Emergence of matched airway and vascular trees from fractal rules

Lung endothelium, tau, and amyloids in health and disease

Lung endothelia in the arteries, capillaries, and veins are heterogeneous in structure and function. Lung capillaries in particular represent a unique vascular niche, with a thin yet highly restrictive alveolar-capillary barrier that optimizes gas exchange. Capillary endothelium surveys the blood while simultaneously interpreting cues initiated within the alveolus and communicated via immediately adjacent type I and type II epithelial cells, fibroblasts, and pericytes. This cell-cell communication is necessary to coordinate the immune response to lower respiratory tract infection. Recent discoveries identify an important role for the microtubule-associated protein tau that is expressed in lung capillary endothelia in the host-pathogen interaction. This endothelial tau stabilizes microtubules necessary for barrier integrity, yet infection drives production of cytotoxic tau variants that are released into the airways and circulation, where they contribute to end-organ dysfunction. Similarly, beta-amyloid is produced during infection. Beta-amyloid has antimicrobial activity, but during infection it can acquire cytotoxic activity that is deleterious to the host. The production and function of these cytotoxic tau and amyloid variants are the subject of this review. Lung-derived cytotoxic tau and amyloid variants are a recently discovered mechanism of end-organ dysfunction, including neurocognitive dysfunction, during and in the aftermath of infection.

The control of lung branching morphogenesis

Branching morphogenesis generates epithelial trees which facilitate gas exchange, filtering, as well as secretion processes with their large surface to volume ratio. In this review, we focus on the developmental mechanisms that control the early stages of lung branching morphogenesis. Lung branching morphogenesis involves the stereotypic, recurrent definition of new branch points, subsequent epithelial budding, and lung tube elongation. We discuss current models and experimental evidence for each of these steps. Finally, we discuss the role of the mesenchyme in determining the organ-specific shape.

Fgf10/Fgfr2b Signaling Orchestrates the Symphony of Molecular, Cellular, and Physical Processes Required for Harmonious Airway Branching Morphogenesis

Airway branching morphogenesis depends on the intricate orchestration of numerous biological and physical factors connected across different spatial scales. One of the key regulatory pathways controlling airway branching is fibroblast growth factor 10 (Fgf10) signaling via its epithelial fibroblast growth factor receptor 2b (Fgfr2b). Fine reviews have been published on the molecular mechanisms, in general, involved in branching morphogenesis, including those mechanisms, in particular, connected to Fgf10/Fgfr2b signaling. However, a comprehensive review looking at all the major biological and physical factors involved in branching, at the different scales at which branching operates, and the known role of Fgf10/Fgfr2b therein, is missing. In the current review, we attempt to summarize the existing literature on airway branching morphogenesis by taking a broad approach. We focus on the biophysical and mechanical forces directly shaping epithelial bud initiation, branch elongation, and branch tip bifurcation. We then shift focus to more passive means by which branching proceeds, via extracellular matrix remodeling and the influence of the other pulmonary arborized networks: the vasculature and nerves. We end the review by briefly discussing work in computational modeling of airway branching. Throughout, we emphasize the known or speculative effects of Fgfr2b signaling at each point of discussion. It is our aim to promote an understanding of branching morphogenesis that captures the multi-scalar biological and physical nature of the phenomenon, and the interdisciplinary approach to its study.

Fractal Analysis of Lung Structure in Chronic Obstructive Pulmonary Disease

Chest CT is often used for localizing and quantitating pathologies associated with chronic obstructive pulmonary disease (COPD). While simple measurements of areas and volumes of emphysema and airway structure are common, these methods do not capture the structural complexity of the COPD lung. Since the concept of fractals has been successfully applied to evaluate complexity of the lung, this review is aimed at describing the fractal properties of airway disease, emphysema, and vascular abnormalities in COPD. An object forms a fractal if it exhibits the property of self-similarity at different length scales of evaluations. This fractal property is governed by power-law functions characterized by the fractal dimension (FD). Power-laws can also manifest in other statistical descriptors of structure such as the size distribution of emphysema clusters characterized by the power-law exponent D. Although D is not the same as FD of emphysematous clusters, it is a useful index to characterize the spatial pattern of disease progression and predict clinical outcomes in patients with COPD. The FD of the airway tree shape and the D of the size distribution of airway branches have been proposed indexes of structural assessment and clinical predictions. Simulations are also useful to understand the mechanism of disease progression. Therefore, the power-law and fractal analysis of the parenchyma and airways, especially when combined with computer simulations, could lead to a better understanding of the structural alterations during the progression of COPD and help identify subjects at a high risk of severe COPD.

