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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh

Here, we present a comprehensive workflow to simulate single-phase flow and transport in fractured porous media using the discrete fracture matrix approach. The workflow has three primary parts: (1) a method for conforming mesh generation of and around a three-dimensional fracture network, (2) the discretization of the governing equations using a second-order mimetic finite difference method, and (3) implementation of numerical methods for high-performance computing environments. A method to create a conforming Delaunay tetrahedralization of the volume surrounding the fracture network, where the triangular cells of the fracture mesh are faces in the volume mesh, that addresses pathological cases which commonly arise and degrade mesh quality is also provided. Our open-source subsurface simulator uses a hierarchy of process kernels (one kernel per physical process) that allows for both strong and weak coupling of the fracture and matrix domains. We provide verification tests based on analytic solutions for flow and transport, as well as numerical convergence. We also provide multiple expositions of the method in complex fracture networks. In the first example, we demonstrate that the method is robust by considering two scenarios where the fracture network acts as a barrier to flow, as the primary pathway, or offers the same resistance as the surrounding matrix. In the second test, flow and transport through a three-dimensional stochastically generated network containing 257 fractures is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Impact of artificial topological changes on flow and transport through fractured media due to mesh resolution

Abstract We performed a set of numerical simulations to characterize the interplay of fracture network topology, upscaling, and mesh refinement on flow and transport properties in fractured porous media. We generated a set of generic three-dimensional discrete fracture networks at various densities, where the radii of the fractures were sampled from a truncated power-law distribution, and whose parameters were loosely based on field site characterizations. We also considered five network densities, which were defined using a dimensionless version of density based on percolation theory. Once the networks were generated, we upscaled them into a single continuum model using the upscaled discrete fracture matrix model presented by Sweeney et al. (2019). We considered steady, isothermal pressure-driven flow through each domain and then simulated conservative, decaying, and adsorbing tracers using a pulse injection into the domain. For each simulation, we calculated the effective permeability and solute breakthrough curves as quantities of interest to compare between network realizations. We found that selecting a mesh resolution such that the global topology of the upscaled mesh matches the fracture network is essential. If the upscaled mesh has a connected pathway of fracture (higher permeability) cells but the fracture network does not, then the estimates for effective permeability and solute breakthrough will be incorrect. False connections cannot be eliminated entirely, but they can be managed by choosing appropriate mesh resolution and refinement for a given network. Adopting octree meshing to obtain sufficient levels of refinement leads to fewer computational cells (up to a 90% reduction in overall cell count) when compared to using a uniform resolution grid and can result in a more accurate continuum representation of the true fracture network.

58 GEOSCIENCES↗
DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗
DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗
DOE OSTI2022

Fracture Adjacent Matrix Permeability: Insights from a Direct Experimental Approach

Description of a measurement technique, using a triple-pressure tap Hassler Style Core holder, that facilitates pressure measurement perpendicular to a fracture. Through the measurement of permeability changes at multiple distances from the fracture, this system enables an understanding of how end effects and localized ‘skin effects’ can impact the ability of fluids to move to and from the bulk matrix. Measurements of this type may lead to improved input values for reservoir simulations involving discrete fractures and/or dual-permeability.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗
DOE OSTI2020

A Method to Represent a Well in a Three‐Dimensional Discrete Fracture Network Model

Abstract In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three‐dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high‐resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real‐world case study.

