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Mesh Analysis

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...

Mesh Analysis with Current Sources

Mesh Analysis with Current Sources

Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law (KVL)...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...

Mesh Analysis for AC Circuits

Mesh Analysis for AC Circuits

In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...

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Related Experiment Video

Updated: Jul 8, 2026

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

Published on: April 18, 2018

A dual mesh scheme for finite element based reconstruction algorithms.

K D Paulsen¹, P M Meaney, M J Moskowitz

¹Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH.

IEEE Transactions on Medical Imaging

|January 1, 1995

Summary

This summary is machine-generated.

The dual mesh method enhances microwave imaging by using a dense mesh for electric fields and a less dense mesh for dielectric properties. This improves temperature estimation in biological tissues during therapies like hyperthermia.

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Last Updated: Jul 8, 2026

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Area of Science:

* Computational electromagnetics
* Biomedical imaging
* Applied physics

Background:

* Microwave imaging offers potential for thermal estimation in biological tissues.
* Temperature variations in tissue dielectric properties are key to monitoring therapies like hyperthermia.
* Finite element (FE) methods are computationally intensive for accurately representing rapidly varying electric fields.

Purpose of the Study:

* To introduce and evaluate a dual mesh scheme for microwave imaging using the hybrid element (HE) method.
* To improve the reconstruction of complex wavenumbers (k(2)) and tissue properties.
* To demonstrate the effectiveness of the dual mesh approach compared to single mesh methods in FE-based imaging.

Main Methods:

* Employed the hybrid element (HE) method with a dual mesh strategy for 2-D TM polarization microwave imaging.
* Utilized a uniformly dense mesh for calculating electric fields and a non-uniform, less dense mesh for representing k(2) distributions.
* Tested the method on dielectric distributions in both large and small problem scales.

Main Results:

* The dual mesh scheme significantly improved reconstructed images of tissue properties compared to a single mesh approach.
* Demonstrated flexibility in handling complex dielectric distributions and varying mesh densities.
* Showcased the method's capability in recovering smoother property profiles from rapidly varying physical quantities.

Conclusions:

* The dual mesh method is critical for FE-based microwave imaging, particularly for biological tissues.
* This approach enhances accuracy in deducing temperature distributions by effectively imaging dielectric property changes.
* The dual mesh strategy offers a more efficient and accurate solution for complex imaging problems in biomedical applications.