Pulmonary capillary perfusion: intra-alveolar fractal patterns and interalveolar independence

A perpetual switching system in pulmonary capillaries

Of the 300 billion capillaries in the human lung, a small fraction meet normal oxygen requirements at rest, with the remainder forming a large reserve. The maximum oxygen demands of the acute stress response require that the reserve capillaries are rapidly recruited. To remain primed for emergencies, the normal cardiac output must be parceled throughout the capillary bed to maintain low opening pressures. The flow-distributing system requires complex switching. Because the pulmonary microcirculation contains contractile machinery, one hypothesis posits an active switching system. The opposing hypothesis is based on passive switching that requires no regulation. Both hypotheses were tested ex vivo in canine lung lobes. The lobes were perfused first with autologous blood, and capillary switching patterns were recorded by videomicroscopy. Next, the vasculature of the lobes was saline flushed, fixed by glutaraldehyde perfusion, flushed again, and then reperfused with the original, unfixed blood. Flow patterns through the same capillaries were recorded again. The 16-min-long videos were divided into 4-s increments. Each capillary segment was recorded as being perfused if at least one red blood cell crossed the entire segment. Otherwise it was recorded as unperfused. These binary measurements were made manually for each segment during every 4 s throughout the 16-min recordings of the fresh and fixed capillaries (>60,000 measurements). Unexpectedly, the switching patterns did not change after fixation. We conclude that the pulmonary capillaries can remain primed for emergencies without requiring regulation: no detectors, no feedback loops, and no effectors-a rare system in biology. NEW & NOTEWORTHY The fluctuating flow patterns of red blood cells within the pulmonary capillary networks have been assumed to be actively controlled within the pulmonary microcirculation. Here we show that the capillary flow switching patterns in the same network are the same whether the lungs are fresh or fixed. This unexpected observation can be successfully explained by a new model of pulmonary capillary flow based on chaos theory and fractal mathematics.

Lung Structure and the Intrinsic Challenges of Gas Exchange

Structural and functional complexities of the mammalian lung evolved to meet a unique set of challenges, namely, the provision of efficient delivery of inspired air to all lung units within a confined thoracic space, to build a large gas exchange surface associated with minimal barrier thickness and a microvascular network to accommodate the entire right ventricular cardiac output while withstanding cyclic mechanical stresses that increase several folds from rest to exercise. Intricate regulatory mechanisms at every level ensure that the dynamic capacities of ventilation, perfusion, diffusion, and chemical binding to hemoglobin are commensurate with usual metabolic demands and periodic extreme needs for activity and survival. This article reviews the structural design of mammalian and human lung, its functional challenges, limitations, and potential for adaptation. We discuss (i) the evolutionary origin of alveolar lungs and its advantages and compromises, (ii) structural determinants of alveolar gas exchange, including architecture of conducting bronchovascular trees that converge in gas exchange units, (iii) the challenges of matching ventilation, perfusion, and diffusion and tissue-erythrocyte and thoracopulmonary interactions. The notion of erythrocytes as an integral component of the gas exchanger is emphasized. We further discuss the signals, sources, and limits of structural plasticity of the lung in alveolar hypoxia and following a loss of lung units, and the promise and caveats of interventions aimed at augmenting endogenous adaptive responses. Our objective is to understand how individual components are matched at multiple levels to optimize organ function in the face of physiological demands or pathological constraints.

Microvascular perfusion heterogeneity contributes to peripheral vascular disease in metabolic syndrome

A major challenge facing public health is the increased incidence and prevalence of the metabolic syndrome, a clinical condition characterized by excess adiposity, impaired glycaemic control, dyslipidaemia and moderate hypertension. The greatest concern for this syndrome is the profound increase in risk for development of peripheral vascular disease (PVD) in afflicted persons. However, ongoing studies suggest that reductions in bulk blood flow to skeletal muscle may not be the primary contributor to the premature muscle fatigue that is a hallmark of PVD. Compelling evidence has been provided suggesting that an increasingly spatially heterogeneous and temporally stable distribution of blood flow at successive arteriolar bifurcations in metabolic syndrome creates an environment where a large number of the pre-capillary arterioles have low perfusion, low haematocrit, and are increasingly confined to this state, with limited ability to adapt perfusion in response to a challenged environment. Single pharmacological interventions are unable to significantly restore function owing to a divergence in their spatial effectiveness, although combined therapeutic approaches to correct adrenergic dysfunction, elevated oxidant stress and increased thromboxane A2 improve perfusion-based outcomes. Integrated, multi-target therapeutic interventions designed to restore healthy network function and flexibility may provide for superior outcomes in subjects with metabolic syndrome-associated PVD.