Pham, Hai (ORCID:0000000310164394)↗
NASA NTRS2003

High-Performance Acousto-Ultrasonic Scan System Being Developed

Acousto-ultrasonic (AU) interrogation is a single-sided nondestructive evaluation (NDE) technique employing separated sending and receiving transducers. It is used for assessing the microstructural condition and distributed damage state of the material between the transducers. AU is complementary to more traditional NDE methods, such as ultrasonic cscan, x-ray radiography, and thermographic inspection, which tend to be used primarily for discrete flaw detection. Throughout its history, AU has been used to inspect polymer matrix composites, metal matrix composites, ceramic matrix composites, and even monolithic metallic materials. The development of a high-performance automated AU scan system for characterizing within-sample microstructural and property homogeneity is currently in a prototype stage at NASA. This year, essential AU technology was reviewed. In addition, the basic hardware and software configuration for the scanner was developed, and preliminary results with the system were described. Mechanical and environmental loads applied to composite materials can cause distributed damage (as well as discrete defects) that plays a significant role in the degradation of physical properties. Such damage includes fiber/matrix debonding (interface failure), matrix microcracking, and fiber fracture and buckling. Investigations at the NASA Glenn Research Center have shown that traditional NDE scan inspection methods such as ultrasonic c-scan, x-ray imaging, and thermographic imaging tend to be more suited to discrete defect detection rather than the characterization of accumulated distributed microdamage in composites. Since AU is focused on assessing the distributed microdamage state of the material in between the sending and receiving transducers, it has proven to be quite suitable for assessing the relative composite material state. One major success story at Glenn with AU measurements has been the correlation between the ultrasonic decay rate obtained during AU inspection and the mechanical modulus (stiffness) seen during fatigue experiments with silicon carbide/silicon carbide (SiC/SiC) ceramic matrix composite samples. As shown in the figure, ultrasonic decay increased as the modulus decreased for the ceramic matrix composite tensile fatigue samples. The likely microstructural reason for the decrease in modulus (and increase in ultrasonic decay) is the matrix microcracking that commonly occurs during fatigue testing of these materials. Ultrasonic decay has shown the capability to track the pattern of transverse cracking and fiber breakage in these composites.

Roth, Don J.↗
NASA NTRS2003

High-Performance Acousto-Ultrasonic Scan System Being Developed

Acousto-ultrasonic (AU) interrogation is a single-sided nondestructive evaluation (NDE) technique employing separated sending and receiving transducers. It is used for assessing the microstructural condition and distributed damage state of the material between the transducers. AU is complementary to more traditional NDE methods, such as ultrasonic cscan, x-ray radiography, and thermographic inspection, which tend to be used primarily for discrete flaw detection. Throughout its history, AU has been used to inspect polymer matrix composites, metal matrix composites, ceramic matrix composites, and even monolithic metallic materials. The development of a high-performance automated AU scan system for characterizing within-sample microstructural and property homogeneity is currently in a prototype stage at NASA. This year, essential AU technology was reviewed. In addition, the basic hardware and software configuration for the scanner was developed, and preliminary results with the system were described. Mechanical and environmental loads applied to composite materials can cause distributed damage (as well as discrete defects) that plays a significant role in the degradation of physical properties. Such damage includes fiber/matrix debonding (interface failure), matrix microcracking, and fiber fracture and buckling. Investigations at the NASA Glenn Research Center have shown that traditional NDE scan inspection methods such as ultrasonic c-scan, x-ray imaging, and thermographic imaging tend to be more suited to discrete defect detection rather than the characterization of accumulated distributed micro-damage in composites. Since AU is focused on assessing the distributed micro-damage state of the material in between the sending and receiving transducers, it has proven to be quite suitable for assessing the relative composite material state. One major success story at Glenn with AU measurements has been the correlation between the ultrasonic decay rate obtained during AU inspection and the mechanical modulus (stiffness) seen during fatigue experiments with silicon carbide/silicon carbide (SiC/SiC) ceramic matrix composite samples. As shown in the figure, ultrasonic decay increased as the modulus decreased for the ceramic matrix composite tensile fatigue samples. The likely microstructural reason for the decrease in modulus (and increase in ultrasonic decay) is the matrix microcracking that commonly occurs during fatigue testing of these materials. Ultrasonic decay has shown the capability to track the pattern of transverse cracking and fiber breakage in these composites.