Hemodynamic function of the right ventricular-pulmonary vascular-left atrial unit: normal responses to exercise in healthy adults

With each heartbeat, the right ventricle (RV) inputs blood into the pulmonary vascular (PV) compartment, which conducts blood through the lungs at low pressure and concurrently fills the left atrium (LA) for output to the systemic circulation. This overall hemodynamic function of the integrated RV-PV-LA unit is determined by complex interactions between the components that vary over the cardiac cycle but are often assessed in terms of mean pressure and flow. Exercise challenges these hemodynamic interactions as cardiac filling increases, stroke volume augments, and cycle length decreases, with PV pressures ultimately increasing in association with cardiac output. Recent cardiopulmonary exercise hemodynamic studies have enriched the available data from healthy adults, yielded insight into the underlying mechanisms that modify the PV pressure-flow relationship, and better delineated the normal limits of healthy responses to exercise. This review will examine hemodynamic function of the RV-PV-LA unit using the two-element Windkessel model for the pulmonary circulation. It will focus on acute PV and LA responses that accommodate increased RV output during exercise, including PV recruitment and distension and LA reservoir expansion, and the integrated mean pressure-flow response to exercise in healthy adults. Finally, it will consider how these responses may be impacted by age-related remodeling and modified by sex-related cardiopulmonary differences. Studying the determinants and recognizing the normal limits of PV pressure-flow relations during exercise will improve our understanding of cardiopulmonary mechanisms that facilitate or limit exercise.

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood-gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions (DF) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined DF values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded DF values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess-Murray law or 'the principle of minimum work'.

Space colonization by branching trachea explains the morphospace of a simple respiratory organ

Branching morphogenesis helps increase the efficiency of gas and liquid transport in many animal organs. Studies in several model organisms have highlighted the molecular and cellular complexity behind branching morphogenesis. To understand this complexity, computational models have been developed with the goal of identifying the "major rules" that globally explain the branching patterns. These models also guide further experimental exploration of the biological processes that execute and maintain these rules. In this paper we introduce the tracheal gills of mayfly (Ephemeroptera) larvae as a model system to study the generation of branched respiratory patterns. First, we describe the gills of the mayfly Cloeon dipterum, and quantitatively characterize the geometry of its branching trachea. We next extend this characterization to those of related species to generate the morphospace of branching patterns. Then, we show how an algorithm based on the "space colonization" concept (SCA) can generate this branching morphospace via growth towards a hypothetical attractor molecule (M). SCA differs from other branch-generating algorithms in that the geometry generated depends to a great extent on its perception of the "external" space available for branching, uses few rules and, importantly, can be easily translated into a realistic "biological patterning algorithm". We identified a gene in the C. dipterum genome (Cd-bnl) that is orthologous to the fibroblast growth factor branchless (bnl), which stimulates growth and branching of embryonic trachea in Drosophila. In C. dipterum, this gene is expressed in the gill margins and areas of finer tracheolar branching from thicker trachea. Thus, Cd-bnl may perform the function of M in our model. Finally, we discuss this general mechanism in the context of other branching pattern-generating algorithms.

