ORACLE: An analytical approach for T1, T2, proton density, and off-resonance mapping with phase-cycled balanced steady-state free precession

To develop and validate a novel analytical approach simplifying T 1 $$ {T}_1 $$ , T 2 $$ {T}_2 $$ , proton density (PD), and off-resonance Δ f $$ \Delta f $$ quantifications from phase-cycled balanced steady-state free precession (bSSFP) data. Additionally, to introduce a method to correct aliasing effects in undersampled bSSFP profiles.PURPOSETo develop and validate a novel analytical approach simplifying T 1 $$ {T}_1 $$ , T 2 $$ {T}_2 $$ , proton density (PD), and off-resonance Δ f $$ \Delta f $$ quantifications from phase-cycled balanced steady-state free precession (bSSFP) data. Additionally, to introduce a method to correct aliasing effects in undersampled bSSFP profiles.Off-resonant-encoded analytical parameter quantification using complex linearized equations (ORACLE) provides analytical solutions for bSSFP profiles. which instantaneously quantify T 1 $$ {T}_1 $$ , T 2 $$ {T}_2 $$ , proton density (PD), and Δ f $$ \Delta f $$ . An aliasing correction formalism was derived to allow undersampling of bSSFP profiles. ORACLE was used to quantify T 1 $$ {T}_1 $$ , T 2 $$ {T}_2 $$ , PD, T 1 $$ {T}_1 $$ / T 2 $$ {T}_2 $$ , and Δ f $$ \Delta f $$ based on fully sampled ( N = 20 $$ N=20 $$ ) bSSFP profiles from numerical simulations and 3T MRI experiments in phantom and 10 healthy subjects' brains. Obtained values were compared with reference scans in the same scan session. Aliasing correction was validated in subsampled ( N = 4 $$ N=4 $$ ) bSSFP profiles in numerical simulations and human brains.THEORY AND METHODSOff-resonant-encoded analytical parameter quantification using complex linearized equations (ORACLE) provides analytical solutions for bSSFP profiles. which instantaneously quantify T 1 $$ {T}_1 $$ , T 2 $$ {T}_2 $$ , proton density (PD), and Δ f $$ \Delta f $$ . An aliasing correction formalism was derived to allow undersampling of bSSFP profiles. ORACLE was used to quantify T 1 $$ {T}_1 $$ , T 2 $$ {T}_2 $$ , PD, T 1 $$ {T}_1 $$ / T 2 $$ {T}_2 $$ , and Δ f $$ \Delta f $$ based on fully sampled ( N = 20 $$ N=20 $$ ) bSSFP profiles from numerical simulations and 3T MRI experiments in phantom and 10 healthy subjects' brains. Obtained values were compared with reference scans in the same scan session. Aliasing correction was validated in subsampled ( N = 4 $$ N=4 $$ ) bSSFP profiles in numerical simulations and human brains.ORACLE quantifications agreed well with input values from simulations and phantom reference values (R2 = 0.99). In human brains,