In our last post, we discussed the basic physics underlying magnetic resonance imaging, or MRI. But we havenât built the complete picture yet-- even with all of the physics that we talked about last time, weâre still only left with the ability to use a magnetic field to create a smaller magnetization vector inside the body that can then be measured by the electric current it induces in a loop of wire. How do we use this to create images of different types of tissue?
If you recall from our last post, we talked about the MRI producing an excess of spin up protons in your body, the magnetic moments of which sum to the measureable net magnetization vector, or NMV. To make this easier to visualize, letâs think of each excess spinning proton as a top, just like the mind-blowing eternally spinning one from Inception. As a result of the big magnetic field B0 pointing toward your head in the MRI, each of these little tops is lined up along B0 with its stem pointing toward your head and its tip toward your feet.  Letâs also think of the magnetic moment produced by the spinning proton, which we can visualize as an arrow pointing along its axis of rotation, as essentially analogous to the topâs angular momentum-- take a look at the arrow labeled L in the diagram below. In the absence of other forces, each proton acts just like a top set spinning with its stem perfectly vertical. It would keep spinning forever, precisely parallel to B0.
However, letâs say your top tips over just slightly, as it inevitably will in the real world-- now the force of gravity isnât perfectly aligned with the topâs axis of rotation. In fact, gravity now has a component perpendicular to the topâs angular momentum, as in the diagram above. This perpendicular component applies a torque that causes the topâs axis of rotation to rotate around its tip, changing the direction of the topâs spin without changing its speed. This phenomenon, called precession, is actually what you see in that wobbling circular motion of a top-- see how its stem traces a circle, if viewed from birdâs-eye view?
We actually make use of precession for MRI. Remember how we said that the coil of wire at the head of the MRI can only measure changes in the z-component of the NVM? Well, we can change the z-components of our protonsâ magnetic moments by making the protons precess. You see, when the magnetic moment is inclined so that it is no longer perfectly parallel to B0, its z-component shrinks. This is a simple matter of the Pythagorean theorem: try working it out to convince yourself that each leg of a triangle must be shorter than the hypotenuse. In fact, if we can get the proton to precess so that it is perpendicular to B0, its z-component will be 0.
We can cause precession by applying a little pulse of a magnetic force in the x- or y-direction, perpendicular to B0, to âpullâ the protonâs magnetic moment (which lies along its axis of rotation) down and to the side. Letâs imagine we applied a little force to the right of the proton so that its magnetic moment tilts just a little to the right. Now, as its magnetic moment tilts forward and around to the left, we have to pull to the left in order to pull the magnetic moment further downward. So as the proton begins to precess, we have to apply an oscillating magnetic field, called a radiofrequency (RF) pulse, to pull its magnetic moment to the right as it rotates past the right, then left as it rotates past the left, then right again, left again, etc. in a swirl-- all the while pulling it downward until it lies perpendicular to B0. This can be a little hard to visualize, so if youâre lost, try watching the first half of this video (until 0:03)!
For this RF pulse to be effective in rotating the protonâs magnetic moment to a desired angle, it has to come as close as possible to matching the frequency of the protonâs precession, which is called the Larmor frequency in MRI. If the RF pulse is out of sync with the Larmor frequency, it will be ineffective, kind of like pushing a swing at the wrong time. Now, a protonâs Larmor frequency depends on the strength of B0, the big magnetic field, at the specific location of the proton in question. This is a very important concept for what weâre going to be talking about in Part III, so keep this in mind!
After we use an RF pulse at the Larmor frequency of the proton long enough to force it to precess around the z-axis at a 90 degree angle, we just have to work out how to turn this precession into something measurable that we can use to differentiate between tissues. One way to do so is to use the density of protons, usually from water, in that tissue. Another way, which weâll be discussing in further detail, is to use relaxation times, like T1 and T2.
At the beginning of the MRI, when we just have B0 without any other magnetic forces, our magnetization vector (which is, again, just a fancy name for the sum of the protonsâ little magnetic moments) lies completely along the z-axis, so it has a really large z-component. Then, we use the RF pulse to force a 90 degree precession, so all of the protons precess in the XY-plane and the z-component of the magnetization vector decreases to a much smaller value. After we stop the RF pulse, however, these protons will gradually precess back to align with B0, essentially doing the opposite of the video above. As the protons do so, the NVMâs z-component exponentially increases back to its initial value. T1, or spin-lattice, relaxation measures the time constant of this recovery, marking the time at which approximately 63% of the original z-component. Because other atoms nearby can affect how easy it is for protons to precess back upward to align with B0, T1 varies between different types of tissues. Watch the second half of the video above (after 0:03) to see T1 in action.
In addition, when we apply the RF pulse to rotate the protonsâ magnetic moments into the XY-plane, all of our protons precess in sync, with all of their magnetic moments aligned so that the magnetization vector oscillates between having a really large x-component and a really large y-component. As time passes, though, the protons dephase, getting out of sync with each other so that the x- and y-components of their magnetic moments cancel out. T2, or spin-spin, relaxation measures the time that it takes for the x- and y-components of the magnetization vector to decrease by 63%. This value also depends on the protons nearby, so T2, like T1, varies between tissues. You can see a birdâs eye view of T2 dephasing in the video below, in which the translucent arrows represent individual magnetic moments, which sum to the big bright yellow arrow, or the magnetization vector.Â
Wow, that was a doozy. We zoomed in on individual protons, combining physics and math to figure out how to change their rotation to produce something that our wire coils can pick up and measure. In our next post, we just have to worry about the easy part-- how to localize different tissues to specific locations in your body. Stay tuned!
https://en.wikipedia.org/wiki/Angular_momentum
http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html
https://en.wikipedia.org/wiki/Physics_of_magnetic_resonance_imaging