Awesome. So welcome back everybody. So computational MRI parallel imaging part two. Before we get

started, I just wanted to check in how the exercises are going. How was it last week?

Okay, people are nodding. The reason I'm asking is that out of my experience, this exercise

from last week is the hardest for people out of all the exercises. So it seems to be the

most complicated implementation and if that has been going well, then that's good news

and rest assured that from now on this was the hardest, we made it to the hardest.

Unless this particular group is an outlier and sense was very easy.

All right, so we're gonna do a second lecture on parallel imaging and the reason for this is,

as I said last week, there are two ways how you can see parallel imaging. Either operations

doing in image space and or operations doing in case space. And the research field has really

split up into these groups 20 years ago when these two methods were developed and one group

did one approach, the other group did the other approach, the manufacturers followed.

So these two approaches are out there and you have to understand them because you will encounter them

if you work in MRI, but never forget that under the hood what's really happening is essentially

the same thing. It's just using the coil sensitivities as a mean of additional spatial

encoding and then it's just a way of how you formulate the operations to do that.

So what we're going to do is we're going to do just a little bit of a review of parallel MRI

and a little bit of sense just in two minutes or so to recap and get everybody on the same page.

And then we're going to look in detail at two case-based parallel imaging methods and those two

are SMESH and KRAPA. And the reason why we are looking at those two is SMESH was the very very first parallel

imaging development out of all of them. So we just have to cover it if we talk about parallel

imaging this was really the first method that was invented. It's not flexible enough and

to be actually be used. So the one parallel imaging case-based method that does work

and is used is KRAPA and you can see here from the timeline SMESH was invented in 97. Then

that inspired sense. So sense came two years later but with a different formulation of the

problem and then in 2002 KRAPA was developed that really made case-based parallel imaging work.

And when you said that any MRI scanner in the world of any of the major manufacturers

the two methods that you will see implemented there are sense and KRAPA. They all have them

with different flavors of refinement on Siemens and on GE scanners. KRAPA is the one that is far

better developed and works way better on Phillips scanner sense is way more developed and works

better. So we're going to cover those two and I'm going to show you the derivations. I'll show you

a little bit of math and then at the end I'm yeah we're going to discuss a little bit what

the advantages and disadvantages of case-based based versus image-based methods are. When should

you use sense? When should you use KRAPA to get a little bit of information?

Okay so this is just to recap the basic problem. We are dealing with this

equidistant Cartesian case-based sampling. So no Cartesian sampling today, no non-Cartesian sampling

today. And we know now very very well that our distance between those two sampling lines and

case-based defines our field of view. We want to accelerate our acquisition so we skip half of the

lines. We double the distance between them that halves our field of view that leads to aliasing

and now we need the coil sensitivities to undo this aliasing and still get full information back

even though we have half this kenta. Everybody is clear on that.

So this is just another example here of these multi-channel receive coils. So this is a brain

image and you can see that they are circling oriented around the brain with different receive

coil sensitivities and that means that they encode spatial information.

So if you just see it from a very very high level what happens in the two operation sense and KRAPA,

then it all comes down to when do you do your computational techniques in relation to the Fourier

transform. Do you do your algorithmic approaches before you do the Fourier transform?

Or do you do it after the Fourier transform? And in sense you do the Fourier transform first,

it means you get an image with aliasing artifacts because you have the sampling

theorem so that's what you get. Then you run your computations, you use the receive coil