Using random matrix theory to quantify pulmonary fibrosis: Investigating the effect of time window duration

Abstract

Random matrix theory (RMT) exploits the distribution of singular values of the inter-element response matrix (IRM). If multiple scattering dominates the propagation, the singular value distribution follows the quarter circle law. However, dominance of single scattering results in Henkel function behavior of the singular value distribution. In our previous work, we have shown that this can be exploited to estimate severity of bleomycin-induced fibrosis (measured by histology) in rodent lungs. We showed that E(x), the expected value of the singular value distribution, as well as the singular value with the highest probability, correlated significantly with histology scores. Here, we investigate the sensitivity of these metrics to the time window duration used for the Singular Value Decomposition of the IRM, which is performed in the frequency domain, using overlapping time windows. A linear transducer with a central frequency of 7.8 MHz and a Verasonics scanner were used to obtain IRMs in 24 rat lungs. Different degrees of pulmonary fibrosis were induced using bleomycin in 18 rats while 6 rats were left as controls. The IRMs were time-windowed with different duration of 2T, 4T, and 6T where T is the transmitted pulse period. E(x) and were evaluated for each time window duration for all rat lungs. For all time window durations significant correlations were observed between and E(x), and histology scores. Wilcoxon ranksum tests show that the distributions obtained for and E(x) are not affected by the time window duration.