Fractal nature of regional ventilation distribution

Methodology of murine lung cancer mimics clinical lung adenocarcinoma progression and metastasis

Lung cancer is the leading cause of cancer-related deaths, of which adenocarcinoma is the most common subtype. Despite this, lung adenocarcinoma and its metastasis are poorly understood, due to difficulties in feasibly recapitulating disease progression and predicting clinical benefits of therapy. We outline a methodology to develop immunogenic orthotopic lung adenocarcinoma mouse models, by injecting cell-specific cre viruses into the lung of a genetically engineered mouse, which mirrors cancer progression defined by the International Association for the Study of Lung Cancer. Evaluation of different cre virus/concentrations models demonstrate remarkable consistency in cancer initiation and metastasis, allowing for high throughput, while showing differences in timing and severity, offering greater flexibility when selecting models. Histological and immune profiles reflect clinical observations suggesting similar mechanisms are recapitulated and preliminary data show resultant tumors to be responsive to clinical treatments. We present a clinically relevant, next-generation murine model for studying lung adenocarcinoma.

The Pulmonary Vasculature

The pulmonary circulation is a low-pressure, low-resistance circuit whose primary function is to deliver deoxygenated blood to, and oxygenated blood from, the pulmonary capillary bed enabling gas exchange. The distribution of pulmonary blood flow is regulated by several factors including effects of vascular branching structure, large-scale forces related to gravity, and finer scale factors related to local control. Hypoxic pulmonary vasoconstriction is one such important regulatory mechanism. In the face of local hypoxia, vascular smooth muscle constriction of precapillary arterioles increases local resistance by up to 250%. This has the effect of diverting blood toward better oxygenated regions of the lung and optimizing ventilation-perfusion matching. However, in the face of global hypoxia, the net effect is an increase in pulmonary arterial pressure and vascular resistance. Pulmonary vascular resistance describes the flow-resistive properties of the pulmonary circulation and arises from both precapillary and postcapillary resistances. The pulmonary circulation is also distensible in response to an increase in transmural pressure and this distention, in addition to recruitment, moderates pulmonary arterial pressure and vascular resistance. This article reviews the physiology of the pulmonary vasculature and briefly discusses how this physiology is altered by common circumstances.

Modeling the influence of gravity and the mechanical properties of elastin and collagen fibers on alveolar and lung pressure-volume curves

The relationship between pressure (P) and volume (V) in the human lung has been extensively studied. However, the combined effects of gravity and the mechanical properties of elastin and collagen on alveolar and lung P-V curves during breathing are not well understood. Here, we extended a previously established thick-walled spherical model of a single alveolus with wavy collagen fibers during positive pressure inflation. First, we updated the model for negative pressure-driven inflation that allowed incorporation of a gravity-induced pleural pressure gradient to predict how the static alveolar P-V relations vary spatially throughout an upright human lung. Second, by introducing dynamic surface tension and collagen viscoelasticity, we computed the hysteresis loop of the lung P-V curve. The model was tested by comparing its predicted regional ventilation to literature data, which offered insight into the effects of microgravity on ventilation. The model has also produced novel testable predictions for future experiments about the variation of mechanical stresses in the septal walls and the contribution of collagen and elastin fibers to the P-V curve and throughout the lung. The model may help us better understand how mechanical stresses arising from breathing and pleural pressure variations affect regional cellular mechanotransduction in the lung.

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

Fractal analysis reveals functional unit of ventilation in the lung

Ventilation is inhomogeneous in the lungs across species. It has been hypothesized that ventilation inhomogeneity is largely determined by the design of the airway branching network. Because exchange of gases at the alveolar barrier is more efficient when gas concentrations are evenly distributed at subacinar length scales, it is assumed that a 'functional unit' of ventilation exists within the lung periphery, where gas concentration becomes uniform. On the other hand, because the morphology of pulmonary airways and alveoli, and the distribution of inhaled fluorescent particles show self-similar fractal properties over a wide range of length scales, it has been predicted that fractal dimension of ventilation approaches unity within an internally homogeneous functional unit of ventilation. However, the existence of such a functional unit has never been demonstrated experimentally due to lack of in situ gas concentration measurements of sufficient spatial resolution in the periphery of a complex bifurcating network. Here, using energy-subtractive synchrotron radiation tomography, we measured the distribution of an inert gas (Xe) in the in vivo rabbit lung during Xe wash-in breathing manoeuvres. The effects of convective flow rate, diffusion and cardiac motion were also assessed. Fractal analysis of resulting gas concentration and tissue density maps revealed that fractal dimension was always smaller for Xe than for tissue density, and that only for the gas, a length scale existed where fractal dimension approached unity. The length scale where this occurred was seen to correspond to that of a rabbit acinus, the terminal structure comprising only alveolated airways. KEY POINTS: Gas ventilation is inhomogeneous in the lung of many species. However, it is not known down to what length scales this inhomogeneity persists. It is generally assumed that ventilation becomes homogeneous at subacinar length scales, beyond the spatial resolution of commonly available imaging techniques, hence this has not been demonstrated experimentally. Here we measured the distribution of inhaled Xe gas in the rabbit lung using synchrotron radiation energy-subtractive imaging and used fractal analysis to show that ventilation becomes internally uniform within regions about the size of rabbit lung acini.

