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Optimal SSFP Pulse-Sequence Design for Tissue Density Estimation Zhuo Zheng Advanced Optimization Lab McMaster University Joint Work with C. Anand, R. Sotirov, T. Terlaky
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Overview Motivation Model Optimization Problem Numerical Results
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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.
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MRI Basics (Step-by-step Illustration)
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The Dynamic System Magnetization is dependent on several parameters and. The dynamic system satisfies: The system can be built up from several components.
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SSFP Pulse-Sequence Fast scanning and good signal-to-noise ratio. Steady-state is achieved if Denoted as, we have with and.
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Model Components Based on the physical mechanisms, we have
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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.
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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.
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SDO Problem Exerting SVD
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Relaxation We replace the sines and cosines in the components by unit vectors and and add the constraints: Then relax the constraints to:
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Complete System Adding upper and lower bounds for the repetition times we have now the system: s.t.
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where
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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.
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A Clinical Application Carotid artery tissue densities estimation We reconstruct the densities based on the optimal solutions obtained by our formulation.
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Comparison Reconstructed gray-scale images obtained by optimal solutions and grid-search.
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Numerical Results
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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.
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Future Work Formulating the mixed imaging pulse- sequence selection problems. Making the robust formulation possible. Developing an embedded solver to improve performance.
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