Triple-cell lineage tracing by a dual reporter on a single allele

Genetic lineage tracing is widely used to study organ development and tissue regeneration. Multicolor reporters are a powerful platform for simultaneously tracking discrete cell populations. Here, combining Dre-rox and Cre-loxP systems, we generated a new dual-recombinase reporter system, called Rosa26 traffic light reporter (R26-TLR), to monitor red, green, and yellow fluorescence. Using this new reporter system with the three distinct fluorescent reporters combined on one allele, we found that the readouts of the two recombinases Cre and Dre simultaneously reflect Cre⁺Dre^-, Cre^-Dre⁺, and Cre⁺Dre⁺ cell lineages. As proof of principle, we show specific labeling in three distinct progenitor/stem cell populations, including club cells, AT2 cells, and bronchoalveolar stem cells, in Sftpc-DreER;Scgb1a1-CreER;R26-TLR mice. By using this new dual-recombinase reporter system, we simultaneously traced the cell fate of these three distinct cell populations during lung repair and regeneration, providing a more comprehensive picture of stem cell function in distal airway repair and regeneration. We propose that this new reporter system will advance developmental and regenerative research by facilitating a more sophisticated genetic approach to studying in vivo cell fate plasticity.

In Vitro Study of Particle Transport in Successively Bifurcating Vessels

To reach a predictive understanding of how particles travel through bifurcating vessels is of paramount importance in many biomedical settings, including embolization, thromboembolism, and drug delivery. Here we utilize an in vitro model in which solid particles are injected through a rigid vessel that symmetrically bifurcates in successive branching generations. The geometric proportion and fluid dynamics parameters are relevant to the liver embolization. The volumetric flow field is reconstructed via phase-contrast magnetic resonance imaging, from which the particle trajectories are calculated for a range of size and density using the particle equation of motion. The method is validated by directly tracking the injected particles via optical imaging. The results indicate that, opposite to the common assumption, the particles distribution is fundamentally different from the volumetric flow partition. In fact, the amount of delivered particles vary substantially between adjacent branches even when the flow is uniformly distributed. This is not due to the inertia of the particles, nor to gravity. The particle distribution is rather rooted in their different pathways, which in turn are linked to their release origin along the main vessel cross-section. Therefore, the tree geometry and the associated flow streamlines are the prime determinant of the particle fate, while local changes of volumetric flow rate to selected branches do not generally produce proportional changes of particle delivery.

Spatial Heterogeneity of Lung Strain and Aeration and Regional Inflammation During Early Lung Injury Assessed with PET/CT

INTRODUCTION

Spatial heterogeneity of lung aeration and strain (change volume/resting volume) occurs at microscopic levels and contributes to lung injury. Yet, it is mostly assessed with histograms or large regions-of-interest. Spatial heterogeneity could also influence regional gene expression. We used positron emission tomography (PET)/computed tomography (CT) to assess the contribution of different length-scales to mechanical heterogeneity and to direct lung injury biological pathway identification.

MATERIALS AND METHODS

Sheep exposed to mild (n = 5, supine and n = 3, prone) and moderate (n = 6, supine) systemic endotoxemia were protectively ventilated. At baseline, 6 hours and 20 hours length-scale analysis was applied to aeration in CT (mild groups) and PET transmission (moderate group) scans; and voxel-level strain derived from image registration of end-inspiratory and end-expiratory CTs (mild). 2-deoxy-2-[(18)F]fluoro-d-glucose (18F-FDG)-PET kinetics parameters in ventral and dorsal regions were correlated with tissue microarray gene expression (moderate).

RESULTS

While aeration and strain heterogeneity were highest at 5-10 mm length-scales, larger length-scales contained a higher fraction of strain than aeration heterogeneity. Contributions of length-scales >5-10 mm to aeration and strain heterogeneity increased as lung injury progressed (p < 0.001) and were higher in supine than prone animals. Genes expressed with regional correlation to 18F-FDG-PET kinetics (|r| = 0.81 [0.78-0.85]) yielded pathways associated with immune system activation and fluid clearance.

CONCLUSION

Normal spatial heterogeneity of aeration and strain suggest larger anatomical and functional determinants of lung strain than aeration heterogeneity. Lung injury and supine position increase the contribution of larger length-scales. 18F-FDG-PET-based categorization of gene expression results in known and novel biological pathways relevant to lung injury.

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.