Complexity and emergent phenomena

Complex biological systems operate under non-equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power-law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory-related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed.

Determinants of pulmonary blood flow distribution

The primary function of the pulmonary circulation is to deliver blood to the alveolar capillaries to exchange gases. Distributing blood over a vast surface area facilitates gas exchange, yet the pulmonary vascular tree must be constrained to fit within the thoracic cavity. In addition, pressures must remain low within the circulatory system to protect the thin alveolar capillary membranes that allow efficient gas exchange. The pulmonary circulation is engineered for these unique requirements and in turn these special attributes affect the spatial distribution of blood flow. As the largest organ in the body, the physical characteristics of the lung vary regionally, influencing the spatial distribution on large-, moderate-, and small-scale levels.

Distribution of perfusion

Local driving pressures and resistances within the pulmonary vascular tree determine the distribution of perfusion in the lung. Unlike other organs, these local determinants are significantly influenced by regional hydrostatic and alveolar pressures. Those effects on blood flow distribution are further magnified by the large vertical height of the human lung and the relatively low intravascular pressures in the pulmonary circulation. While the distribution of perfusion is largely due to passive determinants such as vascular geometry and hydrostatic pressures, active mechanisms such as vasoconstriction induced by local hypoxia can also redistribute blood flow. This chapter reviews the determinants of regional lung perfusion with a focus on vascular tree geometry, vertical gradients induced by gravity, the interactions between vascular and surrounding alveolar pressures, and hypoxic pulmonary vasoconstriction. While each of these determinants of perfusion distribution can be examined in isolation, the distribution of blood flow is dynamically determined and each component interacts with the others so that a change in one region of the lung influences the distribution of blood flow in other lung regions.

Separating in vivo mechanical stimuli for postpneumonectomy compensation: imaging and ultrastructural assessment

Following right pneumonectomy (PNX), the remaining lung expands and its perfusion more than doubles. Tissue and microvascular mechanical stresses are putative stimuli for compensatory lung growth and remodeling, but their relative contribution remains uncertain. To temporally separate expansion- and perfusion-related stimuli, we replaced the right lung of adult dogs with a customized inflated prosthesis. Four months later, the prosthesis was either acutely deflated (DEF) or kept inflated (INF). Thoracic high-resolution computed tomography (HRCT) was performed pre- and post-PNX before and after prosthesis deflation. Lungs were fixed for morphometric analysis ∼12 mo post-PNX. The INF prosthesis prevented mediastinal shift and lateral lung expansion while allowing the remaining lung to expand 27-38% via caudal elongation, associated with reversible capillary congestion in dependent regions at low inflation and 40-60% increases in the volumes of alveolar sepal cells, matrix, and fibers. Delayed prosthesis deflation led to further significant increases in lung volume, alveolar tissue volumes, and alveolar-capillary surface areas. At postmortem, alveolar tissue volumes were 33% higher in the DEF than the INF group. Lateral expansion explains ∼65% of the total post-PNX increase in left lung volume assessed in vivo or ex vivo, ∼36% of the increase in HRCT-derived (tissue + microvascular blood) volume, ∼45% of the increase in ex vivo septal extravascular tissue volume, and 60% of the increase in gas exchange surface areas. This partition agrees with independent physiological measurements obtained in these animals. We conclude that in vivo signals related to lung expansion and perfusion contribute separately and nearly equally to post-PNX growth and remodeling.

