Research

I study how mechanics shapes and regulates living biological systems. My focus is in the modelling of growth in living elastic tissues, both at the large-scale continuum level, and at the cell scale. I am particularly interested in growth laws, i.e. feedback laws between growth, mechanical stress, and chemical fields. Growth laws can be used to model how developing organs dynamically attain their shape (morphogenesis), how the final size of an organ is "controlled" through growth, and how failure of such a control mechanism may lead to cancer-like exponential growth. My interest is both in the theory and modelling of growth laws:

To derive growth laws that link the shape of a tissue to its cellular structure by using fundamental theories like thermodynamics and finite elasticity, poroelasticity and mixture theory, and dynamical systems theory.
To study growth and elasticity in concrete biological systems such as the the Ammonite seashell, the Drosophila wing disc, or the giant Amazonian water lily.

Below are some more details on these two categories.

Theory and application of growth laws in morphogenesis

Couplings between growth and mechanics

How do growth laws affect tisse size? Growth anisotropy decides if an organ grows in a controlled way, or switches to cancer-like growth.

A. Erlich, G. W. Jones, F. Tisseur, D. E. Moulton, A. Goriely. The role of topology and mechanics in uniaxially growing cell networks. Proceedings of the Royal Society A https://doi.org/10.1098/rspa.2019.0523 (2020)

A. Erlich, D. E. Moulton, A. Goriely. Are homeostatic states stable? Dynamical stability in morphoelasticity. Bull Math Biol. 81: 3219 doi: https://doi.org/10.1007/s11538-018-0502-7 (2018)

A. Erlich, T. Lessinnes, D. E. Moulton, A. Goriely. A short introduction to morphoelasticity: the mechanics of growing elastic tissues. In: Bigoni D. (eds) Extremely Deformable Structures. CISM International Centre for Mechanical Sciences, vol 562. Springer, Vienna https://doi.org/10.1007/978-3-7091-1877-1_6 (2015)

Modelling of seashell morphogenesis

How do Ammonites get their typical ribbing? The answer is in the growth and elasticity of the mantle which builds the shell layer by layer.

A. Erlich, D. E. Moulton, A. Goriely, R. Chirat. Morphomechanics and developmental constraints in the evolution of ammonites shell form. J. Exp. Zool. (Mol. Dev. Evol.) 00B:1–14 https://doi.org/10.1002/jez.b.22716 (2016)

A. Erlich, R. Howell, A. Goriely, R. Chirat, D.E. Moulton. Mechanical feedback in seashell growth and form. The ANZIAM Journal, 59(4), 581-606. https://doi.org/10.1017/S1446181118000019 (2018)

How stress is built up in Drosophila

The Drosophila wing disc gets its curvature by differential growth between two elastic layers, as we show through modelling and experiments.

A. Erlich, D. E. Moulton, A. Goriely, R. Chirat. Morphomechanics and developmental constraints in the evolution of ammonites shell form. J. Exp. Zool. (Mol. Dev. Evol.) 00B:1–14 https://doi.org/10.1002/jez.b.22716 (2016)

A. Erlich J. Étienne, J. Fouchard, T. Wyatt. How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale. Interface Focus https://royalsocietypublishing.org/doi/10.1098/rsfs.2022.0038 (2022)

Computational modelling of plants and animals

How do water lilies stay afloat when you put a human on them?

The Amazonian water lily carries a surprising amount of weight. Is it just a rigid floating elastic sheet? There is more, the answer lies in the leaf’s intricate vascular network. Computational modeling and experiments at the Oxford Botanical Gardens explain how the lily stores so much weight.

F. Box, A. Erlich, J. H. Guan, C. Thorogood. Gigantic floating leaves occupy a large surface area at an economical material cost. Science Advances https://www.science.org/doi/10.1126/sciadv.abg3790 (2022)

Simulation of blood flow and oxygen transport

The fetus gets oxygen from the mother via an intricate placental vasculature network. These papers explain what makes a placenta "healthy".

A. Erlich, G. A. Nye, P. Brownbill, O. E. Jensen, I. L. Chernyavsky. Quantifying the impact of tissue metabolism on solute transport in feto-placental microvascular networks. Interface Focus https://doi.org/10.1098/rsfs.2019.0021 (2019)