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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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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.
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Quantitative Susceptibility Mapping (QSM) Algorithms: Mathematical Rationale and Computational Implementations.

Youngwook Kee1, Zhe Liu2, Liangdong Zhou1

  • 1Department of Radiology, Weill Cornell Medical College, New York, USA.

IEEE Transactions on Bio-Medical Engineering
|September 9, 2017
PubMed
Summary
This summary is machine-generated.

Quantitative susceptibility mapping (QSM) addresses MRI inverse problems with noisy data. Advanced algorithms, including Bayesian methods and preconditioning, improve artifact reduction and efficiency for better tissue susceptibility mapping.

Keywords:
Bayes methodsInverse problemsKernelMagnetic resonance imagingMagnetic susceptibilityPartial differential equationsResource description framework

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Area of Science:

  • Medical Imaging
  • Computational Physics
  • Biomedical Engineering

Background:

  • Quantitative susceptibility mapping (QSM) is crucial for solving the magnetic field-to-magnetization inverse problem in MRI.
  • QSM deals with noisy and incomplete field data, necessitating sophisticated algorithms to address its ill-posed nature.

Purpose of the Study:

  • To review sophisticated algorithms for quantitative susceptibility mapping (QSM).
  • To discuss challenges in QSM, including artifact reduction and computational efficiency.

Main Methods:

  • The forward problem is modeled using integral forms or partial differential equations (PDEs).
  • Bayesian maximum a posteriori (MAP) estimation is employed, incorporating morphological and biomedical priors.
  • Gradient-based optimization algorithms are used for robust computation of convex cost functions.
  • Prior knowledge-based preconditioners are utilized to accelerate Bayesian QSM and reduce shadow artifacts.

Main Results:

  • Algorithmic strategies are reviewed to mitigate streaking and shadow artifacts inherent in QSM.
  • Bayesian QSM, enhanced with priors, offers robust solutions and improved artifact reduction.
  • Preconditioning techniques demonstrate potential for accelerating QSM and increasing shadow reduction effectiveness.

Conclusions:

  • Sophisticated algorithms are essential for accurate QSM from noisy MRI data.
  • Bayesian methods and preconditioning represent promising avenues for improving QSM accuracy and efficiency.
  • Further research into preconditioning is needed to fully analyze its impact on QSM performance.