Functional and structural optimization of the respiratory system of the bat Tadarida brasiliensis (Chiroptera, Molossidae): does airway geometry matter?
1 Departamento de Ciencias Ecológicas, Facultad de Ciencias,
Universidad de Chile, Casilla 653, Santiago, Chile
2 Departamento de Botánica, Facultad de Ciencias Naturales y
Oceanográficas, Universidad de Concepción, Concepción,
Chile
3 Departamento de Ciencias Biológicas Animales, Facultad de Ciencias
Veterinarias y Pecuarias, Universidad de Chile
* Author for correspondence (e-mail: mcanals{at}uchile.cl)
Accepted 1 August 2005
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key words: bat, rodent, airway, lungs, diffusion capacity, optimization
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Animals with high energetic requirements have physiological and structural
compromise solutions for the required energetic efficiency, environmental
demands and lifestyle constraints
(Schmidt-Nielsen, 1997).
Because flight is one of the most energetically expensive forms of locomotion,
these compromises are particularly evident in flying animals. For example,
birds and bats increase oxygen consumption 10- to 20-fold from rest to flight
(Bartholomew et al., 1964
) and
their mass-specific aerobic capacities are 2.53 times higher than those
of non-flying mammals of the same size
(Thomas, 1987
). To satisfy
these high oxygen demands, flying animals must optimize the structure of the
respiratory tract (Maina,
2000a
,b
,
2002
) and the cardiovascular
system (Greenewalt, 1975
;
Johansen et al., 1987
;
Mathieu-Costello et al., 1992
;
Maina,
2000a
,b
).
Bat lungs are similar to those of non-flying mammals, but may be highly
refined to operate at near maximum values. Maina
(1998) identified the bats as
having a `narrow-based high-keyed strategy'. This strategy includes: (i)
larger heart and cardiac output
(Jürgens et al., 1981
;
Canals et al., 2005a
), (ii)
high hematocrit, high hemoglobin concentration and high blood oxygen transport
capacity (Wolk and Bogdanowics, 1985) and (iii) optimization of respiratory
structural parameters (Lechner,
1985
; Maina, 1998
,
2000a
,b
;
Jürgens et al., 1981
;
Maina et al., 1991
).
Little is known, however, about possible refinements or adjustments of the
lungs' airways as related to high energetic requirements. Recent studies on
the physical optimality of the airway of rats showed a gradual approach
towards the physical optimum from proximal to distal zones, which could be
explained by a transition from a central distributive zone to a physical
domain along the successive bifurcations of the airway
(Canals et al., 2004). Canals
et al. (2004
) developed a
geometric pattern for the branching tree, and deduced useful relationships to
estimate departures from both the physical and the geometrical optima of each
bronchial bifurcation. They analyzed the bronchial tree of rabbits
Oryctolagus cuniculus, rats Rattus norvegicus, a small
rodent Abrothrix olivaceus and the bat Tadarida
brasiliensis. They demonstrated that distances to optimum values decrease
from proximal to distal zones of the bronchial tree, and that the distance to
the physical optimum value is always lower than that to the geometrical
optimum value.
In the present studies, we examine the structural and functional parameters that characterize the respiratory system of the bat Tadarida brasiliensis. We expected the respiratory system to respond to energetic demands as a complete system. Thus, we expected high maximum oxygen consumption alongside optimal design in both lungs and airways. To contrast the findings with those obtained using the same methodology in other animals with high energetic requirements, we compared the bat's structure with those of Abrothrix olivaceus, a common rodent of low altitude lands, and the high-Andean Abrothrix andinus.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Oxygen consumption
Resting and maximum metabolic rates were estimated by oxygen consumption
using a modified closed-circuit automatic system, based on a manometric design
of Morrison (Rosenmann and Morrison,
1974). Resting metabolic rate (RMR) was measured at 30°C, in
post-absorptive resting animals. Maximal metabolic rate
(
O2max) was
measured at 5°C in a HeO2 (8020%) atmosphere,
following Rosenmann and Morrison's protocol. Metabolic scope MS was estimated
as
O2maxRMR.