Ventilation heterogeneity imaged by multibreath wash-ins of hyperpolarized 3 He and 129 Xe in healthy rabbits

KEY POINTS

Multibreath imaging to estimate regional gas mixing efficiency is superior to intensity-based single-breath ventilation markers, as it is capable of revealing minute but essential measures of ventilation heterogeneity which may be sensitive to subclinical alterations in the early stages of both obstructive and restrictive respiratory disorders. Large-scale convective stratification of ventilation in central-to-peripheral directions is the dominant feature of observed ventilation heterogeneity when imaging a heavy/less diffusive xenon gas mixture; smaller-scale patchiness, probably originating from asymmetric lung function at bronchial airway branching due to the interaction of convective and diffusive flows, is the dominant feature when imaging a lighter/more diffusive helium gas mixture. Since detecting low regional ventilation is crucial for characterizing diseased lungs, our results suggest that dilution with natural abundance helium and imaging at higher lung volumes seem advisable when imaging with hyperpolarized ¹²⁹ Xe; this will allow the imaging gas to reach slow-filling and/or non-dependent lung regions, which might otherwise be impossible to distinguish from total ventilation shunt regions. The ability to differentiate these regions from those of total shunt is worse with typical single-breath imaging techniques.

ABSTRACT

The mixing of freshly inhaled gas with gas already present in the lung can be directly assessed with heretofore unachievable precision via magnetic resonance imaging of signal build-up resulting from multiple wash-ins of a hyperpolarized (HP) gas. Here, we used normoxic HP ³ He and ¹²⁹ Xe mixtures to study regional ventilation at different spatial scales in five healthy mechanically ventilated supine rabbits at two different inspired volumes. To decouple the respective effects of density and diffusion rates on ventilation heterogeneity, two additional studies were performed: one in which ³ He was diluted with an equal fraction of natural abundance xenon, and one in which ¹²⁹ Xe was diluted with an equal fraction of ⁴ He. We observed systematic differences in the spatial scale of specific ventilation heterogeneity between HP ³ He and ¹²⁹ Xe. We found that large-scale, central-to-peripheral convective ventilation inhomogeneity is the dominant cause of observed heterogeneity when breathing a normoxic xenon gas mixture. In contrast, small-scale ventilation heterogeneity in the form of patchiness, probably originating from asymmetric lung function at bronchial airway branching due to interactions between convective and diffusive flows, is the dominant feature when breathing a normoxic helium gas mixture, for which the critical zone occurs more proximally and at an imageable spatial scale. We also showed that the existence of particular underventilated non-dependent lung regions when breathing a heavy gas mixture is the result of the density of that mixture - rather than, for example, its diffusion rate or viscosity. Finally, we showed that gravity-dependent ventilation heterogeneity becomes substantially more uniform at higher inspired volumes for xenon gas mixtures compared to helium mixtures.

Combined Assessment of Pulmonary Ventilation and Perfusion with Single-Energy Computed Tomography and Image Processing

RATIONALE AND OBJECTIVES

To establish a proof-of-principle for combined assessment of pulmonary ventilation and perfusion using single-energy computed tomography (CT) and image processing/analysis (denoted as single-energy CT ventilation/perfusion imaging).

MATERIALS AND METHODS

Breath-hold CT scans were acquired at end-expiration and end-inspiration before injection of iodinated contrast agents, and repeated at end-inspiration after contrast injection for 17 canines (8 normal and 9 diseased lung subjects). Ventilation images were calculated with deformable image registration to map the end-expiratory and end-inspiratory CT images and quantitative analysis for regional volume changes as surrogates for ventilation. Perfusion images were calculated by subtracting the end-inspiratory precontrast CT from the deformably registered end-inspiratory postcontrast CT, yielding a map of regional Hounsfield unit enhancement as a surrogate for perfusion. Ventilation-perfusion matching, spatial heterogeneity, and gravitationally directed gradients were compared between two groups using a Wilcoxon rank-sum test.

RESULTS

The normal group had significantly higher Dice similarity coefficients for spatial overlap of segmented functional volumes between ventilation and perfusion (median 0.40 vs. 0.33, p = 0.05), suggesting stronger ventilation-perfusion matching. The normal group also had greater Spearman's correlation coefficients based on 16 regions of interest (median 0.58 vs. 0.40, p = 0.09). The coefficients of variation were comparable (median, ventilation 0.71 vs. 0.91, p = 0.60; perfusion 0.63 vs. 0.75, p = 0.27). The linear regression slopes of gravitationally directed gradient were also comparable for ventilation (median, ventilation -0.26 vs. -0.18, p = 0.19; perfusion -0.17 vs. -0.06, p = 0.11).

CONCLUSION

These findings provide proof-of-principle for single-energy CT ventilation/perfusion imaging.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

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.

Positional Therapy and Regional Pulmonary Ventilation

BACKGROUND

Prone ventilation redistributes lung inflation along the gravitational axis; however, localized, nongravitational effects of body position are less well characterized. The authors hypothesize that positional inflation improvements follow both gravitational and nongravitational distributions. This study is a nonoverlapping reanalysis of previously published large animal data.

METHODS

Five intubated, mechanically ventilated pigs were imaged before and after lung injury by tracheal injection of hydrochloric acid (2 ml/kg). Computed tomography scans were performed at 5 and 10 cm H2O positive end-expiratory pressure (PEEP) in both prone and supine positions. All paired prone-supine images were digitally aligned to each other. Each unit of lung tissue was assigned to three clusters (K-means) according to positional changes of its density and dimensions. The regional cluster distribution was analyzed. Units of tissue displaying lung recruitment were mapped.

