Biomechanics
Motivation
Biological tissues — epithelial sheets, liver parenchyma, the tunics of the eye, ductal structures in the breast — are soft elastic bodies whose mechanics directly influences their biological function. Abnormal mechanics, in turn, is both a symptom and a driver of disease: cancer cells soften or stiffen their neighborhood, and the resulting stress landscape feeds back into growth and migration. Continuum mechanics provides a language for quantifying these effects: tissue elasticity, surface tension at cell–cell junctions, residual stress, fluid–solid coupling, and vibration dynamics can all be expressed in the same framework.
My contributions to biomechanics are spread across four distinct biological contexts, each arising from collaboration with experimentalists or biomedical engineers who brought the mechanical questions to the table.
Details
Fiber morphogenesis in the liver (2020)
The liver parenchyma is crisscrossed by a network of collagen fibers that form around bile ducts during organ development. The question of why the fibers adopt their observed spatial patterns — star-shaped arrays around ducts, preferential alignment along flow directions — was the subject of:
- Recrosi, Repetto, Tatone & Tomassetti (2020) — Mechanical model of fiber morphogenesis in the liver. The tissue surrounding a duct was modeled as an elastic medium with a preferred fiber direction that evolves according to a remodeling law driven by the local stress state. A key finding is that the stress field induced by the duct’s internal pressure is sufficient to explain the observed fiber orientation: fibers align with the circumferential principal stress and form the characteristic star-like patterns seen in histological sections.
Epithelial tissue elasticity and cancer morphogenesis (2022–2025)
Epithelial cells form monolayers that act as barriers and signal integrators. Their mechanical properties — stiffness, surface tension, contractility — control collective behavior such as wound healing and tumor spreading. Three papers, all with Favata and Paroni as co-authors, build a coherent line from a mechanical model of the epithelium to an observable prediction about cancer:
- Favata, Paroni, Recrosi & Tomassetti (2022) — Competition between epithelial tissue elasticity and surface tension in cancer morphogenesis (International Journal of Engineering Science, 176, 103677). The epithelium is modeled as a thin hyperelastic layer bounded by two material surfaces endowed with surface tension. The equilibrium thickness is determined by the competition between surface tension and bulk elasticity, and when the apico-basal tension imbalance reaches a critical value a subcritical bifurcation triggers the physiological folding of the epithelium.
- Favata, Paroni, Recrosi & Tomassetti (2022) — Young modulus of healthy and cancerous epithelial tissues from indirect measurements (Mechanics Research Communications, 124, 103952). Building on the model of the first paper, this work derives a formula for the ratio between the Young modulus of healthy and cancerous tissue in terms of apico-basal pMLC2 intensity and tissue thickness — quantities accessible to direct observation. When applied to available data, the formula confirms that cancerous epithelial tissues are softer than healthy ones.
- Ambrosi, Favata, Paroni & Tomassetti (2025) — Oncogenic transformation of tubular epithelial ducts: How mechanics affects morphology (European Journal of Mechanics – A/Solids, 117, 105984). The modulus ratio established in the previous paper is now used as input to study how the softening of cancerous cells translates into observable morphological changes at the scale of a ductal structure, closing the loop from tissue-level mechanics to organ-level geometry.
The logical thread across the three papers: build the mechanical model → extract the cancer/healthy modulus ratio → use that ratio to predict duct morphology.
Cell reorientation under cyclic stretch (2026)
Endothelial and other cells subjected to cyclic mechanical stretch reorganize their cytoskeleton and reorient their stress fibers. The deterministic models proposed in the literature account for the mean orientation but not for the experimentally observed spreading of the orientation distribution. This paper addresses that gap using the framework of Stochastic Thermodynamics with Internal Variables:
- Abeyaratne, Dharmaravam, Saccomandi & Tomassetti (2026) — Using stochastic thermodynamics with internal variables to capture orientational spreading in cell populations undergoing cyclic stretch (Proceedings of the Royal Society A, 20250705). Starting from the Langevin dynamics proposed by Loy & Preziosi (2023) for fluctuations in cell orientation, the STIV framework of Leadbetter et al. (2023) is applied to derive a two-dimensional ODE system governing the mean orientation $\mu(t)$ and an order parameter $\kappa(t)$ that quantifies the sharpness of the orientation distribution. Phase-plane analysis of this reduced system reveals a two-stage reorientation phenomenon: when a cell population initially aligned near an energy maximum is subjected to stretch, the distribution first broadens before concentrating around the energy minimum. This non-intuitive prediction — not previously reported in the literature — suggests a concrete new experiment (switch the stretching axis on a pre-aligned population and observe the transient broadening). The reduced model is validated against numerical solutions of the full Fokker–Planck equation and against published experimental data on human mesenchymal stem cells.
Ocular biomechanics: bulb vibrations (2024)
The mechanical dynamics of the eye are relevant both for diagnostic purposes (acoustic-based tonometry) and for understanding barotrauma from blast waves. The geometry — a nearly spherical shell filled with nearly incompressible fluid — makes this an unusual structural problem.
- Tambroni, Tomassetti, Lombardi & Repetto (2024) — A mechanical model of ocular bulb vibrations and implications for acoustic tonometry, PLOS ONE 19(1): e0294825. This paper modeled the eye as an elastic spherical shell (the sclera and cornea) enclosing an incompressible fluid (the vitreous humor and aqueous humor). The vibrational frequencies and mode shapes were computed analytically for a simplified geometry, showing that the intraocular pressure has a significant effect on the fundamental frequency. The results suggest that acoustic resonance measurements could be used as a non-contact method for intraocular pressure estimation.
Summary and connections
The four research threads within biomechanics — liver morphogenesis, epithelial mechanics and cancer (a three-paper arc), ocular dynamics, and cell reorientation under cyclic stretch — share a common methodology: formulate a continuum model, derive analytical solutions or asymptotic approximations, and extract mechanistic insight that is not accessible from purely computational approaches. The threads are connected by shared mathematical tools (thin-shell theory from the thin structures thread, accretion mechanics from the surface growth thread) and by the recurring theme that geometry amplifies mechanics: the curvature of a duct, the hexagonal tiling of an epithelium, or the near-spherical shape of the eye all lead to qualitatively different responses than a flat slab would exhibit.