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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

DNS of Flame Stabilization Dynamics of a Swirl-Stabilized Spray Burner Using Sustainable Aviation Fuels

Concern for emission reduction has motivated the development of new cost-effective alternative sustainable aviation fuels (SAFs). Drop-in SAFs with blends of the certified and the alternative fuels are beneficial because they do not require engine modifications for use in current aviation engines. Combustion characteristics are of particular concern when comparing a new fuel with Jet-A. Lean blow-off and flame stabilization have been identified to be governed by the fuel propensity to autoignition, i.e. derived cetane number. However, fundamental investigation is required to identify the impact of derived cetane number on the combustion mode of flame stabilization in a realistic combustor. The combustion mode has also a direct impact on turbulent combustion modeling closures. DNS simulations are performed in the low-Mach solver of the Pele Suite called PeleLMeX. Lagrangian multi-phase modeling is used to capture the liquid spray injection of Jet-A (reference fuel) and C1 as a representative of a low cetane number SAF. Adaptive Mesh Refinement (AMR) is used to enable a more efficient simulation of a more realistic domain size and embedded boundary treatment is used to model a bluff-body geometry. Local extinction and edge flame propagation were observed for both fuels. The edge flame propagation mode was quantified in terms of a Damkohler number defined as the ratio between progress variable reaction rate and its diffusive flux. Initial analysis suggests that a mixed mode combustion occurs for the edge flame propagation, with flame propagation assisted by ignition and autoignition co-existing for both Jet-A and C1 flames. The analysis of the extinction region shows a larger progress variable for Jet-A which can further increase the local displacement speed and present a faster reignition of the stoichiometric mixture fraction.

adaptive mesh refinement↗
DOE OSTI2025

A Computational Workflow of Elucidating Viral Impact on Mediating Microbial Response to In-situ Experimental Warming: Bridging microbial modeling to carbon and mineral modeling

Viruses are abundant in soils and shape microbial communities in ways that can potentially influence ecosystem processes, yet their contributions to carbon cycling and mineral transformations remain poorly understood. Here we present a multi-phase framework that links virus-host interactions to soil biogeochemistry by combining ecological simulations, genome- and community-scale metabolic modeling, and statistical and machine-learning analyses. We first calibrated microbial abundance profiles under explicit infection scenarios to capture how viral pressure alters community structure, then explored alternative interaction strategies, including kill-the-winner, piggyback-the-winner, and mixed lytic-lysogenic modes, through forward simulations. These ecological shifts were translated into metabolic consequences using exchange fluxes summarized into biologically meaningful categories, while integrated statistical and machine-learning screens elevated subtle but consistent signals. Application of this framework revealed that viral infections shift the balance between organic and inorganic fluxes, redirecting metabolism from diffuse organic transformations toward inorganic pools such as protons and CO 2 , directly linking viral regulation to respiration and soil carbon balance. The roll-up analysis also isolated perturbations in critical mineral ions, including magnesium, manganese, zinc, and copper, which serve as essential enzymatic cofactors. In piggyback-the-winner scenarios, uptake of these ions was strongly suppressed. Contrasting viral strategies produced distinct community structures and metabolic outcomes, from broad suppression under kill-the-winner dynamics to dramatic redistributions under high-lytic and high-gain lysogenic regimes that collapsed vulnerable microbial populations while promoting opportunists. Together, these results provide a tractable path to trace viral perturbations from host abundance shifts to metabolic flux adjustments and ecosystem-scale processes, offering a practical way to include viruses in earth system models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Liquid Hydrogen Tank Chill and No-Vent Fill Prediction using Computational Fluid Dynamics

Cryogenic tank chill and fill is an important cryogenic fluid management technology that supports and enables many of NASA’s long-duration space missions. For no-vent fill, the receiver tank pressure remains below the supply tank pressure during the entire duration of the fill so that the tank does not require venting. This is especially advantageous for tank fill operations in low gravity where the position of the liquid is not always known and venting the tank may cause loss of propellant by venting liquid. In lieu of expensive tests conducted on-orbit, accurate computational models capable of predicting receiver tank pressure during cryogenic propellant tank fill may be used to reduce system and propellant mass as well as mission risk. However, these numerical models must be validated or anchored to test data. This study presents computational fluid dynamics (CFD) models with conjugate heat transfer that are used to predict a liquid hydrogen tank chill and no-vent fill ground test conducted at Lewis Research Center (now Glenn Research Center) in 1991. The specific test case chosen for model validation implemented an upward-facing jet near the bottom of a cylindrical 34-liter tank. CFD predictions are compared to experimental measurements of tank pressure, fill level, and wall temperature. The CFD results show reasonable agreement to the test data but overpredict the pressure collapse near the end of the fill despite the liquid jet penetrating the liquid-vapor interface.