RESULTS

We characterized three tissue clusters on computed tomography: deflation (increased tissue density and contraction), limited response (stable density and volume), and reinflation (decreased density and expansion). The respective clusters occupied (mean ± SD including all studied conditions) 29.3 ± 12.9%, 47.6 ± 11.4%, and 23.1 ± 8.3% of total lung mass, with similar distributions before and after lung injury. Reinflation was slightly greater at higher PEEP after injury. Larger proportions of the reinflation cluster were contained in the dorsal versus ventral (86.4 ± 8.5% vs. 13.6 ± 8.5%, P < 0.001) and in the caudal versus cranial (63.4 ± 11.2% vs. 36.6 ± 11.2%, P < 0.001) regions of the lung. After injury, prone positioning recruited 64.5 ± 36.7 g of tissue (11.4 ± 6.7% of total lung mass) at lower PEEP, and 49.9 ± 12.9 g (8.9 ± 2.8% of total mass) at higher PEEP; more than 59.0% of this recruitment was caudal.

CONCLUSIONS

During mechanical ventilation, lung reinflation and recruitment by the prone positioning were primarily localized in the dorso-caudal lung. The local effects of positioning in this lung region may determine its clinical efficacy.

EDITOR’S PERSPECTIVE

Ventilation/Perfusion Relationships and Gas Exchange: Measurement Approaches

Ventilation-perfusion ( V ˙ A / Q ˙ ) matching, the regional matching of the flow of fresh gas to flow of deoxygenated capillary blood, is the most important mechanism affecting the efficiency of pulmonary gas exchange. This article discusses the measurement of V ˙ A / Q ˙ matching with three broad classes of techniques: (i) those based in gas exchange, such as the multiple inert gas elimination technique (MIGET); (ii) those derived from imaging techniques such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), magnetic resonance imaging (MRI), computed tomography (CT), and electrical impedance tomography (EIT); and (iii) fluorescent and radiolabeled microspheres. The focus is on the physiological basis of these techniques that provide quantitative information for research purposes rather than qualitative measurements that are used clinically. The fundamental equations of pulmonary gas exchange are first reviewed to lay the foundation for the gas exchange techniques and some of the imaging applications. The physiological considerations for each of the techniques along with advantages and disadvantages are briefly discussed. © 2020 American Physiological Society. Compr Physiol 10:1155-1205, 2020.

The fractal geometry of bronchial trees differs by strain in mice

Fractal biological structures are pervasive throughout the plant and animal kingdoms, with the mammalian lung being a quintessential example. The lung airway and vascular trees are generated during embryogenesis from a small set of building codes similar to Turing mechanisms that create robust trees ideally suited to their functions. Whereas the blood flow pattern generated by these fractal trees has been shown to be genetically determined, the geometry of the trees has not. We explored a newly established repository providing high-resolution bronchial trees from the four most commonly studied laboratory mice (B6C3F1, BALB/c, C57BL/6 and CD-1). The data fit a fractal model well for all animals with the fractal dimensions ranging from 1.54 to 1.67, indicating that the conducting airway of mice can be considered a self-similar and space-filling structure. We determined that the fractal dimensions of these airway trees differed by strain but not sex, reinforcing the concept that airway branching patterns are encoded within the DNA. The observations also highlight that future study design and interpretations may need to consider differences in airway geometry between mouse strains.NEW & NOTEWORTHY Similar to larger mammals such as humans, the geometries of the bronchial tree in mice are fractal structures that have repeating patterns from the trachea to the terminal branches. The airway geometries of the four most commonly studied mice are different and need to be considered when comparing results that employ different mouse strains. This variability in mouse airway geometries should be incorporated into computer models exploring toxicology and aerosol deposition in mouse models.

Ventilation/Perfusion Matching: Of Myths, Mice, and Men

Despite a huge range in lung size between species, there is little measured difference in the ability of the lung to provide a well-matched air flow (ventilation) to blood flow (perfusion) at the gas exchange tissue. Here, we consider the remarkable similarities in ventilation/perfusion matching between species through a biophysical lens and consider evidence that matching in large animals is dominated by gravity but in small animals by structure.

Small Cell Lung Cancer Therapeutic Responses Through Fractal Measurements: From Radiology to Mitochondrial Biology

Small cell lung cancer (SCLC) is an aggressive neuroendocrine disease with an overall 5 year survival rate of ~7%. Although patients tend to respond initially to therapy, therapy-resistant disease inevitably emerges. Unfortunately, there are no validated biomarkers for early-stage SCLC to aid in early detection. Here, we used readouts of lesion image characteristics and cancer morphology that were based on fractal geometry, namely fractal dimension (FD) and lacunarity (LC), as novel biomarkers for SCLC. Scanned tumors of patients before treatment had a high FD and a low LC compared to post treatment, and this effect was reversed after treatment, suggesting that these measurements reflect the initial conditions of the tumor, its growth rate, and the condition of the lung. Fractal analysis of mitochondrial morphology showed that cisplatin-treated cells showed a discernibly decreased LC and an increased FD, as compared with control. However, treatment with mdivi-1, the small molecule that attenuates mitochondrial division, was associated with an increase in FD as compared with control. These data correlated well with the altered metabolic functions of the mitochondria in the diseased state, suggesting that morphological changes in the mitochondria predicate the tumor’s future ability for mitogenesis and motogenesis, which was also observed on the CT scan images. Taken together, FD and LC present ideal tools to differentiate normal tissue from malignant SCLC tissue as a potential diagnostic biomarker for SCLC.

