HEART RATE OF THE LAND CRAB, CARDZSOMA GUANHUMZ (LATREILLE), DURING AQUATIC AND AERIAL RESPIRATION GHULAM M. SHAH and’ CLYDE E. HERREID II Department of Physiology, Medical College. Shrinagar, Kashmir, India, and Department of Biological Sciences, State University of New York at Buffalo, NY, U.S.A. (Received 8 August 1977) Abstract-l. EKG’s were obtained on the land crab Cardisoma g~u~~~~j. The heart rate after electrode implantation was initially high. (Rates up to lOO/min were measured.) Within I.5 hr after implantation. rates reached 80/min and I5 hr later, averaged 7O/min. 2. A diurnal rhythm in heart rate appeared, with rates highest in the late afternoon and evening. 3. Periods of brief cardiac arrest were common and without known cause. Cardisoma were not particularly sensitive to tactile and visual stimuli; heart rate did not change with mild disturbances. 4. Heart rate was not a function of body weight. 5. Submergence of Cardisoma in normoxic water typically caused a brief tachycardia, followed by a bradycardia. Bradycardia may be a response to the relatively lower levels of oxygen in water compared to air. When crabs re-emerged from water, heart rates rapidly rose to resting levels or above, suggesting a possible response to payment of an O2 debt. 6. Heart rates of crabs submerged in 50% seawater were lower than those submerged in freshwater, 25”’0 and lOIF0 seawater.
INTRODUCTION
The cardiovascular system in decapod Crustacea is poorly understood. The anatomy of the system has only been studied generally in a few species and little info~at~on is available about the basic physiology (Maynard, 1960). The paucity of information has become particularly apparent in recent years, as investigators have become interested in the respiratory system of crabs. With the development of a general theory of aquatic gas exchange (Hughes, 1963; Rahn, 1966; Steen, 1971; Dejours, 1975) and the increasing knowledge of fish respiration, several investigators have applied these principles to respiration in crabs with considerable success (Johansen er al., 1970; Howell et n/., 1973; Taylor, 1976). Nevertheless, it has been clear from such reports that there are great gaps in our knowledge about the role that the cardiovascular system plays in respiration. For instance, we have almost no information about the flow patterns and hemodynamics in the open circulatory system of crabs. Also, considerable controversy exists about the extent to which blood is saturated with oxygen in the prebanchial and postbranchial blood (compare the reports of Redmond, 1955 and Larimer, 1964 with those of Johansen et af., 1970, Taylor rr ai., 1973 and McMahon & Wilkens, 1975). The crustacean heart has received considerable attention. Heart beat frequency has been studied in numerous Crustacea with the conclusion that alterations in heart rate occur readily with changes in the environment. Tactile ‘and visual stimuli influence heart rate significantly. Temperature, Pco,, PO, and the salinity of the water all can have an impact upon the EKG pattern and heart rate of aquatic crabs. (See Maynard, 1960; Larimer, 1962; Ashby & Larimer, 1964; Larimer & Tindel, 1966; Florey & Kriebel,
1974; Hill & Koopowitz, 1975; Hume & Berlind, 1976). Air-breathing crabs have received little attention. Studies of the coconut crab, Birgus, and the land crab, Gecarcinus later& (Cameron, 1975; Cameron & Mecklenburg, 1973) have provided some information about the respiratory system, but little is known about the cardiovascular system of these species. Nor is there much data on those amphibious crabs capable of surviving in both air and water, although several important contributions have been made on the intertidal form, Car&us maenus {e.g. Ahsanullah & Newell, I971 ; Taylor et at., 1973 ; Hume & Berlind, 1976; Taylor, 1976). In view of the need for basic information about crabs, and especially those that are air breathers or amphibious, the purpose of this paper is to measure the heart rate of the crab Cardisoma guanhumi (Latreille) under various environmental conditions. This land crab exists as a ominivore in tropical areas and is found in only a few locations in the U.S.A., most notably southern Florida (Gifford, 1962; Herreid & Gifford. 1963). Although primarily an air breather, Cardisoma enters water readily and must periodically moisten its gills in water at the bottom of its burrow in order to survive. As one of the examples of biomodal breathers in the Crustacea, Cardisoma is of interest for several reasons. It moves back and forth from an aquatic to aerial environment with apparent ease. Also, it experiences great differences in salinities without obvious effect. Herreid & Gifford (1963) reported that water at the bottom of their burrows can be either fresh- or seawater and that the crabs enter the ocean as well as canal-water near their burrows. What effect these changes have upon the crab’s respiratory and cardiovascular systems are of interest. Hence, in this paper we report
335
336
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on the basic resting heart rate of crabs. its diurnal variation and the response to air and water encironments of different salinities.
