What can imaging tell us about physiology? Lung growth and regional mechanical strain

Abstract

The interplay of mechanical forces transduces diverse physico-biochemical processes to influence lung morphogenesis, growth, maturation, remodeling and repair. Because tissue stress is difficult to measure in vivo, mechano-sensitive responses are commonly inferred from global changes in lung volume, shape, or compliance and correlated with structural changes in tissue blocks sampled from postmortem-fixed lungs. Recent advances in noninvasive volumetric imaging technology, nonrigid image registration, and deformation analysis provide valuable tools for the quantitative analysis of in vivo regional anatomy and air and tissue-blood distributions and when combined with transpulmonary pressure measurements, allow characterization of regional mechanical function, e.g., displacement, strain, shear, within and among intact lobes, as well as between the lung and the components of its container—rib cage, diaphragm, and mediastinum—thereby yielding new insights into the inter-related metrics of mechanical stress-strain and growth/remodeling. Here, we review the state-of-the-art imaging applications for mapping asymmetric heterogeneous physical interactions within the thorax and how these interactions permit as well as constrain lung growth, remodeling, and compensation during development and following pneumonectomy to illustrate how advanced imaging could facilitate the understanding of physiology and pathophysiology. Functional imaging promises to facilitate the formulation of realistic computational models of lung growth that integrate mechano-sensitive events over multiple spatial and temporal scales to accurately describe in vivo physiology and pathophysiology. Improved computational models in turn could enhance our ability to predict regional as well as global responses to experimental and therapeutic interventions.

all iteratively branching structures develop as a result of persistent physical forces acting against the resistance of one or more media. The lung continuously balances internal and external pressure gradients created by the interdependent actions of two pumps at the interface of two media: air movement generated by the respiratory muscles and blood flow generated by the entire cardiac output. The adult human lung moves ∼9,000 liters of air and ∼7,000 liters of blood daily. In addition to rhythmic stretching of alveolar septa and pulsatile flow within the bronchovasculature, lung tissue experiences cyclic mechanical strain and shear distortion caused by its weight and asymmetric deformation, as well as surface tension at air-tissue interfaces. Since mechanotransduction—the conversion of mechanical load into a cellular response—is a fundamental and universal mechanism regulating diverse physico-biochemical processes from membrane permeability, ion transport, gene transcription, enzymatic reactions, protein synthesis to cell proliferation, and differentiation [reviewed in refs. (1, 15, 49, 62, 68)], it is not surprising that the interplay of mechanical forces critically shapes fetal lung morphogenesis, postnatal growth and maturation, and compensatory growth and remodeling following the loss of functioning lung units. Here, we review 1) the clinical and experimental evidence supporting mechanical stresses as major stimuli for lung growth, 2) the evolution of imaging approaches for quantifying lung strain in relation to alveolar-capillary and bronchovasuclar growth using pneumonectomy (PNX) as an example where quantitative imaging has been applied to gain insight into mechano-sensitive adaptation, 3) the limitations and new developments in relevant imaging approaches, and 4) the continuing challenges in quantifying tissue stress and developing imaging-based computational models to interpret deformation measurements and integrate the mechanical events that occur over multiple spatial scales during growth and development.

LUNG STRESS-STRAIN DURING DEVELOPMENT AND COMPENSATORY GROWTH

Lung stress-strain during development.

Structure of the growing lung has been described in detail elsewhere (6). The newborn human lung contains only a fraction (up to 50 million) (16, 17, 48) of the alveoli in the adult lung (∼400 million) (57), with millions of “saccules”—peripheral airspaces bound by septa containing a thick, connective tissue layer between two capillary sheets. Transformation from “saccular” to “alveolar” and then “mature” morphology requires not only the addition of alveolar septa but also new capillary formation and transition from a double- to a single-capillary profile, accompanied by increased gas-exchange surface area and reduced resistance of the diffusion barrier. New alveolar subdivisions arise as secondary septae emerge from the primary alveolar walls. This process is most rapid in the first 6 mo of life and continues during the next 2-3 years (5). Some studies suggested that new alveoli continue to appear throughout somatic maturation (6). New capillary beds may arise by “intussusception” (46), a process where tissue pillars form a bridge across the lumen of an existing capillary, eventually dividing it in two.