Airway fractal dimension predicts respiratory morbidity and mortality in COPD

BACKGROUND

Chronic obstructive pulmonary disease (COPD) is characterized by airway remodeling. Characterization of airway changes on computed tomography has been challenging due to the complexity of the recurring branching patterns, and this can be better measured using fractal dimensions.

METHODS

We analyzed segmented airway trees of 8,135 participants enrolled in the COPDGene cohort. The fractal complexity of the segmented airway tree was measured by the Airway Fractal Dimension (AFD) using the Minkowski-Bougliand box-counting dimension. We examined associations between AFD and lung function and respiratory morbidity using multivariable regression analyses. We further estimated the extent of peribronchial emphysema (%) within 5 mm of the airway tree, as this is likely to affect AFD. We classified participants into 4 groups based on median AFD, percentage of peribronchial emphysema, and estimated survival.

RESULTS

AFD was significantly associated with forced expiratory volume in one second (FEV1; P < 0.001) and FEV1/forced vital capacity (FEV1/FVC; P < 0.001) after adjusting for age, race, sex, smoking status, pack-years of smoking, BMI, CT emphysema, air trapping, airway thickness, and CT scanner type. On multivariable analysis, AFD was also associated with respiratory quality of life and 6-minute walk distance, as well as exacerbations, lung function decline, and mortality on longitudinal follow-up. We identified a subset of participants with AFD below the median and peribronchial emphysema above the median who had worse survival compared with participants with high AFD and low peribronchial emphysema (adjusted hazards ratio [HR]: 2.72; 95% CI: 2.20-3.35; P < 0.001), a substantial number of whom were not identified by traditional spirometry severity grades.

CONCLUSION

Airway fractal dimension as a measure of airway branching complexity and remodeling in smokers is associated with respiratory morbidity and lung function change, offers prognostic information additional to traditional CT measures of airway wall thickness, and can be used to estimate mortality risk.

TRIAL REGISTRATION

ClinicalTrials.gov identifier: NCT00608764.

FUNDING

This study was supported by NIH K23 HL133438 (SPB) and the COPDGene study (NIH Grant Numbers R01 HL089897 and R01 HL089856). The COPDGene project is also supported by the COPD Foundation through contributions made to an Industry Advisory Board comprised of AstraZeneca, Boehringer Ingelheim, Novartis, Pfizer, Siemens, Sunovion and GlaxoSmithKline.

In silico modeling of oxygen-enhanced MRI of specific ventilation

Specific ventilation imaging (SVI) proposes that using oxygen-enhanced 1H MRI to capture signal change as subjects alternatively breathe room air and 100% O2 provides an estimate of specific ventilation distribution in the lung. How well this technique measures SV and the effect of currently adopted approaches of the technique on resulting SV measurement is open for further exploration. We investigated (1) How well does imaging a single sagittal lung slice represent whole lung SV? (2) What is the influence of pulmonary venous blood on the measured MRI signal and resultant SVI measure? and (3) How does inclusion of misaligned images affect SVI measurement? In this study, we utilized two patient-based in silico models of ventilation, perfusion, and gas exchange to address these questions for normal healthy lungs. Simulation results from the two healthy young subjects show that imaging a single slice is generally representative of whole lung SV distribution, with a calculated SV gradient within 90% of that calculated for whole lung distributions. Contribution of O2 from the venous circulation results in overestimation of SV at a regional level where major pulmonary veins cross the imaging plane, resulting in a 10% increase in SV gradient for the imaging slice. A worst-case scenario simulation of image misalignment increased the SV gradient by 11.4% for the imaged slice.

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.

Assessment of regional bone tissue perfusion in rats using fluorescent microspheres

Disturbances in bone blood flow have been shown to have deleterious effects on bone properties yet there remain many unanswered questions about skeletal perfusion in health and disease, partially due to the complexity of measurement methodologies. The goal of this study was use fluorescent microspheres in rats to assess regional bone perfusion by adapting mouse-specific fluorescent microsphere protocol. Ten fifteen-week old Sprague Dawley rats were injected with fluorescent microspheres either via cardiac injection (n = 5) or via tail vein injection (n = 5). Femora and tibiae were harvested and processed to determine tissue fluorescence density (TFD) which is proportional to the number of spheres trapped in the tissue capillaries. Right and left total femoral TFD (2.77 ± 0.38 and 2.70 ± 0.24, respectively) and right and left tibial TFD (1.11 ± 0.26 and 1.08 ± 0.34, respectively) displayed bilateral symmetry in flow when assessed in cardiac injected animals. Partitioning of the bone perfusion into three segments along the length of the bone showed the distal femur and proximal tibia received the greatest amount of perfusion within their respective bones. Tail vein injection resulted in unacceptably low TFD levels in the tibia from 4 of the 5 animals. In conclusion this report demonstrates the viability of cardiac injection of fluorescent microspheres to assess bone tissue perfusion in rats.

Relaxation dynamics of Sierpinski hexagon fractal polymer: Exact analytical results in the Rouse-type approach and numerical results in the Zimm-type approach

In this paper, we focus on the relaxation dynamics of Sierpinski hexagon fractal polymer. The relaxation dynamics of this fractal polymer is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, by performing real-space renormalization transformations, we determine analytically the complete eigenvalue spectrum of the connectivity matrix. Based on the eigenvalues obtained through iterative algebraic relations we calculate the averaged monomer displacement and the mechanical relaxation moduli (storage modulus and loss modulus). The evaluation of the dynamical properties in the Rouse-type approach reveals that they obey scaling in the intermediate time/frequency domain. In the Zimm-type approach, which includes the hydrodynamic interactions, the relaxation quantities do not show scaling. The theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results.