MATERIALS
AND
METHODS
The experiments were conducted on the land crab c‘~rdi.~~~~u guunhumi obtained from Southern Florida. well acclimated to the laboratory environment. All animals were males. with weights ranging from 90 to 19Og and a carapace width of 6&10cm. They were housed in large aquaria which contained 46 in. of moist dirt and sand. A large pan of 25”,, seawater was provided as the source of water. The temperature of the aquarium ranged from 24 to 27’C. They were fed twice weekly with lettuce, puppy chow. egg shells and occasionally clams. Elrctroc~urdiogrupkic
srudim
The location of the heart can easily be determined bq certain naturally-occurring surface markings in the crab. There is an obvious transverse groove limited at each end by a longitudinal groove in the dorsal carapace just anterior to the heart. Electrocardiograms were obtained by a pair of steel electrodes. 5-6 mm long, made from steel insect pins soldered to 22.gauge, stranded. shielded copper wire leads. Two holes. one above the middle of the heart and another 0.5-I cm anterior or posterior 10 it. were drilled in the carapace just short of completely piercing the shell to prevent leakage of hemolymph. but such that the electrodes could easily pierce it. The electrodes were than inserted into the holes and quickly sealed with sticky wax. The leads were held in position by adhesive tape to prevent drag on the electrodes and accidental pulling out by the animal during experimental maneuvers. Once the electrodes were implanted. the crab was placed m a IO-I. Plexiglas box covered on all sides with opaque paper to obscure visual stimuli. The EKG leads were brought out through a hole in the center of the lid of the box and connected to a Gilson MP5 Polygraph, where a differential recording between electrodes was obtained. The crab was free to move during the course of the experiments. Most EKG determinations were made on C‘clrdi.sotnu resting In air for variable periods of time specified in the results section. During such tests. room air was passed into the crab’s box: the air was supplied from a compressor and the flow was regulated at 625 mlimin by a calibrated flow-meter. In those experiments where it was necessary to submerge the crab, water was gradually passed into the crab’s box via a tube entering near the bottom of the box. The water gradually filled the box covering the crab completely in about IOmin. Water could be rapidly drained from the box in about IOmin. In those experiments where water of dlfferent salimties was tested. the following procedure was used: after implantation of EKG electrodes. the crabs were allowed to rest in the test box overnight. Approximately I6 hr later. resting heart rates were monitored for 1hr. Aerated water of a particular salinity was gradually added to the tank. submerging the crab for I hr. After the water was drained away. the crab rested in air for I hr before water of another salinity was fed into the tank. This procedure was followed for several test salimties; the number varied in different experiments. “Instant Ocean” was used to make up solutions of different seawater concentrations using a dechlorinated freshwater source. Air was bubbled into the water supply through an air stone for 2 hr before the run and throughout the period of submersion. All experiments were carried out at room temperature of 24-27°C. with water at the came temperature.
