I can obviously tell you're a busy guy, but you teased the 4th video too much for me not bug you about it. WE WANT ANOTHER LECTURE ON MRIS, DAMMIT!! your teaching is just too good!!
I needed to understand k-space for my solid state physics class, a pretty much unrelated context, but your explanation of k-space was so intuitive that I was able to 'translate' to what I needed! Thank you!! To anyone in the same situation needing a bit more help: at 43:00, we have the physical setup on the right, where the surface represents the complex wavefunction of a given state, and on the left is its corresponding encoding in k-space. For crystals, we have three spatial dimensions instead of two but of course the idea is identical. So, when we look at a point in k-space, we are looking at a wavefunction that oscillates within the unit cell. Due to quantisation, these oscillations must fit an integer number of times within the crystal unit cell size, so our k-space is discretised: k_n = (2 * pi * n) / a.
I’m a medical student who study physics of medical instruments in high school but never finished it! Now I’m studying it for entertainment in my free time. Thank you for make it all easier for me and many people to learn!
I don`t think I`ve ever been this exited to see a video. Just finished part 2 and really hoped you had made the one about the Fourier Transform. You are really helping me conseptualise MRI and its inner workings! So glad you followed up on your plans, hope the fourth video also gets made and uploaded. Thank you! 😄
I am a new MRI tech and your video series have been invaluable to understanding the NMR phenomenon. It's kind of mind blowing. I think if I watch your videos a few hundred more times I might finally understand it 😜. I can't wait for the next video!
@@ahmadaljazeeri9287 It is not at all required... but it is certainly helpful in educating individuals such as resident M.D's as to why they should not order MRI hip scans to rule out osteomyelitis on patients that have undergone total hip arthroplasties...
This is incredible, I know the DFT and FFT functions from an electrical engineers perspective and your explanations are so good it's clear you've worked very hard to present the topic in this way. Amazing, thank you .
Your explanations are so helpful. I am doing a course on MRI Sequence Programming in my university FAU Erlangen, and now I feel more confident on the topics. Really looking forward to the next video on gradients. It would be great if you can talk about compressed sensing methods.
I'm very happy to see that great imagination and animation for one of the most difficult physics topics, despite all equations which I'm not interested due to my designation as MRI technologist but I passed through to next step in my To do list
At 53:42, for anyone confused about why delta k_x=1/FOV_x, note that each horizontal coordinate (for some fixed vertical coordinate k_y) in k-space is expressed as some integer number of cycles per FOV_x. Therefore, between two consecutiv discrete points on the given horizontal line in the discrete k-space grid, we have that k_n=n/FOV_x and k_(n+1)=(n+1)/FOV_x. Subtracting the bigger from the lesser gives: (n+1)/FOV_x - n/FOV_x = 1 /FOV_x. Similarly, to understand the "pixel dimension_x", which I will refer to as "delta w", relationship to the k_(x,Nyquist), consider the following: There are 3 relevant formulas: 1) sampling rate_x = (# of pixels_x)/ FOV_x 2) (sampling rate_x)/2 = k_(x,Nyquist) 3) (# of pixels_x) * (delta w)=FOV_x. Putting all of this together gives us the following sequence of algebra: (sampling rate_x)/2 = k_(x,Nyquist) = (# of pixels_x) / (2* FOV_x) =(# of pixels_x) / (2*# of pixels_x * delta w)= 1/(2 delta w). This gives us: k_(x,Nyquist)=1/(2 delta w)...multiplying by 2 and then inverting gives us: delta w = 1/ (2* k_(x,Nyquist)
An interesting bit: the FFT was in fact invented by... Gauss! It was found in his notes after he died, he apparently thought the result was cute but not important enough to warrant publication (he was right: without computers it's practically useless and with nothing terribly illuminating about it from the POV of pure mathematics either).
Amazing intuition of fourier transform. Could you please make some videos on control engineering? Why we use step and impulse response? The real meaning and reason behind using of laplace transform, state-space model etc. Thank you
Really excellent !!!! best course ever I watched on youtube ! You have a talent, really !!! Can't wait to see your next "chef d'oeuvre" :) :) Please, hurry ! We are all addicted now !!!!
