Mark Adams

Cortical and Trabecular Load Sharing in the Human Vertebral Body

The biomechanical role of the vertebral cortical shell remains poorly understood. Using high‐resolution finite element modeling of a cohort of elderly vertebrae, we found that the biomechanical role of the shell can be substantial and that the load sharing between the cortical and trabecular bone is complex. As a result, a more integrative measure of the trabecular and cortical bone should improve noninvasive assessment of fracture risk and treatments.

High-Resolution Peripheral Quantitative Computed Tomography Can Assess Microstructural and Mechanical Properties of Human Distal Tibial Bone

High‐resolution peripheral quantitative computed tomography (HR‐pQCT) is a newly developed in vivo clinical imaging modality. It can assess the 3D microstructure of cortical and trabecular bone at the distal radius and tibia and is suitable as an input for microstructural finite element (µFE) analysis to evaluate bones mechanical competence. In order for microstructural and image‐based µFE analyses to become standard clinical tools, validation with a current gold standard, namely, high‐resolution micro‐computed tomography (µCT), is required. Microstructural measurements of 19 human cadaveric distal tibiae were performed for the registered HR‐pQCT and µCT images, respectively. Next, whole bone stiffness, trabecular bone stiffness, and elastic moduli of cubic subvolumes of trabecular bone in both HR‐pQCT and µCT images were determined by µFE analysis. The standard HR‐pQCT patient protocol measurements, derived bone volume fraction (BV/TVd), trabecular number (Tb.N*), trabecular thickness (Tb.Th), trabecular spacing (Tb.Sp), and cortical thickness (Ct.Th), as well as the voxel‐based direct measurements, BV/TV, Tb.N*, Tb.Th*, Tb.Sp*, Ct.Th, bone surface‐to‐volume ratio (BS/BV), structure model index (SMI), and connectivity density (Conn.D), correlated well with their respective gold standards, and both contributed to µFE‐predicted mechanical properties in either single or multiple linear regressions. The mechanical measurements, although overestimated by HR‐pQCT, correlated highly with their gold standards. Moreover, elastic moduli of cubic subvolumes of trabecular bone predicted whole bone or trabecular bone stiffness in distal tibia. We conclude that microstructural measurements and mechanical parameters of distal tibia can be efficiently derived from HR‐pQCT images and provide additional information regarding bone fragility.

Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone

The microstructure of trabecular bone is usually perceived as a collection of plate-like and rod-like trabeculae, which can be determined from the emerging high-resolution skeletal imaging modalities such as micro-computed tomography (μCT) or clinical high-resolution peripheral quantitative CT (HR-pQCT) using the individual trabecula segmentation (ITS) technique. It has been shown that the ITS-based plate and rod parameters are highly correlated with elastic modulus and yield strength of human trabecular bone. In the current study, plate-rod (PR) finite element (FE) models were constructed completely based on ITS-identified individual trabecular plates and rods. We hypothesized that PR FE can accurately and efficiently predict elastic modulus and yield strength of human trabecular bone. Human trabecular bone cores from proximal tibia (PT), femoral neck (FN) and greater trochanter (GT) were scanned by μCT. Specimen-specific ITS-based PR FE models were generated for each μCT image and corresponding voxel-based FE models were also generated in comparison. Both types of specimen-specific models were subjected to nonlinear FE analysis to predict the apparent elastic modulus and yield strength using the same trabecular bone tissue properties. Then, mechanical tests were performed to experimentally measure the apparent modulus and yield strength. Strong linear correlations for both elastic modulus (r(2) = 0.97) and yield strength (r(2) = 0.96) were found between the PR FE model predictions and experimental measures, suggesting that trabecular plate and rod morphology adequately captures three-dimensional (3D) microarchitecture of human trabecular bone. In addition, the PR FE model predictions in both elastic modulus and yield strength were highly correlated with the voxel-based FE models (r(2) = 0.99, r(2) = 0.98, respectively), resulted from the original 3D images without the PR segmentation. In conclusion, the ITS-based PR models predicted accurately both elastic modulus and yield strength determined experimentally across three distinct anatomic sites. Trabecular plates and rods accurately determine elastic modulus and yield strength of human trabecular bone.

HPGMG 1.0: A Benchmark for Ranking High Performance Computing Systems

This document provides an overview of the benchmark ? HPGMG ? for ranking large scale general purpose computers for use on the Top500 list [8]. We provide a rationale for the need for a replacement for the current metric HPL, some background of the Top500 list and the challenges of developing such a metric; we discuss our design philosophy and methodology, and an overview of the specification of the benchmark. The primary documentation with maintained details on the specification can be found at hpgmg.org and the Wiki and benchmark code itself can be found in the repository https://bitbucket.org/hpgmg/hpgmg.