Each metabolic run was conducted for 2 h after an acclimation period of
1530 min during the active circadian phase of each species. Body
temperature was measured at the end of each measurement using an intra-rectal
copperconstantan thermocouple. We measured MS,
O2max and RMR of
34 individuals of A. olivaceus, 9 A. andinus and 20 T.
brasiliensis. Comparisons between species were analyzed with a one-way
analysis of variance (ANOVA) followed by Tukey's multiple range tests.
Pulmonary structure
We removed the lungs of three individuals of each species
(Mb=11.3±0.5 g, 26.3±2.0 g and
25.5±1.9 g for T. brasiliensis, A. olivaceus and
A. andinus, respectively) and measured the thickness of the
bloodgas barrier and the alveolar surface. We also estimated the lung's
volume using the radiographic method
(Canals et al., 2005b) in four
or five other individuals of each species.
We followed Maina's methodology (Maina,
2002) to fixate lung tissues. We used sections of each lobule of
both lungs to prepare 410 blocks, from which small pieces (12 mm
thick) were obtained. These samples were fixed in glutaraldehyde (2.3%
glutaraldehyde in phosphate buffer) for 2 h at 4°C, washed in buffer and
postfixed with 1% osmium tetroxide, and then dehydrated in gradually
increasing concentrations of ethanol. Semithin sections (1 µm thick) were
prepared and stained with 1% Toluidine Blue. Ultrathin sections (6090
nm) were prepared and contrasted with lead citrate before examination by
transmission electron microscopy (JEOL/JEM 100SX, Musashino, Tokyo, Japan)
The images were digitalized and studied using SCION IMAGE software
(Frederick, MD, USA). The harmonic mean thickness of the bloodgas
barrier (h) was estimated by means of point-and-line counting
in a grid, as suggested by Weibel
(1970/71
) and Maina
(2002
). Twelve measurements of
h in different parts of the lungs were obtained for each
individual and the species effect on
h was analyzed by
repeated-measures ANOVA. Alveolar surface density was estimated by measuring
directly the alveolar perimeter in three fields of each lung section per
individual in the optical microscope. We considered the ratio of alveolar
perimeter to field area (R) as a good estimator of the alveolar
surface density, following the principle of stereological methodology
(Weibel, 1970/71
;
Weibel at al., 1981
). Lung
volume was estimated from radiographs of four individuals of T.
brasiliensis (Mb=11.95±1.4 g), four
individuals of A. olivaceus (Mb=26.0±4.3
g) and five individuals of A. andinus
(Mb=25.4±3.0 g). On lung images, we traced a
straight line (RL) between the costophrenic recesses, and measured: (i) the
width of RL (W) as a lateral measurement; (ii) the height between RL
and the top of the left (H1) and the right
(H2) lung; and (iii) left (w1) and
right (w2) lung width at the middle point of diaphragm
domes. Recently, Canals et al.
(2005b
), showed that
LV*=0.496VRX
1/2VRX is a
good estimator of lung volume in small mammals, where
VRX=W[(H1+H2)/2]x[(w1+w2)/2]
represents the volume of a box containing the lungs. The parenchymal lung
volume was estimated as LVp=0.9LV* (Maina,
2000a
,b
).
From these structural measurements the morphometric oxygen diffusion capacity
was estimated using:
DtO2=
(DsaxLVp)/
h,
where DtO2 is the oxygen diffusion capacity of the
bloodgas barrier (tissue),
is the Krogh's diffusion coefficient
=4.1x108 cm2 s1
Pa1 (Maina,
2002
) and Dsa is the alveolar surface
density.