Very nice video. One very common mistake though @34:38, only frequencies *below* the Nyquist frequency can be sampled. => "make sure your sample rate is *more than twice* as high as your max frequency"
These are all made in Powerpoint. The animations are gifs I made in either R or Blender. Maybe if people are interested I'll show my process in a future video.
you're an amazing lecturer! can't wait for part 4 even though I don't understand 90% of the video. May I ask what software did you use to animate the graphs? also thank you!
38:15 Note: The Nyquist frequency is as stated in 52:45 is half of the Sampling frequency \omega_s. Thus the total frequency space will vary between (- \omega_s/2) to (+ \omega_s/2). Where \omega_s = Sampling Frequency.
@50:30 if the complex conjugate phasors have the same magnitude wouldn't it be possible to just collect half k-space and get the original magnitude with: ∣A∣^2=AA∗ to reconstruct the "prefect" real image instead of a "reasonable reconstruction" ?
Thank you for the video. At 43:34, you say the following: "...the 2D function we're describing, f(x,y), will increase in phase, and thus sinusoidal wiggles, according to the sum of phases k_x*x and k_y*y". What do you mean by this? Why are you describing the terms k_x*x and k_y*y as 'phases'? Aren't these terms analogous to omega*t...rather than phi? Why would 'increases in phases' have anything to do with 'sinusoidal wiggles'
It's perhaps not the best phrasing, but the point is that k_x *x + k_y*y is indeed the phase of the complex exponential (units of k are rad/m or cycles/m) which is actually the spatial analog of phi = omega*t (units of omega are rad/s or cycles/s). Hope that helps? Cheers
For to do the wavelet transform or Function Wave i am not requiere the complex number or Fourier series. Just I need the new methodoly I discovered.I left this video to compare: ruclips.net/video/3Ebvypj577E/видео.html
I just discovered this series couples of days ago , am so lucky 😂
After a long wait, the third episode finnaly came. And it was well worth the wait. Cant wait for the next episode in a year.
I can obviously tell you're a busy guy, but you teased the 4th video too much for me not bug you about it. WE WANT ANOTHER LECTURE ON MRIS, DAMMIT!! your teaching is just too good!!
What a coincidence! 2days before my medical imaging systems exam😂 thank you so much. I appreciate the godlike visualisations.
Best series of videos on MRI. Thank you.
The best RUclips channel for academic. Thank you so much.
I needed to understand k-space for my solid state physics class, a pretty much unrelated context, but your explanation of k-space was so intuitive that I was able to 'translate' to what I needed! Thank you!!
To anyone in the same situation needing a bit more help: at 43:00, we have the physical setup on the right, where the surface represents the complex wavefunction of a given state, and on the left is its corresponding encoding in k-space. For crystals, we have three spatial dimensions instead of two but of course the idea is identical. So, when we look at a point in k-space, we are looking at a wavefunction that oscillates within the unit cell. Due to quantisation, these oscillations must fit an integer number of times within the crystal unit cell size, so our k-space is discretised: k_n = (2 * pi * n) / a.
We need more videos like this, on quantum mechanics and Lagrangian Mechanics. Awesome video!!
I’m a medical student who study physics of medical instruments in high school but never finished it! Now I’m studying it for entertainment in my free time. Thank you for make it all easier for me and many people to learn!
Finally, part 3 comes. Thank you for very good lecture of MRI series.
I don`t think I`ve ever been this exited to see a video. Just finished part 2 and really hoped you had made the one about the Fourier Transform. You are really helping me conseptualise MRI and its inner workings! So glad you followed up on your plans, hope the fourth video also gets made and uploaded. Thank you! 😄
I am a new MRI tech and your video series have been invaluable to understanding the NMR phenomenon. It's kind of mind blowing. I think if I watch your videos a few hundred more times I might finally understand it 😜. I can't wait for the next video!
Is this level of understanding required for MRI techs or is it an engineering level of understanding?
@@ahmadaljazeeri9287 It is not at all required... but it is certainly helpful in educating individuals such as resident M.D's as to why they should not order MRI hip scans to rule out osteomyelitis on patients that have undergone total hip arthroplasties...