Seeing the forest for the trees: fractal dimensions measure COPD airway remodeling

Chronic obstructive pulmonary disease (COPD) is extremely heterogenous in its effects on airway remodeling. Parsing the complex and interrelated morphologic changes and understanding their contribution to disease severity has posed a significant challenge to the field. In the current issue of the JCI, Bodduluri et al. measured the complex effects of COPD on the airway tree using airway fractal dimension (AFD) on computerized tomography in a large cohort of smokers with and without COPD. They found that lower AFD was independently associated with disease severity and mortality in COPD. This work highlights AFD as a noninvasive approach to analyze complex changes in airway geometry.

Regulation of vascular signalling by nuclear Sprouty2 in fetal lung epithelial cells: Implications for co-ordinated airway and vascular branching in lung development

Sprouty2 (Spry2) acts as a central regulator of tubular growth and branch patterning in the developing mammalian lung by controlling both magnitude and duration of growth factor signalling. To determine if this protein coordinates airway and vascular growth factor signalling, we tested the hypothesis that Spry2 links the primary cue for airway outgrowth, fibroblast growth factor-10 (FGF-10), to genomic events underpinning the expression and release of vascular endothelial growth factor-A (VEGF-A). Using primary fetal distal lung epithelial cells (FDLE) from rat, and immortalised human bronchial epithelial cells (16HBE14o-), we identified a nuclear sub-population of Spry2 which interacted with regions of the rat and human VEGF-A promoter spanning the hypoxia response element (HRE) and adjacent 3' sites. In FDLE cultured at the PO₂ of the fetal lung, FGF-10 relieved the Spry2 interaction at the HRE region by promoting clearance of a 39 kDa form and this was accompanied by histone-3 S10K14 phosphoacetylation, promoter de-methylation, hypoxia inducible factor-1α activation and VEGF-A expression. This repressive characteristic of nuclear Spry2 was relieved in 16HBE14o- by shRNA knockdown, and stable expression of mutants (C218A; C221A) that do not interact with the VEGF-A promoter HRE region. We conclude that nuclear Spry2 acts as a molecular link which co-ordinates airway and vascular growth of the cardiopulmonary system. This identifies Spry2 as a contributing determinant of design optimality in the mammalian lung.

Gravity outweighs the contribution of structure to passive ventilation-perfusion matching in the supine adult human lung

Gravity and matched airway/vascular tree geometries are both hypothesized to be key contributors to ventilation-perfusion (V̇/Q̇) matching in the lung, but their relative contributions are challenging to quantify experimentally. We used a structure-based model to conduct an analysis of the relative contributions of tissue deformation (the "Slinky" effect), other gravitational mechanisms (weight of blood and gravitational gradient in tissue elastic recoil), and matched airway and arterial tree geometry to V̇/Q̇ matching and therefore to total lung oxygen exchange. Our results showed that the heterogeneity in V̇ and Q̇ were lowest and the correlation between V̇ and Q̇ was highest when the only mechanism for V̇/Q̇ matching was either tissue deformation or matched geometry. Heterogeneity in V̇ and Q̇ was highest and their correlation was poorest when all mechanisms were active (that is, at baseline). Eliminating the contribution of matched geometry did not change the correlation between V̇ and Q̇ at baseline. Despite the much larger heterogeneities in V̇ and Q̇ at baseline, the contribution of in-common (to V̇ and Q̇) gravitational mechanisms provided sufficient compensatory V̇/Q̇ matching to minimize the impact on oxygen transfer. In summary, this model predicts that during supine normal breathing under gravitational loading, passive V̇/Q̇ matching is predominantly determined by shared gravitationally induced tissue deformation, compliance distribution, and the effect of the hydrostatic pressure gradient on vessel and capillary size and blood pressures. Contribution from the matching airway and arterial tree geometries in this model is minor under normal gravity in the supine adult human lung. NEW & NOTEWORTHY We use a computational model to systematically analyze contributors to ventilation-perfusion matching in the lung. The model predicts that the multiple effects of gravity are the predominant mechanism in providing passive ventilation-perfusion matching in the supine adult human lung under normal gravitational loads, while geometric matching of airway and arterial trees plays a minor role.