HESI
Resting
hcurt
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md
1.1’S
Eh G pur~~~rtr
Electrocardiograms \arh. depending upon thr placement of electrodes in the crab (e.g. Ozawa (‘I 111.. 1955: Dubuisson. l9.U: Larimer. 1962). In the present study we obtained monophasic records. such as those displayed in Fig. I. by positioning the first electrode over the heart and the second electrode 5 mm to I cm anterior to the heart. Biphasic records
were obtained when one electrode was placed above the middle of the heart and the second electrode wab situated 5 mm to I cm postrrior or lateral to the heart. Such voltage spikes represent EKG patterns and accompany heart contraction5 (Larimer. 1962). We have not attempted to explain the origin of the electrical changes. The number of major voltage spikes wcrc counted as the index of heart beat frequency. Immediately after implantation of the electrodes and handling of the crab. heart heat frcquenc) was high. reaching rates over l00!min on occasion. The rates commonly decreased to around X0 beatsimin within I.5 hr after implantation. When these crabs were tested on the following day. I6 hr after implantation of the electrodes. rates averaged about 7Olmin. although some individuals had rates as low as 50 or as high as XO/min. Such data reflect the commonlyobserved individual variahilit\ 111 heart rate seen among crustaceans. During long periods of recording we commonly found changes in EKG signal; generally the voltage spike decreased through time. Figure I displays records on a crab taken several hours apart. It is obvious that the spike amplitude on the last record is less than half of that seen in the EKG pattern taken 2 hr earlier. We do not know the cause of such a decline. Perhaps the electrodes are affecting the heart function, altering the stroke volume or electrical conduction pattern, or the heart may have shifted relative to electrode position. Alternatively. the performance of the electrodes might have been affected; possibly hemolymph clotting around the electrode tips could account for the amplitude shift. It is worth noting in this regard, that sometimes the record gradually disappeared completely : however. implantation of
recordings for each crab (A) Record obtained at 9 a.m.. 30 min after implantation of EKG electrodes. Heart rate = 77 beats/min. (B) EKG at 1Oa.m.. 1.5 hr after electrode implantation. Heart rate = 63 beats/min. Note brief period of cardiac arrest. (C) EKG at I I a.m.. 2.5 hr after electrode implantation. Heart rate = 69 beats/min. Note cardiac arrest. Also compare the amplitude of the spikes in records A. B and C. Fig.
I.
(Cardisomu
Electrocardiograph guanhumi).
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Heart rate in land crabs
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Fig. 2. Daily variation in heart rate of crabs in five experiments. Note the gradual increase of heart rate throughout the day.
new electrodes in slightly altered positions usually picked up a clear EKG pattern. Periods of apparent cardiac arrest (up to 15 set in duration) were noted in resting crabs. Figure 1 shows two such cases. In most instances, the EKG prior to the pause and just after the pause seems relatively unaltered; cardiac arhythmia does not seem to be evident. Cases of cardiac arrest seem to be the result of one or more missed heart beats. Although it is possible that the pause in the EKG record is the result of a recording anomaly, such records have been frequently obtained for Crustacea by many investigators and interpreted as cardiac arrest (Brandt. 1865; Jolyet & Viallanes, 1893 ; Johansen et nl., 1970; Florey and Kriebel. 1974; Stiffler & Pritchard, 1972). Heart rate varied in a consistent pattern during the day. As Fig. 2 shows, heart rate in the morning (16 hr after electrode implantation) was around 70 beats/ min. There was a gradual increase in frequency, with TIME
go.? 80-
the highest records occurring in the afternoon and early evening. All of the records were obtained in the laboratory setting, subject to variations in natural lighting. Although the records graphed in Fig. 2 are our most complete experiments on resting crabs, on many other occasions we noted distinctly higher heart rates in afternoon and early evening compared to rates obtained in the morning. Several investigators have shown that heart rate depends upon the body size of the crab (Schwartzkopff, 1955; Ahsanullah & Newell, 1971). When resting rates for C. guanhumi were related to wet body weight in these studies, no significant effect of body size was apparent. The least-squares regression equation was as follows: Y = 7.36 - 0.037 X where Y is heart beat in beats/min and X is in the body weight in grams. The standard error of the slope (0.076) and the correlation coefficient (0.114) indicate that there is little reason to suspect an important relationship between body size and heart rate in our specimens. However, the weights of the experimental animals only varied from 90 to 190 g and perhaps this conclusion would be modified with greater extremes in weight. Nevertheless, Spaargaren (1973) did not find a correlation between heart rate and body size in the shrimp. Effect
of submergenceon
heart rate
Several crabs were gradually submerged in water while their heart rate was monitored. On the basis of these pilot runs, where it appeared that a distinct bradycardia occurred when the crab was under water, more extensive experiments were established. Two such experiments are shown in Fig. 3. The procedure of the experiments required the EKG electrodes to be placed in position and the crab to be put into its test chamber for a period of equilibration. 16 hr later, in the morning, resting heart rates were established. Then aerated freshwater was run into the tank. After exposure for 1 hr, the freshwater was drained away and fresh air admitted for 1 hr. Solutions of 25% seawater, 50% seawater and 100% seawater were placed into the box for I-hr periods, always separated with a rest of I hr in air. That is, the crabs submer-
(hr)
I
1
is ?o&
2 60? 50-
s 40& a 3oY 20-
AIR
Fig. 3. Heart C.&P
ho 3n-c
FRESH WATER
AIR
25% SEA WATER
rate of 2 crabs sequentially exposed submerged in freshwater,
SEA WATER
100% SEA WATER
to air and water for I-hr intervals. 25, 50 and 100°/(, seawater.
