This work proposes "Spin-3/2 Bloch Equation" (SBE), a consolidated formalism for spin-3/2 dynamics in biological environments. The formalism encapsulates excitation, relaxation, and off-resonance with accessible matrix representation for a straightforward implementation with high computational efficiency. Theory: The SBE is derived using spherical tensor operators to encapsulate the spin-3/2 dynamics in biological systems in a single system matrix, a formalism akin to the well-known Bloch Equations (BE). Methods: Using the proposed SBE, simulations of three classical 23 Na pulse sequences were performed to demonstrate the versatility and applicability of the model, returning the evolution of the 23 Na spin system during these experiments: soft rectangular and adiabatic inversion recovery (IR) and triple-quantum filtering. IR simulations were compared with two existing spin-3/2 simulators and the adaptive BE as a first-order approximation. Results: The proposed SBE is straightforward to implement and facilitates accurate and fast simulations of the underlying higher order coherence in sodium experiments of biological tissues. SBE simulations and comparison spin-3/2 simulators outperform the BE simulations as expected, with the SBE offering superior computational efficiency achieved by the single system matrix formalism.
Conclusion:The proposed SBE enables comprehensive and accurate simulations for spin-3/2 systems in biological tissue. With a one-line call to an ordinary differential equation solver, it offers a computationally efficient and accessible method for use in 23 Na pulse sequence design.
This work implements 2D ultra-short TE (UTE) imaging for 23Na using half-pulse excitation. The sequence was examined in numerical simulations and phantom experiments at 7T. 2D UTE 23Na imaging is shown to be less prone to partial volume effects than conventional radial 3D sodium imaging and able to produce high in-plane resolution 23Na images.
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