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Integrative Computational Models of Lung Structure‐Function Interactions

Alys R. Clark, Kelly S. Burrowes, Merryn H. Tawhai

10.1002/cphy.c200011

Source: Volume 11, Issue 2, April 2021

Published online: February 2021

Full Article on Wiley Online Library



Abstract

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.

Figure 1. Figure 1. The respiratory system components and their interactions that are necessary to consider for simulating basic integrated ventilation‐perfusion and gas exchange function.
Figure 2. Figure 2. High order finite element (FE) meshes for the lung. (A) FE mesh embedded within the volumetric imaging data from which it is derived. Surface nodes (numbering in the order of 10s) are shown. (B) A geometry‐fitted surface mesh with high‐order interpolation functions to represent the highly curved surface with relatively few elements.
Figure 3. Figure 3. Anatomically based models for an airway (A) and arterial (C) tree in one subject generated using the method of Tawhai et al. 200. The central airways (from trachea to first generation of subsegmental bronchi) and central arteries (pulmonary artery to first generation of subsegmental arteries) were segmented from volumetric HRCT. Rather than generating an independent arterial model, the airway tree was copied, offset, and then merged with the central arteries over several generations of branching (B). Reused, with permission, from Tawhai MH, et al., 2004 200.
Figure 4. Figure 4. Different configurations for models of intra‐acinar blood vessel geometry. (A) and (B) illustrate series models, where the capillary beds all sit at the same arteriole branching level. (C) provides a “ladder‐like” geometry, with capillary beds distributed at side‐branches from the arterioles, and drained by a matching venule structure. Reused, with permission, from Clark AR, et al., 2010 42.
Figure 5. Figure 5. The multi‐scale nature of the multiple components that contribute to organ‐level tissue mechanical properties in the lungs. Each component—from protein to cell and tissue—makes an important contribution to how the lung deforms with posture and during breathing. Reused, with permission, from Burrowes KS, et al., 2019 29.
Figure 6. Figure 6. Rib cage motion simulated using a FE model for the rib cage and intercostal muscle activation. The model in blue shows the resting configuration, and in gold shows the displacement of the rib cage after muscle activation. (A‐C) show inspiratory displacement, and (D‐E) expiratory displacement. Reused, with permission, from Zhang G, et al., 2016 232.
Figure 7. Figure 7. A multi‐scale model for force balance across the actively contracting airway wall. Models at the organ, tissue, cell, and molecule scales interact through (A) anisotropic strain from an organ‐level continuum model is linearized to an expression for airway‐parenchymal tethering, (B) shortening velocity of the smooth muscle is limited by the balance of active and passive forces, (C) coupling of calcium to force generation via activation of myosin light chain kinase (MLCK), (D) active and passive force generation from cross‐bridges and cross‐linkers in the airway smooth muscle, (E) airway constriction and redistribution of tissue expansion in a ventilation model coupled to elastic tissue. The sub‐figure shows the actin‐myosin cycle. After actin (A) and phosphorylated myosin (Mp) bind (→ AMp) they can transition to a “latch state” that maintains force but cannot generate additional force. Actin unbinds with rate constant g(x), to end up with unphosphorylated myosin (M) and actin again. The ? represents an unknown rate constant for the theoretical situation of latch bridge formation from unphosphorylated myosin and actin, which is likely to be minimal. Reused, with permission, from Lauzon AM, et al., 2012 126.
Figure 8. Figure 8. Ventilation distribution simulated in an upright airway tree model coupled to elastic acini. (A) shows the flow to each acinus in a craniocaudal slice through the central lung. The color scale extends from 2.8 mm3/s (blue) to 4.6 mm3/s (red). (B) compares the ventilation distribution for coupling to uniform or linearly distributed initial acinar volumes, or to a finite deformation elasticity simulation of initial tissue distribution. For the resting ventilation considered in this study, the difference between the finite deformation and linear volume initializations was not large. Reused, with permission, from Swan AJ, et al., 2012 195.
Figure 9. Figure 9. Example of a multiscale model of the pulmonary circulation. This includes the largest vessels derived from high‐resolution computed tomography imaging and distal vessels generated using a volume‐filling branching algorithm. The arterioles and venules within the acini are represented using a “ladderlike” structure where a capillary sheet model (a “rung” on the ladder) links each arteriole‐venule pair to provide a full‐circuit perfusion model that predicts regional recruitment and distension. Reused, with permission, from Tawhai MH, and Bates JH, 2011 199.
Figure 10. Figure 10. V̇/Q̇ matching simulated in a supine model for the human lung that includes soft tissue deformation under gravitational load, airflow coupled to peripheral elastic tissue units, and blood flow through a full circulation model that includes the effect of hydrostatic pressure. (A) shows the distribution of V̇/Q̇ for the full model; (B) is simulated without tissue deformation; (C) is simulated without hydrostatic pressure; and (D) is for zero gravity. Reused, with permission, from Kang W, et al., 2017 110.