The crabs
AIR
were
338
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and
gence in water was always preceded by a rest of I hr in air, and followed by 1 hr recovery in air. The order in which the various salinities were presented to the crab varied and did not have any noticeable influence on the results. Figure 3 displays two extremes in response to submergence. Crab C. with an initial low heart rate of around 40 beatsimin, showed rather striking changes in frequency with sequential exposure to air and water. Crab E, with an initial rate of near 75 beats! min. showed more modest changes. On the basis of these records, and others not shown, we may make the following generalizations. Cardisomu quankurni displayed great individual variability in their heart rate in response to the air and water submersion. Many crabs showed at least a slight trachycardia as water (regardless of the salinity) was admitted into the chamber. Frequently during this time the crab rose high on its walking legs in an apparent attempt to keep its respiratory openings (the Milne-Edwards opening and mouth parts) above water. After an initial tachycardia. heart rate usually fell during submergence. The change in rate was due to an increase in the interbeat interval. rather than to instances of cardiac arrest. In some cases, bradycardia was profound whereas in other instances the effect was minor (compare for example, the different responses of crabs C and E to freshwater.) Once water was drained from the crab’s chamber. there was generally a rapid increase in heart rate. If the previous bradycardia in water was profound, such as in Crab C, the heart rate in air seemed to rebound much more vigorously than if the bradycardia were modest. In most cases. the heart rate during recovery was at least as high and in many cases higher than the initial heart rate. This suggests that some compensatory tachycardia may occur when the crab reemerges into air. To obtain the heart rate in air just prior to submergence, 6 readings (at 5-min intervals) covering 30min were used. 12 readings (5-min intervals) were averaged to cover the period of 1 hr submergence. To obtain the rate during air recovery, the 6 readings (at 5-min intervals) for the 30min just after water was drained were used. Using this procedure, the hour’s rest in air after any period of submergence was arbitrarily divided in half, the first 30min was considered as the recovery period for the previous exposure to water. and the next 30min was considered the initial air exposure for the next submergence period. This procedure of data analysis admittedly masks individual it provides a variations seen in Fig. 2: nevertheless. more objective basis for noting the average effect of air and water exposure on heart rate. Figure 3 shows that there was an average modest bradycardia in all solutions tested. The standard deviations are rather high, reflecting the considerable variation among crabs and between readings of individual crabs, In spite of such variations there are statistically significant differences between the heart rates seen in air and in water. A comparison of the average heart rate seen in air just before exposure to water and during recovery reveals that the values are similar. However, in two cases---exposure to 25”,, and IOO”, seawater -the recovery rate was significantly higher than the initial rate (P < 0.05 and P < 0.01 respectively).
C‘LLI)I b. HIKKIII)
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:hc heal c I,,,~’ :‘/ Uo progrc\\l\ c patern is obvious. The heart ralc W;IXdcpres\ed h) .m average of 7 lo”,, in all 5alinille\ ~\cept To”, ‘,c‘~,water; in the latter. heart r;ltc \\;t\ i-~~ltrc~~lht. 3~’ from the initial rate In .iu Finally.
