Optimization of Pulse Sequences in MRI Scheme

In this paper we investigate a fractional generalization of the Bloch equation that includes both fractional derivatives and time delays. The appearance of the fractional derivative on the left side of the Bloch equation encodes a degree of system memory in the dynamic model for magnetization. The introduction of a time delay on the right side of the equation balances the equation by also adding a degree of system memory on the right side of the equation. The analysis of this system shows different stability behavior for the T"1 and the T"2 relaxation processes. The T"1 decay is stable for the range of delays tested (1-100 @ms), while the T"2 relaxation in this model exhibited a critical delay (typically 6 @ms) above which the system was unstable. Delays are expected to appear in NMR systems, in both the system model and in the signal excitation and detection processes. Therefore, by including both the fractional derivative and finite time delays in the Bloch equation, we believe that we have established a more complete and more realistic model for NMR resonance and relaxation.

Fractional Bloch equation with delay

Purpose
To develop a T1ρ-prepared balanced gradient echo (b-GRE) pulse sequence for rapid 3D T1ρ relaxation mapping within the time constraints of a clinical exam (< 10 minutes), examine the effect of acquisition on the measured T1ρ relaxation time and optimize 3D T1ρ pulse sequences for the knee joint and spine.

Optimization of Pulse Sequences in MRI Scheme

References

Fractional Bloch equation with delay

T1ρ‐prepared balanced gradient echo for rapid 3D T1ρ MRI

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization.

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