparently sound and informative conclusions without considering possible phylogenetic effects, we believe this validates our approach in this particular case. We do not deny that phylogenetic and ecological effects may play a role, but we do not think that such effects would influence the conclusions drawn.
Materials and methods
Measurement of breathing rate
The study was performed on mammals ranging in size from Mongolian gerbils (Meriones unguiculartus) (0.073 kg) to white rhinoceros (Ceratotherium simum) (1600 kg), running at speeds from just beyond the trot-gallop transition to a full gallop. The gerbil and horses (Equus caballas) running on a treadmill were just beyond the trot-gallop transition. Free-running horses were filmed exercising on a lunge at speeds just beyond the trot-gallop transition. Greyhounds (Canis familiaris) were running at a full gallop in a race. Rabbits (Oryctolagus cuniculus, mixed domestic), rhinoceros and the remaining dogs (labrador and mongrel) were galloping at some indeterminate speed. Since stride frequency at the preferred galloping speed and at the trot-gallop transition are described by very similar allometric equations (Heglund and Taylor, 1988), it was not important to control the exact galloping speed at which measurements were taken.
Ventilation and stride frequencies were derived from synchronized recordings of breathing flow and ciné film of racehorses exercising upon a treadmill (full details in I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, in preparation). A battery-powered camcorder was used to film the riderless, cantering standard-bred horses on cold days, so that the exhaled breath was also filmed. Similar video recordings were made of exercising dogs and free-running rabbits. The framing rate of the camcorder was checked by filming a stopwatch and timing the replay. Breathing frequency during galloping was obtained from film sequences in which breathing was clearly visible. High-speed ciné film of racing greyhounds and running white rhinoceros (courtesy of Professor R. McN. Alexander) was analysed on a photo-optical data analyser, and the breathing rate was determined from respiratory movements of the jaws (greyhounds) or nostrils (rhinoceros).
To investigate the possibility of locomotor/respiratory linkage in small mammals, gerbils were trained to run on a treadmill. The frequency and phase of the breathing and locomotory cycles just beyond the trot-gallop transition were obtained from video film, using a NACHSV400 high-speed video system (on loan from the SERC). With stroboscopic illumination, synchronised to the frame rate of the video system, respiratory movements of the nose could be filmed. The video film was taken at 200 frames per second, and the tape was analysed on the video processor frame by frame.
Smaller mammals (gerbils-dogs) were weighed, and the masses of the horses were estimated by experienced owners, or measured in the case of those running on the treadmill. Mean masses of the individual greyhounds analysed were taken from Jayes and Alexander (1982) and of the three rhinoceros from Owen-Smith (1988).
The numbers of animals used in the analysis were as follows (with mean mass in kg): gerbils 1 (0.073); rabbits 3 (2.72); dogs 4 (28.1); horses 6 (500); white rhinoceros 3 (1600). Of the six horses, three were free-running and three ran on the treadmill. Allometric relationships were determined from species means of body mass and breathing frequency. Mean breathing frequency ±s.E. values for each species are given in the text. Values for each individual are the means of at least six experimental runs: intra-individual variation was less than intraspecific variation. Measurements were taken while animals were running steadily, with no change in gait, when breathing frequency showed no tendency to increase or decrease.
Measurements of the mechanical properties of the intact thorax
Measurements were carried out on 11 mice (Mus musculus, white laboratory, mean mass±standard error=0.026 ±0.001 kg), nine rats (Rattus norvegiens, white laboratory, 0.23±0.02kg), one rabbit (Oryctolagus cuniculus, laboratory, 4.5 kg) and four red-necked wallabies (Macropus rufogriseus, 16.13±1.25 kg) of known mass. Mice and rats were killed by cervical dislocation, the rabbit by a fatal dose of KC1 when under anaesthetic (after use by other researchers for different purposes). Wallabies were zoo specimens that had to be shot because of injury or illness. Fresh and previously frozen specimens were used with similar results. In all cases, the viscera were removed from the abdomen and weighed. To measure the elastic properties of the thorax and diaphragm of mice and rats, the thorax was pinned down to a dissection board (Fig. 1A). Awls pinning the lumbar spine, the dorsal abdominal musculature, the cervical vertebrae and beneath the axillae prevented lateral movement of the trunk but allowed free movement of the rib cage. An isometric force transducer (natural frequency 90Hz, compliance errors <5 %), with a large, blunt probe attached, and mounted on a micromanipulator, was manoeuvred until just touching the abdominal face of the diaphragm and withdrawn until the force was zero. The end of the probe was modelled (from airsetting modelling clay) to make it as wide as possible so that, without touching the rib cage, it would contact a large area of the diaphragm, thus minimising stress concentrations. The resisting force of the thorax and diaphragm was measured as the probe was moved against the diaphragm in 0.5 mm increments.
