Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips
The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/6/688 |
| _version_ | 1827697006711144448 |
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| author | Elishan Christian Braun Gabriella Bretti Roberto Natalini |
| author_facet | Elishan Christian Braun Gabriella Bretti Roberto Natalini |
| author_sort | Elishan Christian Braun |
| collection | DOAJ |
| description | The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains. |
| first_indexed | 2024-03-10T12:59:12Z |
| format | Article |
| id | doaj.art-a8f3dd3086e84be881d43ed34ef1bb11 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:59:12Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a8f3dd3086e84be881d43ed34ef1bb112023-11-21T11:37:57ZengMDPI AGMathematics2227-73902021-03-019668810.3390/math9060688Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic ChipsElishan Christian Braun0Gabriella Bretti1Roberto Natalini2Department Mathematics, University of Rome 3, 00146 Rome, ItalyIstituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, ItalyIstituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, ItalyThe present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains.https://www.mdpi.com/2227-7390/9/6/688multi-domain networktransmission conditionsfinite difference schemeschemotaxisreaction-diffusion models |
| spellingShingle | Elishan Christian Braun Gabriella Bretti Roberto Natalini Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips Mathematics multi-domain network transmission conditions finite difference schemes chemotaxis reaction-diffusion models |
| title | Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips |
| title_full | Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips |
| title_fullStr | Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips |
| title_full_unstemmed | Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips |
| title_short | Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips |
| title_sort | mass preserving approximation of a chemotaxis multi domain transmission model for microfluidic chips |
| topic | multi-domain network transmission conditions finite difference schemes chemotaxis reaction-diffusion models |
| url | https://www.mdpi.com/2227-7390/9/6/688 |
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