J Appl Physiol 110: 1119–1129, 2011.
First published December 16, 2010; doi:10.1152/japplphysiol.01293.2010.
HIGHLIGHTED TOPIC
Review
Emergent Behavior in Lung Structure and Function
Emergence of matched airway and vascular trees from fractal rules
Robb W. Glenny
Departments of Medicine and of Physiology and Biophysics, University of Washington School of Medicine,
Seattle, Washington
Submitted 5 November 2010; accepted in final form 6 December 2010
fractal; symmorphosis; ventilation; perfusion; branching morphogenesis
mammalian lung is to distribute
fresh air and blood to a vast surface area, thereby facilitating
diffusion and exchange of respiratory gases. Blood and air are
delivered to the alveolar capillary surface through intimately
interwoven airway and vascular trees. These trees, which
begin as single trunks, undergo serial branching and ramify
into complex structures with ⬃70 million precapillary arterioles (22), 480,000 alveoli (47), and 280 billion capillary
segments (62).
The design of these trees is central to efficient gas exchange
and must, therefore, have robust building instructions to ensure
that the airway and vascular trees are accurately constructed in
each individual. However, individual instructions cannot exist
for each airway and vascular segment in the human lung, and
investigators have suggested that that the bronchial and vascular trees are built recursively by invoking basic branching rules
at developing lung buds (34, 38). With the advent of fractal
geometry, in which complex structures can be created through
simple recursive rules, the airway and vascular trees in the lung
have been recognized as fractal structures (34, 61).
Emergent structures arise from limited numbers of forces
interacting with each other to produce recognizable patterns
and structures, such as sand dunes and snowflakes (46). Furthermore, these patterns could not have been predicted by
THE PRIMARY FUNCTION OF THE
Address for reprint requests and other correspondence: R. Glenny W., Univ. of
Washington School of Medicine, Division of Pulmonary and Critical Care Med.,
P.O. Box 356522, Seattle, Washington 98195-6522 (e-mail: [email protected]).
http://www.jap.org
knowing the details of the individual forces. Only through
complex and initially unexpected interactions does the structure emerge. As will be discussed in this highlighted topic, the
fractal geometry of mammalian airway and vascular trees
could be considered emergent behavior in that their complex
and interwoven geometries are determined through the interaction of only a few proteins.
However, the general concept of emergence does not depend
on the final structure having any benefits, such that one structure should be more likely to be created than other forms. In
contrast to nonliving structures in nature, organisms and animals that acquire structures through emergent processes are
more likely to retain these structures, if they confer an advantage to the organism. Hence evolutionary advantages can
reinforce development of complex structures that are created
through emergent processes, as long as the interacting processes are coded by genetic material. It is, therefore, more
appropriate to consider the airway and vascular trees as having
emergent adaptive behavior.
This review will integrate the concepts of emergence, fractals, and evolution to demonstrate how the complex branching
geometries of the airway and vascular trees are ideally suited
for gas exchange in the lung. In contrast to emergent processes,
where resultant structures may be vastly different each time
structures and patterns are formed, development of the mammalian lung must be both robust and closely regulated to
ensure precise structure and function. One of the major disadvantages of vascular and airway trees is that small asymmetries
8750-7587/11 Copyright © 2011 the American Physiological Society
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Glenny RW. Emergence of matched airway and vascular trees from fractal
rules. J Appl Physiol 110: 1119 –1129, 2011. First published December 16, 2010;
doi:10.1152/japplphysiol.01293.2010.—The bronchial, arterial, and venous trees of
the lung are complex interwoven structures. Their geometries are created during
fetal development through common processes of branching morphogenesis. Insights from fractal geometry suggest that these extensively arborizing trees may be
created through simple recursive rules. Mathematical models of Turing have
demonstrated how only a few proteins could interact to direct this branching
morphogenesis. Development of the airway and vascular trees could, therefore, be
considered an example of emergent behavior as complex structures are created
from the interaction of only a few processes. However, unlike inanimate emergent
structures, the geometries of the airway and vascular trees are highly stereotyped.
This review will integrate the concepts of emergence, fractals, and evolution to
demonstrate how the complex branching geometries of the airway and vascular
trees are ideally suited for gas exchange in the lung. The review will also speculate
on how the heterogeneity of blood flow and ventilation created by the vascular and
airway trees is overcome through their coordinated construction during fetal
development.
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in parent branches create heterogeneous distributions of blood
flow and ventilation at their terminal branches, potentially
causing inefficient gas exchange. A possible mechanism for
matching local ventilation and perfusion is the coordinated and
matched construction of the airway and vascular trees during
fetal development.
