Virtual Physiological Human and a Lung Physiome Model
The International Union of Physiological Physiome project was the foundation for the Virtual Physiological Human (VPH) initiative and the human physiome. The term physiome describes the physiology of the whole organism.
The concept of computational physiology and the human physiome is to have mathematicians and bioengineers, working together with physiologists and molecular biologists, link together the different scales of human biology quantitative models beginning with genomic and proteomic databases, and linking these to higher levels of organization at the cell, tissue, organ, and whole organism level. The mathematical and engineering tools needed to develop quantitative models of physiological dynamics and functional behavior of the intact organism need to account for inhomogeneous, anisotropic, and nonlinear behavior of biological materials.
A complete computational model of lung function will need to span multiple spatial and temporal scales (multiscale model). This is necessary to understand how dynamic molecular interactions at small spatial dimensions link to whole lung function at large spatial dimensions. A multiscale model will use a computationally efficient strategy to capture the important functions for each spatial and temporal scale.
Physical forces acting on the surface of the lung through coupling with the chest wall are transmitted to the level of the gas exchange tissue, pulmonary acinus, where this force holds the blood vessels and airways open. The lung surface forces are further transmitted to the level of cells and molecules within the lung tissue where the local stress produced by the lung surface force modulates local cellular and molecular functions.
The stretching of lung tissue produces secretion of surfactant from the type II alveolar epithelial cells that line the pulmonary acinus along with the type I alveolar epithelial cells. The release of surfactant reduces the surface tension of the air-tissue surface of the pulmonary acinus, which decreases the lung surface forces needed to keep the acinar lumen from collapsing and, in this way, alters global lung mechanics.
Pulmonary airway antagonists, such as inhaled allergens (e.g., pollen), act at the cellular level by inducing airway smooth muscle contraction. This results in a subsequent larger-scale narrowing of airway lumens. The narrowed airway lumens in turn produce increases in airway resistance. The increase in airway resistance then produces an even larger scale decrease in whole lung ventilation.
The obstruction of a pulmonary artery lumen by acute thromboemboli, blood clot, induces local disruption of pulmonary artery blood flow that alters the shear stress of endothelial cells on a small scale in the area of the blood clot where pulmonary blood flow has decreased. This decrease in shear stress on the endothelial cells activates the release of nitric oxide by the endothelium, which is a potent vasodilator. The nitric oxide dilates on a larger scale the pulmonary vessels. The dilation of the pulmonary vessels alters on an even larger scale whole lung blood flow.
This chapter will discuss a sophisticated human lung physiome model that includes patient-specific 3D lung CT images as the structural input to a patient-specific multiscale lung model that predicts whole lung physiology of the patient. In previous chapters we have seen how different lung CT AI can assess lung density for the presence of emphysema and pulmonary fibrosis. We have discussed how combining information from inspiratory and expiratory chest CT scans can be used to assess ventilation at different scales in the lung (e.g., whole lung, lobe, voxel). We have also seen how powerful limited memory AI algorithms can be used to detect and assess different texture patterns produced by diffuse lung disease and to assess whether a lung nodule is benign or malignant. In this chapter, we will see how the 3D lung CT structure of the lung including airways, pulmonary arteries, and veins can be used to construct a patient-specific multiscale finite element model of the lung that can predict hypoxemic risk due to acute pulmonary emboli.
Tawhai et al. published details of their lung physiome/VPH model. We will refer to this model as the LP model in this chapter. The LP model builds a complete model of lung structure and how this structure interacts with lung function across a wide range of spatial scales, physical functions, and their integration. The robustness of the LP model is applicable to a wide range of physiological and pathophysiological areas of interest.
The LP model is applicable not only to the risk of gas exchange impairment elevating right ventricular pressure in patients with acute pulmonary embolism but also to the mechanics of airway hyperresponsiveness at the scale of airway smooth muscle to the scale of whole lungs. The LP model can also assess the effects of normal aging on tissue mechanics and optimize methods of mechanical ventilation of the lungs.
Finite Element Model of Lung Structure and Function
There are several major steps in building the LP model of the lung. High-quality 3D chest CT scan is acquired of the thorax and the lungs are segmented from the rest of the thoracic anatomy. The airway tree and pulmonary arteries and veins are segmented from the lung CT images. A 3D finite element mesh of the lungs is generated and bounded by the 3D lung CT volume. The airways are placed into the 3D finite element model and attached to the 3D finite element mesh of the lungs. The extra-acinar and intra-acinar pulmonary arteries and veins are placed into the model. The model then computes known biophysical properties of the lung and includes them in the LP model ( Box 8.1 ).
