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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
Future Blog Post
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Blog Post number 4
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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 3
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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 2
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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 1
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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
publications
The distance between the hamstring grafts and the physis and apophysis of the proximal tibia – implications for pediatric ACL reconstruction and physeal arrest
Published in Journal of ISAKOS: Joint Disorders & Orthopaedic Sports Medicine, 2018
Recommended citation: Richmond C.G., Green D.W., Cannamela P.C., Martinson W.D., Shea K.G. (2018). The distance between the hamstring grafts and the physis and apophysis of the proximal tibia – implications for pediatric ACL reconstruction and physeal arrest. Journal of ISAKOS: Joint Disorders & Orthopaedic Sports Medicine, 3 (6), 318-322. DOI: 10.1136/jisakos-2018-000222 http://www.doi.org/10.1136/jisakos-2018-000222
Variation in the medial patellofemoral ligament origin in the skeletally immature knee: An anatomic study.
Published in The American Journal of Sports Medicine, 2018
Recommended citation: Shea, K.G., Martinson W.D., Cannamela P.C., Richmond C.G., Fabricant P.D., Anderson A.F., Polousky J.D., Ganley T. J. (2018). "Variation in the medial patellofemoral ligament origin in the skeletally immature knee: An anatomic study." The American journal of sports medicine 46 (2), 363-369. DOI: 10.1177/0363546517738002 http://www.doi.org/10.1177/0363546517738002
Multiscale modeling and simulation of traveling waves in biology: A review.
Published in Rendiconti di Matematica e delle sue Applicazioni, 2019
Recommended citation: Martinson W.D., Byrne H.M., Maini P.K. (2019). "Multiscale modeling and simulation of traveling waves in biology: A review." Rendiconti di Matematica e delle sue Applicazioni 40 (7), 191-216. http://wdmartinson.github.io/files/2019-multiscale-modeling.pdf
Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling
Published in Physical Review E, 2020
Recommended citation: Martinson W.D., Byrne H.M., Maini P.K. (2020). "Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling." Physical Review E 102 (6), 062417. DOI: 10.1103/PhysRevE.102.062417 http://www.doi.org/10.1103/PhysRevE.102.062417
Comparative analysis of continuum angiogenesis models
Published in Journal of Mathematical Biology, 2021
Recommended citation: Martinson W.D., Ninomiya H., Byrne H.M., Maini P.K. (2021). "Comparative analysis of continuum angiogenesis models." Journal of Mathematical Biology 82 (21), online. DOI: 10.1007/s00285-021-01570-w http://www.doi.org/10.1007/s00285-021-01570-w
Dynamic fibronectin remodeling prevents collective cell jamming in a cell-based mathematical model
Published in eLife, 2023
Recommended citation: Martinson W.D., McLennan R., Teddy J.M., McKinney M.C., Davidson L.A., Baker R.E., Byrne H.M, Kulesa P.M., Maini P.K. (2023). "Dynamic fibronectin remodeling prevents collective cell jamming in a cell-based mathematical model." eLife 12, e83792. arXiv:2209.07794. DOI: 10.7554/eLife.83792 http://www.doi.org/10.7554/eLife.83792
Soliton approximation in continuum models of leader-follower behavior
Published in Physical Review E, 2023
Recommended citation: Terragni F., Martinson W.D., Carretero M., Maini P.K., Bonilla L.L. (2023). "Soliton approximation in continuum models of leader-follower behavior." Physical Review E 108 (5), 054407. DOI: 10.1103/PhysRevE.108.054407 http://www.doi.org/10.1103/PhysRevE.108.054407
Linking continuous and discrete models of cell birth and migration
Published in Royal Society Open Science, 2024
Recommended citation: Martinson W.D., Volkening A., Schmidtchen M., Venkataraman C., Carrillo J. (2024). "Linking continuous and discrete models of cell birth and migration." Roy Soc Open Sci 11, 232002. arXiv:2308.16093. DOI: 10.1098/rsos.232002 https://royalsocietypublishing.org/doi/full/10.1098/rsos.232002
Collective transitions from orbiting to matrix invasion in 3D multicellular spheroids
Published in bioRxiv, 2025
Recommended citation: Kim J., Jeong H., Falco C., Hruska A.M., Martinson W.D., Marzoratti A., Araiza M. Yang H., Franck C., Carrillo J.A., Guo M., Wong I.Y. (preprint). "Collective transitions from orbiting to matrix invasion in 3D multicellular spheroids." bioRxiv bioRxiv:2025.02.10.636936. DOI: 10.1101/2025.02.10.636936 https://www.biorxiv.org/content/10.1101/2025.02.10.636936v1
research
talks
Establishing zebrafish as a model to screen genetic factors of hormone-induced thrombosis
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Revisiting a classical continuum model of angiogenesis: Novel insights using in silico data
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Revisiting a classical continuum model of angiogenesis: Novel insights using in silico data
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Traveling wave analysis of angiogenesis models and its implications
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Recipient of a travel grant to support my attendance.
