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. 2018 Nov 2;8:16296. doi: 10.1038/s41598-018-34261-6

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© The Author(s) 2018

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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Groups identified using the K-means clustering analysis of the 3D spinal curvatures at three different time-points. The projections of the cluster centers of the spinal curves are shown in the sagittal, frontal, and axial planes for cluster 1 (red), cluster 2 (blue), and cluster 3 (green) at three different time-points (A) The pre-operative (PO), (B) early post-operative (EP), and (C) two-year outcome (2Y). The PO 3D curve patterns are characterized as follows. These characteristics were in the sagittal view cluster 1: hypokyphotic range with no proximal kyphosis, cluster 2: normal-hypokyphotic range with no proximal kyphosis and a high inflection point (T11), cluster 3: normal-hypokyphotic range with proximal kyphosis and a lower level inflection point (L1). In frontal view cluster 1: balanced, cluster 2: unbalanced, and cluster 3: balanced. In the axial view cluster 1: closed V shape, cluster 2: V shaped, and cluster 3: S shaped. The two EP clusters in the three views are shown in (B). The sagittal characteristics of cluster 1 are flat, and of cluster 2 are normal-hypo kyphotic range with proximal kyphosis and a low-level inflection point (L1). The Frontal characteristics are as follows. Cluster 1: lateral shift and cluster 2: balanced. The axial characteristics are cluster 1: closed loop, cluster 2: S shape. The sagittal characteristics are: cluster 1: hyperkyphosis backward shift, for cluster 2: normal-hypo kyphotic, and for cluster 3: flat. The frontal characteristics are cluster 1: unbalance, cluster 2: balance, and cluster 3: unbalance. The axial characteristics are cluster 1: S shaped, cluster 2: S shaped, cluster 3: S shaped-closed.