Lukas Buschle^{1}, Christian Ziener^{1}, Thomas Kampf^{2}, Volker Sturm^{3}, Ke Zhang^{1}, Sabine Heiland^{3}, Martin Bendszus^{3}, Heinz-Peter Schlemmer^{1}, and Felix Kurz^{3}

Magnetic resonance imaging of lung tissue is strongly influenced by susceptibility effects between spin-bearing water molecules and air-filled alveoli. The measured lineshape, however, also depends on the blood-flow around alveoli that can be approximated as pseudo-diffusion. Both effects are quantitatively described by the Bloch-Torrey-equation, which was so far only solved for dephasing on the alveolar surface. In this work, we extend this model to the whole range of physiological relevant air volume fractions. The results agree very well with in vivo measurements in human lung tissue.

Magnetic resonance imaging of lung tissue is cumbersome due to macroscopic field inhomogeneities, short relaxation times and motion artefacts. While the lineshape of the water peak in most other organs is narrow and Lorenzian-shaped, a broad and asymmetric lineshape is present in lung tissue [1]. On the other hand, an analysis of this broad lineshape reveals microscopic changes of the lung structure [2]. To obtain microstructural parameters from measured lineshapes, it is necessary to understand the signal formation in lung tissue. Previously, a shell model was used to describe the spin dephasing in the magnetic dipole field around alveoli (see [3] and Fig. 1c). However, the signal evolution is not only influenced by the air-filled alveoli but also strongly depends on the blood flow in the highly-vascularized interstitial lung tissue, which can be described as pseudo-diffusion, see Fig. 1d). In this work, both, pseudo-diffusion and susceptibility effects are considered in the so-called extended alveolar surface model that reveals a good agreement with measured lineshapes.

The susceptibility difference between air-filled alveoli with radius $$$R$$$ and surrounding tissue causes local dipole fields of the form:

$$\omega(\mathbf{r}) = \delta\omega R^3 \frac{3\cos^2(\theta)-1}{r^3},$$where $$$\delta\omega$$$ denotes the dipole field strength. Pseudo-diffusion and susceptibility effects are described by the Bloch-Torrey-equation that, however, is not analytically solvable for the given form of the magnetic field inhomogeneity. Since the air volume fraction $$$\eta$$$ in lung tissue is typically very high, most spin-bearing particles are located close to the surface of the alveoli, see Fig. 1. Thus, the alveolar surface model assumes that all spins are located on the surface of the alveoli, which allows solving the Bloch-Torrey-equation [4]. For a pathological decrease of the air volume fraction $$$\eta$$$, however, the relaxation time $$$T_2^\prime$$$ is significantly underestimated in this model, see Fig. 2. Therefore, this work extends the alveolar surface model to smaller air volume fractions.

The results are compared with in vivo measurements in a healthy volunteer. Images were acquired with a Magnetom Aera 1.5T (Siemens Healthcare, Erlangen, Germany). A cubic $$$[15\text{mm}]^3$$$ voxel as visualized in Fig. 1a) was selected to acquire the free induction decay in expiration using the PRESS sequence [5] with TR = 1.5 s, echo time TE = 30 ms and twenty averages, see Fig. 1a).

[1] R.Mulkern, S. Haker, H. Mamata, E. Lee, D. Mitsouras, K. Oshio, M. Balasubramanian, and H. Hatabu. Lung parenchymal signal intensity in MRI: A technical review with educational aspirations regarding reversible versus irreversible transverse relaxation effects in common pulse sequences. Concepts Magn Reson Part A, 43A:29–53, 2014.

[2] J. Zapp, S. Domsch, S. Weingärtner, and L. R. Schad. Gaussian signal relaxation around spin echoes: Implications for precise reversible transverse relaxation quantification of pulmonary tissue at 1.5 and 3 Tesla. Magn Reson Med, 77(5):1938–1945, 2017.

[3] A. G. Cutillo. Application of magnetic resonance to the study of lung. Futura Publishing Company, Inc., Armonk, NY,1996.

[4] L. R. Buschle, F. T. Kurz, T. Kampf, W. L. Wagner, J. Duerr, W. Stiller, P. Konietzke, F. Wünnemann, M. A. Mall, M. O.Wielpütz, H. P. Schlemmer, and C. H. Ziener. Dephasing and diffusion on the alveolar surface. Phys Rev E, 95(2-1):022415, 2017.

[5] P. A. Bottomley. Spatial Localization in NMR Spectroscopy in Vivo. Ann N Y Acad Sci, 508:333–348, 1987.

Fig. 1: (a) MR imaging of lung tissue highly depends on microscopic field inhomogeneities caused by alveoli (b). A single alveolus is typically described as spherical object (c), where spin-bearing particles are located close to the surface. Blood flow in the highly vascularized tissue, however, also contributes to the signal formation, and can be considered as pseudo-diffusion (d).

Fig. 2: Relaxation times $$$T_2^\prime$$$ for negligible diffusion effects. In the alveolar surface model (ASM), the relaxation rates are significantly underestimated for intermediate air volume fractions $$$\eta$$$ when compared to the exact relaxation rate, whereas the extended alveolar surface model (EASM) is better applicable for small air volume fractions.

Fig. 3: Lineshapes in the extended alveolar surface model for different pseudo-diffusion strength $$$\tau=R^2/D^*$$$. The lineshape is approximately symmetric for strong pseudo-diffusion and becomes more asymmtric with decreasing pseudo-diffusion strength.

Fig. 4: Comparison of the measured lineshape in a healthy subject (red line), the lineshape in the alveolar surface model (blue line) and the lineshape in the newly developed extended alveolar surface model (black line). For realistic values of the peripheral lung tissue, the extended alveolar surface model allows a better description of the flanks of the peak. Please note that no fitted parameters were used.