The major transitions of life from a network perspective

Many attempts have been made to understand the origin of life and biological complexity both at the experimental and theoretical levels but neither is fully explained. In an influential work, Maynard Smith and Szathmáry (1995) argued that the majority of the increase in complexity is not gradual, but it is associated with a few so-called major transitions along the way of the evolution of life. For each major transition, they identified specific mechanisms that could account for the change in complexity related to information transmission across generations. In this work, I propose that the sudden and unexpected improvement in the functionality of an organism that followed a major transition was enabled by a phase transition in the network structure associated with that function. The increase in complexity following a major transition is therefore directly linked to the emergence of a novel structure-function relation which altered the course of evolution. As a consequence, emergent phenomena arising from these network phase transitions can serve as a common organizing principle for understanding the major transitions. As specific examples, I analyze the emergence of life, the emergence of the genetic apparatus, the rise of the eukaryotic cells, the evolution of movement and mechanosensitivity, and the emergence of consciousness. Finally, I discuss the implications of network associated phase transitions to issues that bear relevance to the history, the immediate present and perhaps the future, of life.

Modelling pulmonary blood flow

Computational model analysis has been used widely to understand and interpret complexity of interactions in the pulmonary system. Pulmonary blood transport is a multi-scale phenomenon that involves scale-dependent structure and function, therefore requiring different model assumptions for the microcirculation and the arterial or venous flows. The blood transport systems interact with the surrounding lung tissue, and are dependent on hydrostatic pressure gradients, control of vasoconstriction, and the topology and material composition of the vascular trees. This review focuses on computational models that have been developed to study the different mechanisms contributing to regional perfusion of the lung. Different models for the microcirculation and the pulmonary arteries are considered, including fractal approaches and anatomically-based methods. The studies that are reviewed illustrate the different complementary approaches that can be used to address the same physiological question of flow heterogeneity.

Spatial and temporal heterogeneity of regional pulmonary blood flow in piglets

Regional pulmonary blood flow (PBF) in adult animals varies over space and time, following a fractal pattern. We hypothesized that PBF would follow a fractal pattern in young animals. Five, two-week old piglets were sedated and mechanically ventilated. After stabilization, fluorescent microspheres were injected via the right atrium at baseline and then again at 5, 20, 20.5, 40 and 60 min. The lungs were subsequently excised, dried, inflated, and cored into 0.12-cm3 pieces (mean n=561+/-106 per animal) with the spatial coordinates recorded for each piece. Regional PBF was spatially and temporally heterogeneous with a spatial coefficient of variation of 43.3+/-7.9% and a temporal coefficient of variation of 14.3+/-0.4%. PBF followed a fractal pattern with a fractal dimension of 1.20+/-0.06 at 20 min, remaining stable throughout the experiment. PBF decreased with distance from the hilum but did not follow a lobar pattern. Temporal heterogeneity did not significantly increase with time but low flow regions demonstrated the greatest temporal variability throughout the study. Hence, PBF in young piglets was characterized both spatial and temporal heterogeneity.

Biologically variable ventilation improves gas exchange and respiratory mechanics in a model of severe bronchospasm*

OBJECTIVE

Mechanical ventilation can be lifesaving for status asthmaticus, but how best to accomplish mechanical ventilation is unclear. Biologically variable ventilation (mechanical ventilation that emulates healthy variation) and conventional control mode ventilation (monotonously regular) were compared in an animal model of bronchospasm to determine which approach yields better gas exchange and respiratory mechanics.

DESIGN

A randomized prospective trial of biologically variable ventilation vs. control mode ventilation in swine.

SETTING

University research laboratory.

SUBJECTS

Eighteen farm-raised pigs.

INTERVENTIONS

Methacholine was administered as a nebulized aerosol to initiate bronchospasm, defined as doubling of peak inspiratory pressure and respiratory system resistance, and then randomized (n = 9 each group) to either continue control mode ventilation or switch to biologically variable ventilation at the same minute ventilation. Over the next 4 hrs, hemodynamics, blood gases, respiratory mechanics, and carbon dioxide expirograms were recorded hourly. At end-experiment, tracheobronchial lavage was undertaken to determine interleukin-6 and -10 concentrations.