Extracellular matrix remodelling by neural crest cells provides a robust mechanism for collective migration
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Awarded the 2021 UCR Contributed Talk Award from the Society for Mathematical Biology in recognition of outstanding research presentation.
Extracellular matrix remodelling by neural crest cells provides a robust signal for collective migration
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Also co-organiser of two mini-symposia with Dr. Sara Bernardi (“Insights on collective migration using agent-based modeling”, “Non-local mathematical models for collective migration: insights from analytical methods”).
Extracellular matrix remodeling by neural crest cells provides a robust signal for collective migration
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Recipient of a Society for Mathematical Biology travel grant to support my attendance.
Multiscale modelling of collective behaviour: insights, challenges, and future perspectives
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Multiscale modelling of collective behaviour: insights, challenges, and future perspectives
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Multiscale modelling of collective behaviour: insights, challenges, and future perspectives
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Multiscale modelling of collective behaviour: insights, challenges, and future perspectives
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teaching
University of Oxford Mathematical Institute Graduate Teaching Assistant
Undergraduate teaching, Mathematical Institute, University of Oxford, 2018
- Assessed student problem sheets and co-taught biweekly problem classes for the following third-year undergraduate/graduate courses:
- Further Mathematical Biology, Michaelmas term 2018 (October 2018 – January 2019)
- Numerical Solutions to Differential Equations I, Michaelmas term 2018 (October 2018 – January 2019)
- Further Mathematical Biology, Michaelmas term 2019 (October 2019 – January 2020)
- Nonlinear Systems, Hilary term 2020 (January 2020 – March 2020)
- Mathematical Modelling, Michaelmas term 2020 (October 2020 – January 2021)
- Worked up to 20 hours per week during term time.
Balliol College Graduate Mentor
Undergraduate teaching, Balliol College, University of Oxford, 2019
- Led one-on-one tutoring sessions with a student in Balliol College for the following third-year classes in the Mathematical Institute:
- Further Mathematical Biology
- Applied PDEs
- Nonlinear Systems
- Worked up to 5 hours per week during term time.
Balliol College Graduate Teaching Assistant
Undergraduate teaching, Balliol College, University of Oxford, 2020
- Assisted senior fellows in the teaching and assessment of weekly problem sheet classes for the following first-year mathematics modules:
- Statistics & Data Analysis, Trinity term 2022 (April 2022 – June 2022)
- Multivariable Calculus, Hilary term 2022 (January 2022 – April 2022)
- Probability, Michaelmas term 2021 (October 2021 – January 2022)
- Statistics & Data Analysis, Trinity term 2021 (April 2021 – June 2021)
- Multivariable Calculus, Hilary term 2021 (January 2021 – April 2021)
- Probability, Michaelmas term 2020 (October 2020 – January 2021)
- Introductory Calculus, Michaelmas term 2020 (October 2020 – January 2021)
- Worked up to 20 hours per week during term time.
Oxford University Mathematical Institute Tutor
Tutor, Mathematical Institute, University of Oxford, 2022
- Led biweekly problem sheet classes for the following fourth year/graduate module:
- Perturbation Methods, Michaelmas term (October 2022 – January 2023)
Dissertation Project Supervisor
Master's student supervision, Mathematical Institute, University of Oxford, 2022
- Supervised thesis dissertation projects for three graduate (Master’s level) students during the 2022-2023 academic year. These projects aimed to rigorously derive and analyse solutions to systems of aggregation-diffusion equations for three or more cell types.
Stipendiary Lecturer in Applied Mathematics
Lecturer, Balliol College, University of Oxford, 2023
- Led weekly classes and small group tutorial sessions for the following first- and second-year modules:
- Multivariable Calculus, Hilary term (January 2023 – March 2023)
- Numerical Analysis, Hilary term (January 2023 – March 2023)
- Marked termly examinations and problem sheets.
- Led outreach sessions for prospective applicants to the undergraduate mathematics programmes at Balliol.