Mechanical interactions between the thorax and lungs are crucial for normal lung maturation and function (26, 33). In fluid-filled fetal lungs, a high level of distention is normally maintained by breathing-like movements and by upper-airway resistance during apnea. Any sustained perturbation that reduces lung expansion causes fetal lung hypoplasia, leading to postnatal compromise in function. Premature birth compromises airway and alveolar formation by shortening the duration of intrauterine lung expansion (23). Abolishing rhythmic respiratory movements decreases fetal lung liquid volume, developmental gene expression, and structural growth (24, 84). Reduced lung fluid in oligohydramnios (52, 53) or inadequate space for lung expansion in congenital diaphragmatic hernia (CDH) impedes fetal lung development, whereas severe kyphoscoliosis impedes postnatal lung growth (3, 54). Conversely, increasing lung distention by fetal tracheal occlusion (31, 81) or postnatal perfluorocarbon instillation accelerates lung development (18, 20, 56, 82) via transduction of growth-related pathways. Exposure to continuous positive airway pressure (CPAP) during maturation increases lung capacity, lung weight, protein, and DNA contents (92). These data support stress-induced acceleration of parenchyma growth and remodeling. Clinically, long-term survivors of CDH repair exhibit only a mild reduction of forced vital capacity with normal total lung capacity, airway function, and exercise performance compared with age-matched control subjects (50), suggesting that the maturing lung undergoes “catch-up” growth and compensation once mechanical stress-strain relationships between the thorax and lung are normalized.

Lung stress-strain during compensatory growth.

Mechanical thoraco-pulmonary interactions also mediate adaptation to lung disease and the reinitiation of alveolar-capillary growth in mature lungs. In a robust model of restrictive lung disease by surgical removal of lung units, e.g., unilateral PNX, the remaining units expand ∼90% to fill the thoracic cavity, whereas ventilation and perfusion/lung unit increase by a factor of one/fractional lung remaining, causing the recruitment of existing alveoli and capillaries. The resulting tissue and capillary stress transduces nearly all major homeostatic pathways (1, 2, 21, 47, 60, 72, 86, 91), leading to increased permeability and remodeling of the remaining alveolar septa and acinar airspaces and if the signal intensity exceeds a critical threshold, reinitiation of cell proliferation, protein synthesis, and matrix deposition, culminating in the generation of new gas-exchange tissue as reviewed in refs. (1, 33). The remaining conducting airways and vessels become distorted and elongated, followed by slow dilatation that partially counteracts the increase in flow resistance (11, 74). Preventing post-PNX lung expansion using a customized inflatable prosthesis significantly impairs, whereas subsequent reimposition of lung expansion upregulates, growth-related pathways and facilitates compensatory alveolar growth and function (37, 38, 87, 91). Application of CPAP in isolated lungs elicits many of the same biochemical changes seen following PNX (71). Therefore, PNX is a useful model for examining the extent and the mechanisms of mechanosensitive compensation. Conversely, the diminished mechanical interactions associated with air trapping and loss of elastic recoil in emphysema may at least partly explain the difficulty in reinducing compensatory lung growth in this condition.

QUANTIFYING REGIONAL LUNG VOLUME, STRESS AND STRAIN

Imaging regional lung volume and deformation.