it is posslblc
tc) compari
C. pmhumi in different salinities.
Heart rate varies greatly among different C‘ardisortlcl yuanhurni and, from time to time. 111the same individual (Figs 2 and 3). Some of these differences can be attributed to changes in the cn~~ronmcnt. while other differences are prcsumahl> of endogenou\ physiological origin. One notable result of the stud) was that ImpIantation of the electrodes and handling of the crab> often lead to heart rates approaching or exceeding 100 beats/min. Within an hour or two after electrode implantation. the rates decreased to near X0 heats min; however, many hours of recovery were required to approach rates that we judge to be normal (50 70 beatsimin). Most investigators have ignored such periods of adjustment when they report on cardiovascular studies. Diurnal variations in heart rate should also be taken into account by physiologists. Ctrrdismm yuunhumi showed lower rates in the mid-morning than in the afternoon and evening. It is questionable whether such variations in heart rate can be realistically correlated with field behavior. Cc~v&~orntr arc most active in the evening hours. However. the experimental crabs had been maintained in the laboratory for months, under a combination of natural and artificial lighting. One must be cautious in assuming that the daily variations in heart rate seen in Fig. 2, reflect a normal state. Nevertheless. the data should make us alert as to the possibility of such variations and the influence they might have upon cardiovascular studies. Periods of apparent cardiac arrest were noted on many occasions (see Fig. I). The longest period of cardiac arrest in resting Curdisomu wah about 15 sec. Such circulatory pauses may have only a negligible effect on the metabolism. Johansen PI (I/. (1970) and Florey & Kriebcl (1974) have calculated thar period\ of cardiac arrest up to 3 mln should not impost :I significant effect upon the aerobic metabolism of the crab, Cuncrr. because of the oxygen rcscrw h&i m the hemolymph. Cardiac arrest is produced m home Crustacea by changes in environmental stimuli; although such change cannot be ruled out in the present experiments. no obvious changes wt’rc apparent which could be correlated with periods of cardiac arrest. In fact. in contrast to variou, other authors working with different specie.4 of crustaceans (moxt notably Larimer & Tindel. 1966: t‘lorc) 6i Krrchel. 1974), C. yuanh~rni appeared remarkabl) insensitive to visual and gentle tactile stimuli. Alteration\ in heart rate were not common in our experiments. even when the crab could see out of the ILW chamber Inlo the laboratory or when the laboratory bench on which the crab was resting was disturbed. HOU.IVX. it must be noted that these crabs had been maintained in such laboratory conditions for several months. and undoubtedly were habituated to minor disturbances
Heart rate in land crabs The importance of a change in heart rate to the total cardiovascular system in crabs is poorly understood. Since crabs have an open circulatory system without obvious modes of changing resistance, authors have argued that the circulatory system must be necessarily controlled exclusively via changes in the heart (e.g. Florey & Kriebel, 1974). In addition to such conjecture, another assumption made by many authors is that changes in heart rate reflect changes in cardiac output. There is little evidence for such an assumption, and in fact this view has been challenged. Florey & Kriebel (1974) suggest that the increase in heart rate seen in Cancer when placed into warm temperatures is accompanied by decrease in stroke volume and reduced cardiac output. They also discuss the implications of a change in EKG amplitude. An increased EKG spike may mean an increased force of contraction and a greater stroke volume, but data are few on this point. Therefore. caution must be exercised in interpreting changes in rate and amplitude such as those seen in Fig. 1. These caveats should be kept in mind in the ensuing discussion. Cardisoma guanhumi exist on land and are primarily air-breathers (Gifford, 1962; Cameron, 1975) although they are capable of breathing water (Standaerdt, 1970; O’Mahoney, 1977); however, their oxygen consumption in water is somewhat less (85%) than that in air. When C. guanhumi are gradually submerged, their first response is to try and avoid coverage of their respiratory openings, hence they rise out of the water as much as possible. These activities may be the cause of the brief tachycardia seen when water was admitted into the crab chamber (Fig. 3). Once the crab was completely submerged, a bradycardia developed. The extent of the bradycardia was variable-some individuals showed a mild response
Fig. 4. Heart rate of crabs exposed
339
and others a profound effect (Fig. 3). What stimulates bradycardia? Bradycardia has been reported when crabs are subjected to hypoxic environments. Ambient PO, levels obviously affect hemolymph PO1 and oxygen content. It has been argued that low oxygen levels are detected by internal sensors, and reflex inhibition of the heart occurs. Also. there is evidence that low PO, levels in the hemolymph inhibit the heart directly (Stiffler & Pritchard, 1972). It does not seem likely that differences in the Pco2 of the hemolymph can account for the changes in heart rate seen in water and air. even though it is known that there are differences in hemolymph Pco, of crabs in air and water (Howell et al., 1973; O’Mahoney & Herreid, 1974). The Pcol drops from 16.6 to 8.5 torr when the crab, Cardisoma, is moved from air to water for 48 hr (O’Mahoney, 1977). However, unpublished data by Shah & Herreid show that C. guanhumi do not alter their heart rate when the P,, levels in air are raised from 0.3 to 38 torr. Therefore, it seems most likely that the bradycardia seen in water was a response to decreased O2 levels. As mentioned above, the decrease in heart rate during submersion cannot be assumed definitely to mean a decrease in cardiac output. However, if stroke volume remained constant, then cardiac output would have decreased by about 89% in water as compared to air. Thus, the 85% reduction in oxygen consumption in water seen by O’Mahoney (1977) can be accounted for simply by a decrease in the change of perfusion rate of the tissues. For this to occur, the hemolymph would have to be equally saturated in air and water at these temperatures. Also, the arterial-venous difference in oxygen content would have to remain constant. Whether these assumptions are accurate must await further study. The heart rate rapidly increased after the crab
to water of various salinities. The bars represent the mean heart rate of crabs in air (30min) followed by submersion in water (60min) and during recovery in air (30 min). The numbers in parentheses represent the standard deviation of the readings. Students’ t-tests between air and water readings were significant at the P < 0.01 level.
