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Related Concept Videos

Multicompartment Models: Overview01:14

Multicompartment Models: Overview

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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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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.
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Compartment Models: Single-Compartment Model01:14

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The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...
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Compartment Models: Two-Compartment Model01:20

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The two-compartment model divides the body into central and peripheral compartments to account for varying blood perfusion rates among organs and tissues, affecting drug distribution. The central compartment includes blood and highly perfused tissues with rapid drug distribution, while the peripheral compartment contains tissues with slower drug distribution. After a single IV bolus dose, the drug concentration is high in plasma and low in tissues. The drug distribution between compartments...
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Three-Compartment Open Model01:06

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The three-compartment open model is a pharmacokinetic model used to describe the distribution and elimination of drugs following extravascular administration. It comprises a central compartment representing the plasma and two peripheral compartments. The highly perfused peripheral compartment represents organs and tissues with a rich blood supply, such as the liver, kidneys, and lungs. The scarcely perfused peripheral compartment represents tissues with lower blood supply, such as adipose...
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Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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A mixed virtual element method for Biot's consolidation model.

Feng Wang1, Mingchao Cai2, Gang Wang3

  • 1Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China.

Computers & Mathematics with Applications (Oxford, England : 1987)
|July 21, 2023
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Summary
This summary is machine-generated.

This study introduces a weak virtual element method for poroelasticity problems. The new method achieves optimal convergence rates for both mesh size and time step, offering robust solutions for complex simulations.

Keywords:
Poroelasticity equationsVirtual element methodsWeak Galerkin

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Area of Science:

  • Computational mechanics
  • Geophysics
  • Applied mathematics

Background:

  • Poroelasticity problems are crucial in geophysics and engineering.
  • Existing numerical methods face challenges with complex geometries and heterogeneous materials.
  • Efficient and accurate computational techniques are needed for simulating fluid flow and solid deformation.

Purpose of the Study:

  • To develop and analyze a novel weak virtual element method (WVEM) for the three-field poroelasticity problem.
  • To discretize poroelasticity equations on general polytopal meshes.
  • To establish the convergence properties of the proposed numerical scheme.

Main Methods:

  • The weak virtual element method is employed for spatial discretization.
  • Low-order virtual elements approximate flux velocity and pressure.
  • Higher-order virtual elements with tangential polynomials discretize elastic displacement.
  • Backward Euler scheme is used for time discretization.

Main Results:

  • The fully discrete scheme achieves a convergence order of 1 with respect to mesh size.
  • The time step also yields a convergence order of 1.
  • The hidden constants in the convergence analysis are independent of problem parameters.
  • Numerical experiments validate the theoretical convergence rates.

Conclusions:

  • The proposed weak virtual element method is effective for solving the three-field poroelasticity problem.
  • The method demonstrates optimal convergence, providing a reliable tool for computational geophysics and engineering.
  • The technique is suitable for complex polytopal meshes, enhancing simulation capabilities.