MEASUREMENTS AND MAIN RESULTS

Measurements of physiologic variables and inflammatory cytokines showed that biologically variable ventilation significantly improved gas exchange, with greater arterial oxygen tensions (p = .006; group x time interaction), lower arterial carbon dioxide tensions (p = .0003; group effect), lower peak inspiratory pressures (p = .0001; group x time), greater static compliance (p = .0001; group x time), greater dynamic compliance (p = .0001; group x time), and lower total respiratory system resistance (p = .028; group x time), compared with conventional ventilation. The appearance of inflammatory cytokines in bronchoalveolar lavage fluid (interleukin-6 and -10) was not affected by mode of ventilation.

CONCLUSIONS

In this experimental model, biologically variable ventilation was superior to control mode ventilation in terms of gas exchange and respiratory mechanics during severe bronchospasm.

Blood flow switching among pulmonary capillaries is decreased during high hematocrit

Pulmonary capillary perfusion within a single alveolar wall continually switches among segments, even when large-vessel hemodynamics are constant. The mechanism is unknown. We hypothesize that the continually varying size of plasma gaps between individual red blood cells affects the likelihood of capillary segment closure and the probability of cells changing directions at the next capillary junction. We assumed that an increase in hematocrit would decrease the average distance between red blood cells, thereby decreasing the switching at each capillary junction. To test this idea, we observed 26 individual alveolar capillary networks by using videomicroscopy of excised canine lung lobes that were perfused first at normal hematocrit (31–43%) and then at increased hematocrit (51–62%). The number of switches decreased by 38% during increased hematocrit ( P < 0.01). These results support the idea that a substantial part of flow switching among pulmonary capillaries is caused by the particulate nature of blood passing through a complex network of tubes with continuously varying hematocrit.

Heterogeneous capillary recruitment among adjoining alveoli

Pulmonary capillaries recruit when microvascular pressure is raised. The details of the relationship between recruitment and pressure, however, are controversial. There are data supporting 1). gradual homogeneous recruitment, 2). sudden and complete recruitment, and 3). heterogeneous recruitment. The present study was designed to determine whether alveolar capillary networks recruit in a variety of ways or whether one model predominates. In isolated, pump-perfused canine lung lobes, fields of six neighboring alveoli were recorded with video microscopy as pulmonary venous pressure was raised from 0 to 40 mmHg in 5-mmHg increments. The largest group of alveoli (42%) recruited gradually. Another group (33%) recruited suddenly (sheet flow). Half of the neighborhoods had at least one alveolus that paradoxically derecruited when pressure was increased, even though neighboring alveoli continued to recruit capillaries. At pulmonary venous pressures of 40 mmHg, 86% of the alveolar-capillary networks were not fully recruited. We conclude that the pattern of recruitment among neighboring alveoli is complex, is not homogeneous, and may not reach full recruitment, even under extreme pressures.

Umbilical flow distribution to the liver and the ductus venosus in human fetuses during gestation: an anatomy-based mathematical modeling

The partitioning of umbilical vein blood flow between fetal liver and ductus venosus may be an indicator of the fetal well-being, because the goal of the ductus venosus is to supply oxygen and nutrients to heart and brain. Both distribution and blood flow rate of the umbilical vein are functions of the local vascular impedances that, in turn, depend on the anatomical features of the related vessels. In order to investigate the venous blood flows in human fetuses during a normal gestation, a simple lumped parameter mathematical model was developed on the basis of some information achievable by ultrasonographic techniques. Particularly, the diameter and length of umbilical vein and ductus venosus and the volume of the liver were used to derive the vascular impedances. Three different impedance models were adopted for the umbilical vein, the ductus venosus and the hepatic circulation. A linear model described viscous hydraulic dissipations through the umbilical vein, while a quadratic pressure-flow relationship was used for the ductus venosus due to the irregular local hemodynamics at its inlet. Finally, the equivalent impedance of the whole hepatic network was related to the hepatic volume assuming a tree-like, symmetric and self-similar fractal geometry. The hepatic vascular resistances predicted according to the fractal analysis were quite consistent with some experimental measurements in fetal lambs. In agreement with clinical observations, the model predicted blood flows through the ductus venosus and umbilical vein increasing (from about 25 to 75 ml/min and from about 45 to 370 ml/min, respectively) throughout the gestation (20-40 weeks), while the flow fraction shunted via the ductus venosus diminishes (from about 50 to 20%).

