00:00:07
any questions
00:00:09
about spatial
00:00:17
localization um so do you just image the
00:00:22
quter of kpace if it's you can get all
00:00:24
your same
00:00:26
information why would you why would you
00:00:29
all
00:00:31
well two things first of all so what
00:00:33
you're what what we're talking about
00:00:36
here
00:00:40
is that if we
00:00:42
divide our
00:00:47
kpace into four quadrants okay H this
00:00:52
this question oh same question see that
00:00:54
imagine that so that if we divide this
00:00:57
into four quadrants like this
00:01:00
that there is this conjugate
00:01:04
symmetry
00:01:06
okay so if I have the top half of kpace
00:01:11
I
00:01:13
can
00:01:21
right I can reproduce the
00:01:24
bottom or if I have the left half I can
00:01:27
reproduce the right half it's not not
00:01:30
one thing you said is not true if you
00:01:32
have
00:01:34
25% you can't do
00:01:36
anything okay because it's not mirror
00:01:40
symmetry right so if you have this 25%
00:01:44
all you can do is generate the lower
00:01:47
right
00:01:48
25% so let's understand that first now
00:01:52
that being said so in terms of if Time
00:01:56
Savings is the reason why you're doing
00:01:58
this we in a second we talk about
00:02:00
another reason why you might do do this
00:02:02
if you're interested in Saving Time you
00:02:04
would be interested in acquiring only
00:02:06
the first 50% in terms of the number of
00:02:09
rows in
00:02:10
kpace right so if you can do that right
00:02:14
if you can do it in half the time why
00:02:17
would you ever bother to acquire the
00:02:20
whole
00:02:22
thing okay so everyone hear the
00:02:24
question okay so the
00:02:28
reason is that while it's true that you
00:02:32
can do what is called
00:02:38
a half fora acquisition
00:02:42
sometimes uh there are other names that
00:02:44
different vendors use for it but if you
00:02:47
only acquire that fir it's actually not
00:02:49
just the first half it's the first half
00:02:50
plus at least the first line of the
00:02:52
second half that you can what we call
00:02:56
interpolate the second half of kpace
00:03:00
but in re while in theory it would be
00:03:03
possible to actually reproduce it right
00:03:06
in reality because of right
00:03:10
variabilities that are inherent in the
00:03:11
way that we collect the data and noise
00:03:15
there are always going to be some errors
00:03:17
in reproducing that second half so the
00:03:20
image quality and in particular the
00:03:22
signal to noise of the image is never
00:03:24
going to be quite the same when you take
00:03:27
this approach now that being said it's
00:03:30
it's pretty good so this is a technique
00:03:33
that you would use where you really need
00:03:35
the time so in other words if you're
00:03:38
doing something like breath hold Imaging
00:03:40
or if you're trying to image something
00:03:43
for example in in some applications in
00:03:46
diffusion Imaging where any kind of
00:03:49
motion uh even physiologic motion is
00:03:52
going to limit your ability to get a
00:03:54
diagnostic quality image then it's an
00:03:58
option and you really need to exercise
00:04:01
that option but if you have the
00:04:03
opportunity to acquire a complete data
00:04:05
set your image quality is going to be
00:04:07
better
00:04:10
yeah okay so any questions about slice
00:04:18
selection from this
00:04:20
morning is everyone okay with that how
00:04:23
we select a
00:04:25
slice determine orientation location
00:04:31
thickness yes
00:04:34
no
00:04:36
okay now once we have our slice
00:04:40
selected and we talked about localizing
00:04:44
signal in the frequency
00:04:47
direction is everyone clear about how we
00:04:49
do
00:04:52
that Smitha what do you
00:04:56
say um not Crystal not Crystal
00:05:01
okay
00:05:03
so but slice selection we're okay with
00:05:06
pistol okay
00:05:10
so
00:05:13
so slice selection simply means that we
00:05:17
have a signal that comes from everywhere
00:05:19
in this slice and we have no idea where
00:05:21
it comes from okay when we talk about
00:05:25
frequency
00:05:27
encoding we turn on a gr magnetic
00:05:31
field parallel to one of the inplane
00:05:33
dimensions of the slice and by the way
00:05:35
to be clear I've always been showing you
00:05:37
frequency coding left to right and
00:05:39
phasing coding top to bottom it could be
00:05:42
the other way around it's totally your
00:05:45
choice uh we'll talk hopefully a little
