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. 2020 Aug 5;7:89. doi: 10.3389/frobt.2020.00089

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Copyright © 2020 Porat, Tedone, Palladino, Marcati and Meroz.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Schematic of the governing equations. We present the main stages involved in the model. (A) Organ shape parametrization, section 2.1: the Frenet Serret local frame in Equations (1)–(3), and Frenet-Serret equations that also define κ and τ, introduced in Equation (4). (B) Response vector to external signal, section 2.3: assuming a vector field signal, we find the projected signal (Equation 10) and calculate the response vector (Equation 11), which affects the growth response. (C) Differential growth vector (Equation 12); includes terms representing external cues (the response vector), internal cues (circumnutations), and proprioception for posture control. (D) Implementing growth dynamics, section 2.2. The centerline is updated using Equations (6) and (9), using the constructed differential growth vector.