Figure 1. The respiratory system components and their interactions that are necessary to consider for simulating basic integrated ventilation‐perfusion and gas exchange function.


Figure 2. High order finite element (FE) meshes for the lung. (A) FE mesh embedded within the volumetric imaging data from which it is derived. Surface nodes (numbering in the order of 10s) are shown. (B) A geometry‐fitted surface mesh with high‐order interpolation functions to represent the highly curved surface with relatively few elements.


Figure 3. Anatomically based models for an airway (A) and arterial (C) tree in one subject generated using the method of Tawhai et al. 200. The central airways (from trachea to first generation of subsegmental bronchi) and central arteries (pulmonary artery to first generation of subsegmental arteries) were segmented from volumetric HRCT. Rather than generating an independent arterial model, the airway tree was copied, offset, and then merged with the central arteries over several generations of branching (B). Reused, with permission, from Tawhai MH, et al., 2004 200.


Figure 4. Different configurations for models of intra‐acinar blood vessel geometry. (A) and (B) illustrate series models, where the capillary beds all sit at the same arteriole branching level. (C) provides a “ladder‐like” geometry, with capillary beds distributed at side‐branches from the arterioles, and drained by a matching venule structure. Reused, with permission, from Clark AR, et al., 2010 42.


Figure 5. The multi‐scale nature of the multiple components that contribute to organ‐level tissue mechanical properties in the lungs. Each component—from protein to cell and tissue—makes an important contribution to how the lung deforms with posture and during breathing. Reused, with permission, from Burrowes KS, et al., 2019 29.


Figure 6. Rib cage motion simulated using a FE model for the rib cage and intercostal muscle activation. The model in blue shows the resting configuration, and in gold shows the displacement of the rib cage after muscle activation. (A‐C) show inspiratory displacement, and (D‐E) expiratory displacement. Reused, with permission, from Zhang G, et al., 2016 232.


Figure 7. A multi‐scale model for force balance across the actively contracting airway wall. Models at the organ, tissue, cell, and molecule scales interact through (A) anisotropic strain from an organ‐level continuum model is linearized to an expression for airway‐parenchymal tethering, (B) shortening velocity of the smooth muscle is limited by the balance of active and passive forces, (C) coupling of calcium to force generation via activation of myosin light chain kinase (MLCK), (D) active and passive force generation from cross‐bridges and cross‐linkers in the airway smooth muscle, (E) airway constriction and redistribution of tissue expansion in a ventilation model coupled to elastic tissue. The sub‐figure shows the actin‐myosin cycle. After actin (A) and phosphorylated myosin (Mp) bind (→ AMp) they can transition to a “latch state” that maintains force but cannot generate additional force. Actin unbinds with rate constant g(x), to end up with unphosphorylated myosin (M) and actin again. The ? represents an unknown rate constant for the theoretical situation of latch bridge formation from unphosphorylated myosin and actin, which is likely to be minimal. Reused, with permission, from Lauzon AM, et al., 2012 126.


Figure 8. Ventilation distribution simulated in an upright airway tree model coupled to elastic acini. (A) shows the flow to each acinus in a craniocaudal slice through the central lung. The color scale extends from 2.8 mm3/s (blue) to 4.6 mm3/s (red). (B) compares the ventilation distribution for coupling to uniform or linearly distributed initial acinar volumes, or to a finite deformation elasticity simulation of initial tissue distribution. For the resting ventilation considered in this study, the difference between the finite deformation and linear volume initializations was not large. Reused, with permission, from Swan AJ, et al., 2012 195.


Figure 9. Example of a multiscale model of the pulmonary circulation. This includes the largest vessels derived from high‐resolution computed tomography imaging and distal vessels generated using a volume‐filling branching algorithm. The arterioles and venules within the acini are represented using a “ladderlike” structure where a capillary sheet model (a “rung” on the ladder) links each arteriole‐venule pair to provide a full‐circuit perfusion model that predicts regional recruitment and distension. Reused, with permission, from Tawhai MH, and Bates JH, 2011 199.


Figure 10. V̇/Q̇ matching simulated in a supine model for the human lung that includes soft tissue deformation under gravitational load, airflow coupled to peripheral elastic tissue units, and blood flow through a full circulation model that includes the effect of hydrostatic pressure. (A) shows the distribution of V̇/Q̇ for the full model; (B) is simulated without tissue deformation; (C) is simulated without hydrostatic pressure; and (D) is for zero gravity. Reused, with permission, from Kang W, et al., 2017 110.
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Article Title: Integrative Computational Models of Lung Structure‐Function Interactions
 

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Alys R. Clark, Kelly S. Burrowes, Merryn H. Tawhai. Integrative Computational Models of Lung Structure‐Function Interactions. Compr Physiol 2021, 11: 1501-1530. doi: 10.1002/cphy.c200011