This is insanely good! Thank you. I just started my section on MRI and this is a life saver
AWW YEAHHHHHH Part 3 is here fellas
Thank you. Really hope the next chapter can come out as soon as possible. These animations are stupidly awesome, for lack of a stronger adjective.
Yes! Awesome, thank you for posting this!
The wait was worth it *-*
Thanks! I have been waiting for this!!
This is incredible, I know the DFT and FFT functions from an electrical engineers perspective and your explanations are so good it's clear you've worked very hard to present the topic in this way. Amazing, thank you .
I thought I would have to wait for another year. This is awesome thank you so much
Your explanations are so helpful. I am doing a course on MRI Sequence Programming in my university FAU Erlangen, and now I feel more confident on the topics. Really looking forward to the next video on gradients. It would be great if you can talk about compressed sensing methods.
This was very helpful! I am doing a talk about MRI scanners and I wanted to get an introductory understanding for it, thank you!
This is pure gold. I just wished I was smart enough to understand it all..
Nice explanation of fourier transforms
I want moreeeeee. This videos are amazing!
This a remarkably thorough and clear-cut presentation. Very well done, congratulations and many thanks for the huge effort that surely went in !
THANK YOU! been waiting for this
Amazing video series. compressed sensing is pretty interesting too
Wau! Very nice. Can't wait for next episode. Thank you. :-)
It's was amazing, Thank you for creating this video. Hoping to see more videos in near future
Part 4? Absolutely amazing content
Can't wait to see the next video, hopefully in a couple months ❤
Thanks for the amazing animations and education! Can't wait for the next episode!!!
So nicely explained. Awaiting the next part eagerly!!
I'm very happy to see that great imagination and animation for one of the most difficult physics topics, despite all equations which I'm not interested due to my designation as MRI technologist but I passed through to next step in my To do list
love it, tnx for another great part in your mri series ❤❤❤❤❤
i’m watching all these before the ARRT exam for extra preparedness
At 53:42, for anyone confused about why delta k_x=1/FOV_x, note that each horizontal coordinate (for some fixed vertical coordinate k_y) in k-space is expressed as some integer number of cycles per FOV_x. Therefore, between two consecutiv discrete points on the given horizontal line in the discrete k-space grid, we have that k_n=n/FOV_x and k_(n+1)=(n+1)/FOV_x. Subtracting the bigger from the lesser gives: (n+1)/FOV_x - n/FOV_x = 1 /FOV_x.
Similarly, to understand the "pixel dimension_x", which I will refer to as "delta w", relationship to the k_(x,Nyquist), consider the following:
There are 3 relevant formulas: 1) sampling rate_x = (# of pixels_x)/ FOV_x 2) (sampling rate_x)/2 = k_(x,Nyquist) 3) (# of pixels_x) * (delta w)=FOV_x.
Putting all of this together gives us the following sequence of algebra: (sampling rate_x)/2 = k_(x,Nyquist) = (# of pixels_x) / (2* FOV_x) =(# of pixels_x) / (2*# of pixels_x * delta w)= 1/(2 delta w). This gives us: k_(x,Nyquist)=1/(2 delta w)...multiplying by 2 and then inverting gives us: delta w = 1/ (2* k_(x,Nyquist)
This is absolutely amazing
Excited for the next one! These are great
Can’t wait for the 4th episode!!
Worth mentioning, that for the FFT to work best, the range should be a power of two. So 32 pixels would have been better than 30. 🤓
An interesting bit: the FFT was in fact invented by... Gauss! It was found in his notes after he died, he apparently thought the result was cute but not important enough to warrant publication (he was right: without computers it's practically useless and with nothing terribly illuminating about it from the POV of pure mathematics either).
Yessss. Been waiting!
Fantastic video! Thanks!
Hi, this serious is so great! Is there any way to support you in continuing this work?
Amazing intuition of fourier transform. Could you please make some videos on control engineering? Why we use step and impulse response? The real meaning and reason behind using of laplace transform, state-space model etc.
Thank you
Thank youuu!!! Your videos are great
Craving for part 4 now
How did you animate this and how much work was it?
Its so fantastic
This was amazing!!
