Complex Three-dimensional Geometries Research Articles

Predicting lift and drag coefficients during hypersonic Mars reentry using hyStrath

During hypersonic reentry, a spacecraft experiences several different fluid flow regimes, which usually require the application of different software frameworks to simulate the respective regimes. This study aims to evaluate the hyStrath library for predicting aerodynamic lift and drag coefficients of complex three-dimensional (3D) geometries during hypersonic Mars reentry, using flight data of the Viking 1 mission as reference. A range of altitudes (h=30−140 km) and Mach numbers (M=13−24) where flight data is available is considered, covering the rarefied, transitional, and continuum fluid flow regimes. The hyStrath library contains a set of modified solvers and state-of-the-art thermophysical and chemistry models within the framework of OpenFOAM, dedicated to modeling high-enthalpy hypersonic flow problems. Depending on the flow regime, the computational fluid dynamics solver hy2Foam or direct-simulation Monte Carlo solver dsmcFoam+ are employed in the study. Because hyStrath is based on OpenFOAM, it allows the use of an unstructured adaptive mesh refinement approach for arbitrary geometries. We obtain excellent results throughout all investigated flow regimes and Mach numbers with an average deviation of 1.5% and 2% from the measured lift and drag coefficients, respectively. The applicability of the framework for accurately modeling both rarefied and continuum Mars reentry problems of complex 3D geometries such as the Viking capsule is demonstrated.

Exploring Aesthetic Outcomes and Complications in Auricular Reconstruction Utilising Autologous Cartilage: A Systematic Review and Narrative Synthesis.

Auricular reconstruction remains a challenging procedure, requiring a high degree of manual dexterity and attention to detail in order to reconstruct the complex three-dimensional geometry of the ear successfully. Most techniques will rely on autologous cartilage for auricular framework fabrication, carrying a risk of donor and recipient site morbidity. The aim of this report is to investigate the complications and aesthetic outcomes associated with autologous cartilage harvest in auricular reconstruction. A systematic review protocol was registered with theInternational Prospective Register of Systematic Reviews (PROSPERO) and reported in accordance with the Preferred Reporting for Items for Systematic Reviews and Meta-Analyses. Comprehensive electronic search strategies for four databases were developed. Studies were screened according to the inclusion and exclusion criteria by two independent reviewers. The literature search identified 7171 articles. Filtering for relevance and duplication reduced the number of articles to 52. A total of 12,215 patients underwent auricular reconstruction utilising autologous cartilage. Indications included 11,696 patients due to microtia, 334 patients due to burns or trauma, 70 patients due to constricted ears, and 115 patients due to prominent ears. The most commonly reported donor site complications included chest wall deformities (n = 159). The most commonly reported recipient site complications included hypertrophic or keloid scars (n = 279), haematoma (n = 155), tissue expander exposure (n = 111), cartilage or framework exposure (n = 122), and cartilage framework deformation or resorption (n = 50). Although a challenging procedure, auricular reconstruction utilising autologous cartilage is possible. Exceptional aesthetic results can be achieved when performed by a skilled surgeon on appropriately selected individuals. However, the potential risks and complications associated with the procedure should be discussed with the patient and family beforehand.

Anodization as a scalable nanofabrication method to engineer mechanobactericidal nanostructures on complex geometries.

Bacterial contamination of implant surfaces is one of the primary causes of their failure, and this threat has been further exacerbated due to the emergence of drug-resistant bacteria. Nanostructured mechanobactericidal surfaces that neutralize bacteria via biophysical forces instead of traditional biochemical routes have emerged as a potential remedy against this issue. Here, we report on the bactericidal activity of titania nanotubes (TNTs) prepared by anodization, a well-established and scalable method. We investigate the differences in bacterial behavior between three different topographies and demonstrate the applicability of this technique on complex three-dimensional (3D) geometries. It was found that the metabolic activity of bacteria on such surfaces was lower, indicative of disturbed intracellular processes. The differences in deformations of the cell wall of Gram-negative and positive bacteria were investigated from electron micrographs Finally, nanoindentation experiments show that the nanotubular topography was durable enough against forces typically experienced in daily life and had minimal deformation under forces exerted by bacteria. Our observations highlight the potential of the anodization technique for fabricating mechanobactericidal surfaces for implants, devices, surgical instruments, and other surfaces in a healthcare setting in a cheap, scalable way.