DESIGN OF THE MAMMALIAN LUNG
EMERGENCE OF FRACTAL STRUCTURES AND SPATIAL
PATTERNS OF PERFUSION AND VENTILATION
In its most simple form, emergence is demonstrated when
limited numbers of forces interact with each other to produce
discernable patterns and structures. Furthermore, these patterns
Fig. 1. Latex cast of human airway (white),
arterial tree (red), and venous tree (blue) provided with permission from Ewald Weibel. Note
that the three trees are complex interwoven structures that arise from single trunks. Also note that
the airway and arterial trees mirror each other all
of the way out to the terminal branches. [From
personal correspondence with Ewald Weibel]
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The primary function of the mammalian lung is to efficiently
exchange respiratory gases between the environment and the
organism. Because mammals breathe air, a number of constraints
and requirements are imposed on the respiratory system. To
minimize water and heat loss, humidity and heat must be added to
the incoming air and reclaimed on exhalation. The volume of the
conducting system must be minimized to decrease wasted ventilation and the work of breathing. The surface area for gas exchange must be maximized while being constrained to the volume
of the chest cavity. Similarly, blood needs to be delivered through
a vascular system that minimizes resistance to decrease the work
that the right heart needs to perform. The vascular system, while
constrained by the chest cavity, also must maximize the surface
area it creates for gas exchange. In a remarkable feat of engineering, all of these design requirements are met through a system of
interwoven branching trees (Fig. 1).
The adult human airway begins at the trachea with a crosssectional area of ⬃5 cm2 and, through a series of bifurcations,
ramifies into a tree with ⬃17 million branches (62) that connect
the environment to 480,000,000 alveoli (47), with a total surface
area of 130 m2 (62). Similarly, the arterial tree begins as a single
trunk from the right ventricle, and, through a series of bifurcations, branches into ⬎250,000 arterioles that then connect to the
alveolar capillaries, spreading the 200 ml of capillary blood
volume over the entire alveolar surface area. Blood is then drained
from the alveolar capillaries through the venous tree back to the
left atrium. These three trees and their terminal branches of
capillaries and alveoli must fit within the thoracic cavity that has
a volume of ⬃5– 6 liters. Packing these trees and the alveolar
surface into the thoracic cavity is the equivalent of folding a
standard piece of paper so that it fits into a thimble (63).
The geometries of the human airway and vascular trees are
optimized for their functions. Horsfield (21), Phalen et al. (50),
and Weibel (62) have provided detailed measurements of the
bronchial tree in humans and demonstrated that the branching
pattern remains similar across generations, with the diameter of
daughter branches being reduced by a nearly constant factor. The
observed branching diameter ratios of the airways turn out to be
very close to the idealized branching ratio formulated in Murray’s
law for the vascular tree (42) that tends to minimize the volume
within the conducting segments, as well as the resistance to fluid
or air movement. The morphometry of the vascular tree has also
been carefully described by Weibel (62), Huang et al. (24), and
Singhal et al. (55) and has also been shown to adhere to Murray’s
law of hemodynamics, such that resistance is minimized while
also decreasing the volume of blood in the conducting vessels
(42). The stereotypical geometry of these branching trees lead
Lefevre (30) to hypothesize that the pulmonary vascular tree is a
fractal structure. He demonstrated that such bifurcating trees
followed a principle of adequate design (53) “to expend minimal
energy and materials to build, repair, and operate its components
and to retain these qualities under many conditions.”
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EMERGENCE OF AIRWAY AND VASCULAR TREES
daughter branches remains relatively constant throughout all
orders of the bronchial (23) and pulmonary vascular trees (22).
With the introduction of fractal analysis, Horsfield (21) reanalyzed his own data and confirmed that the bronchial tree is
fractal with the diameter and lengths of branches related to the
branch order by a log-log relationship. He did note (21) that the
first three orders of the trees do not conform to the fractal
pattern of the rest of the lung. Recent observations on lung
morphogenesis have shed light on this observation (see
BRANCHING MORPHOGENESIS section below). The vascular tree
also deviates from a purely fractal structure in that supernumerary arteries (4) branch off at all levels of the arterial tree.
These are vessels that sprout directly from large pulmonary
blood vessels to supply the nearest acinar unit.
The mammalian bronchial and pulmonary vascular trees are
richly arborizing structures that, despite their complexity, are
generated through simple iterative processes (17, 45, 66). The
trachea bifurcates to form the right and left bronchi, and
subsequent generations are formed by a repetitive bifurcation
of the most distal airways. In this manner, a dichotomously
branching network is produced, filling the available space. In
his initial description of potential fractal structures in nature,
Mandelbrot (34) described a simple rectangular branching
algorithm, which bore a striking resemblance to the bronchial
tree. Nelson and Manchester (44) created a more realistic
fractal branching tree by including boundary conditions on the
branching angles and perimeter of the lung (Fig. 2). They
argued that these boundary conditions had analogs in lung
development because of the closed space in which the lung
develops. Kitaoka and colleagues (27) extended their computer
modeling to three-dimensional space and needed to incorporate
a number of new branching rules to fill the thoracic cavity.