The asymmetry of intrathoracic structures and rigidity of the mediastinum predispose to nonuniform distributions of mechanical stress, lobar expansion, and tissue deformation that could impact regional parenchyma structure and function. It is difficult to relate lung mechanics to structure assessed from a few selected postmortem-fixed specimens. To quantitatively relate regional as well as global anatomy to function in vivo, early studies used chest X-ray and biplane cineradiography to estimate regional volume and stress-strain relationships in canine lungs by determining the three-dimensional (3D) spatial coordinates of radio-opaque markers implanted into the parenchyma or affixed onto pleural surfaces (41, 58, 70). Mechanical deformation is measured as strain, which is usually a tensor (a geometric representation that quantifies fractional length change relative to initial length in 3D space) that can be decomposed into its stretch and shear components. Strain must be quantified relative to an initial unloaded or prestretched state; hence, the calculation of strain requires identifying unique material points within the tissue and tracking their displacement between successive images following intervention. In the studies using implanted lung markers, deformation of tetrahedrons formed by any four noncoplanar markers was expressed as strain along 3D orthogonal axes; regional mechanical properties were estimated from the tetrahedron volume changes and expressed at the centroid of each tetrahedron. These invasive studies demonstrated relatively uniform respiratory expansion of normal lobes, posture-dependent shape changes in the diaphragm and lung, displacement of the lobes relative to each other (9), differential patterns of regional ventilation and diaphragm motion during mechanical ventilation compared with spontaneous breathing, and a nonlinear relationship between regional ventilation and volume changes (40). Regional parenchyma strain exhibits volume-, posture-, and lobe-dependent variations in supine but not prone posture (70), which is partly due to mechanical interaction between the lung and diaphragm via a shift in the abdominal contents with posture. A recent computational study of human lung stress-strain also reported supine-prone differences in lung density and pleural pressure gradients that can be explained by posture-related lung-shape change in the absence of any change in gross lung shape (77). Thus components of the “container”—heart and mediastinum, rib cage, diaphragm, and abdominal content—constrain the shape and direction in which the lungs could deform. Mechanical interactions between lung and chest wall and the relative motion between lobes are significant determinants of regional ventilation, whereas heterogeneity in expansion, compliance, and strain among small lung regions could explain the gravity-independent nonuniform regional ventilation (58) and gas mixing within lobes (85).

Quantitative analysis of volumetric chest computed tomography.

Early chest computed tomography (CT), using the dynamic spatial reconstructor, noninvasively demonstrated a ventral-to-dorsal gradient of decreasing fractional lung air content at FRC in supine but not prone posture; regional differences were caused by gravitational effects as well as structural differences and the rigidity of mediastinal contents (27, 29, 30). Subsequently, CT attenuations of air and air-free tissue were used to estimate lung weight, gas volume, and expansion. In children of different ages, volumetric CT-derived gas volume and lung weight correlated with predicted values of functional residual capacity (FRC) and postmortem lung weight, respectively; the estimated rates of lung expansion with age are consistent with the view that postnatal lungs grow initially by addition of alveolar septa, followed by gradual increases of both tissue volume and airspace size (13). Airway wall and lumen and arterial area were exponentially related to body height, whereas airway surface length/area ratio was linearly related to alveolar surface/volume ratio (12).

With the use of high-resolution CT (HRCT) and combining the attenuation of lung parenchyma with the calibrated attenuations of intrathoracic air and air-free blood-containing tissue, it is possible to partition any given volume of parenchyma into air (V_air) and tissue (V_tiss; including microvascular blood) volumes (75) and to derive the fractional tissue volume (FTV) as FTV = V_tiss/(V_tiss + V_air). This analysis can be applied voxel-by-voxel to yield topographical gradients of V_air, V_tiss, and FTV, expressed along standardized 3D coordinate axes (65, 66, 88, 89). Recently developed semiautomated lobar fissure-detection algorithms (67, 88, 90) may be added, allowing separate analysis of each natural functioning unit (lobe) as well as comparisons of regional changes with respect to their relative positions within and among lobes before and after intervention, even in the presence of gross distortion. Adding simultaneous measurement of transpulmonary pressure (P_tp) during HRCT performed at two or more inflation levels allows estimation of regional lung compliance. A more accurate assessment of regional compliance (or more complex expressions of stress distribution) requires knowledge of the constitutive properties of the lung and the precise distribution of loads that are acting on the tissue: neither of these has yet been achieved. State-of-the-art open-source nonrigid registration and analytical tools are available to match natural landmarks on successive scans and warp or “morph” paired images and permit voxelwise analysis of regional deformation characteristics by generating 3D vector field maps of displacement (motion) and strain, as well as the estimation of lobar shear (55, 89). These evolving techniques have significantly advanced our state-of-the-art ability to monitor regional anatomy noninvasively in relation to regional function.

Functional lung growth assessed by HRCT.

