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Mathematical modelling of growth factor induced cell migration in 3D engineered matrices
Cells mechanically interact with their environment to sense, for example, topography, elasticity, mechanical cues from other cells, and chemical signals. Multi-signalling stimuli have profound effects on cellular behaviour, including migration. The current study aims to develop a mathematical model...
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| Format: | Thesis |
| Language: | English |
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Department of Human Biology
2024
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| _version_ | 1867613181474504704 |
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| access_status_str | Open Access |
| author | Ahmed, Riham K I |
| author2 | Franz, Thomas |
| author_browse | Ahmed, Riham K I Franz, Thomas |
| author_facet | Franz, Thomas Ahmed, Riham K I |
| author_sort | Ahmed, Riham K I |
| collection | Thesis |
| description | Cells mechanically interact with their environment to sense, for example, topography, elasticity, mechanical cues from other cells, and chemical signals. Multi-signalling stimuli have profound effects on cellular behaviour, including migration. The current study aims to develop a mathematical model for chemo-mechanically induced migration of individual cells in a collective in three-dimensional engineered extracellular matrices governed by the mechanical properties of the matrix and a growth factor gradient. In the developed model, each cell is assumed to transmit a traction force that locally deforms a planar elastic substrate, resulting in spatially varying strain energy density gradients. The magnitude and direction of strain energy density gradients define cell migration. Cell-substrate adhesion and partial random motion are included. Further, the Green function and Duhamel principle are used to solve the diffusion equation to describe the presence of a growth factor and represent chemo-mechanically induced deterministic collective cell migration on planar elastic substrates. Finally, three-dimensional strain energy density gradients due to local matrix deformation by embedded cells are obtained using finite element methods and implemented in the model to describe chemo-mechanically induced collective cell migration in extracellular matrices. Deterministic and random migration of up to 50 cells on planar substrates and threedimensional extracellular matrices with spatially uniform and varying stiffness is predicted. The effect of varying growth factor productivity and diffusivity is explored for cell migration on a planar substrate induced by a growth factor only and combined with mechanical cues. The model predicts that the maximum velocity of a cell migrating towards the growth factor source increases with increasing productivity and decreasing diffusivity of the growth factor. Collective cell migration due to mechanical cell interactions in the extracellular matrix is studied with sequential and non-sequential changes in matrix stiffness. The overall migration is directed towards the stiffest region for the sequential stiffness change and the softest region for the non-sequential stiffness change in the matrix. The chemo-mechanically induced cell migration is presented in three sequential extracellular matrices with an overall migration direction towards the growth factor in the softest region. The mathematical models can adequately simulate the chemo-mechanically induced collective cell migration in elastic planar substrates and three-dimensional extracellular matrices. The models provide qualitative results demonstrating collective cell migration in complex environments with several cues increasing the potential and capabilities to replace in vitro and in vivo experiments with in silico simulations in, for example, wound healing, cancer treatment, and regenerative medicine. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/40743 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:03.909Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Department of Human Biology |
| publisherStr | Department of Human Biology |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/40743 Mathematical modelling of growth factor induced cell migration in 3D engineered matrices Ahmed, Riham K I Franz, Thomas Abdalrahman, Tamer Davies, Neil H Vermolen, Fred Human Biology Cells mechanically interact with their environment to sense, for example, topography, elasticity, mechanical cues from other cells, and chemical signals. Multi-signalling stimuli have profound effects on cellular behaviour, including migration. The current study aims to develop a mathematical model for chemo-mechanically induced migration of individual cells in a collective in three-dimensional engineered extracellular matrices governed by the mechanical properties of the matrix and a growth factor gradient. In the developed model, each cell is assumed to transmit a traction force that locally deforms a planar elastic substrate, resulting in spatially varying strain energy density gradients. The magnitude and direction of strain energy density gradients define cell migration. Cell-substrate adhesion and partial random motion are included. Further, the Green function and Duhamel principle are used to solve the diffusion equation to describe the presence of a growth factor and represent chemo-mechanically induced deterministic collective cell migration on planar elastic substrates. Finally, three-dimensional strain energy density gradients due to local matrix deformation by embedded cells are obtained using finite element methods and implemented in the model to describe chemo-mechanically induced collective cell migration in extracellular matrices. Deterministic and random migration of up to 50 cells on planar substrates and threedimensional extracellular matrices with spatially uniform and varying stiffness is predicted. The effect of varying growth factor productivity and diffusivity is explored for cell migration on a planar substrate induced by a growth factor only and combined with mechanical cues. The model predicts that the maximum velocity of a cell migrating towards the growth factor source increases with increasing productivity and decreasing diffusivity of the growth factor. Collective cell migration due to mechanical cell interactions in the extracellular matrix is studied with sequential and non-sequential changes in matrix stiffness. The overall migration is directed towards the stiffest region for the sequential stiffness change and the softest region for the non-sequential stiffness change in the matrix. The chemo-mechanically induced cell migration is presented in three sequential extracellular matrices with an overall migration direction towards the growth factor in the softest region. The mathematical models can adequately simulate the chemo-mechanically induced collective cell migration in elastic planar substrates and three-dimensional extracellular matrices. The models provide qualitative results demonstrating collective cell migration in complex environments with several cues increasing the potential and capabilities to replace in vitro and in vivo experiments with in silico simulations in, for example, wound healing, cancer treatment, and regenerative medicine. 2024-11-28T06:33:54Z 2024-11-28T06:33:54Z 2024 2024-11-26T12:34:39Z Thesis / Dissertation Doctoral PhD http://hdl.handle.net/11427/40743 eng application/pdf Department of Human Biology Faculty of Health Sciences University of Cape Town |
| spellingShingle | Human Biology Ahmed, Riham K I Mathematical modelling of growth factor induced cell migration in 3D engineered matrices |
| thesis_degree_str | Doctoral |
| title | Mathematical modelling of growth factor induced cell migration in 3D engineered matrices |
| title_full | Mathematical modelling of growth factor induced cell migration in 3D engineered matrices |
| title_fullStr | Mathematical modelling of growth factor induced cell migration in 3D engineered matrices |
| title_full_unstemmed | Mathematical modelling of growth factor induced cell migration in 3D engineered matrices |
| title_short | Mathematical modelling of growth factor induced cell migration in 3D engineered matrices |
| title_sort | mathematical modelling of growth factor induced cell migration in 3d engineered matrices |
| topic | Human Biology |
| url | http://hdl.handle.net/11427/40743 |
| work_keys_str_mv | AT ahmedrihamki mathematicalmodellingofgrowthfactorinducedcellmigrationin3dengineeredmatrices |