00:05:48
bit about why you might make one choice
00:05:50
or the other depending on the body part
00:05:52
and the orientation of the image but it
00:05:53
could be either one so just to make the
00:05:56
diagram easy I've chosen left to right
00:05:59
so what what does this mean that we've
00:06:00
turned that that we've drawn this
00:06:03
oblique Arrow here I'm just causing a
00:06:06
gradient along that which means that if
00:06:08
we compare what's going on in the tissue
00:06:11
at each of a variety of locations along
00:06:13
this Dimension what's changing as we
00:06:16
move from left to
00:06:19
right it's not really left to right well
00:06:23
no it is left or right this is the this
00:06:24
is the image okay okay so if I say let's
00:06:29
look at all of the tissue within this
00:06:33
column okay and let's compare that to
00:06:38
all of the tissue
00:06:40
in this
00:06:43
column when I turn on this gradient
00:06:46
magnetic field what does that mean
00:06:48
what's a different exactly so the
00:06:51
magnetic field strength at each of these
00:06:53
locations is different now at a given
00:06:56
location like right here no matter where
00:06:59
you are top to bottom the field strength
00:07:02
is the same now since we've altered the
00:07:05
field strength between these two
00:07:06
locations it follows that these spins at
00:07:09
these two locations press at different
00:07:12
frequencies okay so the way this is
00:07:17
happening is that we turn on our RF with
00:07:22
our slice select
00:07:23
gradient right and at that point we have
00:07:27
transverse magnetization coming coming
00:07:29
from everything in this
00:07:31
slice okay so at this point in time we
00:07:35
have a signal right which we could
00:07:39
measure which is the composite of all of
00:07:43
the transverse magnetization in the
00:07:45
slice
00:07:46
okay and everything in the slice
00:07:50
beginning at this point in time is
00:07:52
pressing at what
00:07:54
frequency I haven't turned this on yet
00:07:57
so it be zero everything is pressing at
00:07:59
the same same frequency at Omega no
00:08:02
right now at some point in time we are
00:08:05
going to turn
00:08:06
on this frequency encoding gradient okay
00:08:11
and while that's on we're going to be
00:08:13
sampling this signal now as soon as we
00:08:16
turn it
00:08:18
on this signal is now composed of
00:08:22
what different groups of
00:08:25
spins that are seeing different field
00:08:28
strengths ande assessing at different
00:08:31
frequencies so essentially this signal
00:08:34
which we detect as a single signal
00:08:36
coming from the whole slice is really
00:08:39
the
00:08:40
sum right
00:08:43
of two different
00:08:50
components okay
00:08:52
okay so all we can detect is one signal
00:08:56
coming out of there but that signal
00:08:59
which which we detect at te because the
00:09:01
frequency encoding gradient is on is
00:09:04
composed of different I'm only showing
00:09:05
you two of them here but there's an
00:09:07
infinite array of different frequencies
00:09:09
because depending on location there is a
00:09:13
different field strength experienced by
00:09:15
those
00:09:16
spins right so when we sample this
00:09:20
signal it really contains all of these
00:09:23
components in
00:09:24
it by taking that signal and sampling it
00:09:30
right over
00:09:34
time measuring a whole bunch of
00:09:38
incremental measurements of signal
00:09:39
amplitude acquired at different points
00:09:41
in
00:09:42
time right which we can write those
00:09:47
down so we can
00:09:50
record over a period of
00:09:53
time right a series of measurements of
00:09:56
signal amplitude now each one of these
00:09:59
measurements of signal
00:10:01
amplitude
00:10:03
contains all of this
00:10:06
information right contain signal coming
00:10:08
from
00:10:12
where each one each time I measure this
00:10:14
where is that signal coming
00:10:21
from I mean it's coming along
00:10:23
each well it's coming from the entire
00:10:27
slice do you see why that that
00:10:30
is because remember we turn on our RF
00:10:34
and we generate transverse magnetization
00:10:37
from all the spins in that entire slice
00:10:40
they all have transverse magnetization
00:10:42
at this point and then we're waiting and
00:10:45
over here we're going to sample whatever
00:10:46
signal happens to be around well that
00:10:49
signal comes from the entire
00:10:53
