A sample size analysis of a mathematical model of longitudinal tumor volume and progression-free survival for Bayesian individual dynamic predictions in recurrent high-grade glioma.

Patients with recurrent high-grade glioma (rHGG) have a poor prognosis with median progression-free survival (PFS) of <7 months. Responses to treatment are heterogenous, suggesting a clinical need for prognostic models. Bayesian data analysis can exploit individual patient follow-up imaging studies to adaptively predict the risk of progression.

Predicting Individual Tumor Response Dynamics in Locally Advanced Non-Small Cell Lung Cancer Radiation Therapy: A Mathematical Modelling Study.

Purpose: To predict individual tumor responses to radiation therapy (RT) in non-small cell lung cancer.

Materials And Methods: The proliferation saturation index (PSI) model, which models tumor dynamics in response to RT as an instantaneous reduction in tumor volume, was fit to n = 162 patients with 4 distinct dose fractionation schedules (30-32 fractions × 2 Gy, 23-24 fractions × 2.75 Gy, 32-42 fractions × 1.

Harnessing Flex Point Symmetry to Estimate Logistic Tumor Population Growth.

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e.

Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues.

The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis.