Harnessing flex point symmetry to estimate logistic tumor population growth

by Stefano Pasetto, Isha Harshe, Renee Brady-Nicholls, Robert A. Gatenby, Heiko Enderling

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Tumor growth dynamics are well-described mathematically by the S-shaped logistic function. Initially exponential growth decelerates as the tumor approaches its carrying capacity – the maximum tumor burden that can be sustained by the local and systemic (micro-)environment. The volume-to-carrying capacity ratio is a major determinant of response to (radio-)therapy; therefore, it is of high importance to estimate the carrying capacity from limited tumor volume measurements. The symmetry around the logistic growth flex point can be used to introduce ghost points symmetric to observed data points to double the available data to calibrate model parameters for an individual patient. With this approach, fewer data points are necessary to identify patient-specific carrying capacities, thereby potentiating shorter times to treatment decisions.