Measurements of stiffness were obtained from the rabbit and wallabies by dissecting out the thorax, together with the intact diaphragm and mounting it diaphragm uppermost in a stiff-walled container (Fig. 1B). The thorax rested upon its vertebral column with the anterior (rostral) processes of the first thoracic vertebra cut to provide a flat base on the bottom of the container and the most posterior (caudal) thoracic vertebrae resting against its side. In the case of the wallaby, the bottom of the container was filled with plaster of Paris to a depth of about 2 cm to prevent slippage. This positioning allowed the rib cage and vertebral column to bend when the diaphragm was loaded, without apparent impedance by the walls of the container. The container was placed upon a pan balance, which was then balanced to read zero, and loads were imposed upon the diaphragm by bringing a round-ended probe upon a manipulator to bear upon its upward facing surface. The diameter of the head of the probe was made as large as possible without touching the rib cage, to reduce the risk of stress concentration. The loads upon the diaphragm displaced the pan balance from zero; the weight required to counter this equalled the force upon the diaphragm due to the imposed displacement, which was measured on the vernier scale of the manipulator.
In Fig. 2 (see also Table 1), breathing frequency (species means) at the preferred galloping speed (fb) is plotted against body mass (M) on logarithmic axes. The relationship between fb and M may be described by the allometric equation:
Summary data for individual species given as [mean fb (HZ)±S.E. (N)] were as follows: gerbils=7.85 (1); rabbits=3.92 ±0.03 (3); dogs=3.20±0.11 (4); horses=2.10±0.04 (6); white rhinoceros=2.02±0.03 (3).
Linkage of locomotion and breathing
A rigorous analysis of the linkage between locomotion and breathing has been performed on the horse (I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, in preparation). This demonstrated a rigid 1:1 coupling (Fig. 3A), the possible mechanical benefits and underlying mechanisms of which are discussed by I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson (in preparation) and below in the Discussion. Briefly, the phase relationship between the respiratory and locomotory cycles indicates that breathing may be assisted by flexion of the lumbo-sacral joint during running, but is unlikely to be assisted by oscillations of the viscera against the diaphragm (I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, in preparation). Analysis of the video film of the exercising gerbil also showed a tight 1:1 locomotor/respiratory coupling and a very similar phase relationship. The nares opened at the same time (or within 20 ms after) as the forelimbs impacted with the treadmill (Fig. 3B). The error involved in estimating the timing of the respiratory events was small (<10ms). Errors in estimating the timing of limb movements were smaller (<5 ms). Forelimb impact coincided with the end of the flight phase of the stride. During the flight phase the back and limbs were extended. After the forelimb impact the back was flexed and the hindlimbs were drawn anteriorly for the next stride. The observed timing of the opening and closing of the nares was consistent with the gerbil breathing out while the back was flexing, and breathing in while the back and limbs were extending. In the case of the rhino, the nares were observed to open and close once per stride, but film quality was not adequate for determination of the exact phase relationship with locomotory movements. 1:1 coupling of breathing and locomotion in rabbits and dogs is already well documented (Bramble and Carrier, 1983).