Geometries of vasculature bifurcation can affect the level of trophic damage during formation of a brain ischemic lesion

Ischemic lesion is a common cause of various diseases in humans. Brain tissue is especially sensitive to this type of damage. A common reason for the appearance of an ischemic area is a stop in blood flow in some branch of the vasculature system. Then, a decreasing concentration gradient results in a low mean level of oxygen in surrounding tissues. After that, the biochemical ischemic cascade spreads. In this review, we examine these well-known events from a new angle. It is stressed that there is essential evidence to predict the formation of an ischemic micro-area at the base of vascular bifurcation geometries. Potential applications to improve neuroprotection are also discussed.

Systems Biology and Clinical Practice in Respiratory Medicine. The Twain Shall Meet

Respiratory diseases are highly complex, being driven by host-environment interactions and manifested by inflammatory, structural, and functional abnormalities that vary over time. Traditional reductionist approaches have contributed vastly to our knowledge of biological systems in health and disease to date; however, they are insufficient to provide an understanding of the behavior of the system as a whole. In this Pulmonary Perspective, we discuss systems biology approaches, especially but not limited to the study of the lung as a complex system. Such integrative approaches take into account the large number of dynamic subunits and their interactions found in biological systems. Borrowing methods from physics and mathematics, it is possible to study the collective behavior of these systems over time and in a multidimensional manner. We first examine the physiological basis for complexity in the respiratory system and its implications for disease. We then expand on the potential applications of systems biology methods to study complex systems, within the context of diagnosis and monitoring of respiratory diseases including asthma, chronic obstructive pulmonary disease (COPD), and critical illness. We summarize the significant advances made in recent years using systems approaches for disease phenotyping, applied to data ranging from the molecular to clinical level, obtained from large-scale asthma and COPD networks. We describe new studies using temporal complexity patterns to characterize asthma and COPD and predict exacerbations as well as predict adverse outcomes in critical care. We highlight new methods that are emerging with this approach and discuss remaining questions that merit greater attention in the field.

Fluctuation Analysis of Peak Expiratory Flow and Its Association with Treatment Failure in Asthma

RATIONALE

Temporal fluctuations have been demonstrated in lung function and asthma control, but the effect of controller therapy on these fluctuations is unknown.

OBJECTIVES

To determine if fluctuations in peak expiratory flow (PEF) are predictive of subsequent treatment failure and may be modified by controller therapy.

METHODS

We applied detrended fluctuation analysis to once-daily PEF data from 493 participants in the LOCCS (Leukotriene Modifier Corticosteroid or Corticosteroid-Salmeterol) trial of the American Lung Association Airways Clinical Research Centers. We evaluated the coefficient of variation of PEF (CVpef) and the scaling exponent α, reflecting self-similarity of PEF, in relation to treatment failure from the run-in period of open-label inhaled fluticasone, and the treatment periods for subjects randomized to (1) continued twice daily fluticasone (F), (2) once daily fluticasone plus salmeterol (F + S), or (3) once daily oral montelukast (M).

MEASUREMENTS AND MAIN RESULTS

The CVpef was higher in those with treatment failure in the F and F + S groups in the run-in phase, and all three groups in the treatment phase. α was similar between those with and without treatment failure in all three groups during the run-in phase but was higher among those with treatment failure in the F and F + S groups during the treatment phase. Participants in all three groups showed variable patterns of change in α leading up to treatment failure.

CONCLUSIONS

We conclude that increased temporal self-similarity (α) of more variable lung function (CVpef) is associated with treatment failure, but the pattern of change in self-similarity leading up to treatment failure is variable across individuals.

Brazilian studies on pulmonary function in COPD patients: what are the gaps?

BACKGROUND

COPD is a major cause of death and morbidity worldwide, and is characterized by persistent airflow obstruction. The evaluation of obstruction is critically dependent on sensitive methods for lung-function testing. A wide body of knowledge has been accumulated in recent years showing that these methods have been significantly refined and seems promising for detection of early disease.

OBJECTIVES

This review focuses on research on pulmonary function analysis in COPD performed in Brazil during this century.

