Cray performance data from five benchmarks

The five benchmark programs discussed in TM-88956, February 1987, were run on the CRAY X-MP/24 under different operating systems and compilers. Performance data is reported for runs under early versions of UNICOS and CFT77. The most recent data includes a system of configuration for a X-MP hardware upgrade. Performance figures for the Y-MP are shown for comparison. Differences in the figures are analyzed and discussed

Construction of solutions for some nonlinear two-point boundary value problems

Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed

A comparison of five benchmarks

Five benchmark programs were obtained and run on the NASA Lewis CRAY X-MP/24. A comparison was made between the programs codes and between the methods for calculating performance figures. Several multitasking jobs were run to gain experience in how parallel performance is measured

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research

The Digital Astronaut Project Computational Bone Remodeling Model (Beta Version) Bone Summit Summary Report

Under the conditions of microgravity, astronauts lose bone mass at a rate of 1% to 2% a month, particularly in the lower extremities such as the proximal femur [1-3]. The most commonly used countermeasure against bone loss in microgravity has been prescribed exercise [4]. However, data has shown that existing exercise countermeasures are not as effective as desired for preventing bone loss in long duration, 4 to 6 months, spaceflight [1,3,5,6]. This spaceflight related bone loss may cause early onset of osteoporosis to place the astronauts at greater risk of fracture later in their lives. Consequently, NASA seeks to have improved understanding of the mechanisms of bone demineralization in microgravity in order to appropriately quantify this risk, and to establish appropriate countermeasures [7]. In this light, NASA's Digital Astronaut Project (DAP) is working with the NASA Bone Discipline Lead to implement well-validated computational models to help predict and assess bone loss during spaceflight, and enhance exercise countermeasure development. More specifically, computational modeling is proposed as a way to augment bone research and exercise countermeasure development to target weight-bearing skeletal sites that are most susceptible to bone loss in microgravity, and thus at higher risk for fracture. Given that hip fractures can be debilitating, the initial model development focused on the femoral neck. Future efforts will focus on including other key load bearing bone sites such as the greater trochanter, lower lumbar, proximal femur and calcaneus. The DAP has currently established an initial model (Beta Version) of bone loss due to skeletal unloading in femoral neck region. The model calculates changes in mineralized volume fraction of bone in this segment and relates it to changes in bone mineral density (vBMD) measured by Quantitative Computed Tomography (QCT). The model is governed by equations describing changes in bone volume fraction (BVF), and rates of changes in bone cell populations that remove and replace bone in packets within the bone region. The DAP bone model is unique in several respects. In particular in takes former models of volume fraction changes one step higher in fidelity and separates BVF into separate equations for mineralized and osteoid volume fractions governed by a mineralization rate. This more closely follows the physiology of the remodeling unit cycles where bone is first resorbed and then followed by the action of osteoblasts to lay down collagen matrix which eventually becomes mineralized. In another respect, the modules allow the functional description of the time rate of change of other parameters and variables in the model during a computational simulation. More detailed description of the model, preliminary validation results, current limitation and caveats, and planned advancements are provided in sections 2 through 5. The DAP bone model is being developed primarily as a research tool, and not as a clinical tool like QCT. Even if it transitions to a clinical tool, it is not intended to replace QCT or any other clinical tool. Moreover, the DAP bone model does not predict bone fracture. Its purpose is to provide valuable additional data via "forward prediction" simulations for during and after spaceflight missions to gain insight on, (1) mechanisms of bone demineralization in microgravity, and (2) the volumetric changes at the various bone sites in response to in-flight and post-flight exercise countermeasures. This data can then be used as input to the Keyak [8] (or equivalent) FE analysis method to gain insight on how bone strength may change during and after flight. This information can also be useful to help optimize exercise countermeasure protocols to minimize changes in bone strength during flight, and improve regain of bone strength post-flight. To achieve this goal, the bone model will be integrated with DAP's exercise countermeasure models to simulate the effect of exercise prescriptions on preserving bone. More specifically, the model will accept loading history due to muscle and joint force on bone and produce quantified remodeling within the bone region under influence of the applied stress. Furthermore, because they tend to respond differently, the bone remodeling model includes both trabecular bone and cortical bone

Predicting Bone Mechanical State During Recovery After Long-Duration Skeletal Unloading Using QCT and Finite Element Modeling

During long-duration missions at the International Space Station, astronauts experience weightlessness leading to skeletal unloading. Unloading causes a lack of a mechanical stimulus that triggers bone cellular units to remove mass from the skeleton. A mathematical system of the cellular dynamics predicts theoretical changes to volume fractions and ash fraction in response to temporal variations in skeletal loading. No current model uses image technology to gather information about a skeletal site s initial properties to calculate bone remodeling changes and then to compare predicted bone strengths with the initial strength. The goal of this study is to use quantitative computed tomography (QCT) in conjunction with a computational model of the bone remodeling process to establish initial bone properties to predict changes in bone mechanics during bone loss and recovery with finite element (FE) modeling. Input parameters for the remodeling model include bone volume fraction and ash fraction, which are both computed from the QCT images. A non-destructive approach to measure ash fraction is also derived. Voxel-based finite element models (FEM) created from QCTs provide initial evaluation of bone strength. Bone volume fraction and ash fraction outputs from the computational model predict changes to the elastic modulus of bone via a two-parameter equation. The modulus captures the effect of bone remodeling and functions as the key to evaluate of changes in strength. Application of this time-dependent modulus to FEMs and composite beam theory enables an assessment of bone mechanics during recovery. Prediction of bone strength is not only important for astronauts, but is also pertinent to millions of patients with osteoporosis and low bone density