Computational Fluid Dynamics↗
NASA NTRSDate not supplied

Liquid Hydrogen Tank Chill and No-Vent Fill Prediction Using Computational Fluid Dynamics

Cryogenic tank chill and fill is an important cryogenic fluid management (CFM) technology that supports and enables many of NASA’s long-duration space missions. For no-vent fill, the receiver tank pressure remains below the supply tank pressure during the entire duration of the fill so that the tank does not require venting. This is especially advantageous for tank fill operations in low gravity where the position of the liquid is not always known and venting the tank may cause loss of propellant by venting liquid. In lieu of expensive tests conducted on-orbit, accurate computational models capable of predicting receiver tank pressure during cryogenic propellant tank fill may be used to reduce system and propellant mass as well as mission risk. However, these numerical models must be validated or anchored to test data. This study presents a computational fluid dynamics (CFD) model with conjugate heat transfer that is used to predict a liquid hydrogen tank chill and no-vent fill ground test conducted at Lewis Research Center (now Glenn Research Center) in 1991. The specific test case chosen for model validation implemented an upward-facing jet near the bottom of a cylindrical 34 liter tank. CFD predictions are compared to experimental measurements of tank pressure, fill level, fluid temperatures, and wall temperatures. The CFD results show reasonable agreement to the test data but overpredict the pressure collapse near the end of the fill despite the liquid jet penetrating the liquid-vapor interface. Several sensitivity studies are considered due to notable uncertainties in the experiment.

Computational Fluid Dynamics↗
DOE OSTI2025

Numerical simulations of liquid jetting with solid inclusions

The dynamics of finite-sized particles in fluids, and their influence on the overall flow, are of great interest across several industrial, environmental, and medical fields. In the context of inkjet printing, the presence of solid inclusions can be either intentional, as in additive manufacturing, or unintentional, as in standard printing processes. These inclusions can strongly impact the jetting process, causing effects such as jet asymmetry, bubble entrapment, and the formation of satellite droplets. Understanding and controlling particle behavior is therefore essential, particularly to predict how and when particles are ejected over multiple jetting cycles. It is therefore critical to develop reliable models that allow for a deeper understanding of the complex interplay between particle and fluid during the whole printing process. To address this, we present a tailored implementation of the Color-Gradient multicomponent Lattice Boltzmann Method for fully resolved three-dimensional (3D) simulations of multicycle liquid jetting with particles. Our method supports realistic parameter settings aligned with industrial inkjet systems, and we provide both qualitative and quantitative validation against experimental data. Additionally, we introduce a simplified model based on the Stokes drag law, in which solid particles are represented as point particles and do not influence the fluid flow. Despite this limitation, the model offers a computationally efficient means to explore the vast parameter space typically encountered in industrial applications, allowing, e.g., identifying critical ejection regions and estimating the number of cycles required for particle release. These qualitative insights are valuable for guiding and complement fully two-way coupled simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

An integrated approach to derive relative permeability from capillary pressure

Surface tension affects all aspects of fluid flow in porous media. Through measurements of surface tension interaction under multiphase conditions, a relative permeability curve can be determined. Relative permeability is a numerical description of the interaction between two or more fluids and the porous media. It is a critical parameter for various tools that characterize subsurface multiphase flow systems, such as numerical simulation for carbon sequestration, oil and gas development, and groundwater contamination remediation. Therefore, it is critical to get a good statistical distribution of relative permeability in the porous media under study. Empirical formula for determining relative permeability from capillary pressure are already well established but do not provide the needed flexibility that is required to match laboratory-derived relative permeability curves. By expanding the existing methods for calculating relative permeability from capillary pressure data, it is possible to create both two and three-phase relative permeability curves. Mercury intrusion capillary pressure (MICP) data from the Morrow 'B' Sandstone coupled with interfacial tension and contact angle measurements were used to create a suite of relative permeability curves. Furthermore, these curves were then calibrated to a small sample of existing laboratory curves to elucidate common fitting parameters for the formation that were then used to create relative permeability curves from MICP data that does not have an associated laboratory-measured relative permeability curve.

