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. 2019 Feb 25;9:2658. doi: 10.1038/s41598-019-39297-w

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© The Author(s) 2019

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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Graphical definition of the tortuosity for a flow parallel to the width (W) direction. The apatite platelets configuration is characterized by an inclination of θ_LT = −20°; θ_LW = −25°; θ_WT = 25° in both cases of V_{f_A} = 0.07 (a,b) and V_{f_A} = 0.42 (c,d). (b,d) Show sections of the model parallel to the WT plane. The green dashed lines illustrate the streamlines of the water molecule along the width direction. The red continuous lines represent the Euclidean distance between the path extremes. Sections of the two mineral content cases are in scale in order to highlight the changes in the geometry with the increase of the mineral VF. In (a,b) we also indicated the variables that characterize the distance between the platelets (a_L, a_W and a_T) and between the collagen fibrils (a_c) of diameter (d).