Fast Trabecular Bone Strength Predictions of HR‐pQCT and Individual Trabeculae Segmentation–Based Plate and Rod Finite Element Model Discriminate Postmenopausal Vertebral Fractures

Although high‐resolution peripheral quantitative computed tomography (HR‐pQCT) has advanced clinical assessment of trabecular bone microstructure, nonlinear microstructural finite element (µFE) prediction of yield strength using a HR‐pQCT voxel model is impractical for clinical use due to its prohibitively high computational costs. The goal of this study was to develop an efficient HR‐pQCT‐based plate and rod (PR) modeling technique to fill the unmet clinical need for fast bone strength estimation. By using an individual trabecula segmentation (ITS) technique to segment the trabecular structure into individual plates and rods, a patient‐specific PR model was implemented by modeling each trabecular plate with multiple shell elements and each rod with a beam element. To validate this modeling technique, predictions by HR‐pQCT PR model were compared with those of the registered high‐resolution micro–computed tomography (HR‐µCT) voxel model of 19 trabecular subvolumes from human cadaveric tibia samples. Both the Youngs modulus and yield strength of HR‐pQCT PR models strongly correlated with those of µCT voxel models (r2 = 0.91 and 0.86). Notably, the HR‐pQCT PR models achieved major reductions in element number (>40‐fold) and computer central processing unit (CPU) time (>1200‐fold). Then, we applied PR model µFE analysis to HR‐pQCT images of 60 postmenopausal women with (n = 30) and without (n = 30) a history of vertebral fracture. HR‐pQCT PR model revealed significantly lower Youngs modulus and yield strength at the radius and tibia in fracture subjects compared to controls. Moreover, these mechanical measurements remained significantly lower in fracture subjects at both sites after adjustment for areal bone mineral density (aBMD) T‐score at the ultradistal radius or total hip. In conclusion, we validated a novel HR‐pQCT PR model of human trabecular bone against µCT voxel models and demonstrated its ability to discriminate vertebral fracture status in postmenopausal women. This accurate nonlinear µFE prediction of the HR‐pQCT PR model, which requires only seconds of desktop computer time, has tremendous promise for clinical assessment of bone strength.

Scaling to 150K cores: recent algorithm and performance engineering developments enabling XGC1 to run at scale

Particle-in-cell (PIC) methods have proven to be effective in discretizing the Vlasov-Maxwell system of equations describing the core of toroidal burning plasmas for many decades. Recent physical understanding of the importance of edge physics for stability and transport in tokamaks has lead to development of the first fully toroidal edge PIC code – XGC1. The edge region poses special problems in meshing for PIC methods due to the lack of closed flux surfaces, which makes field-line following meshes and coordinate systems problematic. We present a solution to this problem with a semi-field line following mesh method in a cylindrical coordinate system. Additionally, modern supercomputers require highly concurrent algorithms and implementations, with all levels of the memory hierarchy being efficiently utilized to realize optimal code performance. This paper presents a mesh and particle partitioning method, suitable to our meshing strategy, for use on highly concurrent cache-based computing platforms.

Vertebral fragility and structural redundancy

The mechanisms of age‐related vertebral fragility remain unclear, but may be related to the degree of “structural redundancy” of the vertebra; ie, its ability to safely redistribute stress internally after local trabecular failure from an isolated mechanical overload. To better understand this issue, we performed biomechanical testing and nonlinear micro‐CT–based finite element analysis on 12 elderly human thoracic ninth vertebral bodies (age 76.9 ± 10.8 years). After experimentally overloading the vertebrae to measure strength, we used nonlinear finite element analysis to estimate the amount of failed tissue and understand the failure mechanisms. We found that the amount of failed tissue per unit bone mass decreased with decreasing bone volume fraction (r2 = 0.66, p < 0.01). Thus, for the weak vertebrae with low bone volume fraction, overall failure of the vertebra occurred after failure of just a tiny proportion of the bone tissue (<5%). This small proportion of failed tissue had two sources: the existence of fewer vertically oriented load paths to which load could be redistributed from failed trabeculae; and the vulnerability of the trabeculae in these few load paths to undergo bending‐type failure mechanisms, which further weaken the bone. Taken together, these characteristics suggest that diminished structural redundancy may be an important aspect of age‐related vertebral fragility: vertebrae with low bone volume fraction are highly susceptible to collapse because so few trabeculae are available for load redistribution if the external loads cause any trabeculae to fail.

Whole-volume integrated gyrokinetic simulation of plasma turbulence in realistic diverted-tokamak geometry

Performance prediction for ITER is based upon the ubiquitous experimental observation that the plasma energy confinement in the device core is strongly coupled to the edge confinement for an unknown reason. The coupling time-scale is much shorter than the plasma transport time-scale. In order to understand this critical observation, a multi-scale turbulence-neoclassical simulation of integrated edge-core plasma in a realistic diverted geometry is a necessity, but has been a formidable task. Thanks to the recent development in high performance computing, we have succeeded in the integrated multiscale gyrokinetic simulation of the ion-temperature-gradient driven turbulence in realistic diverted tokamak geometry for the first time. It is found that modification of the self-organized criticality in the core plasma by nonlocal core-edge coupling of ITG turbulence can be responsible for the core-edge confinement coupling.

Segmental Refinement: A Multigrid Technique for Data Locality

We investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. We present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.