A Computational Model for Simulating Spaceflight Induced Bone Remodeling

An overview of an initial development of a model of bone loss due to skeletal unloading in weight bearing sites is presented. The skeletal site chosen for the initial application of the model is the femoral neck region because hip fractures can be debilitating to the overall performance health of astronauts. The paper begins with the motivation for developing such a model of the time course of change in bone in order to understand the mechanism of bone demineralization experienced by astronauts in microgravity, to quantify the health risk, and to establish countermeasures. Following this, a general description of a mathematical formulation of the process of bone remodeling is discussed. Equations governing the rate of change of mineralized bone volume fraction and active osteoclast and osteoblast are illustrated. Some of the physiology of bone remodeling, the theory of how imbalance in remodeling can cause bone loss, and how the model attempts to capture this is discussed. The results of a preliminary validation analysis that was carried out are presented. The analysis compares a set of simulation results against bone loss data from control subjects who participated in two different bed rest studies. Finally, the paper concludes with outlining the current limitations and caveats of the model, and planned future work to enhance the state of the model

Evaluating Daily Load Stimulus Formulas in Relating Bone Response to Exercise

Six formulas representing what is commonly referred to as "daily load stimulus" are identified, compared and tested in their ability to relate skeletal mechanical loading to bone maintenance and osteogenic response. Particular emphasis is placed on exercise- induced skeletal loading and whether or not the formulas can adequately capture the known experimental observations of saturation of continuous cyclic loading, rest insertion between repetitions (cycles), recovery of osteogenic potential following saturation, and multiple shorter bouts versus a single long bout of exercise. To evaluate the ability of the formulas to capture these characteristics, a set of exercise scenarios with type of exercise bout, specific duration, number of repetitions, and rest insertion between repetitions is defined. The daily load values obtained from the formulas for the loading conditions of the set of scenarios is illustrated. Not all of the formulas form estimates of daily load in units of stress or in terms of strain at a skeletal site due to the loading force from a specific exercise prescription. The comparative results show that none of the formulas are able to capture all of the experimentally observed characteristics of cyclic loading. However, the enhanced formula presented by Genc et al. does capture several characteristics of cyclic loading that the others do not, namely recovery of osteogenic potential and saturation. This could be a basis for further development of mathematical formulas that more adequately approximates the amount of daily stress at a skeletal site that contributes to bone adaptation

Mapping Bone Mineral Density Obtained by Quantitative Computed Tomography to Bone Volume Fraction

Methods for relating or mapping estimates of volumetric Bone Mineral Density (vBMD) obtained by Quantitative Computed Tomography to Bone Volume Fraction (BVF) are outlined mathematically. The methods are based on definitions of bone properties, cited experimental studies and regression relations derived from them for trabecular bone in the proximal femur. Using an experimental range of values in the intertrochanteric region obtained from male and female human subjects, age 18 to 49, the BVF values calculated from four different methods were compared to the experimental average and numerical range. The BVF values computed from the conversion method used data from two sources. One source provided pre bed rest vBMD values in the intertrochanteric region from 24 bed rest subject who participated in a 70 day study. Another source contained preflight vBMD values from 18 astronauts who spent 4 to 6 months on the ISS. To aid the use of a mapping from BMD to BVF, the discussion includes how to formulate them for purpose of computational modeling. An application of the conversions would be used to aid in modeling of time varying changes in vBMD as it relates to changes in BVF via bone remodeling and/or modeling

Computational Analysis of Artificial Gravity as a Possible Countermeasure to Spaceflight Induced Bone Loss

During exploration class missions, such as to asteroids and Mars, astronauts will be exposed to reduced gravity for extended periods. Data has shown that astronauts lose bone mass at a rate of 1% to 2% a month in microgravity, particularly in lower extremities such as the proximal femur. Exercise countermeasures have not completely eliminated bone loss from long duration spaceflight missions, which leaves astronauts susceptible to early onset osteoporosis and greater risk of fracture. Introduction of the Advanced Resistive Exercise Device and other large exercise devices on the International Space Station (ISS), coupled with improved nutrition, has further minimized bone loss. However, unlike the ISS, exploration vehicles will have very limited volume and power available to accommodate such capabilities. Therefore, novel concepts like artificial gravity systems are being explored as a means to provide sufficient load stimulus to the musculoskeletal system to mitigate bone changes that may lead to early onset osteoporosis and increased risk of fracture. Currently, there is minimal data available to drive further research and development efforts to appropriately explore such options. Computational modeling can be leveraged to gain insight on the level of osteoprotection that may be achieved using artificial gravity produced by a spinning spacecraft or centrifuge. With this in mind, NASA's Digital Astronaut Project (DAP) has developed a bone remodeling model that has been validated for predicting volumetric bone mineral density (vBMD) changes of trabecular and cortical bone both for gravitational unloading condition and the equivalent of 1g daily load stimulus. Using this model, it is possible to simulate vBMD changes in trabecular and cortical bone under different gravity conditions. In this presentation, we will discuss our preliminary findings regarding if and how artificial gravity may be used to mitigate spaceflight induced bone loss