They found that they required nine basic and four complementary rules to generate a realistic appearing bronchial tree
(Fig. 2). All of these models exhibit the necessary quality of
self-similarity to be deemed fractal, in that each generation
appears similar to previous generations, regardless of the
level of bifurcation examined. As discussed below, the
emergent form of the airway and vascular trees is created
through the interaction of only a few proteins and could,
therefore, be considered emergent structures. Analogous to
the increasing number of rules needed to form realistic tree
structures through computer simulation, recent studies have
demonstrated that the mechanisms regulating morphogenesis of the lung are considerably more complex than originally thought (37).
Fig. 2. Left: a fractal design of the lung in
which a treelike structure was constructed
through simple recursive branching rules.
Center: Nelson and Manchester created a
more realistic fractal branching tree by including boundary conditions on the branching angles and perimeter of the lung. [Borrowed with permission (44).] Right: Kitaoka
and colleagues incorporated a number of new
branching rules to fill the thoracic cavity with
a three-dimensional model. [From Ref. 27.]
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could not have been predicted by knowing the details of the
individual forces. Only through complex and initially unexpected interactions does the structure emerge. These characteristics are found in many naturally occurring structures, such
as sand dunes, snowflakes, and trees. These latter structures
have also been called fractals (34), because they have topological dimensions that are fractions of integers, and they have a
characteristic form that remains constant over a magnitude of
scales. A structure is considered fractal if its small-scale form
appears similar to its large-scale form. In the parlance of fractal
analysis, this is the quality of self-similarity, also termed scale
independence. Clouds are fractal, with each billowing appendage similar in form to its entirety. In fact, without a reference
scale, it is not possible to estimate the size of a cloud from a
photograph (6). The classical example of fractal structures are
coastlines, which appear to maintain the same degree of irregularity, regardless of the size or detail of the map studied (34).
Tree structures display self-similar characteristics, with their
branching angles and proportionate diameters of branches
remaining constant, regardless of whether one looks at the
main trunk or the terminal branches.
The self-similar nature of the bronchial and vascular trees
suggests that fractal mathematics may afford better models and
provide some insight into their structure and, importantly, their
morphogenesis. Weibel and Gomez (64) initially used a simple
exponential model to describe a unifying scaling relationship
between the change in airway dimension and branch order.
They collected morphometric data from casts of human lungs
and found that an exponential relationship fit their data well, up
to the 10th generation, but deviated significantly thereafter.
Using fractal analysis, West et al. (66) showed that the data of
Weibel and Gomez (64) was better fit over the entire range of
measurements by a fractal relationship between branch generation and branch diameter. Independent of scale or branch
generation, the relationship of diameters between parent and
daughter branches remains similar throughout all levels of the
bronchial tree, demonstrating fractal properties of the airways.
Fractal analysis in this particular example clearly provides a
superior model compared with the original exponential model,
as the bronchial tree is more accurately represented over the
entire range of the morphometric data.
Self-similarity has been recognized within the topology of
the bronchial and pulmonary vascular trees by a number of
other investigators (22, 23, 33, 55). Using topological branching and ordering schemes developed for geographical stream
analysis (Strahler ordering), Horsfield et al. have shown that
the ratio of mean diameters and lengths between parent and
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Fig. 3. First few bifurcations of a fractal (F) vascular tree in
which blood is distributed unevenly with a fraction ␥ going
to one branch and the remaining fraction, 1 ⫺ ␥, to the other
branch. Each of these new branches subsequently divides
into daughter branches using the same branching rules.
EMERGENT PATTERNS FROM FRACTAL TREES
Fig. 4. Right-skewed (log-normal) flow distributions
created from fractal trees with asymmetric branching. Left: modeled data. Right: data from animal
experiment where blood flow was measured in the
lung with microspheres. CV, coefficient of variation.
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In models in which conduit resistance is the major mechanism determining flow distribution, slight asymmetries within
successive branching of these trees necessarily create very
broad distributions of blood flow and ventilation at the terminal
segments (15). Figure 3 depicts the first few bifurcations of a
fractal vascular tree in which blood is distributed unevenly
with a fraction ␥ going to one branch and the remaining
fraction, 1 ⫺ ␥, to the other branch. Each of these new
branches subsequently divides into daughter branches as well,
creating 2n branches, where n is the average number of generations in the tree. In this model, the fraction of flow from
parent to daughter branches is ␥ and 1 ⫺ ␥ at each bifurcation.