Acquire high-quality 3D chest CT scans of the thorax and segment the lungs from the rest of the thoracic anatomy
Segment the airway tree and pulmonary arteries and veins from the lung CT images
Generate a 3D finite element mesh of the lungs that is bounded by the 3D lung CT volume
Place the airway tree into the 3D finite element mesh of the lung and attach the airway tree to the 3D finite element mesh
Place the extra-acinar pulmonary arteries and veins into the 3D finite element mesh
Place the intra-acinar pulmonary arteries and veins into the 3D finite element mesh
Compute known biophysical properties of the lung and include them in the LP model
Generating the 3D Finite Element Mesh of the Lung
The method of developing a finite element model of the lung begins by geometrically fitting a volumetric finite element mesh, tetrahedrons, or some other 3D polygon, to the 3D volume of the lungs obtained from a 3D lung CT scan. The volume mesh is then filled with a grid of uniformly spaced points with each point representing a pulmonary acinus; recall there are about 32,000 pulmonary acini in an adult lung. The acinus grid is uniformly spaced assuming that the lung tissue is uniformly expanded at total lung capacity (TLC). This is a reasonable assumption for an upright human lung where maximal expansion can be attained, however, this is less likely in a supine human lung.
Generating the Airway Tree Within the 3D Mesh of the Lung
An initial 1D finite element mesh is placed along the centerlines of the segmented airways obtained from a 3D chest CT scan and acts as an initial condition for the algorithm. Additional new 1D airway branches are generated at the end of a previous branch by directing a branch toward the center of mass of a subset of the acinus grid points where points in any current subset are those that are closest to the parent branch. This process continues until each acinus grid point is supplied by a single terminal model airway. This models the actual lung anatomy where the terminal bronchiole, approximately airway generation 16, supplies a single lung acinus. Tawhai’s finite element lung model generates a subject-specific airway tree for the larger airways that are visible on the 3D lung CT and a shape constraint of the subject-specific airway tree using the surface of the 3D lung CT. The algorithmically generated airways cannot exactly match the individual’s airway tree beyond those identified by the 3D lung CT; however, the averaged airway geometry of the model is consistent with measured human airway morphometry. Because the anatomically structured airway model is generated within the volumetric finite element model of the lung, the modeled airways are connected to the volumetric finite element model of the lung, and as the lung deforms, so will the airways. This coupling of airway and lung tissue function is a strength of Tawhai’s finite element lung model.
Generating the Pulmonary Vascular Tree
Modeling tractable, anatomy-based, computationally functional models of the pulmonary vasculature that capture the important structural features of the pulmonary circulation is a big challenge. Each of the dichotomously branching bronchial airways is accompanied by a corresponding dichotomously branching pulmonary artery, but there are many more pulmonary artery branches in the lung than there are airway branches. The additional pulmonary arteries that do not accompany an airway and pulmonary veins are referred to as pulmonary supernumerary vessels , and these do not branch dichotomously. The extra-acinar and intra-acinar pulmonary blood vessels have distinct geometric structures that give rise to scale-specific functions. The extraacinar dichotomously branching pulmonary arteries supply blood to the gas exchange units, pulmonary acini, in a parallel arrangement. The intraacinar vascular structure has both series and parallel perfusion. The extraacinar and intraacinar blood vessels need to be modeled differently.
Modeling the Extra-Acinar Pulmonary Vessels
The extra-acinar blood vessels were modeled by Burrowes et al. by constructing models of the extra-acinar blood vessels, including supernumerary vessels, using the 3D lung CT to segment the largest pulmonary vessels and then using a volume filling algorithm, similar to the airway model previously described (See “Generating the Airway Tree Within the 3D Mesh of the Lung” section), to construct the blood vessels accompanying the airways to the level of the terminal bronchiole. The supernumerary vessels were constructed in a postprocessing step using an algorithm designed to mimic the limited known features of supernumerary vessels. The algorithm assumes the supernumerary vessels have a branch angle close to 90 degrees from the parent vessel and bifurcate rapidly to supply the closest lung parenchymal tissue. The blood vessels are represented as 1D finite elements distributed in the 3D finite element model of lung tissue.
Modeling the Intra-Acinar Pulmonary Vessels
Clark has modeled the intra-acinar blood vessels separately from the extra-acinar blood vessels described above (See “Generating the Airway Tree Within the 3D Mesh of the Lung” section). This model of intra-acinar blood flow separates the small arterioles and venules from the capillary vessels of the acinus. The acinar arterioles and venules are represented as distinct elastic vessels following the branching structure of the acinar airways, respiratory bronchioles, and alveolar ducts. These acinar arterioles and venules are assumed to join each other at each intra-acinar airway generation by a capillary sheet that covers the alveoli present at each generation of acinar airways forming a ladderlike structure. This model accounts for both serial and parallel perfusion pathways in the pulmonary acinus so it can reproduce the decrease in blood flow rates in the distal part of the acinus compared to the proximal part. The ladderlike model of the intra-acinar vessels is novel. When the ladderlike model of intra-acinar blood vessels was connected to a symmetric extra-acinar vascular structure, a decrease in pulmonary vascular resistance was observed, compared to a different intra-acinar blood vessel model where each acinus was represented by a single continuous capillary sheet (e.g., only parallel perfusion).