58 GEOSCIENCES↗
DOE OSTI2025

The influence of cooling rates on strain phase diagrams and domain structures of ferroelectric thin films: A case study of PbTiO 3

Strain engineering has been established as an effective approach to control phase equilibria, domain configurations, and functional properties of ferroelectric thin films. Temperature-strain phase diagrams have been used as powerful tools for providing insights into strain engineering. However, almost all existing phase diagrams established using the phase-field approach assume quenching conditions without considering actual cooling rates during the post-deposition annealing process of ferroelectric thin films. Within this work, we systematically investigate the influence of cooling rates on domain structures and the strain-phase diagram of ferroelectric thin films using phase-field simulations, taking PbTiO 3 thin films as a model system. We found that both the position of phase boundaries in the strain phase diagrams and the domain morphology are significantly influenced by the cooling rates. It is revealed that while the paraelectric-ferroelectric phase boundary remains invariant, the phase boundaries between single-phase and multi-phase regions tend to shift toward the corresponding multi-phase region as the cool rate reduces. Slow cooling generally leads to more ordered domain structures with increased domain size. Using the obtained equilibrium domain structures, we calculated effective thermal conductivities and found significant variations that can be tuned by the cooling rates. In conclusion, this work reveals an underexplored yet critical impact of cooling rates on phase equilibria and domain structures in ferroelectric thin films, which may inspire further fine-tuning of domains and domain walls in low-dimensional ferroelectrics for multifunctional applications.

Domain structures↗
DOE OSTI2026

BMINN: Learning chemical potentials and parameters from voltage data for multi-phase battery modeling

Free-energy landscapes and chemical potentials govern the dynamics of phase transitions, transport, and stability in functional materials, yet they remain experimentally inaccessible under realistic operating conditions. Here we introduce a Bayesian model-integrated neural network (BMINN) that embeds physics-based formulations of non-autonomous partial differential-algebraic equations into probabilistic learning. This approach reconstructs hidden thermodynamics directly from macroscopic current-voltage data, providing quantitative access to metastable states, staging transitions, and energy barriers without synchrotron probes. Demonstrated on lithium-graphite electrodes, BMINN recovers full Gibbs free-energy landscapes with fidelity validated against operando X-ray diffraction. The framework generalizes across dynamical regimes, enabling accurate voltage prediction, internal state estimation, and inference of governing parameters. Beyond batteries, BMINN exemplifies a broadly applicable strategy for learning missing physics in multiphase, non-equilibrium systems, offering a new pathway to uncover hidden thermodynamic functions across condensed matter and materials physics.

25 ENERGY STORAGE↗
DOE OSTI2025

Phase-field modeling of diffusion bonding in 316H stainless steel: Impact of processing conditions on grain morphology and bonding quality

A novel multi-phase, multi-component phase‐field model is presented to study the diffusion bonding of 316H stainless steel. Combined with targeted experimental investigations, this model simulates the bond-growth process and predicts the bonding quality. Unlike previous models, our approach captures the simultaneous evolution of voids and grain structures, while quantifying bonding quality using defined bonding ratio. A comprehensive analysis of bond process control is performed by changing temperature, pressure and surface roughness observing the resulting bond structure, which is consistent with experimental observations and analytical predictions. Temperature is determined to be the dominant factor, with the transition from a flat to a robust bond occurring between 1000 °C and 1050 °C. At the ideal bonding temperature of 1050 °C, a surface roughness exceeding 0.6 μm or an applied stress below 4 MPa results in poor bonding quality. Beyond this, higher pressures and smoother surfaces reduce void size, accelerate void shrinkage, and lead to improved bond integrity. This diffuse-interface model can be extended to other material systems if supplied with appropriate thermodynamic and kinetic data. In conclusion, this makes it an effective modeling platform for optimizing high-temperature diffusion bonding and developing reliable bonded components such as compact heat exchangers.

