Quantifying severity of lung fibrosis in rodents using random matrix theory

Abstract

We investigate random matrix theory (RMT) as a tool to detect and quantify pulmonary fibrosis in rodents in vivo. Highly scattering structures such as lung alveoli result in specific characteristics in the distribution of singular values of the inter-element response matrix (IRM). When multiple scattering dominates (healthy lung), the distribution of singular values of the IRM is expected to follow a quarter circle law. However, when single scattering regime dominates, the singular values distribution is closer to a Henkel distribution. We propose to exploit this feature to detect pulmonary fibrosis and quantify its severity. Two metrics are defined to describe the singular value distribution: the expected value E(x), which is the weighted average of all singular values, and, the singular value with the highest probability. A 128-element linear transducer operating at 7.8 MHz and a Verasonics scanner were used to collect IRMs from 6 normal and 18 rat lungs with bleomycin-induced fibrosis in vivo. Significant correlations were observed between E(x) (r = −0.46, p = 0.02) and (r = 0.52, p = 0.01) with the severity of fibrosis independently assessed by histology. These preliminary results show the potential of RMT metrics E(x) and to quantify structural changes in the lung parenchyma.