While this model does not explicitly state the determinants of
asymmetric flow distribution at each branch point, heterogeneities of vascular resistance in the arterial and venous trees
must be the key determinants. Flows at each terminal branch of
the final tree can be calculated and the probability distribution
determined. The terminal flows generated by this network have
a log-normal distribution (51) similar to flow distributions
observed in experimental animals (Fig. 4).
Kitaoka and Suki (26) also used a flow branching tree to
model the airways and distribution of ventilation. They analyzed the diameter distributions of the airway tree from the data
of Raabe et al. (52) and found that the diameters of the airway
segments had a distribution that was consistent with a fractal
structure. Using Murray’s law that links diameters to flows via
a cubic power law, they demonstrated that the distributions of
airflow in each generation also followed a fractal pattern.
The spatial distributions from a dichotomously branching
vascular tree is not random, but rather spatially correlated with
neighboring lung regions having similar magnitudes of flow
and distant pieces exhibiting negative correlation. When regional perfusion is determined to ⬃2-cm3 volumes of lung in
dogs, high-flow regions are adjacent to other high-flow regions,
and low-flow areas are close to other low-flow regions (13).
This pattern is visually apparent when the spatial distribution
of blood flow is presented in a map that retains spatial location
of the lung pieces (Fig. 5). It can be quantified by determining
the correlation in perfusion between all lung pieces as a
function of distance between pieces. Figure 6 demonstrates that
adjacent lung pieces (centers of pieces separated by 1.2 cm)
have flows that are strongly correlated (P ⫽ 0.72), and that, as
the distance between pieces increases, the correlation in flow
decreases. This correlation among neighbors exists because of
the shared heritage within the vascular tree. At the greatest
distances, the correlation becomes negative in all cases. This
occurs because the fixed amount of blood is distributed to a
limited volume and high-flow regions exist at the expense of
flow to other regions. No other examples of negative spatial
correlation have been reported in the natural sciences, suggesting that this observation may be limited to branching vascular
structures. Three-dimensional modeling of pulmonary perfusion by Glenny and Robertson (14) and by Parker et al. (49)
have demonstrated that the spatial distributions of perfusion in
laboratory animals can be replicated using dichotomously
branching structures, and that fractal structures can create
emerging patterns of blood flow and ventilation in the lung.
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1123
Fig. 5. Left: spatial distribution of blood flow
to ⬃2-cm3 lung pieces within an isogravitational plane of a supine dog. High-flow regions are near other high-flow regions, and
low-flow areas neighbor other low-flow areas. Right: a fractal vascular tree demonstrating how neighboring lung pieces would have
similar flows. [Borrowed with permission
from Glenny (12).]
The anatomy of the developing human lung has been well
characterized as a dichotomous branching process for decades.
However, the mechanisms by which branching occurs has only
recently been better understood. Fractal mathematics and concepts of branching morphogenesis developed concurrently and
likely played supporting roles in the progress made in each
field. With the insights that simple processes used repeatedly at
the terminal buds can create branching structures, embryologists began investigating models of cellular signaling that
could initiate branching of tubular structures.
A number of outstanding and complete reviews of branching
morphogenesis in the lung have recently been published, and
the reader should consult these sources for further details (41,
Fig. 6. Correlation (␳) in blood flow between lung regions as a function of the
distance (d) between the regions. Blood flow to neighboring regions (1.2 cm
apart) is highly correlated, but the correlation becomes less as the distance
between regions increases. The correlation eventually becomes negative at
great distances due to the fact that high-flow regions can exist only if there are
low-flow regions and due to the shared heritage up the vascular tree. These
anti-correlated regions are on opposite sides of the tree and furthest apart.
[From Glenny (13).]
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59). This review focuses on the mechanisms of branching
morphogenesis and the coordinated development of the airway
and vascular trees and how their construction can be considered emergent behaviors.
The basic developmental stages of lung development are
well characterized in mice and humans. After the initial lung
diverticulum separates from the foregut, the initial lung buds
form as the precursors to the lobes (3 on the right and 2 on the
left in humans) (29). This stereotypical budding is the same in
all individuals and is thought to be hardwired into the developmental control (38). Further development occurs through
subsequent branching of these initial buds, but the mechanism
for this branching morphogenesis was not known until recently.