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.

Regional Fractional Ventilation by Using Multibreath Wash-in (3)He MR Imaging

Purpose To assess the feasibility and optimize the accuracy of the multibreath wash-in hyperpolarized helium 3 ((3)He) approach to ventilation measurement by using magnetic resonance (MR) imaging as well as to examine the physiologic differences that this approach reveals among nonsmokers, asymptomatic smokers, and patients with chronic obstructive pulmonary disease (COPD). Materials and Methods All experiments were approved by the local institutional review board and compliant with HIPAA. Informed consent was obtained from all subjects. To measure fractional ventilation, the authors administered a series of identical normoxic hyperpolarized gas breaths to the subject; after each inspiration, an image was acquired during a short breath hold. Signal intensity buildup was fit to a recursive model that regionally solves for fractional ventilation. This measurement was successfully performed in nine subjects: three healthy nonsmokers (one man, two women; mean age, 45 years ± 4), three asymptomatic smokers (three men; mean age, 51 years ± 5), and three patients with COPD (three men; mean age, 59 years ± 5). Repeated measures analysis of variance was performed, followed by post hoc tests with Bonferroni correction, to assess the differences among the three cohorts. Results Whole-lung fractional ventilation as measured with hyperpolarized (3)He in all subjects (mean, 0.24 ± 0.06) showed a strong correlation with global fractional ventilation as measured with a gas delivery device (R(2) = 0.96, P < .001). Significant differences between the means of whole-lung fractional ventilation (F2,10 = 7.144, P = .012) and fractional ventilation heterogeneity (F2,10 = 7.639, P = .010) were detected among cohorts. In patients with COPD, the protocol revealed regions wherein fractional ventilation varied substantially over multiple breaths. Conclusion Multibreath wash-in hyperpolarized (3)He MR imaging of fractional ventilation is feasible in human subjects and demonstrates very good global (whole-lung) precision. Fractional ventilation measurement with this physiologically realistic approach reveals significant differences between patients with COPD and healthy subjects. To minimize error, several sources of potential bias must be corrected when calculating fractional ventilation. (©) RSNA, 2016 Online supplemental material is available for this article.

Validating the distribution of specific ventilation in healthy humans measured using proton MR imaging

Specific ventilation imaging (SVI) uses proton MRI to quantitatively map the distribution of specific ventilation (SV) in the human lung, using inhaled oxygen as a contrast agent. To validate this recent technique, we compared the quantitative measures of heterogeneity of the SV distribution in a 15-mm sagittal slice of lung obtained in 10 healthy supine subjects, (age 37 ± 10 yr, forced expiratory volume in 1 s 97 ± 7% predicted) using SVI to those obtained in the whole lung from multiple-breath nitrogen washout (MBW). Using the analysis of Lewis et al. (Lewis SM, Evans JW, Jalowayski AA. J App Physiol 44: 416-423, 1978), the most likely distribution of SV from the MBW data was computed and compared with the distribution of SV obtained from SVI, after normalizing for the difference in tidal volume. The average SV was 0.30 ± 0.10 MBW, compared with 0.36 ± 0.10 SVI (P = 0.01). The width of the distribution, a measure of the heterogeneity, obtained using both methods was comparable: 0.51 ± 0.06 and 0.47 ± 0.08 in MBW and SVI, respectively (P = 0.15). The MBW estimated width of the SV distribution was 0.05 (10.7%) higher than that estimated using SVI, and smaller than the intertest variability of the MBW estimation [inter-MBW (SD) for the width of the SV distribution was 0.08 (15.8)%]. To assess reliability, SVI was performed twice on 13 subjects showing small differences between measurements of SV heterogeneity (typical error 0.05, 12%). In conclusion, quantitative estimations of SV heterogeneity from SVI are reliable and similar to those obtained using MBW, with SVI providing spatial information that is absent in MBW.

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.

Spatial distribution of ventilation and perfusion: mechanisms and regulation

With increasing spatial resolution of regional ventilation and perfusion, it has become more apparent that ventilation and blood flow are quite heterogeneous in the lung. A number of mechanisms contribute to this regional variability, including hydrostatic gradients, pleural pressure gradients, lung compressibility, and the geometry of the airway and vascular trees. Despite this marked heterogeneity in both ventilation and perfusion, efficient gas exchange is possible through the close regional matching of the two. Passive mechanisms, such as the shared effect of gravity and the matched branching of vascular and airway trees, create efficient gas exchange through the strong correlation between ventilation and perfusion. Active mechanisms that match local ventilation and perfusion play little if no role in the normal healthy lung but are important under pathologic conditions.

