# MRIgeneralizedBloch.jl

Documentation for the MRIgeneralizedBloch.jl package, which implements the generalized Bloch model for simulating magnetization transfer (MT), as described in our paper. The key innovation of the model is to generalize the original Bloch model to arbitrary lineshapes, such as the super-Lorentzian lineshape which has been shown to describe brain white matter well. This enables a more accurate description of the spin dynamics during short RF-pulses compared to previous MT models.

The package allows to simulate the dynamics of an isolated semi-solid spin pool during RF-pulses, as well as the dynamics of a coupled spin system with a free spin pool, for which we use the Bloch model, and a semi-solid pool, which we describe with the generalized Bloch model.

Section Simulation of a Single RF Pulse demonstrates the basic and flexible simulation of the spin dynamics during a single RF pulse and Section Balanced Hybrid-State Free Precession Pulse Sequence demonstrates an efficient simulation of a train of RF pulses. Section Non-Linear Least Square Fitting demonstrates a simple method for parameter estimation at the example of a Balanced Hybrid-State Free Precession pulse sequence; and Section Optimal Control outlines the interface for optimizing RF pulse trains for parameter estimation. More details about these topics can be found in the paper Rapid quantitative magnetization transfer imaging: utilizing the hybrid state and the generalized Bloch model.

More details on the implementation are provided in the Section *Generalized Bloch Paper*, which reproduces all simulations, data analyses, and figures of the generalized Bloch paper:

- Green's Functions
- Continuous Wave Simulation
- RF-Pulse Simulation
- Inversion Recovery Experiments
- Continuous Wave Saturation Experiments
- Linear Approximation

The documentation of all exported functions can be found in the API Section.