Few studies have quantitatively measured lung-tissue growth by HRCT in children (12, 13, 22, 63). Reference values for the CT-derived volume of each lung as a function of age and sex are available (22). In infants and toddlers up to ∼3 years of age, HRCT-derived lung air and tissue volumes increase linearly with body length and at a constant rate; central conducting airway caliber also increases in proportion to parenchyma volume and body length (64). These results confirm those from previous studies (12, 13)—that early postnatal lung growth occurs primarily by the addition of new lung units rather than by the expansion of lung units. Following pediatric lung transplantation, the relationship of tracheal diameter to body height remains normal, and the postanastomotic large airways grow similarly to native pre-anastomotic airways (69).

Regional lung growth has been quantified experimentally. In normal canine lungs during maturation (∼6–12 mo of age), growth rates among lobes are relatively uniform. Air volume increases faster than tissue volume in all regions, causing the HRCT-derived FTV to decline at a similar rate among lobes (65). This is consistent with the interpretation that the rate of airspace enlargement exceeds the rate of increase in lung tissue and blood. However, upon reaching adulthood, the lungs exhibit moderate heterogeneity in the distributions of air volume, tissue volume, and specific lung compliance within and among lobes. Mean lobar FTV is higher in the caudal and infracardiac lobes than in the cranial lobes (88), reflecting the known lobar differences in alveolar septal tissue density and in microvascular perfusion and blood volume. In addition, regional CT-derived FTV increases in the ventrodorsal and cephalocaudal directions within all lobes (88).

In young dogs following 55–58% lung resection by right PNX, intensified mechanical signals superimpose upon developmental signals, causing an ∼2.2-fold increase in CT-derived tissue-blood volume in all remaining lobes relative to control lobes of matched animals following sham PNX. The magnitude of compensatory increase in CT-derived tissue volume is consistent with the increase in septal tissue volume assessed at postmortem by morphometry (73). However, when HRCT was repeated 10 mo later upon somatic maturity, the relative increase in lobar tissue volume of the remaining left caudal lobe (twofold) fell behind that of the cranial and middle lobes (2.5- to 2.8-fold) (65). The magnitude of whole-lung post-PNX structural growth was larger and functional compensation more complete in young animals than in adults (35, 39, 73), whereas the pattern of lobar nonuniformity was similar regardless of whether PNX was performed before or after somatic maturity (65, 66). Thus the additive developmental and post-PNX signals vigorously accelerated growth of all remaining lobes but do not alter the nonuniform nature of long-term outcome.

In adult dogs following 42–45% lung resection by left PNX, some lobes expanded, whereas others did not; air and tissue volumes of the right cranial and infracardiac lobes expanded 2.2-fold above and below the heart, but the right middle and caudal lobes did not expand, and overall lung-tissue volume did not increase significantly. Following 55–58% resection by right PNX, lobar expansion was more uniform. Air and tissue volumes increased in all remaining lobes; the left cranial and middle lobes expanded 2.3- to 2.7-fold across the midline anterior to the heart, whereas the caudal lobe expanded 1.9-fold posterior to the heart. Post-PNX changes in lobar FTV estimated by HRCT parallel postmortem estimates by morphometry (66). Thus the presence of mediastinal structures and ligaments dictated the heterogeneous nature and extent of lobar expansion. When lateral lung expansion was prevented by an inflated silicone prosthesis manufactured in the shape and size of the resected lung, the remaining lung still expanded, and overall lung-tissue volume increased by ∼20% via caudal displacement of the ipsilateral hemidiaphragm (87), indicating that the remaining lung did not just passively expand to fill an empty space, but the thorax also adapted to accommodate the actively growing lung when space was not readily available. Ultrastructure evidence supports a graded response to strain-related alveolar-capillary distention and recruitment, whereby following ∼45% resection, type 2 epithelial cells are the first to increase in volume (36); as strain increases further following ∼55% resection, the other septal cells are also activated, resulting in an overt increase of alveolar tissue volume.

