Calibration of Multi-Parameter Models of Avascular Tumor Growth Using Time Resolved Microscopy Data

Abstract

Two of the central challenges of using mathematical models for predicting the spatiotemporal development of tumors is the lack of appropriate data to calibrate the parameters of the model, and quantitative characterization of the uncertainties in both the experimental data and the modeling process itself. We present a sequence of experiments, with increasing complexity, designed to systematically calibrate the rates of apoptosis, proliferation, and necrosis, as well as mobility, within a phase-field tumor growth model. The in vitro experiments characterize the proliferation and death of human liver carcinoma cells under different initial cell concentrations, nutrient availabilities, and treatment conditions. A Bayesian framework is employed to quantify the uncertainties in model parameters. The average difference between the calibration and the data, across all time points is between 11.54% and 14.04% for the apoptosis experiments, 7.33% and 23.30% for the proliferation experiments, and 8.12% and 31.55% for the necrosis experiments. The results indicate the proposed experiment-computational approach is generalizable and appropriate for step-by-step calibration of multi-parameter models, yielding accurate estimations of model parameters related to rates of proliferation, apoptosis, and necrosis.

Environmental stress level to model tumor cell growth and survival

“…The resulting average parameter values can be concluded as biologically reasonable, since we chose a prior distribution ensuring this. Up to some adaptions regarding units and reparametrisation, the reasonableness of the parameters is also supported by comparing their values to the calibration results of [7], where a set of similar models is used together with parts of the same data.…”

“…These measurements are employed to calibrate the unknown model parameters for models M S and M η with Bayesian inversion methods (for details see following Section 2.3). Another experiment in [7] was designed to investigate cell behavior under optimal growth conditions, i.e. the cells were provided with 10% FBS over a period of 21 days.…”

“…For comparison, we present two systems of ordinary differential equations, which model tumor cell population dynamics respectively with and without considering an environmental stress level. To do so, time-resolved in vitro data (from [7]) are used to perform model parameter calibration with Bayesian inversion. The latter approach provides a quantitative estimate of the uncertainty in the estimated parameters and hence brings more information than a deterministic inversion method, at the price of a higher computational cost.…”

Characterization of multicellular breast tumor spheroids using image data-driven biophysical mathematical modeling

“…We assume that the MCTS growth takes the form of a reaction diffusion logistic growth model, a commonly studied model for estimating the growth of tumors and avascular spheroids. We utilize a first-order simplifying approximation by neglecting the convective velocity of cellular mitosis under the assumption that the time scale of tumor growth is sufficiently long such that convection motion driven by cell mitosis is minimal relative to diffusive motility 28 .…”

The Hallmarks of Mathematical Oncology

“…While higher resolution imaging techniques will aid parameterisation of more complex models, parameter estimation remains a major bottleneck to the wider integration of mathematical models into clinical practice. As such, more complex models are often calibrated against experimental data to estimate parameter values which subsequently inform clinical models [72]. Automated image analysis tools can also be integrated into the mathematical modelling process to enable more accurate data fitting and model selection [73].…”