MATERIALS AND METHODS

The literature was searched using a systematic search strategy limited to English language studies that were carried out in Brazil from the year 2000 onward, with study objectives that included a focus on lung function.

RESULTS

After we applied our inclusion and exclusion criteria, 94 articles addressed our stated objectives. Among the new methods reviewed are the forced-oscillation technique and the nitrogen-washout test, which may provide information on small-airway abnormalities. Studies investigating the respiratory muscles and thoracoabdominal motion are also discussed, as well as studies on automatic clinical decision-support systems and complexity measurements. We also examined important gaps in the present knowledge and suggested future directions for the cited research fields.

CONCLUSION

There is clear evidence that improvements in lung-function methods allowed us to obtain new pathophysiological information, contributing to improvement in our understanding of COPD. In addition, they may also assist in the diagnosis and prevention of COPD. Further investigations using prospective and longitudinal design may be of interest to elucidate the use of these new methods in the diagnosis and prevention of COPD.

Forced oscillation, integer and fractional-order modeling in asthma

The purpose of this study was to evaluate the use of fractional-order (FrOr) modeling in asthma. To this end, three FrOr models were compared with traditional parameters and an integer-order model (InOr). We investigated which model would best fit the data, the correlation with traditional lung function tests and the contribution to the diagnostic of airway obstruction. The data consisted of forced oscillation (FO) measurements obtained from healthy (n=22) and asthmatic volunteers with mild (n=22), moderate (n=19) and severe (n=19) obstructions. The first part of this study showed that a FrOr was the model that best fit the data (relative distance: FrOr=4.3±2.4; InOr=5.1±2.6%). The correlation analysis resulted in reasonable (R=0.36) to very good (R=0.77) associations between FrOr parameters and spirometry. The closest associations were observed between parameters related to peripheral airway obstruction, showing a clear relationship between the FrOr models and lung mechanics. Receiver-operator analysis showed that FrOr parameters presented a high potential to contribute to the detection of the mild obstruction in a clinical setting. The accuracy [area under the Receiver Operating Characteristic curve (AUC)] observed in these parameters (AUC=0.954) was higher than that observed in traditional FO parameters (AUC=0.732) and that obtained from the InOr model (AUC=0.861). Patients with moderate and severe obstruction were identified with high accuracy (AUC=0.972 and 0.977, respectively). In conclusion, the results obtained are in close agreement with asthma pathology, and provide evidence that FO measurement associated with FrOr models is a non-invasive, simple and radiation-free method for the detection of biomechanical abnormalities in asthma.

Radiomics-based differentiation of lung disease models generated by polluted air based on X-ray computed tomography data

BACKGROUND

Lung diseases (resulting from air pollution) require a widely accessible method for risk estimation and early diagnosis to ensure proper and responsive treatment. Radiomics-based fractal dimension analysis of X-ray computed tomography attenuation patterns in chest voxels of mice exposed to different air polluting agents was performed to model early stages of disease and establish differential diagnosis.

METHODS

To model different types of air pollution, BALBc/ByJ mouse groups were exposed to cigarette smoke combined with ozone, sulphur dioxide gas and a control group was established. Two weeks after exposure, the frequency distributions of image voxel attenuation data were evaluated. Specific cut-off ranges were defined to group voxels by attenuation. Cut-off ranges were binarized and their spatial pattern was associated with calculated fractal dimension, then abstracted by the fractal dimension -- cut-off range mathematical function. Nonparametric Kruskal-Wallis (KW) and Mann-Whitney post hoc (MWph) tests were used.

RESULTS

Each cut-off range versus fractal dimension function plot was found to contain two distinctive Gaussian curves. The ratios of the Gaussian curve parameters are considerably significant and are statistically distinguishable within the three exposure groups.

CONCLUSIONS

A new radiomics evaluation method was established based on analysis of the fractal dimension of chest X-ray computed tomography data segments. The specific attenuation patterns calculated utilizing our method may diagnose and monitor certain lung diseases, such as chronic obstructive pulmonary disease (COPD), asthma, tuberculosis or lung carcinomas.