Now will have to wait for another year :/
Great video!
thank you for your great tutorial. excellent !!
Bro keep up with RUclips as you are extremely good at explaining (and i have watched many videos of the same genre like 3b1b).
Really excellent !!!! best course ever I watched on youtube ! You have a talent, really !!!
Can't wait to see your next "chef d'oeuvre" :) :) Please, hurry ! We are all addicted now !!!!
I woke up while watching the first minute of this video how in luck I feel
PLease PLEASE bring out the next one
Very nice video. One very common mistake though @34:38, only frequencies *below* the Nyquist frequency can be sampled. => "make sure your sample rate is *more than twice* as high as your max frequency"
Which tool do you use for the visuals?
These are all made in Powerpoint. The animations are gifs I made in either R or Blender. Maybe if people are interested I'll show my process in a future video.
@@thepirl903 Thanks for the reply. I honestly myself would love to see a rundown.
@@thepirl903 Just be sure to make part 4 first! You left us with such a cliffhanger there ;)
If you’re a student, try to get the matlab student license. Matlab is the ULTIMATE platform for doing scientific visualizations. World renowned…
you're an amazing lecturer! can't wait for part 4 even though I don't understand 90% of the video.
May I ask what software did you use to animate the graphs?
also thank you!
would you be able to upload the slides for these videos? I believe it will help a loooot.
more thoughts like this pleaseee
Where can I donate? I need keep these kind of videos coming! Thank you!!!
38:15 Note: The Nyquist frequency is as stated in 52:45 is half of the Sampling frequency \omega_s. Thus the total frequency space will vary between (- \omega_s/2) to (+ \omega_s/2). Where \omega_s = Sampling Frequency.
Is it necessary to watch the previous videos in order to understand this one?
Watch them to find out.
50:43 why do you still lose information despite de asymmetry?
Thank you.
You are great.
your work is amazing! How long did it take you to make this!?!?!
You just summarized the entire electronics engineering degree in one video 😂
awesome!!
@50:30 if the complex conjugate phasors have the same magnitude wouldn't it be possible to just collect half k-space and get the original magnitude with:
∣A∣^2=AA∗
to reconstruct the "prefect" real image instead of a "reasonable reconstruction" ?
What are the main physical differences in MRI and MRSI?
Thank you for the video. At 43:34, you say the following: "...the 2D function we're describing, f(x,y), will increase in phase, and thus sinusoidal wiggles, according to the sum of phases k_x*x and k_y*y". What do you mean by this? Why are you describing the terms k_x*x and k_y*y as 'phases'? Aren't these terms analogous to omega*t...rather than phi? Why would 'increases in phases' have anything to do with 'sinusoidal wiggles'
It's perhaps not the best phrasing, but the point is that k_x *x + k_y*y is indeed the phase of the complex exponential (units of k are rad/m or cycles/m) which is actually the spatial analog of phi = omega*t (units of omega are rad/s or cycles/s). Hope that helps?
Cheers
@@thepirl903 cheers~
Hello sir, will you cover Compressed sensing at some point?
Yessss
Very good
Thank you very much! Could you open source the code of the animation?
Yes, I think I will do this and show my process in a future video.
@@thepirl903 Thank you 😀
@thePIRL Good morning, I am a US-based physician and researcher, is there a way to send you a DM?
@@giovannispeziali1491 Yes, I can be best reached at thePIRL@protonmail.com
Please make a video on 2D NMR of biomolecules . Please 🙏
very very interessting
Is this level of understanding required for MRI techs or is it an engineering level of understanding?
Definitely well beyond the level needed for MRI techs (the math especially). Knowing weighting, spatial localisation and sequences is crucial though.
OMG it's a great Video thank you so much but I need the sources 😭
im sad that this episode was released after my exam
plz! part4 now
Wow
For to do the wavelet transform or Function Wave i am not requiere the complex number or Fourier series. Just I need the new methodoly I discovered.I left this video to compare:
ruclips.net/video/3Ebvypj577E/видео.html
Jumpscare at 40:26
profound........
Me for the tenth time through the video: ruclips.net/video/30Ysa3A2WMU/видео.html
your diagrams only serve to confuse the concepts