Lab 3: Magnetic Resonance –
Excitation and Relaxation

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Information, Preparation, Resources, Etc.

Assigned Readings / Videos:

Pages 21-32 & 38-40 Basic mri:Physics" by Evert J Blink

I would like you to re-read/re-watch the following items from last week. I cannot overstate how helpful it will be to carefully re-read/re-watch these after you've read them once and heard my lecture. I promise I would not have you spend your time re-reading if it didn't have great value. It will go a long way toward helping you cement these ideas. Which, by the way, is something in your best interest seeing as you'll have a quiz on these concepts very very soon!

Pages 1-20 Basic mri:Physics" by Evert J Blink

Watch videos #1, #4, #5, and #8 on on this page.

Pages 4-17 of Introduction to MRI Techniques by Lars G. Hanson

Goals for this lab:

Enhance your understanding of MR physics through an interactive visualization

Software introduced in this lab

Two web-based interactive NMR simulators

http://www.drcmr.dk/CompassMR/

http://www.drcmr.dk/BlochSimulator/

Laboratory Report

Your first lab report is due Jan 30th @ 1:10 pm. Throughout this (and all) lab exercise pages you will find instructions for your lab reports within these boxes.

Housekeeping

none

Part 1: Magnetization and Resonance

In this section we will see a simplified version of the magnetic resonance effect. Rather than visualizing precessing nuclei, we will explore the effect on a virtual compass needle placed in a magnetic field

1. Direct your web browser to the Compass Needle hosted by the Danish Research Centre for Magnetic Resonance.

Press the Proceed button

You will see the following interactive display. By default, the compass needle is placed randomly outside of any magnetic field.

The B0 slider controls the strength of the main magnetic field (by default this is set to 3 mT)

The B1 slider controls the strength of the magnetic field perpendicular to the main field

The Freq slider controls the frequency at which B1 is applied

The Push button…well…pushes. It perturbs the needle out of equilibrium.

The Coil checkbox uses a current passed through a coil, rather than a magnet, to create the B1 field

2. Adjust the B0 slider to its minimum value of 0.0 mT and then press Push.

The needle will slowly spin and ultimately stop at a random location. Do you understand why?

In the next step we'll see what happens when we introduce a magnetic field, B0

3. Adjust the B0 slider to its maximum value of 5.0 mT.

Observe that this causes the needle to align with the direction of the magnetic field.

Importantly, the needle first oscillates around the field direction before reaching equilibrium (i.e., no longer oscillating; being at rest)

The amplitude of the oscillations slowly gets smaller, but the frequency stays constant. That fact – that the frequency is constant and independent of amplitude – is an important one!

It takes about 20 seconds for the needle to reach equilibrium (i.e., stop oscillating).

It takes about 1.66 seconds for one full oscillation. In other words, the needle is oscillating at 0.60 Hz.

Converting between the period (i.e., time it takes for one full oscillation) and frequency is easy: Where = frequency, and = time to complete one oscillation

4. We will now attempt to make the needle oscillate again by applying a weak magnetic field (B1) perpendicular to our stronger main field (B0)

Set the field strength to 5.0 mT and let the needle reach equilibrium.

In one quick motion, increase the the strength of B1 to its maximum strength of 1.0 mT and then back down to 0.0 mT. (i.e., swipe right and then back to the left)

This will cause a magnet perpendicular to the B0 field to appear and then disappear. In other words, we apply and remove a B1 field.

You will observe that it has only a small effect on the needle and it returns to equilibrium fairly quickly.

5. Let's try to continuously add and remove B1 (i.e., create an oscillating magnetic field).

B0 should be set to 5.0 mT and B1 should be set to 0.0 mT

Set the Freq slider to 1 Hz

Now apply the B1 field by putting B1 at its max value of 1.0 mT

You will observe that this results in an extremely weak oscillation of the needle, despite the energetic “pushing” of the B1 magnet. In other words, the force of the perpendicular magnetic field is not being efficiently transferred to the needle. You're frantically trying to push a child on the swing, but are mostly just pushing air!

6. We know that prior to reaching equilibrium the needle was oscillating once every 1.66 seconds in the 5.0 mT field. So let's try applying our B1 at that same frequency. (If you don't recall how we know that it's 1.66 per second, or .6 Hz, see step #3 above.)

Set Freq slider to 0.60 Hz

We now observe that the oscillations become rather large (amplitude increases) over the span of a few seconds, and that the needle continues to oscillate at the max amplitude.

This is the resonance effect in action!! In a field of 5.0 mT our needle oscillates at .60 Hz. Even a small force applied perpendicularly to the needle (note that the B1 field is 1/5th the strength of the B0 field) can cause large effects if applied at .60 Hz; the resonant frequency. Think back to the analogy of a parent pushing their child on a swing. The needle is the child, and the perpendicular magnet is the parent. At .60 Hz the parent is pushing at the correct intervals.

7. Now let's see what happens when we adjust the B0 field strength to 2.5 mT

Set B1 to 0.0 mT

Set Freq to 0.0 Hz

Set field strength to 2.5 mT

Push the needle out of equilibrium by pressing the Push button

Observe that it now takes about 2.2 seconds for one full oscillation.