Concepts about fractal structures, the recursive processes
used to create them, and mathematical models introduced by
Alan Turing (56) have recently been integrated into new ideas
about branching morphogenesis (38). Lefevre (30) and Mandelbrot (34) were among the first to recognize the final form of
the lung as a fractal structure. West et al. (66) were some of the
first to mathematically demonstrate that the geometry of the
airway tree is fractal, and this conclusion was later confirmed
by others (21, 45, 61). Nelson and Manchester (44) speculated
that the recursive process used to create fractal structures could
guide the branching morphogenesis of the lung (see Fig. 2).
Although the signaling that induced branching was not initially
evident, Alan Turing’s work (56) on morphogens provided a
clue that only a few proteins might be involved. Turing
hypothesized, and then demonstrated through mathematical
equations, that two chemicals, which he called “morphogens”,
interacted, and that differences in the rates at which these
chemicals diffused through their surrounding and how the
morphogens interacted could produce spatial patterns, such as
the spots on a leopard’s hide (43). Turing called them “reaction-diffusion equations”, and, by varying diffusion speed and
how the morphogens interacted, different spatial patterns could
be created. The interactions between the morphogens created
coupled nonlinearities in the reaction-diffusion equations that
are necessary for pattern formation and are characteristic of
emergent behavior.
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BRANCHING MORPHOGENESIS
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ilar rules were needed to construct the three-dimensional recursive airway model of Kitaoka et al. (27), demonstrating the
parallel evolution of scientific discovery and computer modeling.
Because the fetal lung is not ventilated with air, it is
commonly assumed that lung morphogenesis occurs independently of mechanical stimuli, and a link between function and
structure is neglected. However, recent studies (10) have demonstrated that mechanical stresses do influence branching morphogenesis, and that fetal respiratory efforts guide lung development. The ability to generate spatial variations in the mechanical force balance between epithelial cells and their
underlying basement membranes, by altering either cytoskeletal tension or extracellular matrix mechanics, could be responsible for the establishment of local growth differentials that
drive tissue patterning in the lung.
Airway peristalsis and fetal breathing efforts play important
roles in lung development. Airway peristalsis is mediated by
spontaneous airway smooth muscles contractions (54). Peristaltic contractions and airway occlusions direct waves of fluid
toward the tips of the developing lung, resulting in rhythmic
stretch and relaxation of growing buds (Fig. 8). Normal development of the lung requires fetal breathing movements and
sufficient volumes of fluid within and surrounding the growing
lung (2, 10). Transecting the phrenic nerve disrupts lung
development in rabbits and sheep by preventing fetal breathing
movements (7, 70). Fetal breathing efforts stretch the developing lungs, which may influence lung development by increasing cell proliferation (7, 31). Fetal breathing movements
also maintain transpulmonary pressure by controlling the volume of fluid within the lung. Decreasing fluid leads to lung
hypoplasia, while increasing fluid volume causes hyperplasia
(1, 28, 40). As the thoracic cavity develops, the chest wall
shape influences local mechanical forces and potentially results
in differential regional growth of the bronchial tree. Such a
mechanism would provide support for symmorphosis within
the lung. Symmorphosis is a concept proposed by Weibel et al.
(65), postulating that structural properties of organ systems are
quantitatively matched to functional demand as a result of
regulated morphogenesis during growth. In the lung, for instance, Weibel and Gomez (64) noted that diameters of airways
Fig. 7. Proposed branching mechanism in the developing lung that requires only two proteins: fibroblast growth factor (Fgf10) and sonic hedgehog (shh). These
proteins act as the morphogens (promoters and inhibitors) described by Turing. [Adapted with permission from Metzger and Krasnow (38).]
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Single-gene knockouts in the Drosophila that prevented
branching provided the first clues as to which signaling proteins might be important in branching morphogenesis. Metzer
and Krasnow (38) recognized that, by combining fractal concepts with reaction-diffusion signaling, a limited number of
proteins might be responsible for all of the branching in the
lung from the trachea to the terminal bronchioles. Figure 7
depicts how a simple model of locally interacting proteins can
induce branching. In this model, fibroblast growth factor
(Fgf10) is secreted by the mesenchyme and induces bronchial
branch outgrowth. It also induces new gene expression in the
cells at the ends of the branches that then transcribes a different
protein, sonic hedgehog (shh), that turns off Fgf10 production
in the neighboring mesenchyme. Mesenchyme cells distant
from the branching tip continue to produce Fgf10, inducing
epithelial growth in that direction. The mathematical modeling
of Turing and computer modeling by Miura and Maini (39)
demonstrate that the extracellular matrix through which these
growth factors and inhibitors diffuse can also influence branching geometries. Although studies have uncovered additional
proteins that are involved in the branching morphogenesis of
the lung, the concept of promoters and inhibitors acting locally
to induce branching is a concept that appears to be conserved
across a number of organs and organisms (38).