NekMesh: An open-source high-order mesh generation framework

High-order spectral element simulations are now becoming increasingly popular within the computational modelling community, as they offer the potential to deliver increased accuracy at reduced cost compared to traditional low-order codes. However, to support accurate, high-fidelity simulations in complex industrial applications, there is a need to generate curvilinear meshes which robustly and accurately conform to geometrical features. This is, at present, a key challenge within the mesh generation community, with only a few open-source tools able to generate curvilinear meshes for complex geometries. We present NekMesh: an open-source mesh generation package which is designed to enable the generation of valid, high-quality curvilinear meshes of complex, three-dimensional geometries for performing high-order simulations. We outline the software architecture adopted in NekMesh, which uses a pipeline of processing modules to provide a flexible, CAD-independent high-order mesh processing tool, capable of both generating meshes for a wide range of use cases, as well as post-processing linear meshes from a range of input formats for use with high-order simulations. A number of examples in various application areas are presented, with a particular emphasis on challenging aeronautical and fluid dynamics test cases. Program summaryProgram title: NekMesh (version 5.4.0)CPC Library link to program files:https://doi.org/10.17632/d82hjm4v6r.1Licensing provisions: MITProgramming language: C++External routines/libraries: Boost, TinyXML, OpenCASCADE, Triangle, TetGen, HDF5Nature of problem: NekMesh is a high-order mesh generation framework with the goal of providing a robust framework to automate the process of generating valid meshes for complex three-dimensional CAD geometries.Solution method: Energy minimisation, solid body models and other techniques based around high-order finite element methods.Additional comments including restrictions and unusual features: The supplied cases require a system with 16384 MB of RAM for the automotive example and 32768 MB of RAM for the variational optimisation example.

Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns

Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, meta-materials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study the hybrid structure formed by combining unit cells of the Miura-ori and eggbox patterns. We find the compatibility constraints required to form the hybrid structure and derive properties of its kinematics such as self-locking and Poisson’s ratio. We then compare the aforementioned properties of the Miura-eggbox hybrid with those of the morph pattern, another generalization of the Miura-ori and eggbox patterns. In addition, we study the structure formed by combining all three unit cells of the Miura-ori, eggbox and morph. Our results show that such patterns have tunable self-locking states and Poisson’s ratio beyond their constituent components. Hybrid patterns formed by combining different origami patterns are an avenue to derive more functionality from simple constituents for engineering applications.

Growth of Nb films on Cu for superconducting radio frequency cavities by direct current and high power impulse magnetron sputtering: A molecular dynamics and experimental study

The use of superconducting radio frequency (rf) cavities in particle accelerators necessitates that copper (Cu) surfaces are coated by thin niobium (Nb) films, predominantly synthesized by magnetron sputtering. A key feature of the rf cavities is that they exhibit a complex three-dimensional geometry, such that during Nb film growth vapor is not deposited on a flat substrate. The latter, combined with the line-of-sight nature of the deposition flux in conventional magnetron sputtering methods (including direct current magnetron sputtering; DCMS) yields films with porous columnar morphologies on surfaces of the cavities that do not face the magnetron source. High-power impulse magnetron sputtering (HiPIMS) is a variant of sputtering that generates highly-ionized fluxes. Using electrical fields, such fluxes can be deflected to trajectories that are closer to the substrate normal and, thereby, dense and uniform layers can be deposited on all surfaces of the rf cavities. In the present work, we use classical molecular dynamics simulations to model Nb film growth on Cu substrates at conditions consistent with those prevailing during DCMS and HiPIMS. Our computational results are in qualitative agreement with experimental data (also generated in the present study), with respect to film morphology. Based on this agreement and by studying the evolution of the simulated systems, we suggest that the morphology of HiPIMS-grown films (as compared to their DCMS counterparts) is the result of the combined effects of deflection of ionized sputtered particles to trajectories parallel to the substrate normal, bombardment-induced interruption of crystal growth, and ballistic atomic rearrangement along with dynamic thermal annealing caused by energetic film-forming species. Moreover, the predictions of our model with respect to dynamic processes at the film-substrate interface and their effect on local epitaxial growth are discussed.