Heterogeneity and matching of ventilation and perfusion within anatomical lung units in rats

Prior studies exploring the spatial distributions of ventilation and perfusion have partitioned the lung into discrete regions not constrained by anatomical boundaries and may blur regional differences in perfusion and ventilation. To characterize the anatomical heterogeneity of regional ventilation and perfusion, we administered fluorescent microspheres to mark regional ventilation and perfusion in five Sprague-Dawley rats and then using highly automated computer algorithms, partitioned the lungs into regions defined by anatomical structures identified in the images. The anatomical regions ranged in size from the near-acinar to the lobar level. Ventilation and perfusion were well correlated at the smallest anatomical level. Perfusion and ventilation heterogeneity were relatively less in rats compared to data previously published in larger animals. The more uniform distributions may be due to a smaller gravitational gradient and/or the fewer number of generations in the distribution trees before reaching the level of gas exchange, making regional matching of ventilation and perfusion less extensive in small animals.

Dependence of ventilation image derived from 4D CT on deformable image registration and ventilation algorithms

Ventilation imaging using 4D CT is a convenient and low-cost functional imaging methodology which might be of value in radiotherapy treatment planning to spare functional lung volumes. Deformable image registration (DIR) is needed to calculate ventilation imaging from 4D CT. This study investigates the dependence of calculated ventilation on DIR methods and ventilation algorithms. DIR of the normal end expiration and normal end inspiration phases of the 4D CT images was used to correlate the voxels between the two respiratory phases. Three different DIR algorithms, optical flow (OF), diffeomorphic demons (DD), and diffeomorphic morphons (DM) were retrospectively applied to ten esophagus and ten lung cancer cases with 4D CT image sets that encompassed the entire lung volume. The three ventilation extraction methods were used based on either the Jacobian, the change in volume of the voxel, or directly calculated from Hounsfield units. The ventilation calculation algorithms used are the Jacobian, ΔV, and HU method. They were compared using the Dice similarity coefficient (DSC) index and Bland-Altman plots. Dependence of ventilation images on the DIR was greater for the ΔV and the Jacobian methods than for the HU method. The DSC index for 20% of low-ventilation volume for ΔV was 0.33 ± 0.03 (1 SD) between OF and DM, 0.44 ± 0.05 between OF and DD, and 0.51 ± 0.04 between DM and DD. The similarity comparisons for Jacobian were 0.32 ± 0.03, 0.44 ± 0.05, and 0.51 ± 0.04, respectively, and for HU they were 0.53 ± 0.03, 0.56 ± 0.03, and 0.76 ± 0.04, respectively. Dependence of extracted ventilation on the ventilation algorithm used showed good agreement between the ΔV and Jacobian methods, but differed significantly for the HU method. DSC index for using OF as DIR was 0.86 ± 0.01 between ΔV and Jacobian, 0.28 ± 0.04 between ΔV and HU, and 0.28 ± 0.04 between Jacobian and HU, respectively. When using DM or DD as DIR, similar values were obtained when comparing the different ventilation calculation methods. The similarity values for the 20% high-ventilation volume were close to those found for the 20% low-ventilation volume. The results obtained with DSC index were confirmed when using the Bland-Altman plots for comparing the ventilation images. Our data suggest that ventilation calculated from 4D CT depends on the DIR algorithm employed. Similarities between ΔV and Jacobian are higher than between ΔV and HU, and Jacobian and HU.

Design of vascular networks: a mathematical model approach

In this paper, methods for the modeling of a realistic vascular tree in 3D space and for hemodynamic calculating throughout the simulated tree structure have been developed. Vascular trees are generated based on the power law relationship. Variations in branching asymmetry and segment length of the vasculature are precisely controlled by the designed gaussian distributions. The resolution limit of current imaging techniques for vessel detectability is simulated by designed pruning technique. On the basis of the generated diameters and lengths, the space locations of the vessel segments are calculated by optimizing the out-of-plane angles of two daughter branches. The generated vascular tree not only follows the power law relationship, but also maximizes the filling volume of the tree structure in 3D space. From the hemodynamic calculation in the simulated vasculature, the processes for which structural changes affect hemodynamic distributions are studied in detail. And also, the fractal nature and resistance of the vascular trees are quantified and compared. The developed method provides some insight into the design of the vascular trees in biology and may be used as a reference for the study of vascular diseases.

Airway exchange of highly soluble gases

Highly blood soluble gases exchange with the bronchial circulation in the airways. On inhalation, air absorbs highly soluble gases from the airway mucosa and equilibrates with the blood before reaching the alveoli. Highly soluble gas partial pressure is identical throughout all alveoli. At the end of exhalation the partial pressure of a highly soluble gas decreases from the alveolar level in the terminal bronchioles to the end-exhaled partial pressure at the mouth. A mathematical model simulated the airway exchange of four gases (methyl isobutyl ketone, acetone, ethanol, and propylene glycol monomethyl ether) that have high water and blood solubility. The impact of solubility on the relative distribution of airway exchange was studied. We conclude that an increase in water solubility shifts the distribution of gas exchange toward the mouth. Of the four gases studied, ethanol had the greatest decrease in partial pressure from the alveolus to the mouth at end exhalation. Single exhalation breath tests are inappropriate for estimating alveolar levels of highly soluble gases, particularly for ethanol.

Imaging lung perfusion

From the first measurements of the distribution of pulmonary blood flow using radioactive tracers by West and colleagues (J Clin Invest 40: 1-12, 1961) allowing gravitational differences in pulmonary blood flow to be described, the imaging of pulmonary blood flow has made considerable progress. The researcher employing modern imaging techniques now has the choice of several techniques, including magnetic resonance imaging (MRI), computerized tomography (CT), positron emission tomography (PET), and single photon emission computed tomography (SPECT). These techniques differ in several important ways: the resolution of the measurement, the type of contrast or tag used to image flow, and the amount of ionizing radiation associated with each measurement. In addition, the techniques vary in what is actually measured, whether it is capillary perfusion such as with PET and SPECT, or larger vessel information in addition to capillary perfusion such as with MRI and CT. Combined, these issues affect quantification and interpretation of data as well as the type of experiments possible using different techniques. The goal of this review is to give an overview of the techniques most commonly in use for physiological experiments along with the issues unique to each technique.

