A Three-Compartment Model Describing Temperature Changes in Tethered Flying Blowflies

Non-invasive temperature measurement of insects with a thermal imaging camera was first applied to honeybees, Apis mellifera, by Cena and Clark (1972), and subsequently by Schmaranzer (1983), Stabentheiner and Schmaranzer (1987, 1988) and Stabentheiner and Hagmüller (1991). That the infrared radiation emitted by the tiny bodies of insects can be accurately monitored over time with considerable spatial resolution was further demonstrated by Schmaranzer and Stabentheiner (1988, 1991; honeybee Apis mellifera, fly Musca domestica, beetle Melolontha melolontha, katydid Conocephalus dorsalis) and Heinrich (1987; moth Eupsilia morrisoni). These results confirmed previous measurements with thermocouples showing that the temperature of the three body compartments, head, thorax and abdomen, can differ substantially (e.g. Heinrich, 1974, 1975, 1980a,b; moth Manduca sexta, bumblebee Bombus terricola, honeybee Apis).

In the present paper we use thermal imaging to investigate the thermal effects of blowfly flight. The experimental results are interpreted using a simple model that explicitly treats the insect body as a three-compartment system. The model is used to quantify the blowfly’s heat budget.

Blowflies (Calliphora vicina) were tethered via a V-shaped aluminium wire glued with a small drop of wax at the junction between the head and thorax (see Fig. 1A). A blowfly, thus tethered dorsally, remains at rest when it is offered a substratum, e.g. a small ball of paper tissue. Taking away the substratum initiates flight and this results in warming up. The reverse process, the end of flight and cooling down, was induced by replacing the substratum.

The changing temperature was monitored by adjusting the fly in the focal plane of a thermal imaging camera system (Fig. 1B–F). This was a Barr and Stroud IR-18 equipped with a telescope. The measured images yielded apparent temperatures that were transformed into body temperatures assuming 100% emissivity of the fly body. Stabentheiner and Schmaranzer (1987) found an emissivity of 99.4±2.8% for the honeybee Apis mellifera. Assuming an emissivity of 97%, a recent estimate by Stabentheiner (personal communication) yields an increase of the steady-state thoracic temperature (30.1°C) of only 0.17°C. The temperatures of the fly body compartments (see Fig. 2) were calculated by taking the average temperature of a selected area, as indicated by the boxes in Fig. 1E.

Fig. 1B shows that the heat radiation from the body compartments at rest is about equal to that of the surroundings, indicating that the temperatures of the head, thorax and abdomen are approximately equal to the ambient temperature. Fig. 1C–F, the images obtained at t=15s, 30s, 60s and 90s after the onset of tethered flight, shows that the radiation of the thorax increases rapidly upon initiation of flight, followed by a more moderate radiation increase from both the head and, to a much lesser extent, the abdomen. The highest intensity of radiation emanates from the dorsal part of the thorax, where the flight muscles are concentrated.

Quantitative evaluation of the thermal images yields the time course of the temperature changes. The three body compartments were sampled in each frame as indicated by the rectangles in Fig. 1E. Fig. 2A demonstrates that the temperatures of the three body compartments in the resting state are close to the ambient temperature of 25.0°C. Flying causes the thoracic temperature to rise, reaching approximately 30°C in steady flight. The time course approximates a simple exponential function with a time constant of 30 s (Fig. 2A).

Fig. 2A shows that the temperatures of the head and abdomen also increase. Presumably, the latter body parts do not produce extra heat themselves, but receive heat from the thorax, because the temperature time courses of both head and abdomen more or less approximate an exponential with a similar time constant of about 30s, except for a distinct delay.

At the end of flight, the temperatures of the fly’s body compartments fall back to the ambient temperature (Fig. 2B). The time course of the cooling phase of the thorax is again approximately exponential, but the process is distinctly slowed down, as the time constant is now about 50s (Fig. 2B). The time courses of head and abdomen temperatures indicate that heat transfer from the thorax continues during the cooling phase.

The findings from the thermal imaging experiments are incorporated in the three-compartment model (see Materials and methods) with the following assumptions: (1) the heat capacities of the head, thorax and abdomen depend solely on their mass; (2) the thermal exchange coefficients of thorax to head and to abdomen are equal, i.e. E_h=E_ab; (3) evaporative heat loss is negligible; and (4) the heat power produced by the thoracic muscles, M, is negligible at rest and at its steady-value during flight. The average masses were: m_h=5.0mg and m_th=m_ab=40mg. Taking a specific heat c_h=c_th=c_ab=3.4 Jg⁻1 K⁻1 (following, for example, Heinrich, 1975), the heat capacities are W_h=17mJ K⁻1 and W_th=W_ab=136mJ K⁻1. The warming-up curves of Fig. 2A can then be approximated satisfactorily using the model, equations 1a–c, by taking, for the produced heat power, M=1.38 J min⁻1=23.0mW (for similar values for the metabolic power of the honeybee, see Nachtigall et al. 1989); for the thermal conductances, C_h=75mJmin⁻1 K⁻1=1.25mW K⁻1, C_th=183mJmin⁻1 K⁻1=3.05mW K⁻1 and C_ab=244mJmin⁻1 K⁻1=4.07mW K⁻1; and for the thermal exchange coefficients, E_h=E_ab=67mJmin⁻1 K⁻1=1.12mW K⁻1 (Table 1). Substitution of these values into equation 1 yields Fig. 3A.

