Understanding patient-derived tumor organoid growth through an integrated imaging and mathematical modeling framework
Fig 1
Overview of mathematical models.
A: The exponential model assumes that all cells in the organoid divide at the same rate a, while the power law model assumes that cell divisions are restricted to a subset of cells, for example at the surface of the organoid. The Gompertz and logistic models each assume that initial growth is exponential at rate a and that the growth slows down over time. This can either be due to the cell division rate decreasing uniformly across the organoid, or due to a decreasing subset of actively dividing cells over time. The von Bertalanffy model assumes that cell proliferation follows the power law model, but in addition that cells die uniformly across the organoid at rate b. B: The exponential and power law models are models of unconstrained growth, while the Gompertz, logistic and von Bertalanffy models all assume that the growth eventually stops, with the organoid reaching a so-called “carrying capacity” K.