Multiscale optical phase fluctuations link disorder strength and fractal dimension of cell structure

Optical methods for examining cellular structure based on endogenous contrast rely on analysis of refractive index changes to discriminate cell phenotype. These changes can be visualized using techniques such as phase contrast microscopy, detected by light scattering, or analyzed numerically using quantitative phase imaging. The statistical variations of refractive index at the nanoscale can be quantified using disorder strength, a metric seen to increase with neoplastic change. In contrast, the spatial organization of these variations is typically characterized using a fractal dimension, which is also seen to increase with cancer progression. Here, we seek to link these two measurements using multiscale measurements of optical phase to calculate disorder strength and in turn to determine the fractal dimension of the structures. First, quantitative phase images are analyzed to show that the disorder strength metric changes with resolution. The trend of disorder strength with length scales is analyzed to determine the fractal dimension of the cellular structures. Comparison of these metrics is presented for different cell lines with varying phenotypes including MCF10A, MCF7, BT474, HT-29, A431, and A549 cell lines, in addition to three cell populations with modified phenotypes. Our results show that disorder strength and fractal dimension can both be obtained with quantitative phase imaging and that these metrics can independently distinguish between different cell lines. Furthermore, their combined use presents a new approach for better understanding cellular restructuring during different pathways.