The warming-up and cooling-down curves of the thorax (Fig. 2A,B) have time constants of 30s and 50s, respectively. This indicates that the thermal conductance of the thorax drops during the cooling phase by a factor of 0.6, or, during the cooling phase C_th=1.83mW K⁻1. Assuming that the exchange coefficients remain unchanged, the three cooling curves of Fig. 2B can be approximated with equations 1a–c, using C_th=1.83mW K⁻1, C_h=1.00mW K⁻1 and C_ab=1.63mW K⁻1 (see Fig. 3B). This indicates that the thermal conductances of the head, thorax and abdomen at rest, after flight, are lowered by factors of 0.8, 0.6 and 0.4, respectively. We presume that the thermal conductances at rest, in still air, are lower than those during flight, owing to air currents around the fly’s body, produced by the wings.

The sudden drop in the thermal conductances at the end of flight results in a seemingly paradoxical temporary temperature increase in the head and abdomen. The same phenomenon was observed in temperature recordings of the abdomen of a tethered flying giant tropical fly (Bartholomew and Lighton, 1986).

Using the parameters obtained from fitting the time courses with the model, we can calculate the energy relationships of the blowfly. Fig. 4 shows that the major part of the total heat loss to the environment (L_tot) occurs through the thorax (L_th). Smaller, but non-negligible, amounts of heat are lost via the head (L_h) and abdomen (L_ab) (see Fig. 4A,B). The latter compartments thus act as a heat sink for the thorax, as in other insects (Heinrich, 1970, 1972). The heat power flowing from thorax to the head (F_h) and abdomen (F_ab) appears to remain rather small (Fig. 4C,D).

After the warming-up phase, in the steady state, L_th=15.6mW, L_h=3.0mW and L_ab=4.4mW. The total heat losses, L_tot, equal the heat power produced, M. Hence, the heat fluxes from the thorax to the head and abdomen in the steady state are F_h=3.0mW and F_ab=4.4mW. With an ambient temperature T_a=25.0°C, the temperatures in steady flight are calculated to be: T_h=27.4°C, T_th=30.1°C and T_ab=26.1°C. Note that the thermal conductances and the exchange coefficients can be conveniently checked with the temperature values in the steady state using equations 2a,b.

Presumably, the heat exchange between the body compartments is mainly due to haemolymph flow (e.g. Heinrich, 1970, 1972). If the haemolymph is mainly water, with a heat capacity of 4.18 Jg⁻1 K⁻1, an exchange coefficient E_h=E_ab=67mJmin⁻1 K⁻1=1.12mW K⁻1 gives a flow rate of 16.0mgmin⁻1. In a 85mg blowfly, this means that about one-fifth of the body mass is transported per minute from thorax to abdomen (see Heinrich, 1976, 1979, for a related calculation in the case of the bumblebee Bombus terricola). If the total haemolymph volume is 15 μl (Normann, 1972), a blood flow of 16mgmin⁻1 means that the total volume circulates through the body in approximately 1min. This is quite compatible with the observations of Weyrauther et al. (1989) on the eyes of a white-eyed mutant blowfly (chalky, Calliphora). After injection of 1–2 μl of the fluorescent dye Lucifer Yellow into the thorax, the fluorescence of the eyes increased within several seconds, apparently due to rapid transport of the injected dye solution into the head.

In summary, the heat distribution in an insect body can be well described with a three-compartment model. The metabolic power calculated for the blowfly appears to be very similar to the value obtained for the honeybee (Nachtigall et al. 1989).

We thank B. Kruizinga and D. Gode for help in the initial phase of this work. J. Winkel and W. van Bommel provided technical support. Software for grabbing and producing images was written by R. A. W. Kemp. S. B. Laughlin and J. H. van Hateren and two anonymous referees gave valuable suggestions for improving the manuscript.

In his recent comprehensive book The Hot-Blooded Insects (1993, Springer Verlag: Berlin, p. 365), Bernd Heinrich presents the thermal contour maps of a few insects immediately after flight, derived from measurements with a thermal imaging camera.