Imaging for lung physiology: what do we wish we could measure?

The role of imaging as a tool for investigating lung physiology is growing at an accelerating pace. Looking forward, we wished to identify unresolved issues in lung physiology that might realistically be addressed by imaging methods in development or imaging approaches that could be considered. The role of imaging is framed in terms of the importance of good spatial and temporal resolution and the types of questions that could be addressed as these technical capabilities improve. Recognizing that physiology is fundamentally a quantitative science, a recurring emphasis is on the need for imaging methods that provide reliable measurements of specific physiological parameters. The topics included necessarily reflect our perspective on what are interesting questions and are not meant to be a comprehensive review. Nevertheless, we hope that this essay will be a spur to physiologists to think about how imaging could usefully be applied in their research and to physical scientists developing new imaging methods to attack challenging questions imaging could potentially answer.

A computational model of the topographic distribution of ventilation in healthy human lungs

The topographic distribution of ventilation in the lungs is determined by the interaction of several factors, including lung shape, airway tree geometry, posture, and tissue deformation. Inter-species differences in lung structure-function and technical difficulty in obtaining high resolution imaging of the upright human lung means that it is not straightforward to experimentally determine the contribution of each of these factors to ventilation distribution. We present a mathematical model for predicting the topological distribution of inhaled air in the upright healthy human lung, based on anatomically structured model geometries and biophysical equations for model function. Gravitational deformation of the lung tissue is predicted using a continuum model. Airflow is simulated in anatomically based conducting airways coupled to geometrically simplified terminal acinar units with varying volume-dependent compliances. The predicted ventilation distribution is hence governed by local tissue density and elastic recoil pressure, airway resistance and acinar compliance. Results suggest that there is significant spatial variation in intrinsic tissue properties in the lungs. The model confirms experimental evidence that in the healthy lungs tissue compliance has a far greater effect than airway resistance on the spatial distribution of ventilation, and hence a realistic description of tissue deformation is essential in models of ventilation.

Lung perfusion measured using magnetic resonance imaging: New tools for physiological insights into the pulmonary circulation

Since the lung receives the entire cardiac output, sophisticated imaging techniques are not required in order to measure total organ perfusion. However, for many years studying lung function has required physiologists to consider the lung as a single entity: in imaging terms as a single voxel. Since imaging, and in particular functional imaging, allows the acquisition of spatial information important for studying lung function, these techniques provide considerable promise and are of great interest for pulmonary physiologists. In particular, despite the challenges of low proton density and short T2* in the lung, noncontrast MRI techniques to measure pulmonary perfusion have several advantages including high reliability and the ability to make repeated measurements under a number of physiologic conditions. This brief review focuses on the application of a particular arterial spin labeling (ASL) technique, ASL-FAIRER (flow sensitive inversion recovery with an extra radiofrequency pulse), to answer physiologic questions related to pulmonary function in health and disease. The associated measurement of regional proton density to correct for gravitational-based lung deformation (the "Slinky" effect (Slinky is a registered trademark of Pauf-Slinky incorporated)) and issues related to absolute quantification are also discussed.

Emergence of matched airway and vascular trees from fractal rules

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.

Fractal physiology and the fractional calculus: a perspective

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks.

Lateral position with the remaining lung uppermost improves matching of pulmonary ventilation and perfusion in pneumonectomized pigs

BACKGROUND

Pneumonectomy is a major surgery. Severe hypoxemia sometimes occurs after pneumonectomy. Effective gas exchange depends on perfect pulmonary ventilation (V˙(A)) and perfusion (Q˙) matching. The effect of position on V˙(A)/Q˙ matching after pneumonectomy is not clear. We therefore conducted this study to examine the effects of supine, left lateral decubitus (LLD), and right lateral decubitus (RLD) positions on V˙(A)/Q˙ matching and gas exchange after pneumonectomy in a porcine model.

METHODS

Twelve pigs were anesthetized and mechanically ventilated; six pigs received right pneumonectomy and six pigs received left pneumonectomy. The positions of the pigs were changed to supine, LLD, and RLD in random order after pneumonectomy. We applied intravenous and aerosolized high-resolution fluorescent microsphere technique (FMT) to mark V˙(A) and Q˙ in conjunction with arterial blood gas analysis to study these variables at different positions. Mechanical ventilation was kept constant throughout.

RESULTS

Different positions after pneumonectomy lead to significant changes in heterogeneity and matching of V˙(A)/Q˙. In right pneumonectomized pigs, the highest PaO(2), lowest V˙(A)/Q˙heterogeneity, and highest matching of V˙(A)/Q˙ was in RLD. In left pneumonectomized pigs, the highest PaO(2), lowest V˙(A)/Q˙ heterogeneity, and highest matching of V˙(A)/Q˙ was in LLD.

CONCLUSIONS

The lateral position with the remaining lung uppermost leads to the highest V˙(A)/Q˙ matching and best gas exchange after pneumonectomy.

