Modelling of endothelial cell migration and angiogenesis in microfluidic cell culture systems
Tumour-induced angiogenesis is a complex biological process that involves growth of new blood vessels within the tumour microenvironment and is an important target for cancer therapies. Significant efforts have been undertaken to develop theoretical models as well as in vitro experimental models to study angiogenesis in a highly controllable and accessible manner. Various mathematical models have been developed to study angiogenesis, but these have mostly been applied to in vivo assays. Recently, microfluidic cell culture systems have emerged as useful and powerful tools for studying cell migration and angiogenesis processes, but thus far, mathematical angiogenesis models have not yet been applied to microfluidic geometries. Integrating mathematical and computational modelling with microfluidic-based assays has potential to enable greater control over experimental parameters, provide new insights into fundamental angiogenesis processes and assist in accelerating design and optimization of operating conditions. Here, we describe the development and application of a combined mathematical and computational modelling approach tailored specifically for microfluidic cell culture systems. The objective was to allow optimization of the engineering design of microfluidic systems, where the model may be used to test the impact of various geometric parameters on cell migration and angiogenesis processes, and assist in identifying optimal device dimensions to achieve desired readouts. We employed two separate continuum mathematical models that treated cell density, vessel length density and vascular endothelial growth factor (VEGF) concentration as continuous average variables, and we implemented these models numerically using finite difference discretization and a Method of Lines approach. We examined the average response of cells to VEGF gradients inside our microfluidic device, including the time-dependent changes in cell density and vessel density, and how they were affected by changes in device geometries including the migration port width and length. Our study demonstrated that mathematical modelling can be integrated with microfluidics to offer new perspectives on emerging problems in biomicrofluidics and cancer biology.
KeywordsMigration Angiogenesis Vessel sprouting Endothelial cells Chemotaxis Mathematical modelling Computational modelling
We acknowledge the financial support from the NSERC—Canada Graduate Scholarship (CGS-M), Ontario Graduate Scholarships (OGS), Weber and Mariano Graduate Scholarship, and Barbara and Frank Milligan Graduate Fellowship to NK, and the Canada Foundation for Innovation (CFI) Leaders Opportunity Fund, Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. 436117-2013) Discovery Grant, Canadian Cancer Society Research Institute (CCSRI) (Grant No. 702525) Innovation Grant, Early Researcher Award from Ontario Ministry of Research and Innovation, and Cancer Research Society (CRS) (Grant No. 20172) Operating Grant to EY.
- Addison-Smith B (2010) Mathematical modelling of tumour-induced angiogenesis. Ph.D. thesis, University of QueenslandGoogle Scholar
- Bischel LL, Young EWK, Mader BR, Beebe DJ (2013) Tubeless microfluidic angiogenesis assay with three-dimensional endothelial-lined microvessels. Biomaterials 34(5):1471–1477. https://doi.org/10.1016/j.biomaterials.2012.11.005 CrossRefGoogle Scholar
- Das A, Lauffenburger D, Asada H, Kamm RD (2010) A hybrid continuum-discrete modelling approach to predict and control angiogenesis: Analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology. Philos Trans R Soc A Math Phys Eng Sci 368(1921):2937–2960. https://doi.org/10.1098/rsta.2010.0085 MathSciNetCrossRefzbMATHGoogle Scholar
- Deakin AS (1976) Model for initial vascular patterns in melanoma transplants. Growth 40(2):191–201Google Scholar
- Grogan J (2018) Microvessel CHASTE. https://jmsgrogan.github.io/MicrovesselChaste/docu. Retrieved from https://jmsgrogan.github.io/MicrovesselChaste/documentation/tutorials.html
- Kim BJ, Wu M (2012) Microfluidics for mammalian cell chemotaxis. Annual Biomed Eng. 40(6):1316–1327. https://doi.org/10.1007/s10439-011-0489-9.Microfluidics CrossRefGoogle Scholar
- Stokes CL, Lauffenburger DA, Williams SK (1991) Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J Cell Sci 99:419–430Google Scholar