Data-driven turbulence modelling of inherently unsteady flow in stratified water storage tanks

The flow and thermal characteristics of thermal stratification appears in a wide range of industrial applications related to energy storage. In a previous study (Xu et al. submitted to Flow, Turbulence and Combustion), it has been shown that linear closure models in unsteady Reynolds averaged Navier–Stokes (RANS) calculations are unable to accurately capture the transient flow and thermal characteristics occurring in stratified water storage tank configurations. In the current study, we extend a data-driven framework to develop turbulence and heat flux closures for a three-dimensional (3D) geometry of a stratified water storage tank, using data from a highly resolved large eddy simulation. The transient high-fidelity data set is partitioned into several time-intervals used for closure development and testing. In detail, we first present the model formulations for 3D buoyant flow. We then use the reference data to extract the most suitable input features, i.e. variables used to regress the data driven model. In order to reduce the complexity of the resulting models and accelerate the training process, a recursive basis function elimination is performed, using alignment of the different basis functions with the target turbulence stress and heat flux as metric. Using the identified features and the subsets of basis functions, novel closures are then developed using a symbolic regression framework, based on Gene Expression Programming (GEP). Models are developed either for each time interval or for all intervals at once. The different machine-learnt turbulence and heat-flux closure models are then tested for two different tank configurations where the thermal stratification is affected by positively/negatively buoyant jets within simple or complex three-dimensional geometries. It is demonstrated that the extended GEP-based data-driven turbulence modelling approach is able to create models that can accurately predict flow with inherent unsteadiness in three dimensional complex-geometry cases.

Simplicity is the ultimate sophistication: One-step forming for thermosensitive solid–solid phase change thermal energy harvesting, storage, and utilization

In light of the growing recognition of low-carbon initiatives, renewable energy is gradually assuming a dominant role within the energy framework. Phase change materials can enhance the efficiency of renewable energy utilization by energy peak shaving and time shifting. However, leakage and inherent rigidity signify that a significant amount of energy input is required for scale-up applications of phase change materials to enhance shape stability and processability during industrial installation. In conventional enhancement strategies, high-quality encapsulation means more intricate processes and higher energy consumption. Here we propose a simplified thermally-initiated encapsulation and molding strategy, which involves grafting the phase change materials onto thermosetting polymer backbones by covalently integrated, to construct self-supported phase change materials with complex three-dimensional geometry. The encapsulation process is macroscopically manifested as a transformation from solid-liquid to solid–solid phase change. Therefore, by imposing restrictions on liquid materials, any ultra-high-precision complex structure can be molded, and mechanical properties are imparted through curing to achieve shape stability, ultimately enables the integration of phase change material encapsulation and casting. The complete process requires no curing agents or organic solvents, and no pollution emissions, making it highly maneuverable and environmentally friendly. Furthermore, we demonstrate the universal high value applications of new materials in different fields. In the ancient thermotherapy experiment, the sample exhibited sustained heat release for 8 min. In the advanced chip cooling simulation, the chip exhibits superior heat dissipation performance, as evidenced by its operating temperature being 50 °C lower than that of natural cooling within 20 min. It confirms the remarkable potential of phase change materials constructed through this approach for thermal energy applications.

Shape sensitivity of thermoacoustic oscillations in an annular combustor with a 3D adjoint Helmholtz solver

We model acoustic oscillations driven by velocity-coupled heat release rate fluctuations. We obtain an inhomogeneous wave equation and convert it to the frequency domain with a modal decomposition. We impose acoustic boundary conditions and, using a finite element discretization with Lagrange elements, express this as a nonlinear eigenvalue problem for the complex angular frequency, ω. We solve this using the open source platform FEniCS combined with the SLEPc, PETSc and OpenMPI libraries. In Hadamard form we write the derivative of the eigenvalue, ω, with respect to generic geometry changes. This requires the solution of the adjoint equation, which we obtain with the same method as the direct equation. The output is a thermoacoustic Helmholtz solver that cheaply calculates the effect of generic shape changes on the growth rate and frequency of thermoacoustic oscillations. We then consider symmetry-preserving and symmetry-breaking geometry modifications. For demonstration we model a 30kW laboratory-scale annular combustor (MICCA from EM2C). We parametrize the surfaces of the three-dimensional geometry with NURBS using control points. For the plenum and the combustion chamber, we find the eigenvalue shape derivatives with respect to the parameters of these control points. We apply two different strategies, perpendicular boundary movements and control point perturbations, to implement shape changes proportional to these shape derivatives, thereby reducing the growth rate of the unstable mode by increasing the phase shift between the pressure and the heat release rate oscillations. This computational method shows how to significantly alter thermoacoustic oscillations by making small geometry changes. The framework in this paper can handle arbitrarily complex three-dimensional geometries, which will be useful for the design of industrial combustion systems.

