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.