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Optimal MR Pulse Sequence Design for Tissue Density and Field Inhomogeneity Estimation

Explore the use of optimization methods for tissue density estimation and field inhomogeneity mapping in medical imaging. Prototype development, objective formulation, clinical applications, numerical experiments, and future work covered. Collaborative research from Advanced Optimization Lab, McMaster University.

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Optimal MR Pulse Sequence Design for Tissue Density and Field Inhomogeneity Estimation

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  1. Optimal MR Pulse Sequence Design forTissue Density and Field Inhomogeneity Estimation Zhuo Zheng Advanced Optimization Lab, McMaster University Joint work with Prof. Christopher Anand and Prof. Tamas Terlaky

  2. Motivation • Tissue density: segmentation v.s. estimation. • Field mapping in order to eliminate inhomogeneities. • Optimization applied to medical imaging area (Multidisciplinary in nature). • Scientific evidence for clinical applications.

  3. Tissue Density Estimation Prototype • For a sample voxel: Tissue types Signals

  4. Pulse Sequence (Steady-State Free Precession) • Fast scanning, high resolution and good SNR. • Tissue Properties Design Variables • The dynamic system satisfies: • Therefore:

  5. Model Components • Based on the physical mechanisms, we have:

  6. Imaging • We have • The transformation from tissue densities to measurements:

  7. Objective and Formulation • Unbiased maximum likelihood estimator: • Error given by , white noise • Objective: Choose design variables so that the error in the reconstructed tissue densities is minimized:

  8. SDO Problem • Applying Singular Value Decomposition:

  9. A Clinical Application • Carotid artery tissue densities estimation • We reconstruct the tissue densities based on the optimal solutions obtained by our formulation.

  10. What if field inhomogeneities exist? • Signal measurements become: • Least squares formulation: Numerical results show that it does work !

  11. Numerical Experiment • We discretize the continuous magnetic field to perform our experiment • We simulate the field inhomogeneity for a random pixel

  12. A priori Information • The field inhomogeneity term : smooth and continuous (Maxwell’s Equation). • Tissue density: piece-wise differentiable • The original image would be the one with the least total variation

  13. Total Variation Based Model

  14. Subproblem for field inhomogeneity estimation

  15. Numerical Results

  16. Conclusions and Future Work • An innovative approach for tissue densities estimation by taking into account many parameters using optimization methods. • An integrated model to estimate both tissue densities and field inhomogeneities. • Many interesting applications of our method, such as brain development studies in infants. • Develop an embedded solver and work with clinical partners.

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