zhuo zheng advanced optimization lab, mcmaster university
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Optimal MR Pulse Sequence Design for Tissue Density and Field Inhomogeneity Estimation. Zhuo Zheng Advanced Optimization Lab, McMaster University Joint work with - PowerPoint PPT PresentationTRANSCRIPT
Optimal MR Pulse Sequence Design
for Tissue Density and Field Inhomogeneity Estimation
Zhuo ZhengZhuo Zheng Advanced Optimization Lab, McMaster University Advanced Optimization Lab, McMaster University
Joint work withJoint work with
Prof. Christopher Anand and Prof. Tamas TerlakyProf. Christopher Anand and Prof. Tamas Terlaky
Motivation
Tissue density: segmentation v.s.v.s. estimation.
Field mapping in order to eliminate inhomogeneities.
Optimization applied to medical imaging area
(Multidisciplinary in nature).
Scientific evidence for clinical applications.
Tissue Density Estimation Prototype For a sample voxel:
Tissue types
Signals
Pulse Sequence (Steady-State Free Precession) Fast scanning, high resolution and good SNR.
Tissue Properties Design Variables
The dynamic system satisfies:
Therefore:
Model Components
Based on the physical mechanisms, we have:
Imaging
We have
The transformation from tissue densities to measurements:
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:
SDO Problem
Applying Singular Value Decomposition:
A Clinical Application Carotid artery tissue densities estimation
We reconstruct the tissue densities based on the optimal solutions obtained by our formulation.
What if field inhomogeneities exist?
Signal measurements become: Least squares formulation:
Numerical results show that it does work !Numerical results show that it does work !
Numerical Experiment• We discretize the continuous magnetic field to perform our experiment
• We simulate the field inhomogeneity for a random pixel
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
Total Variation Based Model
Subproblem for field inhomogeneity estimation
Numerical Results
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.