C;H~ I AM M. SHAH and CLI r)t F. HI RHI I:) II
340
emerged from water into air. In many cases the rate exceeded the original resting rate. at least for a brief time. One is tempted to postulate that this represents an increased cardiac output used to pay off a minor O2 debt aquircd during aquatic respiration. Unpublished data by Herreid. Shah & O’Mahoney show a similar cardiac rebound when Cardisorttu are removed from hypoxic conditions into air. Accompanying this tachycardia is a hyperventilation and increased oxygen consumption. Heart rates were measured on crabs submerged in solutions of different salinities (Figs 3 and 4). Although there was no striking trend. we did note that the lowest heart rate was measured in crabs exposed to So”,, seawater. Hume & Berlind (1976) noted a change in heart rate m the curyhaline crab, Carcinu,s rnuenas, with a change in salinity: heart rates wcrc progressively higher the more dilute the medium was below 75”,, seawater. Spaargaren (1973) noted differences in heart rate with exposure to different salinities in the osmoregulating shrimp. Pulo~~on serratus. which were absent in the osmoconformer Lrsmata aeticaudutrr. Changes in heart rate and salinity are reported for the euryhaline amphipod Gurnmuru.s dwkni (Kinne. 1952). In the above cases it has been argued that the heart rate ma) scrvc as an index of the metabolic etrort required to regulate the body fluids in the face of osmotic and ionic stress. The data gathered for C’. yuunhurni do not appear to support this hypothesis. Gross t”t ol. (1966) have shown that Crrrdi,sorrttr is a relatively good osmoregulator. The crab’s serum hemolymph is isosomotic with it is at this point about 75”,, seawater: consequently. that the work required for osmoregulation should be minimum and the heart rate lowest. linfortunately WCdid not expose crabs to 7S”,, seawater---the lowest heart rates we measured were in W,, seawater. If the osmorcgulatory hypothesis were correct. we would expect the rate in SO and IOO”,, seawater to he alike: both media differ in osmotic concentration from the hcmolymph h> approximately the same amount. Figure 4 shows that this is not the case. Also. the hypothesis does not account for the fact that rates in freshwater and 25” ,~seawater are similar. although the osmoregulation involved must surely differ. ..lc,k,lo~(,/‘,dilr,,tc,,lr.\Our thanks go to David Carlson. Larr\ Lee and Neal Smatresk for asststance during the expeiimcnts. We are indebted to Dr C. Fourtner and Dr P. O’Mahoncl for critically reading the manuscript. REFERENCES
AHSAF.L.LLAH M. Br NFWLLL R. C‘. (1971) Factors
affecting the heart rate of the shore crab Carc,inu.s ,~arnas (L.) c‘o,,~p. Bio&,,r. Phr.\io/. 39A. 777 -287. ASHH~ F. & LARIME-RJ. (1964) Cardiac response of the crayfish. Procmkmrs srmukm. to external and internal carbon dioxide stress. Physrol. %oiil. 37. 21-32. BRAI\IUT A. (1X65) Physiologische Beobachtungen am Herrcn des Flusskrebses. !Meru. Biol. 4cud. SC,;. Sci. Sr. P~~trwhoury
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Princtpla IJ/ C’ompurlltlr~~, Kc\ljlr‘lror L North-Holland, Amsterdam DUBUISS~X M. (1934) Etude de I’electrocardiogramme danh la decoordination des pulyatlons. lrc,h\ irrt. Ph~\rol. 40.
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