Predicting pediatric spinal deformity (PSD) from X-ray images collected on the patient’s initial visit is a challenging task. This work builds on our previous method and provides a novel bio-informed framework based on a mechanistic machine learning technique with dynamic patient-specific parameters to predict PSD. We provide a geometry-based bone growth model that can be utilized in a range of applications to enhance the bio-informed mechanistic machine learning framework. The proposed technique is utilized to examine and predict spine curvature in PSD cases such as adolescent idiopathic scoliosis. The best fit of a segmented 3D volumetric geometry of the human spine acquired from 2D X-ray images is employed. Using an active contour model based on gradient vector flow snakes, the anteroposterior and lateral views of the X-ray images are segmented to derive the 2D contours surrounding each vertebra. Using minimal user input, the snake parameters are calibrated and automatically computed over the dataset, resulting in fast image segmentation and data collection. The 2D segmented outlines of each vertebra are transformed into a 3D image segmentation result. The Iterative Closest Point mesh registration technique is then used to establish a mesh morphing approach and creates a 3D atlas spine model. Using the comprehensive 3D volumetric model, one can automatically extract spinal geometry data as inputs to the mechanistic machine learning network. Moreover, the proposed bio-informed deep learning network with the modified bone growth model achieves competitive or even superior performance against other state-of-the-art learning-based methods.Please check and confirm if the author names and initials are correct for “Yongjie Jessica Zhang” and “Wing Kam Liu”.We confirm they are correct.

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Scoliosis, an abnormal curvature of the human spinal column, is characterized by a lateral deviation of the spine, accompanied by axial rotation of the vertebrae. Adolescent Idiopathic Scoliosis (AIS) is the most common type, affecting children between ages 8 to 18 when bone growth is at its maximum rate. We propose a mechanistic machine learning algorithm in order to study patient-specific AIS curve progression, which is associated with the bone growth and other genetic and environmental factors. Two different frameworks are used to analyse and predict curve progression, one with implementing clinical data extracted from 2D X-ray images and the other one with incorporating both clinical data and physical equations governing the non-uniform bone growth. The physical equations governing bone growth are affiliated with calculating all stress components at each region. The stress values are evaluated through a surrogate finite element simulation and a bone growth model on a detailed patient-specific geometry of the human spine. We also propose a patient-specific framework to generate the volumetric model of human spine which is partitioned into different tissues for both vertebra and intervertebral disc. It is shown that implementing physical equations governing bone growth into the prediction framework will notably improve the prediction results as compared to only using clinical data for prediction. In addition, we can predict curve progression at ages outside the range of training samples.@en

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C² inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C¹ inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids are a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods.

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Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff–Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refinement of regions where increased resolution is needed. The benefits of using ASTS to define shell geometries are at least two-fold: (1) The manual and time-consuming task of building a new mesh from scratch using the CAD geometry as an input is avoided and (2) C¹ or higher inter-element continuity enables the discretization of shell formulations in primal form defined by fourth-order partial differential equations. A complete and state-of-the-art description of the development of ASTS, including extraordinary points and T-junctions, is presented. In particular, we improve the construction of C¹-continuous non-negative spline basis functions near extraordinary points to obtain optimal convergence rates with respect to the square root of the number of degrees of freedom when solving linear elliptic problems. The applicability of the proposed technology to shell analysis is exemplified by performing geometrically nonlinear Kirchhoff–Love shell simulations of a pinched hemisphere, an oil sump of a car, a pipe junction, and a B-pillar of a car with 15 holes. Building ASTS for these examples involves using T-junctions and extraordinary points with valences 3, 5, and 6, which often suffice for the design of free-form surfaces. Our analysis results are compared with data from the literature using either a seven-parameter shell formulation or Kirchhoff–Love shells. We have also imported both finite element meshes and ASTS meshes into the commercial software LS-DYNA, used Reissner–Mindlin shells, and compared the result with our Kirchhoff–Love shell results. Excellent agreement is found in all cases. The complexity of the shell geometries considered in this paper shows that ASTS are applicable to real-world industrial problems.

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