Magnetic Resonance Elastography and Computational Modeling Identify Heterogeneous Lung Biomechanical Properties during Cystic Fibrosis

Abstract

The lung is a dynamic mechanical organ and several pulmonary disorders are characterized by heterogeneous changes in the lung's local mechanical properties (i.e. stiffness). These alterations lead to abnormal lung tissue deformation (i.e. strain) which have been shown to promote disease progression. Although heterogenous mechanical properties may be important biomarkers of disease, there is currently no non-invasive way to measure these properties for clinical diagnostic purposes. In this study, we use a magnetic resonance elastography technique to measure heterogenous distributions of the lung's shear stiffness in healthy adults and in people with Cystic Fibrosis. Additionally, computational finite element models which directly incorporate the measured heterogenous mechanical properties were developed to assess the effects on lung tissue deformation. Results indicate that consolidated lung regions in people with Cystic Fibrosis exhibited increased shear stiffness and reduced spatial heterogeneity compared to surrounding non-consolidated regions. Accounting for heterogenous lung stiffness in healthy adults did not change the globally averaged strain magnitude obtained in computational models. However, computational models that used heterogenous stiffness measurements predicted significantly more variability in local strain and higher spatial strain gradients. Finally, computational models predicted lower strain variability and spatial strain gradients in consolidated lung regions compared to non-consolidated regions. These results indicate that spatial variability in shear stiffness alters local strain and strain gradient magnitudes in people with Cystic Fibrosis. This imaged-based modeling technique therefore represents a clinically viable way to non-invasively assess lung mechanics during both health and disease.

Keywords: Finite Element Modeling; Heterogeneity; Lung Mechanics; Respiratory Disease; Shear Stiffness; Strain Gradients.

Figure 1

Overview of the lung finite element simulation. A) Outlines obtained in each axial MR scan using ImageJ and 3D geometry of lung section obtained by lofting outlines using NURBS toolbox. B) Example MRE stiffness map/measurements used to specify material properties in inner domain. C) Inner and outer domains in the lung section, D) Boundary conditions used in finite element simulations of breathing and E) finite element mesh used to solve governing equations. F) Example of total displacements (top row) and 1st principal strain (second row) calculated by the finite element model in a representative normal subject at end expiration (t=0), mid-respiratory cycle (t=1.5s) and end inspiration (t=2.5s).

Figure 2

Magnetic resonance elastography data A) Wave image and shear stiffness map in representative normal and CF patients B) Shear stiffness distribution in the lung of normal and CF patients C) Shear stiffness distribution in normal lung and in consolidated and non-consolidated regions in a CF patient D) Average median shear stiffness and inter-quartile range in normal and CF subjects. E) Average median shear stiffness and inter-quartile range in the n=6 normal lungs, n=3 consolidated regions and n=6 non-consolidated regions in CF subjects.

Figure 3

1^st principal strain in healthy subjects at end inspiration as calculated from computational models that either assume a homogenous stiffness (uniform) or heterogeneous stiffness based on MRE measurements. (MRE based) A) Representative maps of 1^st principal strain at different axial locations. B) Histograms of strain distributions in a representative subject C) Average of median strain distribution in n=6 normal adult subjects and D) average interquartile range (IQR) of strain distribution in n=6 normal adult subjects. Paired two-tailed t-test was used to document statistical significance with *** p<0.001.

Figure 4

Spatial strain gradient in healthy subjects at end inspiration as calculated from computational models that either assume a homogenous stiffness (uniform) or heterogeneous stiffness based on MRE measurements. (MRE based) A) Representative maps of spatial strain gradient at different axial locations. B) Histograms of spatial strain gradient distributions in a representative subject C) Average of median spatial strain gradient distribution in n=6 normal adult subjects and D) average interquartile range (IQR) of spatial strain gradient distribution in n=6 normal adult subjects. Paired two-tailed t-test was used to document statistical significance with **p<0.01, **** p<1e-4.

Figure 5

1^st principal strain obtained in MRE-based models of normal and CF lungs. A) Representative maps of 1st principal strain at a one axial locations in normal, CF – nonconsolidated and CF consolidated lung regions. B) Histograms of strain distributions in a representative normal and CF subject. C) Average of median of strain distribution in n=6 normal adult lungs, n=6 CF – nonconsolidated lung regions and n=3 CF consolidated lung regions and D) average interquartile range (IQR) of strain distribution in n=6 normal adult lungs, n=6 CF – nonconsolidated lung regions and n=3 CF consolidated lung regions. One-way ANOVA was used to document statistical significance with **p<0.01, *** p<0.001, and ****p<1e-4.

Figure 6

Spatial strain gradient obtained in MRE-based models of normal and CF lungs. A) Representative maps of spatial strain gradient at a one axial location in normal, CF – nonconsolidated and CF consolidated lung regions. B) Histograms of strain gradient distributions in a representative normal and CF subject. C) Average of median of strain gradient distribution in n=6 normal adult lungs, n=6 CF – nonconsolidated lung regions and n=3 CF consolidated lung regions and D) average interquartile range (IQR) of strain gradient distribution in n=6 normal adult lungs, n=6 CF – nonconsolidated lung regions and n=3 CF consolidated lung regions. One-way ANOVA was used to document statistical significance with *p<0.05, **p<0.01 and *** p<0.001.