Where biological tissues grow, and how fast they do, determines the shape and size of a tissue or organ. We are interested in understanding the mechanisms underlying the structure, properties, and growth of biological tissues and using our knowledge to contribute to the optimal design of biomedically engineered implants.
Our vision is to develop the predictive mathematical technologies required to achieve more biomedical control for the correction of congenital flaws, and the regeneration of damaged tissues through the engineering of replacement parts for the human body. At present, our capacity to control tissue growth is limited and relies on experimental trial and error. By providing predictive computational models, our research will help make developmental biology and tissue engineering mathematically predictive sciences.
Biological tissues are at an intermediate scale between cells and organs, which makes them particularly amenable to mathematical analysis. They possess emergent behaviours arising from collective cell behaviours, while they can still be studied in relative isolation from higher-level interactions that involve whole-body functional behaviour.
Tissue engineering implant designs and geometric control of tissue growth
New 3D printing technology is enabling precise tissue engineering scaffold designs and fuels highly reproducible new research in the biofabrication of engineered tissues. We work with tissue engineers, materials scientists, and orthopaedic surgeons to optimise new implant designs. These can be optimised for mechanical properties as well as for tissue growth by predicting how engineered tissues evolve in scaffolds once implanted in the body.
Using computational solid mechanics and structural optimisation, we can predict the mechanical response of engineered scaffolds and the surrounding tissues, and optimise scaffold shape and internal architecture. The amount of space as well as the shape of the space in which tissues grow exert strong geometric control on tissue organisation, speed of growth, and tissue material properties. We develop mathematical models to investigate how this geometric control arises from how successive cell generations crowd or spread in the space available to them as the cells multiply and migrate.
Key publications
- Challis VJ, Roberts AP, Grotowski JF, Zhang LC, Sercombe TB (2014) Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication, Advanced Engineering Materials 12(11):1106-1110; https://doi.org/10.1002/adem.201000154
- Cramer AD, Challis VJ, Roberts AP (2017) Physically realizable three-dimensional bone prosthesis design with interpolated microstructures, Journal of Biomechanical Engineering 139(3):031013; https://doi.org/10.1115/1.4035481
- Alias MA & Buenzli PR (2017) Modeling the effect of curvature on the collective behavior of cells growing new tissue, Biophys J 112:192-204; http://dx.doi.org/10.1016/j.bpj.2016.11.3203
- Buenzli PR, Lanaro M, Wong CS, McLaughlin MP, Allenby MC, Woodruff MA, Simpson MJ (2020) Cell proliferation and migration explain pore bridging dynamics in 3D, Acta Biomaterialia 114:285-295; https://doi.org/10.1016/j.actbio.2020.07.010
- Buenzli PR & Simpson MJ (2021) Curvature dependences of wave propagation in reaction-diffusion models; Preprint available on arXiv: https://doi.org/10.48550/arXiv.2112.00928
Mechanical cell interactions
An open challenge of the continuum mechanics of tissue growth is how to prescribe /growth laws/ based on biological processes. Our work derives growth laws as continuum limits of new cell-based mathematical models that include cell proliferation, mechanics-induced cell transport, and mechanobiological cell signaling.
Key publications
- Murphy RJ, Buenzli PR, Baker RE, Simpson MJ (2020) Mechanical cell competition in heterogeneous epithelial tissues: An individual-based model and its continuum approximation, Bull Math Biol 82:130; https://doi.org/10.1007/s11538-020-00807-x
- Tambyah TA, Murphy RJ, Buenzli PR, Simpson MJ (2020) A free boundary mechanobiological model of epithelial tissues, Proc Roy Soc A 476:20200528; https://doi.org/10.1098/rspa.2020.0528
Osteocyte network regulation of bone
Bone are a feat of biological engineering. They are light and highly under-engineered, but they hold strong because bone tissue is continually replaced and bone microstructure is continually optimised to the mechanical loads. We are developing models of the osteocyte network within bone tissue to understand how they form an embedded control network that senses and responds to mechanics.
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Key publications
- Lerebours C & Buenzli PR (2016) Towards a cell-based mechanostat theory of bone: the need to account for osteocyte desensitisation and osteocyte replacement, J Biomech 49:2600-2606; http://dx.doi.org/10.1016/j.jbiomech.2016.05.012
- Taylor-King JP, Buenzli PR, Chapman SJ, Lynch CC, Basanta D (2020) Modeling osteocyte network formation: Healthy and cancerous environments, Frontiers Bioeng Biotechnol 8:757; https://doi.org/10.3389/fbioe.2020.00757
Chief Investigators