Recent studies by Metzger’s group (37) have demonstrated
that, while the branching process is more complicated than
outlined above, it remains remarkably stereotyped. Through
elegant histological studies, they have parsed the three-dimensional branching pattern of the mouse lung into three principal
subroutines that are used repeatedly to create the entire bronchial tree. Echoing the fractal pattern formation achieved in
mathematical models, these recursive routines include the
following: 1) a master branch generator routine, with three
subroutines driving a periodicity clock that coordinates the
temporal appearance of subsequent branches; 2) a rotational
orientation subroutine, which determines the orientation of the
branches around the axis of the airway; and 3) a branch tip
division subroutine (37, 59). Branching morphogenesis of the
bronchi in the mouse lung can, therefore, be dissected into
three simple geometric forms termed domain branching, planar
bifurcation, and orthogonal bifurcation (37). Interestingly, sim-
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EMERGENCE OF AIRWAY AND VASCULAR TREES
1125
are proportional to the size of the peripheral lung units supplied
by a given branch and hence that the caliber of the airways may
be proportional to the ventilation to the subtended lung.
Although most of the work on branching morphogenesis in
the lung has focused on the bronchial tree, there are elegant
studies indicating that the airway tree acts as a scaffolding to
guide formation of the vascular tree (18 –20, 59). The formation of new capillaries occurs at a similar distance from the
epithelial buds throughout all stages of development, suggesting the advancing epithelial cells exert some control in vascular
development. Vascular endothelial growth factor is known to
be involved in angiogenesis and vasculogenesis and has been
demonstrated in airway epithelial cells of human fetuses (18,
19). Vascular endothelial growth factor signaling from the
epithelium to the developing endothelium is essential for the
primitive hemangioblasts to develop into mature vascular networks. Likewise, the endothelium probably signals back to
coordinate epithelial morphogenesis (59). The earliest pulmonary vessels form de novo in the mesenchyme by a process of
vasculogenesis: differentiation of cells to form single endothelial cells and then capillary tubes. These capillaries coalesce to
form small blood vessels alongside the airways. As each new
airway buds into the mesenchyme, a new plexus forms as a
halo and adds to the peripheral circulation, so extending the
arteries and veins. Thus there is sustained addition of the newly
formed tubules to the existing vessels, and the airways act as a
template for the development of blood vessels (18). The
arteries coalesce and course in close association with the
airway wall, while the veins separate from the airways and
eventually run equidistant between them. Veins seem to be
further separated from the influence of the airways as they
become surrounded by lymphatic channels within the connecJ Appl Physiol • VOL
tive tissue septa (19). The stimulus that differentiates the
arteries from the veins initially is not known, but their newly
formed endothelial cells do have different phenotypes (19).
Comparing lung development to other organs provides insights into the degree of control during branching morphogenesis. Although branching appears to be random in the mammary gland and prostate (32), it appears to be tightly controlled
in the lung (37, 59). Warburton and colleagues (57, 58) have
postulated a clock mechanism that plays a key role in timing
the rate of bud extension and hence the interbranch distance.
They propose that a nested hierarchy of clock routines are
likely to be present throughout lung development, given the
number of oscillating systems intrinsic to the lung. Branching
morphogenesis is accompanied by contractile oscillations (airway peristalsis) that are themselves underpinned by periodic
calcium waves (5, 25). These oscillators appear to be coupled
to lung growth, and their precise relation to the timing of
branching remains to be determined. This relatively greater
control of branching morphogenesis in the lung suggests that
the precise geometry of the airway and vascular tree are very
important to lung function. Mauroy et al. (35) have argued that,
even though the human bronchial tree is optimally designed for
its function of ventilation while minimizing work, small deviations from this idealized geometry would create significant
increases in the work of breathing or inefficiencies of gas
exchange. Hence, while the branching morphogenesis of the
airway and vascular trees are under the control of a limited
number of genes, it may not truly be an emergent system, as its
geometry is highly regulated and predictable.
Rather than being simply emergent, the geometry of the
airway and vascular trees might be considered as demonstrating emergent adaptive behavior. The shapes of the bronchial
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Fig. 8. Mechanicobiology in the developing lung.
Peristalsis and fetal respiratory efforts induce regional mechanical stresses that influence local
cellular proliferation and protein expression. Pressure inside the airway creates stretch at the branch
tips. This stress can induce production of metalloproteinase that degrades the surround extracellular matrix (ECM) to allow the lung bud to
advance. Transpulmonary pressures created by
fetal breathing efforts will also stretch the developing lung buds. [Adapted with permission from
Gjorevski and Nelson (9).]