Diffusion bonding↗
DOE OSTI2025

FreeMHD: Validation and verification of the open-source, multi-domain, multi-phase solver for electrically conductive flows

The extreme heat fluxes in the divertor region of tokamaks may require an alternative to solid plasma-facing components, for the extraction of heat and the protection of the surrounding walls. Flowing liquid metals are proposed as an alternative, but raise additional challenges that require investigation and numerical simulations. Free surface designs are desirable for plasma-facing components, but steady flow profiles and surface stability must be ensured to limit undesirable interactions with the plasma. Previous studies have mainly used steady-state, 2D, or simplified models for internal flows and have not been able to adequately model free-surface liquid metal (LM) experiments. Therefore, FreeMHD has been recently developed as an open-source magnetohydrodynamics (MHD) solver for free-surface electrically conductive flows subject to a strong external magnetic field. The FreeMHD solver computes incompressible free-surface flows with multi-region coupling for the investigation of MHD phenomena involving fluid and solid domains. The model utilizes the finite-volume OpenFOAM framework under the low magnetic Reynolds number approximation. FreeMHD is validated using analytical solutions for the velocity profiles of closed channel flows with various Hartmann numbers and wall conductance ratios. Next, experimental measurements are then used to verify FreeMHD, through a series of cases involving dam breaking, 3D magnetic fields, and free-surface LM flows. These results demonstrate that FreeMHD is a reliable tool for the design of LM systems under free surface conditions at the reactor scale. Furthermore, it is flexible, computationally inexpensive, and can be used to solve fully 3D transient MHD flows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A method for crystallographic mapping of an alpha-beta titanium alloy with nanometre resolution using scanning precession electron diffraction and open-source software libraries

An approach for the crystallographic mapping of two-phase alloys on the nanoscale using a combination of scanned precession electron diffraction and open-source python libraries is introduced in this paper. This method is demonstrated using the example of a two-phase α/β titanium alloy. The data were recorded using a direct electron detector to collect the patterns, and recently developed algorithms to perform automated indexing and analyse the crystallography from the results. Very high-quality mapping is achieved at a 3 nm step size. The results show the expected Burgers orientation relationships between the α laths and β matrix, as well as the expected misorientations between α laths. A minor issue was found that one area was affected by 180° ambiguities in indexing occur due to this area being aligned too close to a zone axis of the α with twofold projection symmetry (not present in 3D) in the zero-order Laue Zone, and this should be avoided in data acquisition in the future. Nevertheless, this study demonstrates a good workflow for the analysis of nanocrystalline two- or multi-phase materials, which will be of widespread use in analysing two-phase titanium and other systems and how they evolve as a function of thermomechanical treatments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

NEXT Generation Energy Technologies for Connected and Automated On-Road Vehicles (NEXTCAR Phase I & II)

The Ohio State University’s ARPA-E NEXTCAR project was a multi-phase, multi-year research, development, and demonstration program focused on improving the energy efficiency of connected and automated vehicles (CAVs). The team developed and validated advanced vehicle motion and powertrain control algorithms that coordinate propulsion and automation systems to optimize energy use. Key technologies included Dynamic Skip Fire engine control, predictive eco-driving functions such as Eco-Approach and Departure (Eco-AND) and Eco-Adaptive Cruise Control (Eco-ACC), and powertrain-agnostic optimization frameworks for hybrid, plug-in hybrid, and battery electric vehicles. The project successfully demonstrated up to 30% energy-efficiency improvement during real-world testing at the Transportation Research Center and the American Center for Mobility. The outcomes provide a foundation for scalable, cost-effective deployment of energy-optimized CAV technologies across the automotive industry.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Development and Application of High-Fidelity Models for Heterogeneous CO2 Frost Formation

