37:57 Adiabatic pulses are a lot more natural to visualize in a frame rotating at the instantaneous frequency of the pulse (where the B1 vector stays stationary in the traverse plane). Then the off-resonance frame means there's an effective Bz component, and the magnetization tracks/precesses about this B effective. In the rotating frame at the larmor frequency (shown) there isn't any Bz component. The black arrow corresponding to B effective only exists when the frame is rotating at the Frequency Modulation (FM) of the RF pulse.

@14:29 I believe the product in the equation for B should range from j=n to i + 1

Great video and illustrations but I found some mistakes: You say ellipse when talking about an ellipsoid at 15:11 the phase diagram in the middle shows the blue vector as having phase 0. If the blue vector has higher frequency it should have phase -pi.

At 7:49, assuming linear gradients, why isn't B_x = 0 at both locations on the left, and of the same magnitude ( = G_x*z) at both locations on the right? (Also, at 17:10, I think that the units for the y-axes is T/m?)

At 18:40, why is it the B_0 eddy current term and not the linear gradient eddy current term that distorts the intended gradient?

At 4:50, are Z_1 and Z_2 both cosines?

At 7:13, should the axes in the bottom lefthand corner be x and y instead of x and z?

why these spins at 6:32 have different magnitude ? ins't the magnitude of these that is giving these spin precessions the elliptical shape ? but it's not explained why these spins have different magnitudes. In all previous lectures we were looking at a group of isochromats for simulations.

hi I am currently studying the EPG formalism. My question centers on the fidelity of the EPG formalism in representing the totalsignal from a group of spins distributed along the z-axis when subjected to a sequence of RF pulses and dephasing gradients. like the ones shown in at 8:00. Assuming a voxel contains 20 or so spins uniformly distributed along a segment of the z-axis all pointing in z direction with unit magnitude. just as in the illustration, I would like to understand the equivalence of the signal outcome between a simulation done using AM+B formalism that was taught in the course earlier and the EPG-based approach under the following conditions: Let's say : We apply a 60 degree excitation rf pulse there is a subsequent dephasing due to field inhomogeneities then a 180-degree refocusing RF pulse is applied. Finally, an additional dephasing occurs. and an echo is generated. Is the signal computed from the individual spin behaviors with AM+B simulation in this scenario-buy summing the Mx My Mz to get bulk magnetization-would quantitatively match the signal derived from a standard EPG simulation. In the EPG simulation, the initial state is represented by a 3x1 vector of F states (F+, F-, Z), which undergo transformations due to RF pulsing and dephasing modeled as shifts in state orders, then we convert the FpFmZ back to Mx My Mz of bulk magnetization ? i hope I formulated my question correctly. thank you

i always get's confused about this simulation, I mean we are looking at the spin magnetic moments in a voxel. so why are all of them at the origin (0,0,0) should they be spread across the voxel at sub-voxel positions ? and and what about the encoding gradients ? if I want to run an MRI simulation on a complete digital phantom do I have to have multiple spin magnetization vectors at each voxel location ?

Actually, T2 and T2* decrease with increasing B0. And that's why lung imaging is possible under low field strength MRI.

thank you so much pro

thanks for the video, it's really helpful. Got a question, it seems that the integral equation of k-space position in terms of gradient field on this slide (kzbin.info/www/bejne/rIfRqIF7opWkbKM) should not have the 2*Pi as denominator

thank you so much pro

Thank you very much for this great lecture series! I would like to point out that on slide 9, there is a small error in the gray equation underneath "Divide out M, rearrange and multiply by sin(beta/2)": in the very last term in the denominator, if my calculations are correct, the M^2 term should not be there! It is only (T1/T2)*sin^2(beta/2). I would appreciate any feedback on that :)

I think there is a typo in the rotation matrix at 14:21 .. I would appreciate if anyone could let me know whether they also get a different result when deriving it ... I will present how I get to my result in the following: The Rx matrix in the (Mx,My,Mz)-basis, according to lecture 03A reads: Rx(A)={{1,0,0}, {0,cos(A),sin(A)}, {0,-sin(A),cos(A)}} . This would turn the vector (0,0,1) to (0,1,0) (=left-handed rotation) when A = 90 deg and would turn the vector (0,0,1) to (0,-1,0) (=right-handed rotation) when A = -90 deg. Now, from lecture 03A we know that, in order to transform this into the complex basis, we calculate: Rxc = T.Rx.Inv(T) where T = {{1,i,0},{1,-i,0},{0,0,1}}. Now, applying this transformation to the general Rx I get: 1/2 + Cos[A]/2 1/2 - Cos[A]/2 i Sin[A] Rxc(A) = 1/2 - Cos[A]/2 1/2 + Cos[A]/2 -i Sin[A] i/2 Sin[A] -i/2 Sin[A] Cos[A] If this is correct, the first two zeroes along the diagonal in the given rotation matrix in the video cannot be right. Given the prefactors in the result for Q after the rotation I assume that, in the lecture's notation, the rotation matrix in this example is Rx(-90 deg) (instead of the given Rx(+90 deg)) and then, inserting A=-90 deg into my result, the rotation matrix in the complex basis reads: 1/2 1/2 - i Rxc(-90) = 1/2 1/2 i -i/2 i/2 0 This does not influence the result, of course ... it just drove me crazy that I did not know how to get to the given matrix. Any feedback would be appreciated!