Airway geometry
We initially dealt with all individuals of each species. Animals were
euthanized and bronchographs were immediately performed, using an 18 g plastic
catheter introduced into the trachea. Water-diluted barium sulfate was
introduced into the airway followed by air, to displace the contrast medium
filling to the thinnest bronchi. The procedure was performed using radioscopic
visualization in the X-ray service of a public hospital in Chile (Hospital Del
Salvador). Radiographs were taken at a distance of 1 m, at 100 mA, 0.04 s and
between 24 and 34 kV. Bronchographs were digitalized in a standard format of
400 pixels from the clavicle plane to the distal bronchi. Bronchi order was
assigned using Horsfield's system
(Horsfield, 1990), which
assigns bronchial order from distal to proximal zones. The distal (fine)
airway has smaller order values than proximal ones. A bronchograph was
considered sufficient whenever more than 12 relative orders were recognized.
The fractal dimensions of the bronchial images were computed by means of the
box-counting method, implemented using BENOIT software (St Petersburg, FL,
USA). We analyzed 15, 7 and 16 individuals of A. olivaceus, A.
andinus and T. brasiliensis, respectively. Comparisons between
the species were analyzed using a one-way ANOVA with Tukey multiple
comparisons.
We selected the best radiographs for subsequent analyses, retaining only
those in which the bronchial junctions were clearly recognizable. We
classified a junction as distal if the relative Horstfield order of the
thinnest bifurcation branch was lower than 3 and as proximal if its order was
larger than 5. Three proximal and three distal junctions were selected to
study the departures from optimality. To avoid underestimation due to
rotations, the junctions selected from a particular level were those that did
not overlap and had the largest bifurcation angle. Only 3, 2 and 4 individuals
of A. olivaceus, A. andinus and T. brasiliensis satisfied
these restrictive criteria and were therefore analyzed. The diameter, length
and bifurcation angles () of the parent and daughter branches of each
bifurcation were measured from digitized images (Figs
1 and
2). The length and diameter
scaling ratios (
and
d) were estimated by dividing
the average diameter of the daughter branches by that of the parent branch.
Also, a diameter and length symmetry ratio (Dr and
Lr, respectively) between the daughter branches were
computed, always using the lower value in the numerator of the ratio, so that
Dr and Lr
1.
|
|
Recently Canals et al.
(2004) proposed that
=60° and
should be
expected for a geometrically optimized bronchial tree. From a physical
perspective, in a symmetric bifurcation with laminar flow,
=74.934°
and
is expected on the basis of minimum energy loss, minimum volume and pumping
power principles (Kamiya et al.,
1974
; Zamir and Bigelow,
1984
; Mauroy et al.,
2004
). Considering these bases, Canals et al.
(2004
) defined estimators of
the physical and geometrical distances to the expected optima for each
junction in the following way: X, Y and Z coordinates as
X=sin(
/2) for both the physical and geometrical domains,
Y=
for the geometrical and Y=
d for
the physical domains; and finally Z=Lr for the
geometrical and Z=Dr for the physical domain, the
latter estimating the symmetry of the bifurcation. With these definitions
these authors expected a geometric optimum point (X0,
Y0, Z0)=(sin30°, 0.7937, 1)=(0.5,
0.7937, 1) and a physical optimum point (X0,
Y0, Z0)=(sin 37.467°, 0.7937,
1)=(0.6083, 0.7937, 1); then by defining the departures from the optima as
dX=XX0,
dY=YY0,
dZ=ZZ0 they proposed geometrical
(dG) and physical (dp) distances to
the optima as Euclidean distances in each domain as:
(Fig. 1).
The pair D=(dG,dp) was first
considered as a single vector, and the species effect on that pair was
analyzed by repeated-measures MANOVA. Then dG,
dp, the bifurcation angle , the
daughterparent length (
) and diameter (
d)
scaling ratios, as well as the symmetry ratios Dr and
Lr, were analyzed using repeated-measures two-way ANOVA
with SNK multiple comparisons.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
|
|
|
|
Geometrical and physical optimization of the airway
Comparing the airway radiographs of the three species, we found that all of
them fill the lung's space to a similar extent. The fractal dimensions of the
species were: A. olivaceus, 1.703±0.021; A. andinus,
1.670±0.012; and T. brasiliensis, 1.682±0.012
(F2,28=0.734; P>0.05). These were slightly
higher than the values of 1.57 for Rattus norvegicus, 1.571.62
for Oryctolagus cuniculus and 1.57 for Homo sapiens,
obtained using a somewhat different methodology by Canals et al.