Lung cancer-a fractal viewpoint

Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.

Fatigue reduces the complexity of knee extensor torque fluctuations during maximal and submaximal intermittent isometric contractions in man

Neuromuscular fatigue increases the amplitude of fluctuations in torque output during isometric contractions, but the effect of fatigue on the temporal structure, or complexity, of these fluctuations is not known. We hypothesised that fatigue would result in a loss of temporal complexity and a change in fractal scaling of the torque signal during isometric knee extensor exercise. Eleven healthy participants performed a maximal test (5 min of intermittent maximal voluntary contractions, MVCs), and a submaximal test (contractions at a target of 40% MVC performed until task failure), each with a 60% duty factor (6 s contraction, 4 s rest). Torque and surface EMG signals were sampled continuously. Complexity and fractal scaling of torque were quantified by calculating approximate entropy (ApEn), sample entropy (SampEn) and the detrended fluctuation analysis (DFA) scaling exponent α. Fresh submaximal contractions were more complex than maximal contractions (mean ± SEM, submaximal vs. maximal: ApEn 0.65 ± 0.09 vs. 0.15 ± 0.02; SampEn 0.62 ± 0.09 vs. 0.14 ± 0.02; DFA α 1.35 ± 0.04 vs. 1.55 ± 0.03; all P < 0.005). Fatigue reduced the complexity of submaximal contractions (ApEn to 0.24 ± 0.05; SampEn to 0.22 ± 0.04; DFA α to 1.55 ± 0.03; all P < 0.005) and maximal contractions (ApEn to 0.10 ± 0.02; SampEn to 0.10 ± 0.02; DFA α to 1.63 ± 0.02; all P < 0.01). This loss of complexity and shift towards Brownian-like noise suggests that as well as reducing the capacity to produce torque, fatigue reduces the neuromuscular system's adaptability to external perturbations.

Extension of the mitochondria dysfunction hypothesis of metabolic syndrome to atherosclerosis with emphasis on the endocrine-disrupting chemicals and biophysical laws

Metabolic syndrome and its component phenotypes, hyperglycemia, hypertension, (abdominal) obesity and hypertriglyceridemia, are major risk factors for atherosclerosis. Recently, associations between exposure to endocrine‐disrupting chemicals (EDCs), mitochondrial dysfunction, metabolic syndrome and atherosclerosis have been established, suggesting a possible common mechanism underlying these phenomena. Extending a previously proposed mitochondria dysfunction theory of metabolic syndrome and using biophysical laws, such as metabolic scaling, Murray's law and fractal geometry of the vascular branching system, we propose that atherosclerosis could be explained as an ill‐adaptive change occurring in nutrient‐supplying arteries in response to the decreasing tissue energy demand caused by tissue mitochondrial dysfunction. Various aspects of this new hypothesis are discussed.

Airflow pattern complexity during resting breathing in patients with COPD: effect of airway obstruction

We investigated the influence of airway obstruction in the complexity of the airflow pattern in COPD and its use as a marker of disease activity. The sample entropy (SampEnV') and the variability (SDV') of the airflow pattern were measured in a group of 88 subjects with various levels of airway obstruction. Airway obstruction resulted in a reduction in the SampEnV' (p<0.0001) that was significantly correlated with spirometric indices of airway obstruction (R=0.50, p<0.001). The early adverse effects in mild airway obstruction were detected by the SampEnV' with an accuracy of 84%. SDV' increased with airway obstruction (p<0.002). We conclude that (1) the airflow patterns in COPD exhibit reduced complexity compared with healthy subjects; (2) this reduction in complexity is proportional to airway obstruction; and (3) the evaluation of SampEnV' may provide novel respiratory biomarkers suitable to facilitate the diagnosis of respiratory abnormalities in COPD.