Meshless Geometric Multigrid Method for Complex Geometries with Improved Cell Coarsening Algorithm

In this paper, we present an improved multicloud methodology to extend the multicloud convergence accelerator, which depends on meshless discretization on coarse level computation of the geometric multigrid method, to cell finite volume (CFV) on three-dimensional space. To achieve this, we first identify the primary challenge in the meshless coarsening application to CFV. Specifically, the challenge lies in the poorly coarsened grid, which results in a degradation of the convergence rate. The reason for this is that the coarsening stencils were coupled with the discretization stencil. To address the issue, we proposed a new coarsening strategy on CFV that adequately utilizes node information on the fine-level mesh. The proposed methodology shows superior coarsening rates compared to the basic meshless cell coarsening, regardless of the dimension and type of mesh elements, resulting in significant speedup in convergence. Various computational fluid dynamics (CFD) simulations with three-dimensional complex geometries are presented, and their results demonstrate approximately seven times faster convergence compared to the single-grid method. The overall results verify that the multicloud method with the proposed coarsening procedure provides a powerful tool for practical CFD simulations by reducing the computation time, and it enables researchers and engineers to simulate and optimize real-world systems more efficiently.

Fabrication and Applications of Electroplated Three-Dimensional, Open-Cell, Noble Metal Electrodes

Noble metal electrodes (Au, Ag, and Pt) have found numerous applications in electroanalysis and electrocatalysis. Noble metal electrodes are typically composed entirely of a bulk noble metal so their cost is high and they have a two-dimensional geometry. This presentation describes the fabrication of inexpensive, electroplated noble metal electrodes that have an open-cell, three-dimensional complex geometry. The electroplated noble metal electrodes exhibit a defect-free layer of a noble metal (i.e., Au, Pt or Ag) deposited onto a copper substrate structure of the desired geometry. The surface roughness of the electrodeposited films was tailored by adjusting the electroplating conditions and the composition of the electroplating solution. The electrochemical performance of the electrodes was fully characterized. The electroplated three-dimensional, open-cell electrodes were used for the detection of heavy metals in aqueous samples and the decontamination of aqueous samples that contained bacteria.

Anisotropic flexure hinges: Manufacturing and mechanical characterization for application in pressure-actuated morphing structures

Shape-morphing structures based on pressure actuation promise efficiency gains and performance improvements in aeronautics, but require complex three-dimensional geometries. The compliance of these morphing structures originates from local areas of reduced wall thickness. However, the required high wall thickness ratios are challenging for integral fabrication from high-performance fiber-reinforced plastics, which are demanded to achieve high load-bearing capacity. This study investigates different woven flexure hinges made from a hybrid yarn of glass fibers and the polyamide PA6 for application in pressure-actuated cellular structures. The flexure hinges are mechanically characterized under pure axial and pure bending loading in a tensile and a column bending test method specifically derived for flexure hinges. The specimen quality is further assessed by permeability testing, optical microscopy, and thermogravimetric analysis. This study shows that the stiffness of anisotropic flexure hinges can be determined in simple mechanical tests without the need for complex modeling of reinforcing fibers or consideration of manufacturing-specific effects. The mechanical properties of a double-layer hinge configuration are superior to those of a single-layer configuration, whereas integrating additively manufactured PA6 inlays into the woven preform offers an effective approach for achieving high wall thickness ratios. The most promising hinge configuration is selected for the integral fabrication of the aeronautical morphing structure, which consists of multiple pressurized cells.

Ultrafast quasi-three-dimensional imaging

Understanding laser induced ultrafast processes with complex three-dimensional (3D) geometries and extreme property evolution offers a unique opportunity to explore novel physical phenomena and to overcome the manufacturing limitations. Ultrafast imaging offers exceptional spatiotemporal resolution and thus has been considered an effective tool. However, in conventional single-view imaging techniques, 3D information is projected on a two-dimensional plane, which leads to significant information loss that is detrimental to understanding the full ultrafast process. Here, we propose a quasi-3D imaging method to describe the ultrafast process and further analyze spatial asymmetries of laser induced plasma. Orthogonally polarized laser pulses are adopted to illuminate reflection-transmission views, and binarization techniques are employed to extract contours, forming the corresponding two-dimensional matrix. By rotating and multiplying the two-dimensional contour matrices obtained from the dual views, a quasi-3D image can be reconstructed. This successfully reveals dual-phase transition mechanisms and elucidates the diffraction phenomena occurring outside the plasma. Furthermore, the quasi-3D image confirms the spatial asymmetries of the picosecond plasma, which is difficult to achieve with two-dimensional images. Our findings demonstrate that quasi-3D imaging not only offers a more comprehensive understanding of plasma dynamics than previous imaging methods, but also has wide potential in revealing various complex ultrafast phenomena in related fields including strong-field physics, fluid dynamics, and cutting-edge manufacturing.