(1998).
The distances to the geometric and physical optima of the bronchial junctions decreased from the proximal zone to the distal zone [F1,8=26.7, P<<0.01 for the geometrical distance; F1,8=58.69, P<<0.01 for the physical distance; and F2,7=10.69, P<0.01 for the vector D=(dG,dp) in the repeated-measures MANOVA]. We did not find interspecific effects in scalar or vector distances in the studied species [F2,8=1.1, P=0.378; F2,8=1.97, P=0.211 and F4,14=2.49, P=0.09 for dG, dp and the vector D=(dG,dp) respectively; Table 3]. However, we found a significant interaction between species and zone factors on the physical distance (F2,8=17.47, P<<0.01). This interaction was the result of a smaller physical distance in the bat than in the rodents in the proximal zone. In contrast, in the distal zone, the distances of all species were very similar (Fig. 6).
|
|
Geometrical distances depend on the bifurcation angle , the ratio
between the length of the daughter and the parent branches (
) and on
the ratio between the lengths of daughter branches (Lr).
Physical distances are determined by the bifurcation angle
, the ratio
between the diameter of the daughter and the parent branches
(
d) and the ratio between the diameters of the daughter
branches (Dr). When we explored the behavior of these
components of both distances we did not find interspecific differences
(F2,14=0.21, P>0.05), but the bifurcation
angle increased from proximal to distal zone (F1,14=16.13,
P<<0.01; Table 4).
Neither of the geometrical components
and Lr
differed among species (F2,8=0.99 and
F2,8=0.49, P>0.05 for
and
Lr, respectively) but both increased from proximal to
distal zones (F1,8=9.3, P<0.05 and
F1,8=15.0, P<0.01) (Tables
5 and
6).
|
|
|
The physical components d and Dr were
similar among species (F2,8=1.12 and
F2,8=1.57, P>0.05 for
d and
Dr, respectively), but both increased from proximal to
distal zones (F2,8=4.2, P<0.05 and
F2,8=23.6, P<0.01). Furthermore,
Dr showed a speciesxzone interaction effect due to
larger Dr values in the proximal zone of T.
brasiliensis (F2,8=7.25, P<0.05).
Although a similar pattern could be observed for
p, the
specieszone interaction was not significant
(Fig. 7).
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Structural lung parameters
The mass-specific alveolar surface was similar to that of several bats such
as Phyllostomus hastatus (37.2 cm2 g1),
Cheiromeles torquatus (33.3 cm2 g1) and
Cynopterus brachyotes (30.0 cm2 g1;
Maina et al., 1991), but lower
than in other small bat species whose mass-specific alveolar surfaces ranged
from 5063.2 cm2 g1 (Maina et al.,
1991
, 2000a,b).
The harmonic mean thickness of the tissue barrier was 0.230 µm, similar
to those of other bats, which range from 0.1204 µm in Phyllostomus
hastatus to 0.3033 in Pteropus poliocephalus
(Maina and King, 1984). The
estimated mass-specific diffusion capacity (tissue), DtO2,
of T. brasiliensis, 6.98x106 ml
O2 s1 Pa1 g1,
is within the range
1.07x10623.4x106 ml
O2 s1 Pa1 g1
reported for bats weighing between 5.1 g and 456.03 g
(Maina and King, 1984
;
Maina et al., 1991
).
Tadarida brasiliensis showed a mass-specific
DtO2 from 23 times higher than those of the studied
rodents. From data of Maina et al.
(1991) and Maina
(2000b
), we observed that
DLO2 is about 1/10 of DtO2
(DLO2/DtO2 ratio=0.092±0.070 in
birds and 0.100±0.031 in bats). Assuming this value, we may compare our
rodent data with those of Gehr et al.
(1981
) for several mammals.
