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Related Concept Videos

Finding Volume Using Cross-Sectional Area01:24

Finding Volume Using Cross-Sectional Area

For solids whose cross-sectional areas vary in a predictable way, volume can be determined by integrating these areas along an axis perpendicular to the slices. This approach is particularly useful for polyhedral solids, where classical geometric formulas may not be immediately applicable. A tetrahedron provides a clear example of how cross-sectional integration can be applied to a three-dimensional object with continuously changing geometry.Consider a tetrahedron with height h and a base that...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Volume of Distribution01:20

Volume of Distribution

The apparent volume of distribution (Vd) is a crucial pharmacokinetic parameter representing the hypothetical body fluid volume into which a drug disperses. It is calculated based on the total amount of drug in the body (estimated from the administered dose and bioavailability) divided by the plasma drug concentration. The total amount of drug in the body does not directly refer to the dose given but is derived by accounting for absorption, distribution, metabolism, and excretion processes.
Applications of the Ideal Gas Law: Molar Mass, Density, and Volume03:43

Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, suggests that the volume of a given quantity of gas and the number of moles in a given volume of gas vary with changes in pressure and temperature. At standard temperature and pressure, or STP (273.15 K and 1 atm), one mole of an ideal gas (regardless of its identity) has a volume of about 22.4 L — this is referred to as the standard molar volume.
Problem Solving: Volume01:13

Problem Solving: Volume

The volume of a fuel tank mounted on the wing of a jet aircraft can be modeled using the concept of solids of revolution. In this case, the tank is formed by rotating a two-dimensional region, defined by a mathematical function, about the x-axis. The region extends along the axis from zero to two meters, and the resulting three-dimensional shape is symmetric about the axis of rotation. Because the boundary curve lies directly against the axis, the disk method is an appropriate technique for...
Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions03:03

Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each gas in a mixture exerts the same pressure that it would exert if it were present alone in the container. The pressure exerted by each individual gas in a mixture is called its partial pressure.

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Related Experiment Video

Updated: Jun 1, 2026

A Workflow for Lipid Nanoparticle (LNP) Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models (SVEM)
13:54

A Workflow for Lipid Nanoparticle (LNP) Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models (SVEM)

Published on: August 18, 2023

Efficient Volume Exploration Using the Gaussian Mixture Model.

Yunhai Wang, Wei Chen, Jian Zhang

    IEEE Transactions on Visualization and Computer Graphics
    |June 15, 2011
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new volume exploration method using Gaussian mixture models (GMM) to simplify transfer function design. This approach aids users in discovering features in volumetric data more efficiently.

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    Quantifying Mixing using Magnetic Resonance Imaging
    07:33

    Quantifying Mixing using Magnetic Resonance Imaging

    Published on: January 25, 2012

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    Last Updated: Jun 1, 2026

    A Workflow for Lipid Nanoparticle (LNP) Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models (SVEM)
    13:54

    A Workflow for Lipid Nanoparticle (LNP) Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models (SVEM)

    Published on: August 18, 2023

    Quantifying Mixing using Magnetic Resonance Imaging
    07:33

    Quantifying Mixing using Magnetic Resonance Imaging

    Published on: January 25, 2012

    Area of Science:

    • Computer Graphics
    • Data Visualization
    • Scientific Computing

    Background:

    • Multidimensional transfer functions are crucial for volume data exploration but designing them is challenging.
    • Current methods often involve a difficult trial-and-error process for users.

    Purpose of the Study:

    • To develop a novel, user-friendly volume exploration scheme for efficient feature discovery in volumetric data.
    • To automate initial feature separation and facilitate interactive manipulation of transfer functions.

    Main Methods:

    • Modeling feature space using Gaussian mixture models (GMM) for automatic feature separation.
    • Mapping GMM components to elliptical transfer functions (ETFs) for pre-integrated volume rendering.
    • Utilizing an incremental GMM estimation algorithm for time-varying data exploration.

    Main Results:

    • Automatic initial feature separation via GMM estimation.
    • Direct mapping of Gaussians to ETFs, enabling fast volume rendering.
    • Coherent, user-guided exploration of time-varying datasets with adjustable ETFs.
    • Interactive performance and scalability demonstrated via GPU implementation.

    Conclusions:

    • The proposed GMM-based scheme simplifies transfer function design and enhances volume data exploration.
    • The approach effectively supports both static and time-varying volumetric datasets.
    • The method empowers users, even inexperienced ones, to discover features interactively.