In adult dogs following two-stage balanced resection of 65–70% of total lung units (removing the caudal, infracardiac ± the middle lobes, or ∼35% from each lung without mediastinal distortion), the remaining cranial (and middle) lobes expanded in a caudal direction around and extending below the heart. HRCT-derived lobar air and tissue-blood volumes and FTV increased within 3 mo by 80–150%, 130–250%, and 30–45%, respectively, above the corresponding preresection values and remained unchanged thereafter, reflecting the increased lobar perfusion plus robust alveolar-capillary growth and resulting in early normalization of whole lung-tissue (including microvascular blood) volume (88, 89) (Fig. 1). Postresection lobar-specific compliance (Cs) doubled within 3 mo and then increased further when studied at 15 mo; consequently, whole-lung Cs normalized by 3 mo and increased further above baseline by 15 mo, suggesting a progressive decrease in tissue-stress postresection. Intralobar FTV increased heterogeneously postresection, particularly in peripheral and caudal regions, where a high FTV is associated with elevated alveolar septal-volume density and septal connective-tissue content on histology (88), suggesting that these sites experienced exaggerated mechanical stress and required greater connective-tissue support. Indeed, during passive inflation, parenchyma displacement within all lobes increased in a craniocaudal gradient, in keeping with the major direction of lobar expansion (Fig. 2). Parenchyma displacement diminished globally 3 mo postresection and then increased back to, or in the caudal regions of remaining lobes exceeded, preresection values by 15 mo. These changes indicate an initial reduction of lobar distensibility with subsequent normalization or even an increase in distensibility. Since there was no further tissue growth between 3 and 15 mo postresection, the later increase in distensibility may be attributed to gradual tissue relaxation and structural remodeling, which improved the static stress-strain relationship of the remaining lobes.

Fig. 1.

Serial high-resolution computed tomography (HRCT) was used to monitor lobar air and tissue volumes as well as specific compliance (Cs) calculated at 2 transpulmonary pressures (P_tp; 15 and 30 cmH₂O), before (PRE) and 3 and 15 mo after (POST) 65–70% lung resection in adult dogs. In the remaining 3 lobes [right (R) and left (L) cranial and L middle], the increase in tissue volume stabilized at 3 mo, whereas Cs continued to increase, consistent with early alveolar-capillary growth and progressive remodeling, leading to continued improvement in mechanical function. Mean ± SD. *P < 0.05 vs. PRE; †P < 0.05 vs. 3 mo post-lung resection [adapted from Yilmaz et al. (89)].

Fig. 2.

Three-dimensional color maps of regional fractional tissue volume (FTV; top panels) and vector field maps of parenchyma displacement (middle panels) and strain (bottom panels) during inflation (from 15 to 30 cmH₂O)—imaged by HRCT in adult dog lung before and 3 and 15 mo after extensive (65–70%) lung resection (POST3 and POST15, respectively)—illustrate the temporal and spatial heterogeneity during early and late phases of compensation. Surgery removed 4 lobes (L and R caudal, R middle, and infracardiac lobes). The remaining 3 lobes (L and R cranial and L middle lobes) expanded markedly in a mainly caudal direction and around the mediastinum. At POST3, patchy increases in FTV, reduction in displacement, and nonuniform increases in strain developed compared with PRE. At POST15, mild, patchy reductions in FTV, markedly increased displacements, particularly in the caudal regions, and nonuniform reductions in regional strain developed compared with POST3 (88, 89).

With the knowledge of the regional parenchyma displacement and P_tp changes during inflation, strain vector maps could be generated and the strain magnitude resolved along orthogonal axes (Fig. 2). In normal and postresection lungs, nonuniform strain preferentially distributes to the lobar periphery, where strong bronchovascular support is lacking; the distribution corresponds to the known pattern of more active cellular proliferation in peripheral than in central lobar regions (21, 51). Postresection strain increased nonuniformly, and the spatial pattern was altered from that preresection; strain increase was largest in the regions that expanded around the heart, especially in the left middle lobe. In normal lobes, shear distortion during inflation was minimal. Postresection, nonuniform lobar shear developed in different planes during inflation in keeping with the directions of stretch and rotation of the expanded lobes. From 3 to 15 mo postresection, there was no further change in lobar shear during inflation, whereas lobar strain either remained unchanged or continued to increase modestly and nonuniformly in different regions. Long-term postresection changes in lobar maximum principal strain and tissue growth correlated inversely—the larger the increase in tissue volume, the smaller the increase in maximum principal strain (Fig. 3).