Our rodents had a mass-specific DtO2 that was slightly
lower than those estimated for Mus musculus (42 g;
5.07x106 ml O2 s1
Pa1 g1), Mus wagneri (13 g;
7.46x106 ml O2 s1
Pa1 g1) and Rattus rattus (140 g;
4.85x106 ml O2 s1
Pa1 g1). Both maximum metabolic rates and
the structurally derived DtO2 showed an increase from low
values in A. olivaceus, medium values in A. andinus to high
values in the bat T. brasiliensis. This may be correlated with the
energetic requirements of the habitats and life styles of these species.
A. olivaceus inhabits grasslands, bushes, open forests and stony
areas from sea level up to 2500 masl, while A. andinus usually dwells
in high-Andean zones between 3500 and 4600 masl. T. brasiliensis is a
flying mammal that usually flies long distances and at high altitude
(Gantz and Martinez, 2000
;
Kunz and Fenton, 2003
).
Geometrical and physical optimization of the airway
Breathing work depends on the resistance of all components of the
respiratory systems to respiratory movements and airflow. Among them, the main
component of the total respiratory resistance is the resistance generated
within the airway (80% in humans). This resistance is generated primarily in
the proximal airway because of its reduced sectional area relative to that of
the distal airways. For example, in humans the airways with bronchial
diameters less than 2 mm are only responsible for 20% of the airway
resistance. Thus, the geometry of the proximal airway is a key factor in
determining the work needed for breathing. Another relevant factor is
breathing frequency. The increments of breathing frequency are paralleled by a
decrease in elastic work, but mainly by increments in the work to overcome the
turbulent flow (turbulent work) and the viscous resistance (viscous work) that
lead an increased total work (West,
2000).
Geometrically, the airways of the studied species approached the optimum
from proximal to distal, sacrificing the angle, but varying the symmetry and
improving . From a physical perspective, the optimum was approached
from proximal to distal, improving the symmetry, bifurcation angle and the
scaling ratio,
d. However, the airway of bats departed from
this pattern, maintaining a better
d in the proximal zone.
In a previous report, Canals et al.
(2004
) found a decrease in both
geometrical and physical distances to the optimum from proximal to distal
zones in the airway of several mammals. The reported distances for rabbits and
rats are in the range of the reported values in the present study. For
example, average values in Oryctolagus cuniculus and Rattus
norvegicus were dp=0.374 and
dp=0.417, respectively.
In T. brasiliensis a decrease was evident in the geometrical
distance but not in the physical distance. This latter was always close to the
physical optimum. The diameter ratio, d, was close to, but
lower than the expected
in both
proximal and distal zones. The bifurcation angle, however, varied from
52.2° to 70.9° from proximal to distal airway zones, respectively. The
first value was near the geometrical optimum angle (60°). This could be
associated with ascendancy of geometrical principles in the distribution of
the proximal airway, which could be related to the need to increase the
branches to fill a space and with the higher flow velocities in the proximal
zone associated with high breathing rate. These imply high Reynold's numbers
and increased energetic costs by increased viscous work and turbulence flow
(Massaro and Massaro, 2002
).
If that is the case, a lower physical optimum angle is expected
(Kamiya et al., 1974
) because
it reduces the probability of turbulent flow. This is possible even in fully
symmetric trees with more than three bifurcation generations
(Andrade et al., 1998
). The
energetic saving for the bat may be relevant because better optimization
values occur in the proximal zone of the airway where the main proportion of
the resistance to air flow is generated. Furthermore, bats can reach very high
breathing frequencies and tidal volumes during flight
(Thomas, 1987
). These increase
both the turbulent and viscous respiratory work and making energetic saving
important.
In the studied species, the average diameter scaling ratio in the distal
zones ranged from 0.716 to 0.752. This feature may be critical because in
symmetrical bronchial trees the flow resistance is highly sensitive to
d (Mauroy et al.,
2004
): low
d implies high resistance. One
explanation for this feature is that the exponent `n=3' in Murray's
law used in the derivation of airway models that predict an optimal
d=0.7937, may be lower than that for transitional or
turbulent air flow, conditioning both a lower bifurcation angle and a lower
d. For example n-exponents have been reported from
2.4 to 2.9 for the airways of four mammals
(Horsfield and Thurlbeck,
1981
), and 2.8 for the human airway
(Kitaota and Suki, 1997
).
