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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