Fig. 3.

Compensatory lung growth correlates with reduced lung strain during inflation. In adult dogs following extensive (65–70%) lung resection, the relative increase in maximum principal strain of the remaining lobes correlated inversely with the relative increase in lobar tissue volume estimated by HRCT. Data are expressed as a ratio between 15-mo postresection and the preresection baseline (POST15/PRE). y = −0.68x + 3.27; R² = 0.62 [adapted from Yilmaz et al. (89)].

Taken together, imaging data in a large mammalian model of compensatory lung growth highlight the chronicity as well as the temporal and spatial heterogeneity of structure-function adaption, which are difficult to define from ex vivo tissue studies alone. Imaging provides visual and quantitative support for mechanotransduction as the initiating signal of compensatory lung growth and remodeling, which in turn, mitigates the expected increase in tissue stress strain in a feedback loop that continues until stress strain in all lung regions falls below some threshold level, at which point, growth and remodeling also cease. Heterogeneity of regional stress-strain responses could prolong the time course of this feedback loop, suggesting a potentially wide window of opportunity, during which the adaptive pathways remain persistently active in all or at least some regions of the remaining lobes and hence, are susceptible to exogenous manipulation (64).

Dysanaptic lung growth assessed by HRCT.

The post-PNX remaining bronchovasculature becomes grossly distorted due to rotation, splaying, and/or mediastinal displacement (11, 19, 89). Flow resistance is elevated at any given total ventilation or perfusion. The chronically elevated wall stress leads to a different kind of growth and remodeling in airway/vascular generations, comprised of lengthening followed by slower progressive dilatation. Long-term post-PNX lobar airway cross-sectional area increased 24% but was insufficient to completely offset the higher viscous resistance due to airway lengthening and a threefold higher flow resistance caused by increased turbulence and convective acceleration. Based on airway dimensions measured on HRCT and the expected increase in lobar airflow, the estimated post-PNX compensatory reduction in work of breathing (∼30%) agreed well with that measured in exercising post-PNX animals (11). With increasing severity of lung resection, work of breathing at a given minute ventilation rose steadily (34). Pulmonary arterial resistance rose in parallel, especially in the presence of mediastinal distortion (34), which can cause bronchovascular kinking and lead to morbidity and mortality. In both young and adult dogs, the slowly and incompletely adapting conducting structures confer limited functional improvement, which lags behind the improvement in gas exchange (34, 73, 74). Consequently, ventilatory resistance and pulmonary arterial resistance remain elevated long after alveolar diffusion-perfusion relationships normalize, signifying the inability to form new conducting branches in contrast to the vigorous formation of new alveolar tissue, capillaries, and surfaces. The disparity in structural adaptability, termed dysanaptic growth, is evident during normal lung development (25, 32), becomes more pronounced with increasing parenchyma stress following PNX, and constitutes the major factor that limits exercise capacity following 65–70% resection. In severe destructive lung disease, dysanaptic growth may impose an upper limit on how much functional improvement could be obtained from growth induction of the remaining alveolar units. This limit has major implications for various therapeutic attempts that aim to stimulate distal lung growth using exogenous growth-promoting compounds or stem cells.

CHALLENGES AND NEW DEVELOPMENTS

Limitations and developments in imaging.

The resolution of air-tissue boundary at or below FRC by HRCT is often inadequate. Without intravenous contrast injection, extravascular tissue cannot be distinguished from microvascular blood. Separate quantification of lung-tissue and microvascular blood volumes following contrast injection remains to be validated. Because of a variable in vivo microvascular blood content, CT-derived lung-tissue volume is systematically larger than ex vivo alveolar extravascular tissue volume measured by morphometry. This observation per se is not a major drawback for the assessment of lung growth, because 1) functionally useful lung growth and compensation require balanced increases in gas-exchange tissue surfaces and capillary blood, and 2) a significant correlation exists between in vivo lung-tissue volume and ex vivo alveolar septal volume during development and post-PNX (Fig. 4) (66); these measurements, under different conditions, yield complementary data. However, in vivo and ex vivo correspondence may or may not hold in other pathophysiology and must be established individually.

