Optimal SSFP PulseSequence Design for Tissue Density Estimation

Optimal SSFP Pulse-Sequence Design for Tissue Density Estimation Zhuo Zheng Advanced Optimization Lab Mc. Master University Joint Work with C. Anand, R. Sotirov, T. Terlaky

Overview n Motivation n Model n Optimization Problem n Numerical Results

Motivation n MRI is widely used in diagnosis, treatment monitoring and research. n Quantitatively determining different tissue types is crucial. n Exploring the applicability of optimization in biomedical engineering research.

MRI Basics (Step-by-step Illustration)

The Dynamic System n Magnetization parameters is dependent on several and. n The dynamic system satisfies: n The system can be built up from several components.

SSFP Pulse-Sequence n Fast scanning and good signal-to-noise ratio. n Steady-state is achieved if n Denoted as with , we have and .

Model Components n Based on the physical mechanisms, we have

Imaging n For simplicity, we write the results of n experiments as a real 2 n 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 n Objective: choose pulse-sequence design variables such that the error in the reconstructed densities is minimized. n Error given by in which white measurement noise. is the

SDO Problem n Exerting SVD

Relaxation n We replace the sines and cosines in the components by unit vectors and add the constraints: n Then relax the constraints to:

Complete System n Adding upper and lower bounds for the repetition times we have now the system: s. t.

where

Trust Region Algorithm for NL-SDO n How to deal with constraint: and semidefinite n Defining a linear SDO-SOCO subproblem by linearizing the nonlinear constraints around the current point. n Linearizing : and its partial derivatives for information.

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

Comparison n Reconstructed gray-scale images obtained by optimal solutions and grid-search.

Numerical Results

Concluding Remarks n Innovative method for tissue densities estimation by taking into account many parameters using optimization methods. n Iteratively solving the problem with semidefinite and highly-nonlinear constraints. n Many interesting applications of our method, such as brain development studies in infants.

Future Work n Formulating the mixed imaging pulsesequence selection problems. n Making the robust formulation possible. n Developing an embedded solver to improve performance.