Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment

Abstract

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a “digital twin” of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance. To this aim, we develop a tumor-immune microfluidic hybrid PDE–ODE model to describe the concentration of chemicals in the Cancer-on-Chip environment and immune cells migration. The development of a trustable simulation algorithm, able to reproduce the immunocompetent dynamics observed in the chip, requires an efficient tool for the calibration of the model parameters. In this respect, the present paper represents a first methodological work to test the feasibility and the soundness of the calibration technique here proposed, based on a multidimensional spline interpolation technique for the time-varying velocity field surfaces obtained from cell trajectories.

Differential Models, Numerical Simulations and Applications

“…In [1] the authors developed a hybrid PDE-ODE mathematical model mimicking the mechanisms observed in cancer-on-chip experiments, where tumor cells are treated with chemotherapy drugs and secrete chemical signals into the environment, attracting multiple immune cell species. The in silico model proposed here goes towards the construction of a "digital twin" of the experimental immune cells and allows the reconstruction of the chemical gradients in the chip environment in order to better understand the complex mechanisms of immunosurveillance.…”

Fractional derivative model for tumor cells and immune system competition

“…Several recent works give an interesting results as showing that optimal therapy can control proliferation to reduce specially cervical cancer [14], the formulating of a hybrid PDE-ODE Model test the feasibility and well-posedness [15] of the cancer velocity, in a stochastic approach to show colorectal cancer prediction [16], SEIR epidemic model with fractional order [17] estimating mutation rates tumor, and with fractional approach [18], eliminating cancer cells with immune system less, an new model is also studied [19] to present and analysis fractional-order tumor virotherapy model with two time delays. In the same sense, we can note that among the recent models, we find the model named the Normal Tumor Immune UNHealthy Diet Model (NTIUNHDM) [20] that describes well the dynamic of cancer with immunity and proposes the system of ordinary differential equations as follow:…”

Sensitivity Analysis of a 2D Stochastic Agent-Based and PDE Diffusion Model for Cancer-on-Chip Experiments

“…In recent publications of some of the authors, the macroscopic modeling of COC experiments and related estimation techniques for model parameters have been proposed [22,23]. Moreover, a discrete-in-continuous hybrid approach was formulated as a PDE reactiondiffusion partial model for the evolution of chemicals, coupled with an ODE particle model for cell motion [24]. Some of the present authors proposed a rather general agent-based cellular automata model for the representation of leukocyte dynamics in COC experiments [25], and a first validation of the model was carried out by visually calibrating the model parameters against aggregated real data (using the time of transition from the right to left compartment and a fraction of leukocytes in the chip's compartments as indicators).…”