Fig. 4.

Correlation of lung-tissue volume measured by HRCT (at 20 cmH₂O P_tp) with alveolar septal volume measured by postmortem morphometry (tracheal instillation of fixatives at 25 cmH₂O airway pressure). Solid line, identity; dashed line, regression through the data range. y = 1.06x + 1.79; R² = 0.526 [adapted from Ravikumar et al. (66)].

Accurate detection of lobar fissures is a crucial and time-consuming step in HRCT image analysis. Ongoing improvement in automated or semiautomated lobar segmentation algorithms should facilitate the analysis. Texture-based image analysis, under development by various groups to aid the discrimination of emphysema and fibrosis (4, 28), may be combined with attenuation-based analysis to enhance the characterization of topographical growth patterns and to follow abnormal patterns. Consistent and accurate nonrigid registration of a well-distributed set of landmarks is crucial for reliable deformation vector field analysis. Lung regions near the pleura are more prone to registration errors than central lung regions (43). A plethora of nonrigid landmark registration algorithms for thoracic CT have been described; 20 of these were evaluated in an ongoing public forum, Evaluation of Methods for Pulmonary Image Registration 2010 (55), in an effort to compare them objectively and to facilitate further advances in their development.

Functional changes are usually inferred from static HRCT, performed at two or more states during breath-holding. Dynamic 4D CT is an alternative modality for functional imaging of the lung throughout the respiratory cycle without the need for breath-holding; it suffers the drawback of a lower resolution and higher radiation dose. Thus far, this modality has been used to assess lung tumor size and motion in the planning of stereotactic radiation therapy (43, 83), sometimes in combination with PET/CT (44).

Radiation exposure limits longitudinal clinical applications of functional HRCT. Alternative radiation-free imaging modalities for monitoring lung growth could be particularly useful in pediatric subjects. For example, conventional MRI with a relatively long echo-delay time cannot visualize the lung parenchyma due to a high air content causing rapid signal decay. Recent advent of 3D ultrashort echo time (UTE) MRI sequence, in conjunction with a projection acquisition of the free induction decay, could reduce echo time to ∼100 μs and allow detection of inherent MRI signal intensity from lung parenchyma. Parenchyma signals have been shown to vary with lung inflation and correlate highly with tissue-blood density (80). Changes in parenchyma MRI signal intensity, due to inhalation of 100% oxygen or intravenous gadolinium contrast injection, may be combined with the UTE sequence to assess regional distributions of ventilation or perfusion, respectively (79). By registering corresponding, mostly vascular features on successive MRIs, voxelwise regional parenchyma motion may be assessed (45) in an approach similar to that used for HRCT. Currently, the resolution of parenchyma details by UTE MRI is inferior to that by HRCT, and lobar fissures cannot be detected. Further technological advances may overcome these obstacles.

Limitations in quantifying lung-tissue stress.

Mechanical stress is a measure of the internal forces that arise within a deformable body as a reaction to external forces. To quantify stress, one must know the constitutive properties of the material that is being studied and the forces that are applied to it to establish a measured strain. For many engineering materials, this is simple, as they have linear elastic properties that allow stress and strain to be related by Hooke's law. However, biological materials are rarely this straightforward because of the nonlinear elastic behavior of their constituent proteins and the complexity of their structural configuration. The lung is no exception. Stress in the context of lung growth is critical, because it is the change in stress and not strain per se that is the signal for mechanotransduction. Estimation of regional lung compliance has stood for many years as a placeholder for quantification of the 3D distribution of tissue stress. Quantifying a constitutive law that relates stress and strain in lung tissue is extremely challenging and remains incompletely addressed. A uniaxial or biaxial stretch of tissue strips can be used to define a constitutive law for other tissues (42, 76). However, because the elastic response of lung tissue depends strongly on both the alveolar configuration and the interfacial forces at the air-liquid interface, it is not clear that tissue-strip experiments, which modify one or both of these, are sufficiently accurate to define the mechanical response of the lung. An alternative approach, proposed by Denny and Schroter (14), is to construct a computational model of the lung's microstructure that includes the alveolar geometry and the spatial distribution of elastin and collagen. Elastic moduli, which are representative of the bulk tissue, can then be derived by analyzing the deformation of a block of “virtual” tissue. This approach has been extended to the emphysematous lung (59), demonstrating a link between degradation in alveolar tissue microstructure and macroscopic tissue behavior. This approach may be extended to the maturing lung or to tissue that is under abnormally high and nonuniform strain, e.g., following PNX.