slice so each time I sample this signal
00:10:57
each sample contains information coming
00:10:59
from the entire
00:11:04
slice you see why that is kind of but
00:11:07
once you once you add the the frequency
00:11:10
gradient don't can't you only sample
00:11:13
from where they're resonating at the the
00:11:16
more frequency or whatever okay so what
00:11:19
what you're asking is that well if I
00:11:22
turn on this frequency encoding gradient
00:11:26
all of a sudden spins press at different
00:11:28
frequencies depending on their
00:11:31
location so maybe we could be like a
00:11:35
little ham radio guy right and we could
00:11:37
tune in on individual frequencies and we
00:11:41
could measure the amplitude of the
00:11:43
signal at specific individual
00:11:47
frequencies you could try to do that
00:11:50
right but your ability to resolve at any
00:11:54
kind of a useful spatial resolution what
00:11:58
was going on at each of these locations
00:12:00
would be very difficult because remember
00:12:02
all you would be doing in that
00:12:04
case you're really doing the same thing
00:12:07
you're taking this big signal which is
00:12:10
composed of a whole bunch of different
00:12:12
frequencies and you're saying let's only
00:12:14
listen to one of them okay so what we're
00:12:18
doing instead is we're saying let's
00:12:20
sample the whole
00:12:22
signal listening to the whole
00:12:24
signal and let's then under put it
00:12:28
through a process
00:12:29
that will be able to tell us what each
00:12:31
of those frequencies are without us
00:12:34
having to go in and try and listen to
00:12:36
them individually okay which probably
00:12:38
wouldn't be physically possible to do
00:12:41
anyway do you hear the difference so
00:12:44
within this signal there are many
00:12:46
different
00:12:47
components right each processing at a
00:12:50
different frequency and in some sense
00:12:52
you could say you know just like when
00:12:53
you're driving your car home tonight
00:12:55
there's a whole bunch of frequencies out
00:12:57
there and you can tune your radio in
00:13:00
so that its sensitivity is limited to a
00:13:03
specific frequency so theoretically you
00:13:06
could think about doing that here with
00:13:08
the types of ranges of frequencies that
00:13:10
we're talking about it's just not going
00:13:11
to be it's not going to be possible so
00:13:14
instead we sample the entire signal
00:13:17
every time we sample it we're open to
00:13:20
everything that's in here so each sample
00:13:22
contains some of each of these
00:13:25
frequencies and each of those component
00:13:28
frequencies of course has some amplitude
00:13:30
that goes with it so do you see how the
00:13:33
spatially differentiated information is
00:13:35
embedded in each of these samples yes
00:13:38
okay I don't know how it pulls it apart
00:13:39
but I okay well at this
00:13:42
point if we take this and we put it
00:13:45
through the 4A transform and don't worry
00:13:47
about how it does it
00:13:51
okay just think of this as a black box
00:13:55
okay
00:13:57
really um
00:14:02
because in terms of what's going to be
00:14:03
useful to you in using this information
00:14:05
to understand the images we're going to
00:14:07
generate it's not going to make a
00:14:09
difference it really won't make a
00:14:11
difference whether you understand what
00:14:13
happens during this phase any more or
00:14:16
less but understanding what happens as
00:14:20
opposed to how it actually happens is is
00:14:23
going to be useful and what happens is
00:14:26
we end up with a bunch of measures of
00:14:28
signal
00:14:30
that now are each assigned to a specific
00:14:33
frequency okay so from a series of
00:14:36
samples acquired over time the for a
00:14:38
transform can tell us what those
00:14:41
component frequencies are right each of
00:14:44
these is unique frequency and can put
00:14:47
the correct amount of the signal
00:14:49
amplitude with each of those component
00:14:52
frequencies now realize that if we took
00:14:55
all of these components and added them
00:14:59
all up right that's our reverse for
00:15:02
transform we would get the composite
00:15:04
signal that we sampled in the first
00:15:06
place all right so this allows us to
00:15:10
accurately localize the signal along
00:15:13
this frequency encoding Direction in one
00:15:15
plane only well I don't know what you
00:15:18
mean by plane the image is a slab okay
00:15:21