Carbon America has developed a cryogenic carbon capture technology ("FrostCC") that separates CO2 from point source emissions by solidifying it at cold temperatures through preferential desublimation. Cooling is achieved through a series of interlinked compression, heat exchange, and expansion operations. In the current system, frosting of CO2 happens in heat exchangers, followed by CO2 recovery in a separate extraction step. In this work, multiphysics computational fluid dynamics (CFD) models are developed and validated for compressible and low Mach flows to simulate the formation of solid CO2 in flue gas flowing in a heat exchanger geometry. The models track the mass transfer rate of CO2 from gas phase to solid phase, heat released from desublimation, and the evolution of the solid CO2 layer. Simulations are used to answer scientific questions related to the angle of heat exchanger pipes, where buoyancy effects from flow velocity and pipe orientation influence CO2 frosting. Results show that upwardly angled pipes produce notably different flow structures compared to horizontal or vertical configurations, and that carbon capture efficiency correlates with buoyancy effects for pipe angles within plus or minus 23 degrees of horizontal.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Analysis and design of a high power, digitally-controlled spacecraft power system

The progress to date on the analysis and design of a high power, digitally controlled spacecraft power system is described. Several battery discharger topologies were compared for use in the space platform application. Updated information has been provided on the battery voltage specification. Initially it was thought to be in the 30 to 40 V range. It is now specified to be 53 V to 84 V. This eliminated the tapped-boost and the current-fed auto-transformer converters from consideration. After consultations with NASA, it was decided to trade-off the following topologies: (1) boost converter; (2) multi-module, multi-phase boost converter; and (3) voltage-fed push-pull with auto-transformer. A non-linear design optimization software tool was employed to facilitate an objective comparison. Non-linear design optimization insures that the best design of each topology is compared. The results indicate that a four-module, boost converter with each module operating 90 degrees out of phase is the optimum converter for the space platform. Large-signal and small-signal models were generated for the shunt, charger, discharger, battery, and the mode controller. The models were first tested individually according to the space platform power system specifications supplied by NASA. The effect of battery voltage imbalance on parallel dischargers was investigated with respect to dc and small-signal responses. Similarly, the effects of paralleling dischargers and chargers were also investigated. A solar array and shunt model was included in these simulations. A model for the bus mode controller (power control unit) was also developed to interface the Orbital replacement Unit (ORU) model to the platform power system. Small signal models were used to generate the bus impedance plots in the various operating modes. The large signal models were integrated into a system model, and time domain simulations were performed to verify bus regulation during mode transitions. Some changes have subsequently been incorporated into the models. The changes include the use of a four module boost discharger, and a new model for the mode controller, which includes the effects of saturation. The new simulations for the boost discharger show the improvement in bus ripple that can be achieved by phase-shifted operation of each of the boost modules.

Lee, F. C.↗
NASA NTRS1997

Comparison of Orbiter PRCS Plume Flow Fields Using CFD and Modified Source Flow Codes

The Space Shuttle Orbiter will use Reaction Control System (RCS) jets for docking with the planned International Space Station (ISS). During approach and backout maneuvers, plumes from these jets could cause high pressure, heating, and thermal loads on ISS components. The object of this paper is to present comparisons of RCS plume flow fields used to calculate these ISS environments. Because of the complexities of 3-D plumes with variable scarf-angle and multi-jet combinations, NASA/JSC developed a plume flow-field methodology for all of these Orbiter jets. The RCS Plume Model (RPM), which includes effects of scarfed nozzles and dual jets, was developed as a modified source-flow engineering tool to rapidly generate plume properties and impingement environments on ISS components. This paper presents flow-field properties from four PRCS jets: F3U low scarf-angle single jet, F3F high scarf-angle single jet, DTU zero scarf-angle dual jet, and F1F/F2F high scarf-angle dual jet. The RPM results compared well with plume flow fields using four CFD programs: General Aerodynamic Simulation Program (GASP), Cartesian (CART), Unified Solution Algorithm (USA), and Reacting and Multi-phase Program (RAMP). Good comparisons of predicted pressures are shown with STS 64 Shuttle Plume Impingement Flight Experiment (SPIFEX) data.

