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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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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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Updated: Mar 5, 2026

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Parameter estimation using weighted total least squares in the two-compartment exchange model.

Anders Garpebring1, Tommy Löfstedt1

  • 1Department of Radiation Sciences, Umeå University, Umeå, Sweden.

Magnetic Resonance in Medicine
|March 29, 2017
PubMed
Summary
This summary is machine-generated.

A new weighted total least squares (WTLS) estimator improves accuracy for the linearized two-compartment exchange model by accounting for correlated noise. While computationally more intensive than linear least squares (LLS), WTLS remains faster than nonlinear least squares (NLLS).

Keywords:
dynamic contrast-enhanced magnetic resonance imagingparameter estimationtwo-compartment exchange modelweighted total least squares

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Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Biomedical Engineering
  • Quantitative Analysis

Background:

  • The linearized two-compartment exchange model is crucial for parameter estimation in various physiological studies.
  • Linear least squares (LLS) offers speed but can be biased by correlated noise in the model's system matrix.
  • Accurate parameter estimation is vital for reliable interpretation of MRI data.

Purpose of the Study:

  • To develop a novel estimator for the linearized two-compartment exchange model that addresses bias from correlated noise.
  • To introduce an estimator that accounts for noise within the system matrix, improving parameter estimation accuracy.

Main Methods:

  • Developed a weighted total least squares (WTLS) estimator to incorporate system matrix noise.
  • Conducted simulations to compare the accuracy and precision of WTLS against linear least squares (LLS) and nonlinear least squares (NLLS) estimators.
  • Evaluated performance across different signal-to-noise ratios (SNR).

Main Results:

  • The WTLS estimator significantly improved accuracy compared to LLS, achieving levels comparable to NLLS.
  • WTLS demonstrated increased computational time over LLS but remained faster than NLLS.
  • Similar precision was observed across all methods at high SNR; results were inconclusive at low SNR.

Conclusions:

  • The proposed WTLS method offers enhanced accuracy for the linearized two-compartment exchange model compared to LLS.
  • This accuracy improvement comes with a moderate increase in computational cost.
  • WTLS presents a viable alternative for accurate parameter estimation in MRI, balancing speed and precision.