Optimal SSFP Pulse-Sequence Design for Tissue Density Estimation

Zhuo ZhengAdvanced Optimization LabMcMaster UniversityJoint Work with C. Anand, R. Sotirov, T. Terlaky

Overview

Motivation

Model

Optimization Problem

Numerical Results

Motivation

MRI is widely used in diagnosis, treatment monitoring and research.

Quantitatively determining different tissue

types is crucial.

Exploring the applicability of optimization

in biomedical engineering research.

MRI Basics (Step-by-step Illustration)

The Dynamic System

Magnetization is dependent on several parameters and .

The dynamic system satisfies: The system can be built up from several

components.

SSFP Pulse-Sequence

Fast scanning and good signal-to-noise ratio.

Steady-state is achieved if

Denoted as , we have

with and .

Model Components

Based on the physical mechanisms, we have

Imaging

For simplicity, we write the results of n experiments as a real 2n vector and m

tissue densities as a real m vector:

MPPI is an unbiased estimator for tissue densities if has full rank.

Objective and Formulation

Objective: choose pulse-sequence design variables such that

the error in the reconstructed densities is

minimized.

Error given by in which is the white measurement noise.

SDO Problem

Exerting SVD

Relaxation

We replace the sines and cosines in the components by unit vectors and

and add the constraints:

Then relax the constraints to:

Complete System

Adding upper and lower bounds for the repetition times we have now the system:

s.t.

where

Trust Region Algorithm for NL-SDO

How to deal with and semidefinite constraint:

Defining a linear SDO-SOCO subproblem

by linearizing the nonlinear constraints

around the current point.

Linearizing :

and its partial derivatives for information.

A Clinical Application

Carotid artery tissue densities estimation

We reconstruct the densities based on the optimal solutions obtained by our formulation.

Comparison Reconstructed gray-scale images obtained

by optimal solutions and grid-search.

Numerical Results

Concluding Remarks

Innovative method for tissue densities estimation by taking into account many parameters using optimization methods.

Iteratively solving the problem with semi-

definite and highly-nonlinear constraints.

Many interesting applications of our method,

such as brain development studies in infants.

Future Work

Formulating the mixed imaging pulse-sequence selection problems.

Making the robust formulation possible.

Developing an embedded solver to improve performance.