JEMRIS  2.8.2
open-source MRI simulations
In depth tutorial - Part 1


In the following, a 2D spatially-selective excitation experiment [Pauly 1989] will be demontrated in detail in three different ways. The first will reflect the flexibility of the symbolic mathematics evaluation capabilities of JEMRIS. In the second part, the use and implementation of external gradient and RF pulses will be demonstrated, and in a third part, the framework will be extended to boost the performance of the simulation process.

The paper describes the spatially-selective small tip angle excitation with the application of two gradients accompanied by an RF pulse.

To start off, let us delete the hard rf pulse and replace it with a 2D selective excitation block consisting of an analytic RF pulse, and two analytic gradient pulses in read and phase direction.

Let us now have a look at the analytical solution for the rf pulse and the k-space trajectory presented by the author, which we want to implement:

B1.png
kx.png
ky.png

The paper investigates the case where beta is 2, n is 8, and A is 1 while the excitation is played out for 2 ms. The following steps will associate the excitation block to the according formulas.

What the last step essentially means, is that some attribute of RF pulse needs to know about its own duration. You can see, the magnitude of the RF pulse is time dependent and varies over the 2 ms pulse duration. The concept of observing oneselfs attribute may appear confusing on a first glance, but is due to the flexibility of the attribute implmentation.

Let us now type in the constants involved in order of apearance. They can be accessed by depending attributes as c1 through c5.

Here, some explanation is needed as to why gamma is set to 1. Simply put, JEMRIS does not simulate the nuclear physics deeper than to the point, where the relaxation times for proton imaging are given. In that case the field strength dependant part is intrinsically built into the sample. So, in order to simulate the effects associated with faster T2 decay at high fields, one changes the value for T2 accordingly.

Let us now type in the formula of the time dependant rf magnitude.

You should now be looking at the GUI in the following state:

jemris_sta_1.png

We are not finished yet. The Gradients are next.

We need to introduce the necessary parameters, all stemming from ERF. As there are the duration, A, and n.

The not obvious step in the last instruction block is the setting of the value for Diff. In this step, the flexibility of the symbolic math library is demonstrated. The formula, that was typed in for the Shape describes the k-space trajectory's time evolution. However, we are interested in the shape of the corresponding gradient. Which is just the first derivative with respect to time or T. Alternatively you may also reset Diff to 0 and set Shape to the formula for the gradients as described in the paper:

Gx.png
Gy.png

It is easily comprehendable that the differentiation will cost simulation time.

In Part 2, we will expand the framework by two very easily coded classes to demonstrate the extensibility of the framework. Additionally, as the use of symbolic mathematics is very appealing and should be the first choice for implementing new ideas, there are some performance issues to be considered. If, however, the computation is shifted to the level of the framework in C++, major speed ups may be gained depending on the complexity of the mathematics involved.

You may now simulate the sequence as described in the first steps tutorial. But! be very careful here. The simulation involves some computation power and, depending on the sample size, some RAM.

Step on to: In depth tutorial - Part 2

[Pauly 1989] Pauly JM, Nishimura DG, Macovski A. A k-Space Analysis of Small-Tip-Angle Excitation. Journal of Magnetic Resonance, 81, 43-56 (1989)


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