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and vascular trees are adaptive because specific geometries are
advantageous to the organism and are, therefore, reinforced
through evolutionary selection. The observation that fractal
branching trees have been conserved throughout the plant and
animal kingdoms is thought to be due to evolutionary advantages conferred through efficient distribution of nutrients (67,
68). The tight regulatory control of the airway and vascular tree
geometries also suggests that these fractal structures are important to the organism.
ADVANTAGES OF FRACTAL TREES
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As discussed above, fractal vascular and airway trees create
heterogeneous distributions of blood flow (15) and ventilation
(26). Just a small asymmetry that is repeated at each bifurcation creates remarkable variability in blood flow at the terminal
branches. For example, a dichotomously branching tree that
diverts 53% of the blood flow to one daughter branch and the
remaining 47% to the other daughter branch will create highflow regions that have 50% more flow than the lowest flow
regions after only three generations. After 26 generations, as
seen in the human lung, the highest flow regions will have 22
times more flow than the lowest flow regions. If this heterogeneity were to occur on both the distributions of ventilation
and perfusion, gas exchange could be severely impaired, if
regional ventilation and perfusion were not somehow matched.
MATCHING OF REGIONAL VENTILATION AND PERFUSION
Given that both perfusion and ventilation are heterogeneously distributed, efficient exchange of respiratory gases is
dependent on intimate matching of local ventilation and perfusion. In a theoretical analysis, Wilson and Beck (71) explored the impact of ventilation and perfusion heterogeneity on
ventilation-perfusion (V̇A/Q̇) inhomogeneity. They determined
that V̇A/Q̇ heterogeneity, expressed as the variance in the V̇A/Q̇
distribution, ␴2log V̇A/Q̇, can be related to ventilation and
perfusion distributions by the equation:
2
2
␴2log(V̇A ⁄ Q̇) ⫽ ␴logV˙ ⫹ ␴logQ˙ ⫺ 2␳␴logV˙ A␴logQ˙
A
where ␴log V̇A and ␴log Q̇ are the standard deviations of ventilation and perfusion distributions, respectively, and ␳ is the
correlation between regional ventilation and perfusion in the
log domains. As the correlation between ventilation and perfusion varies from 0 (complete independence) to 1 (perfect
coupling), the inhomogeneity in the V̇A/Q̇ distribution varies
2
2
from a maximum of ␴log
V̇A ⫹ ␴log Q̇ to a minimum of 0.
Hence, regardless of the heterogeneities in ventilation or perfusion, tight coupling of ventilation and perfusion results in minimal
V̇A/Q̇ inhomogeneity. Studies by Altemeier et al. (3) and by
Melsom and colleagues (36) obtained high spatial resolution
measurements of both regional blood flow and ventilation in the
same animals and demonstrated that blood flow and ventilation
are very heterogeneous but highly correlated (Fig. 9). These
experimental data confirmed the theoretical modeling of Wilson
and Beck (71).
Although the shared effect of gravity has been thought of as
the principle mechanism matching ventilation and perfusion
locally (69), gravitational influences cannot account for the
close matching of heterogeneous ventilation and perfusion
within isogravitational planes. While speculative, the simplest
explanation for efficient gas exchange within isogravitational
planes is that the lung is constructed anatomically to match
regional ventilation and perfusion. Evidence supporting this
hypothesis is that airways and pulmonary arteries branch in
union with each other (60). As described above, this relationship arises during embryology when the primordial airways
signal formation of adjacent endothelial cells into pulmonary
arteries. Active feedback mechanisms, such as hypoxic pulmonary vasoconstriction, are certainly important in the diseased
lung, but it appears that active mechanisms do not play a role
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West et al. (67, 68) noted that fractal vascular and air
distribution systems are used by a broad range of species, from
plants, to insects, to animals. For such structures to be conserved across such a wide array of organisms, there must be a
very strong evolutionary advantage. They proposed that fractal
trees have three important characteristics that confer significant
advantages. First, fractal trees fill three-dimensional space
(such as a chest cavity) with the largest possible surface area
for gas or nutrition exchange. This is central to the lung’s
primary role in gas exchange. Second, a fractal tree requires the
least amount of material (least cost to the organism) to fill the
three-dimensional space. This also means that the volume of
the tree takes up the least amount of volume within the lung,
leaving more space for gas exchange. In addition, this minimizes the pulmonary blood volume and maximizes the circulating blood volume, delivering oxygenated blood via the
systemic circulation. Third, a fractal structure requires the least
amount of energy to transport nutrients through an organ
(pumping blood flow from the right to the left ventricle or
moving air in and out of the lung). Through elegant mathematics, West and colleagues (68) demonstrated that these three
advantages were characteristics of fractal networks. As discussed above, an additional advantage of such structures is that
a minimal amount of genetic code is required to create the
trees.