Furthermore, the airways of most mammals are asymmetrical
(Canals et al., 2002b
). On
average, the symmetry ratios of the studied species varied from 0.688 in the
proximal zone to 0.798 in the distal zone. This feature could contribute
towards decreasing the expected
d optimum, and consequently
to reducing the dead space, thus requiring a lower tidal volume
(Mauroy et al., 2004
).
Tadarida brasiliensis showed evidence of the importance of the
interaction between the diameter asymmetry of the bronchial tree, the diameter
scaling ratio (d) and the distance to the physical optimum
in the proximal airway zone. This species showed the lowest distance, which
was sustained by a better symmetry (larger Dr) and was
accompanied by a scaling ratio closer to the optimum. These findings agree
with the predictions of Mauroy et al.
(2004
), who estimated that a
4% of decrease in
d would nearly double the bronchial tree
resistance, decreasing the air flow by 50%.
In brief, T. brasiliensis showed a high aerobic capacity that was
sustained by modifications of both lungs and airways. The bats show reductions
in the thickness of the bloodgas barrier, and modifications in lung
volume and the geometry of the bronchial tree, but no modifications in the
general design of the mammalian respiratory system. It showed the best
physical optimization values in the proximal zone. This may be an important
feature that saves energy and minimizes energy loss during breathing. Those
features, together with previously reported optimization of cardiovascular
parameters, such as the haematocryt, red blood cell number, heart mass and
heart rate (Maina, 1998),
probably facilitate satisfying the high energetic demands of flight in
bats.
![]() |
List of symbols and abbreviations |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
![]() |
Acknowledgments |
---|
![]() |
Footnotes |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Andrade, J. S., Alencar, A. M., Almeida, M. P., Mendes Filho, J., Buldyrev, S. V., Zapperi, S., Stanley, H. E. and Suki, B. (1998). Asymmetric flow in symmetric branched structures. Phys. Rev. Lett. 81,926 -929.[CrossRef]
Bartholomew, G. A., Leitner, P. and Nelson, J. E. (1964). Body temperature, oxygen consumption and heart rate in three species of Australian flying foxes. Physiol. Zool. 37,179 -198.
Canals, M., Olivares, R., Labra, F., Caputo, L., Rivera, A. and Novoa, F. F. (1998). Caracterización de la geometría fractal del arbol bronquial en mamiferos. Rev. Chil. Anat. 16,237 -244.
Canals, M., Atala, C., Olivares, R., Novoa, F. F. and Rosenmann, M. (2002a). Departures from the physical otimality in the bronchial tree of rats (Rattus norvegicus). Biol. Res. 35,411 -419.[Medline]
Canals, M., Atala, C., Olivares, R., Novoa, F. F. and Rosenmann, M. (2002b). La asimetría y el grado de optimización del árbol bronquial en Rattus norvegicus and Oryctolagus cuniculus. Rev. Chil. Hist. Nat. 75,271 -282.
Canals, M., Iriarte-Díaz, J., Olivares, R. and Novoa, F. F. (2002c). Comparación de la morfología alar de Tadarida brasiliensis (Chiroptera: Molossidae) y Myotis chiloensis (Chiroptera: Vespertilionidae), representantes de dos patrones de vuelo. Rev. Chil. Hist. Nat. 74,699 -704.
Canals, M., Novoa, F. F. and Rosenmann, M. (2004). A simple geometrical pattern for the branching distribution of the bronchial tree, useful to estimate optimality departures. Acta Biotheoretica 52,1 -16.[CrossRef][Medline]
Canals, M., Atala, C., Grossi, B. and Iriarte-Díaz, J. (2005a). Heart and lung size of several small bats. Acta Chiropt. 7,65 -72.