High-resolution spatial measurements of ventilation-perfusion heterogeneity in rats

This study was designed to validate a high-resolution method to measure regional ventilation (VA) in small laboratory animals, and to compare regional Va and perfusion (Q) before and after methacholine-induced bronchoconstriction. A mixture of two different colors of 0.04-microm fluorescent microspheres (FMS) was aerosolized and administered to five anesthetized, mechanically ventilated rats. Those rats also received an intravenous injection of a mixture of two different colors of 15-microm FMS to measure regional blood flow (Q). Five additional rats were labeled with aerosol and intravenous FMS, injected with intravenous methacholine, and then relabeled with a second pair of aerosol and intravenous FMS colors. After death, the lungs were reinflated, frozen, and sequentially sliced in 16-microm intervals on an imaging cryomicrotome set to acquire signal for each of the FMS colors. The reconstructed lung images were sampled using randomly placed 3-mm radius spheres. Va within each sphere was estimated from the aerosol fluorescence signal, and Q was estimated from the number of 15-microm FMS within each sphere. Method error ranged from 6 to 8% for Q and 0.5 to 4.0% for Va. The mean coefficient of variation for Q was 17%, and for Va was 34%. The administration of methacholine altered the distribution of both VA and Q within lung regions, with a change in Va distribution nearly twice as large as that seen for Q. The methacholine-induced changes in Va were not associated with compensatory shifts in Q. Cryomicrotome images of FMS markers provide a high-resolution, anatomically specific means of measuring regional VA/Q responses in the rat.

A computer model of the artificially ventilated human respiratory system in adult intensive care

A multi-technique approach to modelling artificially ventilated patients on the adult general intensive care unit (ICU) is proposed. Compartmental modelling techniques were used to describe the mechanical ventilator and the flexible hoses that connect it to the patient. 3D CFD techniques were used to model flow in the major airways and a Windkessel style balloon model was used to model the mechanical properties of the lungs. A multi-compartment model of the lung based on bifurcating tree structures representing the conducting airways and pulmonary circulation allowed lung disease to be modelled in terms of altered V/Q ratios within a lognormal distribution of values and it is from these that gas exchange was determined. A compartmental modelling tool, Bathfp, was used to integrate the different modelling techniques into a single model. The values of key parameters in the model could be obtained from measurements on patients in an ICU whilst a sensitivity analysis showed that the model was insensitive to the value of other parameters within it. Measured and modelled values for arterial blood gases and airflow parameters are compared for 46 ventilator settings obtained from 6 ventilator dependent patients. The results show correlation coefficients of 0.88 and 0.85 for the arterial partial pressures of the O(2) and CO(2), respectively (p<0.01) and of 0.99 and 0.96 for upper airway pressure and tidal volume, respectively (p<0.01). The difference between measured and modelled values was large in physiological terms, suggesting that some optimisation of the model is required.

Control from an allometric perspective

Control of complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. I have attempted to emphasize the difference between homeostatic control and allometric control mechanisms. Homeostatic control is familiar and has as its basis a negative feedback character, which is both local and relatively fast. Allometric control, on the other hand, is a new concept that can take into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the system variable. Allometric control introduces the fractal character into otherwise featureless random time series to enhance the robustness of physiological networks by introducing the fractional calculus into the control of the networks.

Assessment of peripheral lung mechanics

The mechanical properties of the lung periphery are major determinants of overall lung function, and can change dramatically in disease. In this review we examine the various experimental techniques that have provided data pertaining to the mechanical properties of the lung periphery, together with the mathematical models that have been used to interpret these data. These models seek to make a clear distinction between the central and peripheral compartments of the lung by encapsulating functional differences between the conducing airways, the terminal airways and the parenchyma. Such a distinction becomes problematic in disease, however, because of the inevitable onset of regional variations in mechanical behavior throughout the lung. Accordingly, lung models are used both in the inverse sense as vehicles for extracting physiological insight from experimental data, and in the forward sense as virtual laboratories for the testing of specific hypothesis about mechanisms such as the effects of regional heterogeneities. Pathologies such as asthma, acute lung injury and emphysema can alter the mechanical properties of the lung periphery through the direct alteration of intrinsic tissue mechanics, the development of regional heterogeneities in mechanical function, and the complete derecruitment of airspaces due to airway closure and alveolar collapse. We are now beginning to decipher the relative contributions of these various factors to pathological alterations in peripheral lung mechanics, which may eventually lead to the development and assessment of novel therapies.

Quantification of lung injury using ventilation and perfusion distributions obtained from gamma scintigraphy

This paper explores the potential of isotope V/Q lung scans to quantify lung disease. Areas of restricted perfusion in subjects with a pulmonary embolus (PE) were identified in 3D reconstructions of V/Q images achieved using anatomical data from the Visible Human Project. From these, the extent of lung damage was quantified. Significant differences in the values of both LogSD V and LogSD Q (p > 0.05) obtained from plots of V and Q against Log(V/Q) were found between normal subjects and subjects with a PE, but no correlation was found between either of these parameters and the degree of lung damage in subjects with a PE (p > 0.05). Whilst V/Q values were log normally distributed, the V/Q distributions from the subjects with a PE failed to show the bimodal distribution predicted from theoretical considerations and MIGET measurements previously reported. There was a statistically significant difference in the mean and standard deviation values of the V/Q distributions between normal subject and subjects with a PE (p < 0.05) but not in the median values (p > 0.05). There was no correlation between the mean, median and standard deviation of the distributions from the subjects with a PE and the percentage of damage present (p > 0.05).