Concepts in Magnetic Resonance Part A, Bridging Education and Research / 2019 / Article / Tab 1

Research Article

Quick Reduction of Specific Absorption Rate Constraints in Parallel RF Excitation Pulse Design by Maximum Volume Inscribed Ellipsoids

Table 1

Numerical calculation of maximum volume inscribed ellipsoid for the three examples and the three proposed methods.

Example characteristics

Example number

RF coils 2 8 8
SAR constraints 448480 111939 491

Method : individual SAR constraints

Number of iterations 33 100 22
Overall algorithm [s] 657.7 847.3 0.5
Symbolic factorization [s] 630.8 607.0 0.1
Update Hessian [s] 0.6 127.2 0.2
Compute direction [s] 22.2 97.0 0.1
Acceptable trial point [s] 2.4 0.04 0.0
Number of back steps 15 76 22

Method : single SAR constraint

Number of iterations 100 100 61
Overall algorithm [s] 27.9 129.9 0.9
Symbolic factorization [s] 0.1 0.1 0.1
Update Hessian [s] 0.7 115.5 0.5
Compute direction [s] 0.1 0.06 0.1
Acceptable trial point [s] 26.3 0.001 0.1
Number of back steps 1920 412 117

Method : external active constraint selection

Number of iterations 19 58 46
Overall algorithm [s] 2.9 4.4 0.6
Symbolic factorization [s] 0.1 0.1 0.1
Compute Hessian [s] 0.0 0.3 0.2
Compute direction [s] 0.0 0.2 0.1
Acceptable trial point [s] 0.0 3.6 0.1
Number of back steps 15 127 137

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