LAB REPORT Part 1 - #1 Why is the oscillation frequency at 2.5 mT slower than when the field strength was 5.0 mT?

8. Now let's attempt to add an oscillating B1 field to maximally oscillate the needle.

LAB REPORT Part 1 - #2 At what frequency should we apply B1 to achieve our goal? Is thus value different than the on we used in step #6? If so, why?

9. Finally, let's observe an alternative way to introduce B1.

Law of Induction Physics (or more specifically, Joseph Faraday) tells us that passing current through a conductive coil will create a magnetic field perpendicular to that coil. See here for a 30-second demo. The opposite is also true; passing a magnet through a coil will induce an electric current in the coil. See here for a cool interactive demo.

Given what we now know about the law of induction (see box above) we have another way we can “push” our needle. Rather than presenting a perpendicular magnet to oscillate the needle, let's create a magnetic force along B1 by passing electrical current through a coil wrapped around B1.

Set B0 to 5.0 mT

Set Freq to .60 Hz

Set B1 to 1.0 mT

Check the box next to Coil

You will see that the magnetic field created by the coil does the same job as the physical magnet.

It actually seems to do a better job in this demo. Perhaps that's meant to demonstrate the greater control and precision afforded by using an electrically induced field.

What should you understand before proceeding? The relationship between a magnetic filed and the direction something oscillates within that field. What is equilibrium? The relationship between magnetic field strength and frequency. The independence of amplitude and frequency. What is resonance and why it is important for transferring energy? (e.g., making the needle oscillate as much as possible) How does the law of induction allow us to push our needle with an electric current in a coil rather than a second magnet? The primary magnetic field in which the needle oscillations is called B0 The magnetic field that pushes our needle (regardless of whether it is due to a second magnet or to electricity running through a coil) is called B1 You should feel confident in your understanding of the above items before you proceed!

Part 2: Nuclear Magnetic Resonance

In this section we will take what we learned in the prior section and apply it to a slightly more complex visualization of the net magnetization M of an atomic spin state.

1. Direct your web browser to the Bloch simulator hosted by the Danish Research Centre for Magnetic Resonance. This simulator will allow you to manipulate MR excitation and relaxation parameters and observe the effect they have on net magnetization (M).

In 1946 Felix Bloch formulated a set of equations (the “Bloch equations”) for calculating net magnetization as a function of time in the presence of T1 and T2 relaxation effects.

By default, you will see a precessing white bar, which represents the net magnetization of a sample (not a single proton). It is precessing around a vertical magnetic field. In MR, this would be our static field B0. Note: In this lab I might refer to “the bar”, but remember that the bar represents the net magnetization of gazillions of hydrogen atoms.

You can zoom and change your perspective around the bar by dragging with your mouse.

In the upper left corner of the screen you will see a list of drop down menus for various adjustable parameters:

This is a non-exhaustive list of the options:

Relaxation: This allows you to set the T1 and T2 relaxation constants.

T1: the time constant for longitudinal relaxation (seconds)

T2: the time constant for transverse decay (seconds)

View: This allows you to toggle on/off different views of the phenomenon.

Torque: Show direction of torque when you apply RF waves to generate a B1 field. (this will appear as a red bar atop the precessing white bar)

Mx: This will show you Mx, the amplitude of magnetization in the x direction. (displayed as red line in the plot in the upper right corner)

|Mxy|: This will show you the absolute value of tMxy, the strength of magnetization in the transverse plane. This is our recorded signal. (displayed as a white line in the plot in the upper right corner)

|Mz|: This will show you the amplitude of Mz, the strength of magnetization aligned with B0.(displayed as a grey line in the plot in the upper right corner)

Fields: This allows you adjust the strength of the B0 field and the strength and frequency of the B1 field.

Gradients: This allows you adjust the strength of gradients applied along the x (Gx) and y (Gy) directions.

Frame: This allows you to change your perspective.

Stationary: This is the “rotating frame of reference” (standing on a merry-go-round watching a child going up and down on a horse.

B0: This is the “laboratory frame of reference”. (standing on the ground next to the merry-go-round watching a child going up and down on a horse while also going round and round.)

Along the bottom of the screen you'll see several buttons which allow you to set what kind of environment you want and how you want to manipulate that environment. There are too many options for me to describe here (and we'll only be using a small number of them anyway), so I'll just explain them as we use them.

Take your time and be sure that you have a good understanding of what each display represents and what the adjustable values control before you continue. In a moment we'll make some changes and get the bar to do more interesting things. Before we do you should feel comfortable that you understand what is being displayed and what you might expect to happen when we manipulate these things. For example, what do you think would happen to the |Mxy| line if we tipped the bar? What do you think would happen to Mz if we tipped the bar? You'll do these things in a moment, but it's important that you take a moment to try and think through what you'd expect. If you're correct, great! If you're not, you'll have the opportunity to think through and understand why you were wrong….which is also great! (we might even call that “learning”)

Field Effects

2. Adjust the magnitude of B0 using the slider or by entering a new numeric value.

You should observe the frequency of the bar change relative to field strength. Do you remember why this is?

