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...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-09-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/10/4/243 |
| _version_ | 1797506586946568192 |
|---|---|
| author | Gabriella Bretti Adele De Ninno Roberto Natalini Daniele Peri Nicole Roselli |
| author_facet | Gabriella Bretti Adele De Ninno Roberto Natalini Daniele Peri Nicole Roselli |
| author_sort | Gabriella Bretti |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T04:35:40Z |
| format | Article |
| id | doaj.art-5ac6b6199345442095104b1466f4655f |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:35:40Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5ac6b6199345442095104b1466f4655f2023-11-23T03:48:54ZengMDPI AGAxioms2075-16802021-09-0110424310.3390/axioms10040243Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip ExperimentGabriella Bretti0Adele De Ninno1Roberto Natalini2Daniele Peri3Nicole Roselli4Istituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, ItalyIstituto di Fotonica e Nanotecnologie, 00156 Rome, ItalyIstituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, ItalyIstituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, ItalyDipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, 00161 Rome, ItalyThe 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.https://www.mdpi.com/2075-1680/10/4/243differential equationsmathematical biologycell migrationmicrofluidic chip |
| spellingShingle | Gabriella Bretti Adele De Ninno Roberto Natalini Daniele Peri Nicole Roselli Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment Axioms differential equations mathematical biology cell migration microfluidic chip |
| title | Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment |
| title_full | Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment |
| title_fullStr | Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment |
| title_full_unstemmed | Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment |
| title_short | Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment |
| title_sort | estimation algorithm for a hybrid pde ode model inspired by immunocompetent cancer on chip experiment |
| topic | differential equations mathematical biology cell migration microfluidic chip |
| url | https://www.mdpi.com/2075-1680/10/4/243 |
| work_keys_str_mv | AT gabriellabretti estimationalgorithmforahybridpdeodemodelinspiredbyimmunocompetentcanceronchipexperiment AT adeledeninno estimationalgorithmforahybridpdeodemodelinspiredbyimmunocompetentcanceronchipexperiment AT robertonatalini estimationalgorithmforahybridpdeodemodelinspiredbyimmunocompetentcanceronchipexperiment AT danieleperi estimationalgorithmforahybridpdeodemodelinspiredbyimmunocompetentcanceronchipexperiment AT nicoleroselli estimationalgorithmforahybridpdeodemodelinspiredbyimmunocompetentcanceronchipexperiment |