Natural frequency of the viscera, thorax and diaphragm
In Fig. 4, force versus displacement curves are shown for the rat diaphragm, which are typical for all species measured in this experiment. Stiffness was determined from these characteristic ‘J-shaped’ curves by fitting a model 1, leastsquares linear regression (all r2>0.98). Stiffness values for the four species given as [mean±s.E. Nm-1(N)] were as follows: mouse=23.2±5.6 (11); rat=41.6±11.8 (9); rabbit=576 (1); wallaby=1060±230 (4). A logarithmic plot of the natural frequency of the viscera, thorax and diaphragm (species means) as a function of log body mass gives a relationship described by the equation:
The following variables all show a similar dependence on body mass in terrestrial mammals: stride frequencies at the trot-gallop transition (fs) and the preferred galloping speed (fp, Heglund and Taylor, 1988), breathing frequency during galloping (fb, this study), oscillatory work frequency for maximum muscle power output of the diaphragm (fopt, Altringham and Young, 1991) and the natural frequency of the diaphragm, thorax and viscera (nft, this study) (Fig. 6, Table 1):
It has been suggested that coupling between respiration and locomotion could be due to a mechanical linkage (Bramble and Carrier, 1983; Baudinette et al. 1987; Alexander, 1989). This linkage may be attributable to a ventilation mechanism driven by locomotory movements. Bramble and Carrier (1983) described three possible mechanisms that may be responsible for this linkage: the visceral piston, flexion of the back and loading of the thorax by the forelimbs. Alexander (1989) suggested that breathing may be driven by the visceral piston mechanism in the wallaby and by flexion of the back in the horse. The experiments by I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson (in preparation) on the horse also indicate that back flexion, rather than the visceral piston mechanism, is assisting breathing.
In the visceral piston mechanism, the viscera are regarded as a mass suspended on an internal spring, representing the diaphragm and the thorax. During running, accelerations act upon the trunk, causing displacements of the viscera relative to the body wall. The size and phase of these oscillations depend on the mass of the viscera and the viscoelastic properties of the viscera and the respiratory system. Alexander (1989) suggested that the visceral piston could drive ventilation if its natural frequency were tuned to the frequency of the movements of locomotion. Flexion of the back and the resulting forward sweep of the pelvis with each stride push the viscera towards the diaphragm, compressing the lungs (Alexander, 1989; I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, in preparation). For this mechanism to operate, back flexion must have the same frequency as breathing. As inertial losses are minimised at the natural frequency of a spring/mass system, the back flexion mechanism may operate more efficiently if the predicted natural frequency of the diaphragm/thorax/viscera has the same frequency as stride and breathing. Stride frequency, breathing frequency and the predicted natural frequency of the diaphragm/thorax/viscera have been shown to obey the same allometric relationship. This is consistent with the hypothesis that the visceral piston and the back flexion mechanisms could be assisting ventilation. The mechanical properties of the respiratory system allow either of these mechanisms to operate, but the evidence from Alexander (1989) and I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson (in preparation) shows that the precise phase relationship between locomotory movements and breathing will determine which (if either) of these mechanisms may assist breathing.
In addition to passive mechanical properties, the active properties of the respiratory muscles must constrain the normal physiological operation of the respiratory system. Immediately after the trot-gallop transition, stride frequency (Heglund and Taylor, 1988) and breathing frequency (Bramble and Carrier, 1983) are essentially maximal, increasing only slightly with speed. Increases in ventilation are achieved by increasing its depth; diaphragm muscle should therefore be operating at its maximal in vivo frequency and strain during galloping. If systems evolve towards optimum design, then it is not unexpected that diaphragm muscle should produce its maximum power output at the galloping frequency (Altringham and Young, 1991), when the demands on the respiratory system are greatest.
In conclusion, the results of this study extend the size range of animals in which a 1:1 stride to breathing frequency ratio is observed during galloping to include the gerbil at one end of the range and the rhinoceros at the other. We also show that the gerbil maintains a constant phase relationship between locomotion and ventilation, indicating mechanical linkage. The observed mechanical properties of the respiratory system support the hypothesis of optimal design in the processes driving respiration during locomotion.
We would like to thank Professor R. McN. Alexander for many helpful discussions, and comments on the manuscript, and Chris Smith for technical assistance and cream eggs. Thanks also to Professor John Kessler and Professor Tim Pedley, and the SERC, for the use of the high-speed video camera system. The manuscript was substantially improved by the suggestions of two referees. I.S.Y. was supported by a SERC grant.