3. Select the following items from the View menu: Mx, |Mxy|, Mz, and torque. Remind yourself what each of these are showing you.

4. The sample is continuously precessing around B0. This is because the default setting of the simulator is to have the T1 and T2 relaxation times set to “infinity” (Which is an unrealistic situation in which the atoms would never relax. Lucy would keep swinging on the swing forever!)An actual sample would reach thermal equilibrium after a few seconds. .

We're going to change T1 value–the longitudinal relaxation constant–to have a more realistic relaxation time. But before we do you should predict how this change will affect the Mx and |Mxy| signals.

Change the T1 value to 4. (Incidentally, this is the T1 constant for cerebrospinal fluid in a 1.5T field).

You may notice that changing the T1 value from infinite to 4 causes an automatic change in T2. This is because the rate of longitudinal recovery (T1) is always slower or equal to the rate of transverse decay (T2). In other words, transverse decay will always occur faster, or equal to, longitudinal recovery. See this page for a nice description of why this is so. So remember… (where 'greater than' means longer than)

Tip: To watch it again, re-load the webpage and go back to step #3 above

LAB REPORT Part 2 - #1 Describe the effects of changing T1 from infinite to 4. What happened to Mx (red line) and |Mxy| signal (white line)? Why? What happened to our Mz signal (grey line)? Why? Your answer should include reference to equilibrium, transverse plane, longitudinal magnetization, net magnetization, etc.

Excitation

As we know from lecture, in order to acquire a recordable signal we need to 'tip' the net magnetization out of Mz and into Mxy. We'll attempt to do so in this part of the lab.

5. Let’s see how adding a B1 field (i.e., an RF field perpendicular to B0) affects the net magnetization.

Reset the display by reloading the web page.

Set T1=1 and wait for the bar to relax and become aligned parallel to B0.

After the bar is at equilibrium, set the T1 and T2 times back to “infinity”.

Turn on views of |Mxy|, Mx, and torque

By default, the RF frequency (B1) is set to 5. Let’s leave it that way for now.

Change the RF amplitude (B1) from 0 to .3

We now see a small red bar on top of the white bar. The length of the bar represents the strength of the force (we set this to .3) and the direction of the bar represents the direction along which the force (torque) is being applied to the net magnetization.

Despite applying a B1 field (i.e., RF energy perpendicular to B0), we do not see the net magnetization tipping away very much from Mz into Mxy, and therefore (almost) no recordable signal.

LAB REPORT Part 2 - #2 Why do we not see the net magnetization tipping away from Mz even though we're applying energy along B1?

6. Well that didn't work so well. Let's try again, but this time we'll also change the RF freq.

Change the RF freq to 2 (RF freq is B1)

Remember: this means that we're changing the frequency to match the expected frequency of hydrogen in a 3T field.

Now we observe the net magnetization is more effectively tipped into the transverse plane.

Note that the signal (|Mxy|, white line) reaches its maximum amplitude when the net magnetization is at 90° to B0.

You will also see that the net magnetization continues to tip beyond 90° and will actually go all the way around if the excitation stays on indefinitely. This is because we are using an un-realistic model in which there are no T1 or T2 relaxation effects.

Try doing this again and viewing it using the B0<>/sub> reference frame. 7. Finally, let's see how magnetic field inhomogeneity affects our signal. * Choose Weak Inhomogeneity from the drop down menu. * You should see the sample magnetization (the white bar) at thermal equilibrium in a rotating frame. * Apply a 90 degree RF pulse by pressing the 90x hard button (Remember, a “90° pulse” means applying RF so that then net magnetization tips 90° away from B<sub>0.

You should observe the dephasing of the transverse magnetization due to inhomogeneities in the field.

press the v button on your keyboard to see it from an overhead view.

LAB REPORT Part 2 - #3 What causes this dephasing in an inhomogenous magnetic field? What effect does this dephasing have on the signal? Why? Repeat step #7 a couple of times to ensure you have a good feel for what's going on and how dephasing affects our sample signal.

8. Now let's apply a 180° “refocusing pulse”.

Choose Weak Inhomogeneity from the drop down menu.

Apply a 90 degree RF pulse by pressing the 90x hard button

When the signal drops to around .6, apply a 180 degree RF pulse by pressing the 180y hard button

LAB REPORT Part 2 - #4 What effect did the 180 degree pulse have on the signal? What do you think accounts for this effect? NOTE: We did not cover this in the lecture. I want you to think through the likely cause of the signal change based on what you've observed and what you now know about dephasing in the transverse plane (Mxy). You'll get full credit as long as I see that you made a good effort, even if you ultimately get it wrong.

What should you understand before proceeding? Hydrogen is used to generate signal in MRI imaging. Hydrogen is the most abundant atom with non-zero spin in the human body. Atomic particles with the NMR properties will align to an external magnetic field and precess around the field axis at a particular frequency known as the Larmor frequency. Larmor frequency is proportional to the gyromagnetic ratio and the external magnetic field strength. Application of a perpendicular radiofrequency pulse that matches the hydrogen precessional frequency will cause spins to resonate, and subsequently the net magnetization vector will gain transverse magnetization.