Finite element modeling of ¹²⁹Xe diffusive gas exchange NMR in the human alveoli

Highlights

• Numerical simulation framework established for ¹²⁹Xe gas exchange NMR.

• Flexible 3D capillary model developed for evaluating gas exchange parameters.

• 2D/3D histology/micro-CT based geometries realized for diffusion simulations.

• Implications for NMR applications and lung microstructural modeling.

Abstract

Existing models of ¹²⁹Xe diffusive exchange for lung microstructural modeling with time-resolved MR spectroscopy data have considered analytical solutions to one-dimensional, homogeneous models of the lungs with specific assumptions about the alveolar geometry. In order to establish a model system for simulating the effects of physiologically-realistic changes in physical and microstructural parameters on ¹²⁹Xe exchange NMR, we have developed a 3D alveolar capillary model for finite element analysis. To account for the heterogeneity of the alveolar geometry across the lungs, we have derived realistic geometries for finite element analysis based on 2D histological samples and 3D micro-CT image volumes obtained from ex vivo biopsies of lung tissue from normal subjects and patients with interstitial lung disease. The 3D alveolar capillary model permits investigation of the impact of alveolar geometrical parameters and diffusion and perfusion coefficients on the in vivo measured ¹²⁹Xe CSSR signal response. The heterogeneity of alveolar microstructure that is accounted for in image-based models resulted in considerable alterations to the shape of the ¹²⁹Xe diffusive uptake curve when compared to 1D models. Our findings have important implications for the future design and optimization of ¹²⁹Xe MR experiments and in the interpretation of lung microstructural changes from this data.

Introduction

Hyperpolarized (HP) noble gas magnetic resonance imaging (MRI) with ³He and ¹²⁹Xe permits exquisite visualization of lung ventilation [1], [2], [3] and quantitative assessment of lung microstructure [4], [5], [6]. Despite the predominant application of ³He in previous clinical HP gas lung imaging research, ¹²⁹Xe possesses supplementary interesting properties for studies of lung function [7]. In particular, xenon is soluble in parenchymal tissues and blood (Ostwald solubility 0.1–0.2 [8]) and the ¹²⁹Xe resonance exhibits a wide range of chemical shift values in vivo. Upon inhalation, two distinct resonances of ¹²⁹Xe dissolved in lung parenchyma and blood plasma, and erythrocytes [9] can be observed; these “dissolved-phase” ¹²⁹Xe resonances are separated by a chemical shift of around 200 ppm from the resonance of ¹²⁹Xe gas in the alveoli. Owing to these properties, the diffusive exchange of ¹²⁹Xe across the lung’s physiological gas transfer workface – from the alveoli to the capillaries – can be tracked non-invasively in vivo by NMR methods sensitive to chemical shift, for example, spectroscopy and chemical shift imaging (CSI) techniques [10], [11], [12], [13]. In particular, the chemical shift saturation recovery (CSSR) spectroscopy method permits assessment of the temporal dynamics of diffusive exchange of xenon from the alveoli to the capillaries during a single breath-hold of inhaled HP ¹²⁹Xe [12], [14]. ¹²⁹Xe CSSR data can be modeled using analytical solutions of the one-dimensional diffusion equation in order to obtain quantitative information about gas exchange, including estimates of lung microstructural dimensions [14], [15], [16], [17]. This methodology has been adopted in preliminary clinical studies in humans, and has enabled evaluation of alveolar septal thickening in patients with interstitial lung disease (ILD) [14], [18] and chronic obstructive pulmonary disease (COPD) [19]. The technique has potential clinical impact in the assessment of interstitial and gas exchange pathologies for which there is no universally-accepted gold-standard metric of gas exchange assessment at present [20].

The most widely-employed analytical model of xenon diffusional exchange in the lungs for interpreting ¹²⁹Xe CSSR data was developed by considering a simplistic 1D description of the lungs as alveolar spaces separated by septal (interstitial) tissue [12], [14]. This model was subsequently extended to divide the interstitial region into tissue and capillary compartments [15] (as shown in Fig. 1a) in order to utilize the MR signals arising from the discrete dissolved-phase ¹²⁹Xe resonances that can be spectrally resolved at higher B₀ field strengths. Inherent to this approach is the assumption that the septal thickness separating the alveoli and capillaries is constant throughout the lungs. In addition, a 1D radially-symmetric geometry comprising spherical alveoli sheathed by a uniform tissue layer has been considered in order to formulate a comparable model with similar assumptions [17]. In attempt to validate the applicability of these analytical models, preliminary finite difference simulations have been implemented to model ¹²⁹Xe diffusive exchange in a geometry comprising a single alveolus and a capillary region, however this model also assumed homogeneity of septal tissue [21]. Fundamentally, these approaches do not utilize realistic representations of the lung microstructure to account for the heterogeneity in alveolar geometry and tissue or capillary thickness that is present in the lungs [22] and crucially, is accentuated in many lung diseases (see e.g. [23] and example whole-lung and micro-CT images of the lungs of normal subjects and patients with idiopathic pulmonary fibrosis (IPF) shown in Fig. 2). Additionally, analytical approaches are limited by a high number of interrelated fitting parameters that may obscure the quantitative interpretation of metrics of gas exchange and microstructure [18] so-derived. Thus, realistic geometrical representations of the alveoli, septa and capillary networks should help to advance the current models of ¹²⁹Xe diffusional exchange in the human lungs and strengthen the interpretation of quantitative information about lung microstructure derived from in vivo ¹²⁹Xe NMR.

In this work, ¹²⁹Xe diffusive exchange between the alveoli and pulmonary capillaries is simulated via finite element analysis, adopting a similar methodology to that previously presented for simulating hyperpolarized gas diffusion MR [24], [25], [26], [27]. A number of geometrical approaches are employed, including; 3D cylindrical geometries of the pulmonary capillaries (as an initial model system for validation of numerical simulations), and realistic 2D and 3D “image-based” geometries of the alveolar microstructure, derived from histological sections and volumetric μCT data obtained from normal human lungs and the lungs of patients with ILD. The implications of these simulations for the analysis of ¹²⁹Xe gas exchange NMR data and the future development of associated analytical models of lung microstructure are discussed.