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. 2021 Nov 18;12:6681. doi: 10.1038/s41467-021-26971-9

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 8 — a Schematic illustration of tissue elements with embedded fibers in initial configuration (left), after a short period of stretch and fiber elongation (middle), and after an extended period of stretch and fiber elongation (right). Tissue blocks are not shown to scale since volume increase becomes dramatic over an extended period of stretch. Theoretical behavior of a tissue element subjected to sustained tension in direction e₁ as time approaches infinity is described in b–c. b Volume associated with each tissue component as a function of time, starting from a nondimensionalized total tissue volume (V_total) of 1. V₁ represents volume associated with fibers aligned in the direction of tension (e₁), while V₂ and V₃ represent the volume associated with fibers perpendicular to tension (e₂ and e₃), and V_c represents the volume associated with cells and extracellular matrix. Vertical axis is log scaled to facilitate visualization, as total volume begins to increase dramatically (approximately exponentially) at later time points. c Volume fraction of each tissue component as a function of time, starting from an initial fiber volume fraction of 10% in each direction (f₁ = f₂ = f₃ = 0.1). When tension and fiber growth are allowed to continue indefinitely, fiber volume fraction approaches 1 while the volume fraction of non-fiber components (f_c) approaches 0.