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