A mechanical design principle for tissue structure and function in the airway tree

With every breath, the dynamically changing mechanical pressures must work in unison with the cells and soft tissue structures of the lung to permit air to efficiently traverse the airway tree and undergo gas exchange in the alveoli. The influence of mechanics on cell and tissue function is becoming apparent, raising the question: how does the airway tree co-exist within its mechanical environment to maintain normal cell function throughout its branching structure of diminishing dimensions? We introduce a new mechanical design principle for the conducting airway tree in which mechanotransduction at the level of cells is driven to orchestrate airway wall structural changes that can best maintain a preferred mechanical microenvironment. To support this principle, we report in vitro radius-transmural pressure relations for a range of airway radii obtained from healthy bovine lungs and model the data using a strain energy function together with a thick-walled cylinder description. From this framework, we estimate circumferential stresses and incremental Young's moduli throughout the airway tree. Our results indicate that the conducting airways consistently operate within a preferred mechanical homeostatic state, termed mechanical homeostasis, that is characterized by a narrow range of circumferential stresses and Young's moduli. This mechanical homeostatic state is maintained for all airways throughout the tree via airway wall dimensional and mechanical relationships. As a consequence, cells within the airway walls throughout the airway tree experience similar oscillatory strains during breathing that are much smaller than previously thought. Finally, we discuss the potential implications of how the maintenance of mechanical homeostasis, while facilitating healthy tissue-level alterations necessary for maturation, may lead to airway wall structural changes capable of chronic asthma.

With every breath, mechanical pressures change in the lung and permit air to efficiently traverse the airway tree and undergo gas exchange. These pressure variations also influence cell and tissue function, raising the question: how does the airway tree co-exist within its mechanical environment to maintain normal cell function throughout its branching structure of diminishing dimensions? We introduce a new mechanical design principle for the conducting airway tree in which mechanotransduction, the process that converts mechanical forces on cells to biochemical signals, is driven to orchestrate tissue-level structural changes that can best restore a preferred mechanical microenvironment; a concept termed mechanical homeostasis. We report in vitro mechanical properties for a range of airway sizes and present a mathematical model that describes the data. Our results indicate that airways indeed consistently operate within a preferred mechanical homeostatic state. We further describe how this mechanical homeostasis while facilitating healthy tissue-level alterations necessary for maturation can inadvertently lead to airway wall structural changes capable of chronic asthma.

Fluctuation analysis of respiratory impedance waveform in asthmatic patients: effect of airway obstruction

Fluctuation analysis has great potential to contribute to pulmonary clinical science and practice. We evaluated the relationship between asthma and the respiratory impedance recurrence period density entropy (RPDEnZrs) and the variability (SDZrs). A non-invasive and simple protocol for assessing respiratory mechanics during spontaneous breathing was used in a group of 74 subjects with various levels of airway obstruction. Airway obstruction resulted in a reduction in the RPDEnZrs that was significantly correlated with both spirometric indices of airway obstruction (R = 0.48, p < 0.0001) and mean respiratory impedance (R = -0.83, p < 0.0001). These results suggest that the impedance pattern becomes less complex in asthmatic patients, which may explain the reduction in respiratory systems' adaptability to daily life activities. Preliminary evaluations indicate that RPDEnZrs may contribute to the asthma diagnosis, presenting accuracies of 82 and 87 % in patients with moderate and severe airway obstruction, respectively. On the other hand, SDZrs increased with obstruction (p < 0.0001) and was inversely correlated with spirometric indices of obstruction (R = -0.42, p = 0.0003) and directly associated with mean impedance (R = 0.88, p < 0.0001). This analysis contributes to elucidate previous studies and identified respiratory changes in patients with moderate and severe obstruction with an adequate accuracy (85 and 87 %, respectively).

Branch mode selection during early lung development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modes.

Most organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching. While the branching sequence is identical in mice of identical genetic background it differs between mouse strains. This suggests that the positioning of branch points and the type of branching sensitively depends on information encoded in the genome. Encoding every branching point independently in the genome would require a large number of genes, and it is more likely that a recursive, self-organized process exists that determines the patterning. While many regulatory molecules have been identified an integrated understanding of the regulatory network (program) is missing. Based on available experimental data we have developed a model for lung branching. The model correctly predicts branching phenotypes in mutants and suggests that also the growth speed of the lung tip can affect the positioning and type of the next branching event.