Lung Physiome (LP) Model Applied to the Assessment of Acute Pulmonary Embolism
CT pulmonary angiography (CTPA) is the imaging modality of choice for assessing patients suspected to have acute pulmonary embolism (APE). CTPA is widely available in emergency rooms and hospitals for the assessment of APE. CTPA requires the intravenous injection of iodinated contrast media and is more invasive than the other lung CT methods we have discussed. CTPA has the advantage that it can be performed rapidly and interpreted rapidly by expert imaging physicians. It has largely replaced nuclear scintigraphy for the assessment of acute pulmonary emboli. The identification of acute pulmonary arterial thromboemboli is straightforward; however, the correlation of the size and number of pulmonary emboli does not provide a complete assessment of hypoxemic risk in a given patient with APE.
The LP model is a flexible and reducible model that uses a 3D lung CT to inform a structure-based approach to understand individual patient structure-function interactions. The LP model applied to APE has been helpful in the risk stratification of patients with APE and performs better than the simpler 3D lung CT approach of assessing APE by simply assessing the amount of intravascular clot in the pulmonary arteries. The clot burden, or load, is an example of a “structure”-only approach. There is considerable variation in the severity of APE and patient outcomes in APE who have the same clot burden. The success of the LP model in APE is a good example of how powerful lung physiome models like LP can form the respiratory component of a “virtual patient model (VPM)”.
The LP patient-specific model used to assess APE utilized contrast-enhanced 3D lung CT tailored to the assessment of the pulmonary arteries (CTPA) and patient demographics; data of patients who were being clinically assessed for possible APE at the Auckland City Hospital, Auckland, New Zealand.
The 3D distribution of the pulmonary emboli, blood clots, was a semiautomated process that was validated against visual lung CT assessment of the locations of the clots within both lungs. Each clot was associated with a pulmonary artery, and the degree of obstruction depended on the clot size. The LP model then simulated each subject lung perfusion, lung ventilation, and lung oxygen transfer to assess the “hypoxemic risk” for each patient.
Lung perfusion was modeled using a steady-state blood flow model that assumes Poiseuille flow in the elastic extracapillary pulmonary arterial vessels. The lung perfusion model uses a “ladderlike” model of the intra-acinar blood flow in each acinus. This perfusion model was embedded within an upright elastic model of the lung parenchyma where each pulmonary vessel and intra-acinar capillary sheet was attached to points in the elastic lung model so that each vessel and capillary sheet responds to the local tethering force transmitted through the upright elastic model attachment points. This local tethering force is a function of the 3D position in the lung and lung posture (e.g., upright versus supine). The inclusion in the perfusion model of intra-acinar structure and function allowed the LP model to redistribute blood flow from the area of lung that had occluded pulmonary arteries from APE to other regions of the lung without blood clots.
Lung ventilation was simulated using a quasi-steady-state model of 1D airflow that included energy loss equations in the conducting airways, generations 116, that were subtended by compliant pulmonary acinar tissue units. An equation of motion was calculated to balance the elastic tissue pressure, terminal bronchiole air pressure, and airflow.
Oxygen gas transfer from the air contained within the acinar lumen to the blood in the capillary sheet of the acinar unit was modeled assuming equilibration of oxygen between the air containing acinar lumen and the blood, containing lumen of the capillary within the capillary sheet. The patient was assumed to be hemodynamically stable, having stable blood pressure and pulse. The Kapitan and Hempleman model was used to calculate the steady-state partial pressures of oxygen (O 2 ) and carbon dioxide (CO 2 ) in each acinus. The partial pressures of O 2 and CO 2 within the gas-containing portion of the pulmonary acinus were calculated assuming the steady-state condition and were set equal to their values of the partial pressures of O 2 and CO 2 within the blood containing lumen at the end of each capillary of the acinar capillary sheet. The pulmonary venous partial pressure of O 2 and CO 2 were calculated averages of end-capillary O 2 and CO 2 contents that were then converted to partial pressures of O 2 and CO 2 .
The LP perfusion model needed specific boundary conditions set for cardiac output and left atrial pressure ( Box 8.2 ). The LP ventilation model needed specific boundary conditions set for respiratory rate and respiratory tidal volume ( Box 8.2 ). The baseline boundary conditions were estimated by using the patient age, weight, and height to estimate the metabolic rate, oxygen uptake, ventilation rate (or minute ventilation), and cardiac output. The resting respiratory rate was assumed to be 12 breaths per minute, and the resting heart rate was assumed to be 65 beats per minute. Metabolic demand was assumed to stay at a baseline value so that during the simulation of gas exchange, the values of venous O 2 and CO 2 were updated to maintain a constant baseline metabolic rate. The 3D ventilation of the lung was assumed to be constant. Only constant baseline values of cardiac output and minute ventilation were used in the LP model in assessing hypoxemic risk in individual APE patients. The LP model calculated the maximum derangement in arterial blood O 2 and CO 2 values as the hypoxemic risk and hypercapnic risk, respectively. The LP model also assessed the elevation of mean pulmonary artery pressure (mPAP), which provides a direct indication of right ventricular afterload. The increase in right ventricular afterload is what can produce acute right ventricular failure and death in APE.