Perfusion heterogeneity in rat lungs assessed from the distribution of 4-microm-diameter latex particles

Pulmonary vascular perfusion has been shown to follow a fractal distribution down to a resolution of 0.5 cm(3) (5E11 microm(3)). We wanted to know whether this distribution continued down to tissue volumes equivalent to that of an alveolus (2E5 microm(3)). To investigate this, we used confocal microscopy to analyze the spatial distribution of 4-microm-diameter fluorescent latex particles trapped within rat lung microvessels. Particle distributions were analyzed in tissue volumes that ranged from 1.7E2 to 2.8E8 microm(3). The analysis resulted in fractal plots that consisted of two slopes. The left slope, encompassing tissue volumes less than 7E5 microm(3), had a fractal dimension of 1.50 +/- 0.03 (random distribution). The right slope, encompassing tissue volumes greater than 7E5 microm(3), had a fractal dimension of 1.29 +/- 0.04 (nonrandom distribution). The break point at 7E5 microm(3) corresponds closely to a tissue volume equivalent to that of one alveolus. We conclude that perfusion distribution is random at tissue volumes less than that of an alveolus and nonrandom at tissue volumes greater than that of an alveolus.

Pulmonary capillaries are recruited during pulsatile flow

Capillaries recruit when pulmonary arterial pressure rises. The duration of increased pressure imposed in such experiments is usually on the order of minutes, although recent work shows that the recruitment response can occur in <4 s. In the present study, we investigate whether the brief pressure rise during cardiac systole can also cause recruitment and whether the recruitment is maintained during diastole. To study these basic aspects of pulmonary capillary hemodynamics, isolated dog lungs were pump perfused alternately by steady flow and pulsatile flow with the mean arterial and left atrial pressures held constant. Several direct measurements of capillary recruitment were made with videomicroscopy. The total number and total length of perfused capillaries increased significantly during pulsatile flow by 94 and 105%, respectively. Of the newly recruited capillaries, 92% were perfused by red blood cells throughout the pulsatile cycle. These data provide the first direct account of how the pulmonary capillaries respond to pulsatile flow by showing that capillaries are recruited during the systolic pulse and that, once open, the capillaries remain open throughout the pulsatile cycle.

Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

Selected contribution: measuring the response time of pulmonary capillary recruitment to sudden flow changes

To determine how rapidly pulmonary capillaries recruit after sudden changes in blood flow, we used an isolated canine lung lobe perfused by two pumps running in parallel. When one pump was turned off, flow was rapidly halved; when it was turned on again, flow immediately doubled. We recorded pulmonary capillary recruitment in subpleural alveoli using videomicroscopy to measure how rapidly the capillaries reached a new steady state after these step changes in blood flow. When flow was doubled, capillary recruitment reached steady state in <4 s. When flow was halved, steady state was reached in approximately 8 s. We conclude that the pulmonary microcirculation responds rapidly to step changes in flow, even in the capillaries that are most distant from the hilum.

Pulmonary blood flow remains fractal down to the level of gas exchange

The spatial distribution of pulmonary blood flow is increasingly heterogeneous as progressively smaller lung regions are examined. To determine the extent of perfusion heterogeneity at the level of gas exchange, we studied blood flow distributions in rat lungs by using an imaging cryomicrotome. Approximately 150,000 fluorescent 15-microm-diameter microspheres were injected into tail veins of five awake rats. The rats were heavily anesthetized; the lungs were removed, filled with an optimal cutting tissue compound, and frozen; and the spatial location of every microsphere was determined. The data were mathematically dissected with the use of an unbiased random sampling method. The coefficients of variation of microsphere distributions were determined at varying sampling volumes. Perfusion heterogeneity increased linearly on a log-log plot of coefficient of variation vs. volume, down to the smallest sampling size of 0.53 mm(3). The average fractal dimension, a scale-independent measure of perfusion distribution, was 1.2. This value is similar to that of other larger species such as dogs, pigs, and horses. Pulmonary perfusion heterogeneity increases continuously and remains fractal down to the acinar level. Despite the large degree of perfusion heterogeneity at the acinar level, gases are efficiently exchanged.