Roth, Don J.↗
NASA NTRS1986

Interfaces and failure mechanisms in Al-SiC composites

Aluminum alloys reinforced with silicon carbide whiskers exhibit significantly higher strength and modulus than the unreinforced alloys. However, the composites also exhibit low ductility and poor fracture toughness for reasons which are not well-understood. In this study, high resolution and conventional TEM techniques are used to analyze interface microstructure and failure mechanisms in P/M 2124 and 6061 aluminum alloys reinforced with silicon carbide whiskers. Interfacial oxides are typical of both composite materials, often distributed in clusters or in a discrete layer 2-5 nm thick along the whisker-matrix interface. Highly deformed regions beneath bulk tensile fracture surfaces reveal possible fracture nucleation centers as well as sites of stress concentration where intense plastic strain has occurred. Observations of such highly deformed regions include (1) void initiation at whisker ends, (2) interface decohesion involving the thin oxide layer, (3) transverse cracks in whiskers, and (4) cracks in large constituent particles. TEM results are presented and discussed in relation to mechanisms of composite failure.

Nutt, S. R.↗
NASA NTRS2004

Ultrasonic Guided-Wave Scan System Used to Characterize Microstructure and Defects in Ceramic Composites

Ceramic matrix composites (CMCs) are being developed for advanced aerospace propulsion applications to save weight, improve reuse capability, and increase performance. However, mechanical and environmental loads applied to CMCs can cause discrete flaws and distributed microdamage, significantly reducing desirable physical properties. Such microdamage includes fiber/matrix debonding (interface failure), matrix microcracking, fiber fracture and buckling, oxidation, and second phase formation. A recent study (ref. 1) of the durability of a C/SiC CMC discussed the requirement for improved nondestructive evaluation (NDE) methods for monitoring degradation in these materials. Distributed microdamage in CMCs has proven difficult to characterize nondestructively because of the complex microstructure and macrostructure of these materials. This year, an ultrasonic guided-wave scan system developed at the NASA Glenn Research Center was used to characterize various microstructural and flaw conditions in SiC/SiC (silicon carbide fiber in silicon carbide matrix) and C/SiC (carbon fiber in silicon carbide matrix) CMC samples.

Roth, Don J.↗
DOE OSTI2024

A New Simplified Discrete Fracture Model for Shearing of Intersecting Fractures and Faults

Abstract Shearing of fractures and faults is important because it can result in permeability change or even induce seismicity—both are keys for efficient and safe energy recovery and storage in Earth systems. Quantitative analysis of shearing of intersecting fractures and faults is challenging because it can involve dynamic frictional contacts that are complicated by deformation of the rock matrix. To predict the shearing of intersecting fractures/faults, we attempt to answer the question of how intersections impact the shearing of a fracture network and whether we can simplify the description as compared to classical discrete fracture network (DFN) models. To answer these questions, we conducted a series of numerical simulations on scenarios for variable numbers of intersecting fractures. All these examples yield consistent results: the results of using DFNs are consistent with those of using hypothetical major paths. This leads to a new model, which we name simplified discrete fracture network model , to analyze shearing of intersecting fractures/faults using major path(s). We found that the intersections of fractures do not fundamentally change the shearing of two intersecting fractures if the intersecting angles are small. Furthermore, increasing the number of fractures/faults may relax the stress as more fractures/faults become available for shearing and distributing the stress. The simplified DFN model, which can capture efficiently the shearing behavior of each major paths from a large number of intersecting fractures/faults, will be a promising conceptual model that is complementary to existing equivalent continuum and discrete fracture models to analyze shearing of intersecting fractures/faults.

58 GEOSCIENCES↗
DOE OSTI2020

A Particle-Based Conditional Sampling Scheme for the Simulation of Transport in Fractured Rock With Diffusion Into Stagnant Water and Rock Matrix