Characterization of thin film Parylene C device curvature and the formation of helices via thermoforming

In microfabricated biomedical devices, flexible, polymer substrates are becoming increasingly preferred over rigid, silicon substrates because of their ability to conform to biological tissue. Such devices, however, are fabricated in a planar configuration, which results in planar devices that do not closely match the shape of most tissues. Thermoforming, a process which can reshape thermoplastic polymers, can be used to transform flat, thin film, polymer devices with patterned metal features into complex three-dimensional (3D) geometries. This process extends the use of planar microfabrication to achieve 3D shapes which can more closely interface with the body. Common shapes include spheres, which can conform to the shape of the retina; cones, which can be used as a sheath to interface with an insertion stylet; and helices, which can be wrapped around nerves, blood vessels, muscle fibers, or be used as strain relief feature. This work characterizes the curvature of thin film Parylene C devices with patterned metal features built with varying Parylene thicknesses and processing conditions. Device curvature is caused by film stress in each Parylene and metal layer, which is characterized experimentally and by a mathematical model which estimates the effects of device geometry and processing on curvature. Using this characterization, an optimized process to thermoform thin film Parylene C devices with patterned metal features into 0.25 mm diameter helices while preventing cracking in the polymer and metal was developed.

HBIM-BASED INFORMATION SHARING FOR THE EXCHANGE AND SAFEGUARD OF MODELLING EXPERTISE

Abstract. This paper demonstrates an approach for sharing and safeguarding modelling expertise based on the use of Historic Building Information Modelling (HBIM). The approach involves the exchange of information between subjects involved in the creation of HBIM models, an exchange enhanced by Semantic Web Technologies.HBIM datasets usually contain rich and detailed information about historic buildings and their construction; this experiment, in a slightly unusual way, deals with another type of information regarding something that happens in the background during the definition of an HBIM model: the procedures that create the complex three-dimensional geometries typical of historical architecture. This kind of information does not usually live inside BIM models and is even less likely the subject of semantic enrichment. It is however beneficial to record and make available this kind of information for several reasons, discussed in the text.

Angular-spatial discontinuous Galerkin method for radiative heat transfer with a participating medium in complex three-dimensional geometries

The angular-spatial discontinuous Galerkin method (ASDGM) is a numerical technique developed to solve the radiative transfer equation (RTE) in complex three-dimensional geometries with absorbing, emitting, and scattering media. The ASDGM discretizes both the angular and spatial domains of the RTE using structured quadrilateral elements for the angular domain and unstructured tetrahedral elements for the spatial domain. In the solution process, the Riemann upwind solver separates the input and output information at the tetrahedral element boundary. Moreover, the discontinuous Galerkin (DG) sweep algorithm optimizes the order of the unstructured tetrahedral elements and reduces memory usage caused by the coupling of the discretization in the angular and spatial domains. The performance of the ASDGM has been evaluated using several radiative transfer cases in complex three-dimensional geometries, which demonstrate its good accuracy compared to available data from the literature. Additionally, the computational time in the angular domain for high-order DG is lower than that of the finite element method for the same discrete angles. Furthermore, the DG sweep algorithm provides a faster convergence rate in the spatial domain compared to the original sweep algorithm. Therefore, the ASDGM with the DG sweep algorithm is a preferable method for solving radiative transfer problems in complex three-dimensional geometries.

Quantitative coronary three‐dimensional geometry and its association with atherosclerotic disease burden and composition