Canals, M., Olivares, R. and Rosenmann, M. (2005b). Estimating the lung volume of small rodents from radiographs. Biol. Res. 38, 41-47.[Medline]
Gantz, A. P. and Martinez, D. R. (2000). Chiroptera. In Mamíferos de Chile (ed. A. P. Muñoz and J. V. Yañez), pp. 53-66. Santiago: CEA Ediciones
Gehr, P., Mwangi, D. K., Ammann, A., Maloiy, G. M. O., Taylor, C. R. and Weibel, E. R. (1981). Design of the mammalian respiratory system. V. Scaling morphometric pulmonary diffusing capacity to body mass: wild and domestic mammals. Respir. Physiol. 44, 61-86.[CrossRef][Medline]
Greenewalt, C. H. (1975). The flight of birds: the significant dimensions, their departure from the requirements for dimensional similarity and the effect on flight aerodynamics of that departure. Trans. Am. Phil. Soc. 65, 1-67.
Harrison, J. F. and Roberts, S. P. (2000). Flight respiration and energetics. Annu. Rev. Physiol. 2000,179 -205.[CrossRef]
Horsfield, K. (1990). Diameters, generations
and orders of branches in the bronchial tree. J. Appl.
Physiol. 68,457
-461.
Horsfield, K. and Thurlbeck, A. (1981). Relation between diameter and flow in branches of the bronchial tree. Bull. Math. Biol. 43,681 -691.[CrossRef][Medline]
Iriarte-Díaz, J., Novoa, F. F. and Canals, M. (2002). Biomechanic consequences of differences in wing morphology between Tadarida brasiliensis and Myotis chiloensis.Acta Theriol. 47,193 -200.
Johansen, K., Berger, M., Bicudo, J. E. P. W., Ruschi, A. and de Almeida, P. J. (1987). Respiratory properties of blood and myoglobin in hummingbirds. Physiol. Zool. 60,269 -278.
Jürgens, J. D., Bartels, H. and Bartels, R. (1981). Blood oxygen transport and organ weight of small bats and small non-flying mammals. Respir. Physiol. 45,243 -260.[CrossRef][Medline]
Kamiya, A., Togawa, T. and Yamamoto, A. (1974). Theoretical relationships between the optimal models of the vascular tree. Bull. Math. Biol. 36,311 -323.[CrossRef][Medline]
Kitaota, H. and Suki, B. (1997). Branching
design of the bronchial tree based on a diameter-flow relationship.
J. Appl. Physiol. 82,968
-976.
Kunz, T. H. and Fenton, M. B. (2003). Bat Ecology. Chicago and London: The University of Chicago Press.
Lechner, A. J. (1985). Pulmonary design in a microchiropteran bat (Pipistrellus subflavus) during hibernation. Respir. Physiol. 59,301 -312.[CrossRef][Medline]
Maina, J. N. (1998). The lungs of the flying vertebrates birds and bats: is their structure optimized for this elite mode of locomotion? In Principles of Animal Design: The Optimization and Symmorphosis Debate (ed. E. R. Weibel, C. R. Taylor and L. Bolis), pp. 177-185. Cambridge: Cambridge University Press.
Maina, J. N. (2000a). What it takes to fly: the structural and functional respiratory refinements in birds and bats. J. Exp. Biol. 203,3045 -3064.[Abstract]
Maina, J. N. (2000b). Comparative respiratory morphology: Themes and principles in the design and construction of the gas exchangers. Anat. Rec. 261, 25-44.[CrossRef][Medline]
Maina, J. N. (2002). Some recent advances on the study and understanding of the functional design of the avian lung: morphological and morphometric perspectives. Biol. Rev. 77,97 -152.[Medline]
Maina, J. N. and King, A. S. (1984). The structural functional correlation in the design of the bat lung. A morphometric study. J. Exp. Biol. 111, 43-63.[Abstract]
Maina, J. N., Thomas, S. P. and Dalls, D. M. (1991). A morphometric study of bats of different size: correlations between structure and function of the chiropteran lung. Phil. Trans. R. Soc. Lond. B 333, 31-50.[Medline]
Mann, G. (1978). Los pequeños mamíferos de Chile: marsupials, quirópteros, edentados y roedores. Gayana Zool. 40, 9-342.
