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

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...

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Bibliographic Details
Published in:Axioms 2021-12, Vol.10 (4), p.243
Main Authors: Bretti, Gabriella, De Ninno, Adele, Natalini, Roberto, Peri, Daniele, Roselli, Nicole
Format: Article
Language:English
Subjects:
Algorithms
Calibration
Cancer
cell migration
Chemotherapy
differential equations
Experiments
Immune system
Immunocompetence
In vivo methods and tests
Interpolation
mathematical biology
Mathematical models
Medical prognosis
microfluidic chip
Microfluidics
Ordinary differential equations
Parameter estimation
Partial differential equations
Tumors
Velocity distribution
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10040243