Isolate features of the coronary anatomy have been associated with the pathophysiology of atherosclerotic disease. Computational methods have been described to allow precise quantification of the complex three-dimensional (3D) coronary geometry. The present study tested whether quantitative parameters that describe the spatial 3D coronary geometry is associated with the extension and composition of the underlying coronary artery disease (CAD). Patients with CAD scheduled for percutaneous intervention were investigated with coronary computed tomography angiography (CCTA), and invasive coronary angiography, and virtual histology intravascular ultrasound (IVUS-VH). For all target vessels, 3D centerlines were extracted from CCTA images and processed to quantify 23 geometric indexes, grouped into 3 main categories as follows: (i) length-based; (ii) curvature-based, torsion-based, and curvature/torsion-combined; (iii) vessel path-based. The geometric variables were compared with IVUS-VH parameters assessing the extent and composition of coronary atherosclerosis. A total of 36 coronary patients (99 vessels) comprised the study population. From the 23 geometric indexes, 18 parameters were significantly (p < 0.05) associated with at least 1 IVUS-VH parameter at a univariate analysis. All three main geometric categories provided parameters significantly related with atherosclerosis variables. The 3D geometric indexes were associated with the degree of atherosclerotic extension, as well as with plaque composition. Geometric features remained significantly associated with all IVUS-VH parameters even after multivariate adjustment for clinical characteristics. Quantitative 3D vessel morphology emerges as a relevant factor associated with atherosclerosis in patients with established CAD.

Krylov Methods for Large-Scale Dynamical Systems: Application in Fluid Dynamics

AbstractIn fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is of critical importance for both academic and industrial applications. Different tools from dynamical systems theory can be used for this purpose. In this review, we present a concise theoretical and numerical framework focusing on practical aspects of the computation and stability analyses of steady and time-periodic solutions, with emphasis on high-dimensional systems such as those arising from the spatial discretization of the Navier–Stokes equations. Using a matrix-free approach based on Krylov methods, we extend the capabilities of the open-source high-performance spectral element-based time-stepper Nek5000. The numerical methods discussed are implemented in nekStab, an open-source and user-friendly add-on toolbox dedicated to the study of stability properties of flows in complex three-dimensional geometries. The performance and accuracy of the methods are illustrated and examined using standard benchmarks from the fluid mechanics literature. Thanks to its flexibility and domain-agnostic nature, the methodology presented in this work can be applied to develop similar toolboxes for other solvers, most importantly outside the field of fluid mechanics.

Enhancement of the Robustness on Advancing Layer Method with Trimmed Hexahedral Volume Mesh for the Generation of the Boundary Layer Grids

When performing simulations using computational fluid dynamics, the grid systems in the viscous boundary layer regions are important because the velocity and pressure change very rapidly in these regions. Especially for the turbulent flows, thin grids should be arranged densely in the direction perpendicular to the wall. In this study, the advancing layer method, which has been applied mostly to tetrahedral meshes, is applied to trimmed hexahedral meshes. To generate boundary layer meshes with non-intersecting grid lines near the wall boundaries having concave corners and narrow gaps, the directional vectors of grid lines and faces are smoothed, and the displacement vector fields calculated using the Laplace equation were utilized. Firstly, the details on the newly developed methods are introduced showing simple two-dimensional cases as examples. After applying the methods for a complex three-dimensional geometry to check its applicability and investigating the generated grid systems, the numerical simulations of propeller open water test for INSEAN E779A marine propeller were carried out by simpleFoam, one of the standard solvers of OpenFOAM. The computational results showed good agreement with the experimental results. Therefore, in conclusion, the developed advancing layer method is an appropriate method for generating boundary layer grids of a trimmed hexahedral mesh.

Morphable models of the lumbar spine to vary geometry based on pathology, demographics, and anatomical measurements

The shape of the lumbar spine influences its function and dysfunction. Yet examining the influence of geometric differences associated with pathology or demographics on lumbar biomechanics is challenging in vivo where these effects cannot be isolated, and the use of simple anatomical measurements does not fully capture the complex three-dimensional geometry. The goal of this work was to develop and share morphable models of the lumbar spine that allow geometry to be varied according to pathology, demographics, or anatomical measurements. Partial least squares regression was used to generate statistical shape models that quantify geometric differences associated with pathology, demographics, and anatomical measurements from the lumbar spines of 87 patients. To determine if the morphable models detected meaningful geometric differences, the ability of the morphable models to classify spines was compared with models generated from random labels. The models for disc herniation (p < 0.04), spondylolisthesis (p < 0.001), and sex (p < 0.01) all performed significantly better than the random models. Age was predicted with a root mean square error of 14.1 years using the age-based model. The morphable models for anatomical measurements were able to produce instances with root mean square errors less than 0.8°, 0.3 cm2, and 0.7 mm between desired and resulting measurements. This method can be used to produce morphable models that enable further analysis of the relationship among shape, pathology, demographics, and function through computational simulations. The morphable models and code are available at https://github.com/aclouthier/morphable-lumbar-model.