In question 2, there seems a typo. It should be "Any Z0 after an RF refocusing pulse..." instead of F0. Right? This may cause confusion.

Correction: I think the concomitant field equation in 9:23 should be 1/(2*B_0)*((G_x*z-G_z*x/2)^2+(G_y*z-G_z*y/2)^2). It's a small mistake, the 4 in the denominator should be 2 Source:Bernstein, Mat A., et al. "Concomitant gradient terms in phase contrast MR: analysis and correction." Magnetic resonance in medicine 39.2 (1998): 300-308.

13.12 not sure the labels of ccw and cw are correct

Probably a stupid question: If we go from k space to image, dont we get the axes inverted as (F(F f)) (x) = f(-x). The second fft is applied by computers from k space to xy space, the first one by using nmr, i.e. imaging space in the frequency domain, correct?

3:47 I am a bit confused.. shouldn't the final equation be : M 1 = (1−E 1) /[1−E1cos(α)] instead of : ​M 1 = (1−E 1) /[E1cos(α)] 0.o

Thank you🥰!!!

At 3:58, is it possible that the angle sequence is 90, 360, 810 instead of 90, 180, 810 if k = 1, 2, 3... or did I understand the formula wrong?

Thank you so much pro

Slide-06 (~4:02) has an error in the equation. It should read: \Delta t=\frac{1}{2\Delta f}=\frac{2 \pi}{\gamma G_x\cdot FOV_x}

Can you share a link for the code of simulations (for study aproach)?😅

Thank you

At 14:37 , there is a typo in dMx/dt in the slide 15 of lec02A. The minus should be plus in front of the second term in the right hand side.

At 14:37 , there is a typo in dMx/dt in the slide 15 of lec02A. The minus should be plus in front of the second term in the right hand side.

At 14:37, there is a typo in dMx/dt, as the minus should be plus. Please double check.

Thank you for this video and for your efforts, if you don’t mind i still have some questions about this subject, i look forward to discuss them with you and i’ll be happy if we can Chats about the topic😀 Thank you in advance

Thank you for this video, i have a question ,How can we simulate the spin movement in the laboratory system? do you have any idea, I have a project I should visualize this Movment? could you help me please?

It seems the position-vector r is important. But where is its origin located? By the way, if we integrate over the object, then this equation and the following ones (from 11:38 to 18:21) should end with (dr)^3.

@ 12:45 Let's make that 235 microseconds.

Bulk-magnetization is very nice for the math in MRI, but math tends to obscure reality. Of course, the receiver detects field lines across its entire area and never in just one point of this area (opposite to some x,y-plane).

Really love these MRI-videos: kzbin.info/www/bejne/hYK4o4avoZmWd6s

@ 03:38 In my opinion, this should be 0.150 Tesla. @ 11:05 Not quite rectangular because of the rise-time (4:44) @ 20:01 So the instantaneous phase is relevant? (Their accumulated phase is quite different here)

Inspiring video in all its aspects.

Shouldn't the rotation at 17:26 be clockwise, according to left-hand rule?

RIP sound volume😂😂😂

Thanks this tutorial about gradient amp... perhaps you can provide with answer ... where to find mri gradient amplifier squematic, inner component

Great lecture! Thx

the sound is very low!

Great channel and really clear and helpful lectures. Just wanted to let you know that around 16:00 there seem to be some glitches in the recording. Perhaps they are not in the original and it could be improved. Thank you very much, and I hope to one day visit Stanford University. Also a big fan of Leonard Susskind's lectures.

@15:24, your B matrix is wrong. It should say B3x1

Great lecture with very clear explanations. There is a small typo at 7:44, there should be a "ɣ" coefficient in front of -B1e(t)*sin(θ) .

Thank you some much for those lectures and for making your slides AND repo publicly available!

I finally understood what the Maxwell correction in the recon parameter options of the seqeunce is all about.

Anxiously waiting for the next "episode"

I cannot understand the animation during 14:40. How do you get the phase data using a single point in K-space? Code for this part was missing in github project.