In situ experiments and field-scale characterization studies have pointed out that, in fractured crystalline media, groundwater flow is highly channelized. This implies that, at the scale of a single fracture, only part of the fracture surface area is in contact with flowing water, while the rest of in-plane water is essentially stagnant and can be accessed by solutes via molecular diffusion. Despite their importance for contaminant retention, to date, there are no numerical or analytical approaches that could be used to assess the implication of stagnant water zones on solute transport in realistic large-scale Discrete Fracture Network-based models. In this study, we present an efficient and flexible algorithm for the simulation of transport in fractured rock with diffusion into stagnant water and rock matrix. The algorithm is a generalization of a previously developed numerical framework for time domain particle tracking in sparsely fractured rock. The key of the generalization is that total time in fracture (τ f ) is first evaluated using a Monte Carlo sampling and then a second sampling is performed conditioned on τ f . The algorithm has been successfully validated against existing independent solutions and the implication of diffusion into stagnant water and secondary diffusion into the matrix has been assessed for a realistic modeling scenario. The results show that, due to diffusion into stagnant water, contaminants are more strongly retarded. This increased retention is more significant for sorbing species, as a larger number of sorption sites is accessible. A high sensitivity to the flowing channel/stagnant water zone geometry has also been observed.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2005

Ultrasonic Guided-Wave-Scan System Used to Characterize C-Enhanced Silicon Carbide Composite During Creep- Rupture Tests

Ceramic matrix composites (CMCs) are being developed for advanced aerospace propulsion applications in order to save weight, improve reuse capability, and increase performance. However, mechanical and environmental loads applied to CMCs can cause degradation in the form of discrete flaws and distributed microdamage that can play a significant role in reducing desirable physical properties. Categories of microdamage include fiber/matrix debonding (interface failure), matrix microcracking, fiber fracture and buckling, oxidation, and second-phase formation. Distributed microdamage in CMCs has proven difficult to characterize nondestructively because of the complex microstructure and macrostructure of these materials, and a recent study regarding the durability of a ceramic matrix composite discussed the requirement for improved nondestructive evaluation (NDE) methods for monitoring degradation in these materials.

Roth, Don J.↗
DOE OSTI2020

An embedded 3D fracture modeling approach for simulating fracture-dominated fluid flow and heat transfer in geothermal reservoirs

In this paper, we describe an efficient modeling approach, named embedded discrete fracture method (EDFM), for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology. This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while maintaining enough accuracy. Several numeral simulations are presented to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to the simulation of fractured geothermal reservoirs with both artificial and natural fractures.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗
NASA NTRS2001

Differential expression of neuroleukin in osseous tissues and its involvement in mineralization during osteoblast differentiation

Osteoblast differentiation is a multistep process that involves critical spatial and temporal regulation of cellular processes marked by the presence of a large number of differentially expressed molecules. To identify key functional molecules, we used differential messenger RNA (mRNA) display and compared RNA populations isolated from the defined transition phases (proliferation, matrix formation, and mineralization) of the MC3T3-E1 osteoblast-like cell line. Using this approach, a complementary DNA (cDNA) fragment was isolated and identified as neuroleukin (NLK), a multifunctional cytokine also known as autocrine motility factor (AMF), phosphoglucose isomerase (PGI; phosphohexose isomerase [PHI]), and maturation factor (MF). Northern analysis showed NLK temporal expression during MC3T3-E1 cell differentiation with a 3.5-fold increase during matrix formation and mineralization. Immunocytochemical studies revealed the presence of NLK in MC3T3-E1 cells as well as in the surrounding matrix, consistent with a secreted molecule. In contrast, the NLK receptor protein was detected primarily on the cell membrane. In subsequent studies, a high level of NLK expression was identified in osteoblasts and superficial articular chondrocytes in bone of 1-, 4-, and 8-month-old normal mice, as well as in fibroblasts, proliferating chondrocytes, and osteoblasts within a fracture callus. However, NLK was not evident in hypertrophic chondrocytes or osteocytes. In addition, treatment of MC3T3 cells with 6-phosphogluconic acid (6PGA; a NLK inhibitor) resulted in diminishing alkaline phosphatase (ALP) activity and mineralization in MC3T3-E1 cells, especially during the matrix formation stage of differentiating cells. Taken together, these data show specific expression of NLK in discrete populations of bone and cartilage cells and suggest a possible role for this secreted protein in bone development and regeneration.

NASA Discipline Musculoskeletal↗