Rochelle, Wm. C.↗
NASA NTRS2000

Internet Technology on Spacecraft

The Operating Missions as Nodes on the Internet (OMNI) project has shown that Internet technology works in space missions through a demonstration using the UoSAT-12 spacecraft. An Internet Protocol (IP) stack was installed on the orbiting UoSAT-12 spacecraft and tests were run to demonstrate Internet connectivity and measure performance. This also forms the basis for demonstrating subsequent scenarios. This approach provides capabilities heretofore either too expensive or simply not feasible such as reconfiguration on orbit. The OMNI project recognized the need to reduce the risk perceived by mission managers and did this with a multi-phase strategy. In the initial phase, the concepts were implemented in a prototype system that includes space similar components communicating over the TDRS (space network) and the terrestrial Internet. The demonstration system includes a simulated spacecraft with sample instruments. Over 25 demonstrations have been given to mission and project managers, National Aeronautics and Space Administration (NASA), Department of Defense (DoD), contractor technologists and other decisions makers, This initial phase reached a high point with an OMNI demonstration given from a booth at the Johnson Space Center (JSC) Inspection Day 99 exhibition. The proof to mission managers is provided during this second phase with year 2000 accomplishments: testing the use of Internet technologies onboard an actual spacecraft. This was done with a series of tests performed using the UoSAT-12 spacecraft. This spacecraft was reconfigured on orbit at very low cost. The total period between concept and the first tests was only 6 months! On board software was modified to add an IP stack to support basic IP communications. Also added was support for ping, traceroute and network timing protocol (NTP) tests. These tests show that basic Internet functionality can be used onboard spacecraft. The performance of data was measured to show no degradation from current approaches. The cost to implement is much less than current approaches due to the availability of highly reliable and standard Internet tools. Use of standard Internet applications onboard reduces the risk of obsolescence inherent in custom protocols due to extremely wide use across all domains. These basic building blocks provide the framework for building onboard software to support direct user communication with payloads including payload control. Other benefits are payload to payload communication from dissimilar spacecraft, constellations of spacecraft, and reconfigurability on orbit. This work is funded through contract with the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC).

Rash, James↗
NASA NTRS2004

Gas-liquid Phase Distribution and Void Fraction Measurements Using the MRI

We used a permanent-magnet MRI system to estimate the integral and spatially- and/or temporally-resolved void-fraction distributions and flow patterns in gas-liquid two-phase flows. Air was introduced at the bottom of the stagnant liquid column using an accurate and programmable syringe pump. Air flow rates were varied between 1 and 200 ml/min. The cylindrical non-conducting test tube in which two-phase flow was measured was placed in a 2.67 kGauss MRI with MRT spectrometer/imager. Roughly linear relationship has been obtained for the integral void-fraction, obtained by volume-averaging of the spatially-resolved signals, and the air flow rate in upward direction. The time-averaged spatially-resolved void fraction has also been obtained for the quasi-steady flow of air in a stagnant liquid column. No great accuracy is claimed as this was an exploratory proof-of-concept type of experiment. Preliminary results show that MRI a non-invasive and non-intrusive experimental technique can indeed provide a wealth of different qualitative and quantitative data and is especially well suited for averaged transport processes in adiabatic and diabatic multi-phase and/or multi-component flows.

Daidzic, N. E.↗
NASA NTRS2017

VESsel GENeration Analysis (VESGEN): Innovative Vascular Mappings for Astronaut Exploration Health Risks and Human Terrestrial Medicine

Currently, astronauts face significant health risks in future long-duration exploration missions such as colonizing the Moon and traveling to Mars. Numerous risks include greatly increased radiation exposures beyond the low earth orbit (LEO) of the ISS, and visual and ocular impairments in response to microgravity environments. The cardiovascular system is a key mediator in human physiological responses to radiation and microgravity. Moreover, blood vessels are necessarily involved in the progression and treatment of vascular-dependent terrestrial diseases such as cancer, coronary vessel disease, wound-healing, reproductive disorders, and diabetes. NASA developed an innovative, globally requested beta-level software, VESsel GENeration Analysis (VESGEN) to map and quantify vascular remodeling for application to astronaut and terrestrial health challenges. VESGEN mappings of branching vascular trees and networks are based on a weighted multi-parametric analysis derived from vascular physiological branching rules. Complex vascular branching patterns are determined by biological signaling mechanisms together with the fluid mechanics of multi-phase laminar blood flow.

astronaut↗