Between-tumor and within-tumor heterogeneity in invasive potential
The method used to define a quantitative phenotype for invasion is outlined for an organoid that is highly invasive (panels A, B, C), moderately invasive (panels D,E,F), and weakly invasive (panels G,H,I). These three organoids were selected from the 43 organoids generated from tumor 10, illustrating heterogeneity within a single tumor sample. Differential interference contrast (DIC) microscopy was used for image acquisition, with a scale of approximately 0.5 μm per pixel and a field of view of approximately 530×710 μm (panels A,D,G). Boundaries were segmented manually from DIC images and interpolated to 256 equally spaced points, sufficiently dense to track even the most invasive boundaries (panels B,E,H). A discrete Fourier transform was then applied separately to the x and y components of the discrete points, and the magnitudes of the corresponding Fourier amplitudes were squared and added to obtain the raw spectral power. Fourier mode 0, which represents the centroid of the boundary, was set to 0. The remaining modes were normalized by the power of Fourier mode 1 to provide scale invariance. Filters were applied to smooth effects from discrete pixel size and to emphasize the contributions of higher frequency modes, yielding a smoothed and weighted power spectrum for each organoid (panels C,F,I). The sum of the area under the spectrum, termed the spectral power, provides a single quantitative measure of invasiveness.