Imaging-based models to interpret measurements of deformation.

Imaging-based computational models of the lung have emerged as a means of integrating experimental data across spatial scales into a quantitative framework that is biophysically based and predictive of function (10, 61). These types of model have given new insights into lung physiology and pathophysiology, e.g., Burrowes et al. (7); however, they have been developed almost exclusively for the adult lung. A noted exception from the adult models are computational models for airway morphogenesis, e.g., Tebockhorst et al. (78). The predictive power of these imaging-based models lies in their biophysical basis and their foundation in conservation laws. They can be used to explain the interaction of mechanisms over different spatial scales that give rise to experimental observations, as demonstrated by Politi et al. (61), for force development in bronchoconstriction. Following validation against data from animal studies, they can then be used to predict or explain function in the human lung, where data are less accessible.

Data defining compensatory lung growth are of course more accessible from animal studies than from human. The translation between the animal and human computational model involves no more than a change in the model geometry and definition of physiological conditions that are appropriate to the species; the underlying physics remain the same, and cellular- or molecular-level function is assumed the same across species, unless there is clear evidence that this is not the case (e.g., the behavior of mouse airway smooth muscle in contrast to rat or human). This approach has suggested important species differences in the distribution of blood in the lung related to differences in branching geometry but not the nature of the blood flow itself or the mechanisms that influence its regional delivery (8). The same approach of modeling integrative function can be extended to lung maturation and growth, although ideally, this would involve accounting for events that occur over much longer time scales than are typically considered in current lung-modeling studies.

Existing imaging-based models could be used to estimate the regional distribution of stress during lung growth. The accuracy of this estimation would depend on the accuracy of the constitutive law for the lung tissue (which as described previously, is not yet well characterized) and the accuracy of the boundary conditions that control the lung-tissue deformation. Despite the constitutive law limitation, Tawhai et al. (77) have had some success in predicting the gross response of human lung-tissue deformation to gravity in prone and supine postures using a constitutive law with relatively simple parameterization. This model was developed for human lung but is likely to be valid for animal lungs, as the basic pressure-volume response of the lung tissue is similar between species. Baseline imaging and functional measurements would provide sufficient data to confirm this or to optimize the parameters in the constitutive law to make them species and/or subject specific. The Tawhai et al. (77) model minimizes boundary condition error by using contact and sliding constraints at the lung surface instead of defining the displacement of discrete surface points. With the use of contact constraints, the lung model is free to slide within the thoracic cavity, and asymmetric expansion of lung units, such as that occurring under negative intrapleural pressure following major resection, could be simulated to yield a predicted strain field that could be validated against imaging; the corresponding stress field would also be predicted. Whereas it is not possible to directly validate the spatial distribution of stress, good evidence for its appropriateness would be given by a close correspondence between the predicted and imaged strain distribution.

GRANTS

This work was supported by National Heart, Lung, and Blood Institute Grants RO1 HL40070 and UO1 HL111146 (C. C. W. Hsia) and Ministry of Research, Science and Technology (New Zealand) Grant 20959-NMTS-UOA (M. H. Tawhai).

DISCLOSURES

The contents of this article are solely the responsibility of the authors and do not necessarily represent the official views of the National Heart, Lung, and Blood Institute or of the National Institutes of Health.

AUTHOR CONTRIBUTIONS

Author contributions: C.C.H. and M.H.T. conception and design of research; C.C.H. and M.H.T. performed experiments; C.C.H. and M.H.T. analyzed data; C.C.H. and M.H.T. interpreted results of experiments; C.C.H. and M.H.T. prepared figures; C.C.H. and M.H.T. drafted manuscript; C.C.H. and M.H.T. edited and revised manuscript; C.C.H. and M.H.T. approved final version of manuscript.