However, for the geometries of the airway and vascular trees
to confer evolutionary advantages, they must be heritable traits
that can be passed on to subsequent generations. The observations that branching morphogenesis is controlled by a limited
number of proteins does not necessarily mean that the final
shape of the vascular or airway trees is determined genetically.
To test the hypothesis that the shape of the vascular tree is
heritable in mammals, Glenny et al. (11) studied the spatial
distribution of organ blood flow in armadillos, because they
have genetically identical littermates. It was determined that
the regional distribution of blood flow is strongly correlated
between littermates (r2 ⫽ 0.56) and less correlated between
unrelated animals (r2 ⫽ 0.36). Using an ANOVA model,
Glenny and coworkers estimated that 67% of the regional
variability in organ blood flow is genetically controlled.
They also used fractal analysis to characterize the distribution of organ blood flow and found shared patterns within
the lungs and hearts of related animals, suggesting common
control over the vascular development of these two organs.
They concluded that fractal vascular trees are heritable, and
that optimal geometries could be selected through evolutionary pressures.
DISADVANTAGES OF FRACTAL TREES
Review
EMERGENCE OF AIRWAY AND VASCULAR TREES
1127
in matching ventilation and perfusion in the normal lung when
breathing air at sea level (8). This makes the most sense from
an engineering perspective, because a system that does not
require an active feedback loop to function properly is more
robust and less likely to break down. If the geometries of the
vascular and airway trees were similar and were the primary
determinants of ventilation and blood flow, it is easy to
imagine how ventilation and perfusion could be well
matched, despite having heterogeneous distributions. However, the argument against this hypothesis is that regional
lung compliance is more important than airway caliber in
determining regional ventilation (48). The potential rebuttal
is that regional compliance and airway geometry may be
closely linked during embryological development, when
fetal respiratory efforts or airway oscillations create regional mechanical stresses that can influence local airway
development, so that the caliber of the airways is matched to
(correlated with) the regional ventilation. This relationship
does not mean that airway segment resistances determine
the distribution of ventilation, but rather that the airway
calibers are associated with the compliance of the regions
that they serve and, therefore, are correlated with local
ventilation. This is again the concept of symmorphosis,
developed by Weibel et al. (65), where structural design is
matched to functional demand. Weibel and Taylor (60) have
noted that diameters of airways are grossly proportional to
the size of the peripheral lung supplied by a given branch.
J Appl Physiol • VOL
SUMMARY
The bronchial, arterial, and venous trees of the lung are
complex, interwoven structures that could be considered emergent structures, because they are created through the interactions of only a few proteins. Fractal geometry suggests that
these arborizing trees may be created through simple rules that
are applied recursively at new lung buds during branching
morphogenesis. The mathematical models of Alan Turing have
provided new insights into how a few proteins could interact to
induce branching behavior and how differences in diffusion of
these proteins can alter the branching geometries. These fractal
trees have been conserved across many species, suggesting that
their forms provide evolutionary advantages to the organisms.
Elegant work by Metzger and Krasnow has shown that the
branching routines of the developing lungs are very stereotyped
and hence must be well controlled. It is speculated that the final
form of the airway and vascular trees is so important to their
function of gas exchange that the building code must be tightly
regulated. It may, therefore, be more accurate to consider creation
of these trees to represent emergent adaptive behavior. The major
disadvantage of these fractal trees is that they produce very
heterogeneous distributions of ventilation and perfusion. It is also
speculated that the impairment in gas exchange caused by these
heterogeneities is nullified by the close matching of airway and
vascular geometries during fetal development.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
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Fig. 9. Graphical presentations of ventilation
(V̇A) and perfusion (Q̇) distributions from
one animal in which the lung was dissected
into 850 pieces. Top right: V̇A and Q̇ to each
piece against each other. Top left: the heterogeneity of V̇A can be appreciated by collapsing the V̇A data to the vertical axis and
then viewing as a frequency density distribution. Bottom right: the heterogeneity of Q̇
can be viewed similarly by collapsing the
data to the horizontal axis. Despite the heterogeneous distributions of V̇A and Q̇, their
piece-by-piece matching is quite good (r ⫽
0.80, top right). The top right panel includes
isopleths of V̇A/Q̇ ratios from which gas
exchange can be inferred. Bottom left: the
resultant V̇A and Q̇ distributions with respect
to the V̇A/Q̇ ratio, as popularized by the
multiple inert-gas technique, are presented.
[From Glenny and Robertson (16).]
Review
1128
EMERGENCE OF AIRWAY AND VASCULAR TREES
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