Massaro, D. and Massaro, G. D. (2002). Pulmonary alveoli: formation, the `call of oxygen', and other regulators. Am. J. Physiol. 282,L345 -L358.
Mathieu-Costello, O., Szewcsak, J. M., Logerman, R. B. and Agey, P. J. (1992). Geometry of bloodtissue exchange in bat flight muscle compared with bat hindlimb and rat soleus muscle. Am. J. Physiol. 262,955 -965.
Mauroy, B., Filoche, M., Weibel, E. R. and Sapoval, B. (2004). An optimal brobchial tree may be dangerous. Nature 427,633 -636.[CrossRef][Medline]
Murray, C. D. (1926). The physiological
principle of minimum work. Proc. Natl. Acad. Sci. USA
12,207
-214.
Rezende, E. L., Bozinovic, F. and Garland, T., Jr (2004). Climatic adaptation and the evolution of basal and maximum rates of metabolism in rodents. Evolution 58,1361 -1374.[Medline]
Rohrer, F. (1915). Flow resistance in human air passages and the effect of irregular branching of the bronchial system on the respiratory process in various regions of the lungs. Pflügers Arch. 162,255 -299.
Rosenmann, M. and Morrison, P. R. (1974).
Maximum oxygen consumption and heat loss facilitation in small homeotherms by
He-O2. Am. J. Physiol.
226,490
-495.
Schmidt-Nielsen, K. (1997). Animal Physiology. Adaptation and environment. Cambridge: Cambridge University Press.
Sparti, A. (1992). Thermogenic capacity of shrews (Mammalia, Soricidae) and its relationship with basal rate of metabolism. Physiol. Zool. 65, 77-96.
Thomas, S. P. (1987). The physiology of bat flight. In Recent Advances in the Study of Bats (ed. M. B. Fenton, P. Racey and J. M. V. Rayner), pp.75 -99. Cambridge: Cambridge University Press.
Thomas, S. P., Lust, M. R. and van Riper, H. J. (1984). Ventilation and oxygen extraction in the bat Phyllostomus hastatus during rest and steady flight. Physiol. Zool. 57,237 -250.
Voigt, C. C. and Winter, W. (1999). Energetic cost of hovering flight in nectar feeding bats (Phyllostomidae: Glossophaginae) and its scaling in moths, birds and bats. J. Comp. Physiol. B 169,38 -48.[CrossRef][Medline]
Weibel, E. R. (1970/71). Morphometric estimation of pulmonary diffusion capacity. Respir. Physiol. 11,54 -75.[CrossRef]
Weibel, E. R. (1998). Introduction. In Principles of Animal Design. The Optimization and Symmorphosis Debate (ed. E. R. Weibel, C. R. Taylor and L. Bolis), pp.1 -11. Cambridge: Cambridge University Press.
Weibel, E. R. and Gomez, D. M. (1962). Architecture of the human lung. Science 137,577 -585.[Medline]
Weibel, E. R., Gehr, P., Cruz-Ori, L., Muller, A. E., Mwangi, D. K. and Haussener, V. (1981). Design of the mammalian respiration system. IV. Morphometric estimation of pulmonary diffusing capacity: critical evaluation of a new sampling method. Respir. Physiol. 44,39 -59.[CrossRef][Medline]
West, J. B. (2000). Respiratory Physiology The Essentials. 6th edn. Baltimore: Williams and Wilkins.
Winter, Y., Voigt, C. and Von Helversen, O.
(1998). Gas exchange during hovering flight in a nectar-feeding
bat Glossophaga soricina. J. Exp. Biol.
201,237
-244.
Wolk, E. and Bogdanowics, W. (1987). Hematology of the hibernating bat, Myotis daubentoni. Comp. Biochem. Physiol. 88A,637 -639.[CrossRef]
Zamir, M. and Bigelow, D. C. (1984). Cost of departure from optimality in arterial branching. J. Theor. Biol. 109,401 -409.[Medline]