the signal can only be coming from the
00:15:23
slice so I think what you mean to say is
00:15:25
that along one dimension of the image
00:15:28
right and at any given Dimension we have
00:15:32
an ability
00:15:33
to know that the signal is coming from
00:15:37
here in terms of left to right but we
00:15:39
have no way of knowing where that amount
00:15:42
of signal that comes at this point in
00:15:44
the left to right Dimension where it
00:15:46
comes from in the top to bottom
00:15:48
Dimension and that's what phase encoding
00:15:50
is going to give us okay so at this
00:15:53
point in
00:15:54
time that's all we've got is this
00:15:57
one-dimensional information what going
00:15:59
on from left to right okay okay does it
00:16:03
ever happen that your for
00:16:05
transformation just isn't working
00:16:07
properly how would you
00:16:10
know um what if it
00:16:13
like what if it give you totally bunked
00:16:16
material then what I mean how would you
00:16:17
know well it depends on what you mean
00:16:20
okay so first of all there can be
00:16:22
problems with the there can be problems
00:16:24
with the fora transform or with the
00:16:26
Reconstruction algorithms they can cause
00:16:29
artifacts in the image okay oh that's or
00:16:33
there could be errors in the data which
00:16:35
because of the nature of the way they
00:16:37
interact with the fora transform show up
00:16:39
as artifacts in the image and we'll show
00:16:42
you some of those when we talk about
00:16:44
artifacts tomorrow or Thursday I don't
00:16:46
remember which one um so but in terms of
00:16:51
so for example you're not going to have
00:16:53
the for you transform mess up and give
00:16:54
you like an image of a chipmunk instead
00:16:56
of an image of a child if that's what
00:16:59
you mean it's not going to it's not
00:17:00
going to totally know what if it messes
00:17:03
up and it gives you like the right side
00:17:04
towards the left or like you know
00:17:10
um yeah I mean those things are I I
00:17:13
wouldn't say that that's impos I mean
00:17:15
this right left issue is is an important
00:17:19
issue that uh is is addressed and dealt
00:17:22
with and in the image processing
00:17:24
algorithms that are used on most
00:17:25
commercial scanners I can tell you for
00:17:27
an as an example there are all kinds of
00:17:29
problems sometimes when you work with
00:17:31
research systems that the images can be
00:17:34
flipped right to left if you're not
00:17:37
careful and you don't know exactly
00:17:38
what's going on so it's it's not totally
00:17:42
a non-c concern but but pretty much the
00:17:45
the math does does
00:17:48
work PE you had a so um are we Imaging
00:17:53
the same slab at different times or are
00:17:55
we Imaging different slabs at different
00:17:57
times and if Imaging the same slab at
00:18:01
different times just is it at multiple
00:18:03
TVs what do you mean by the same
00:18:06
slab I guess so that CU right now just
00:18:08
so we're all on the same page we excited
00:18:11
a slice once only one time and then we
00:18:15
sample the signal several times after
00:18:18
that single excitation that's all we're
00:18:21
doing here is that what you're referring
00:18:23
to I think so are you into phase
00:18:26
encoding we're going to repeat this and
00:18:27
do it again and again why can't it just
00:18:30
uh like I guess I just don't understand
00:18:33
if we're Imaging the entire slab why why
00:18:35
does it need to be imaged what do you
00:18:36
mean by the slab or I guess the the
00:18:38
slice
00:18:39
SCE why why do why do we need to sample
00:18:42
it at multiple times is it to get the
00:18:44
multiple lines of why do we need
00:18:47
multiple samples here yeah okay well we
00:18:50
need multiple samples because the nature
00:18:52
of the for
00:18:53
transform the nature of the digital for
00:18:56
transform that we're looking that we're
00:18:57
using is that you must provide it a
00:19:01
sample of the signal for each component
00:19:04
you want it to
00:19:06
deliver okay so it has multiple Parts in
00:19:08
the beginning it puts it all together
00:19:09
and then before you transform decomposes
00:19:12
it into its individual Parts exactly
00:19:14
okay and the more information you give
00:19:16
it the better able it is to but how does
00:19:18
how does the the um composite of these
00:19:21
waves from time one time two differ
00:19:24
aren't they aren't they the same but
00:19:25
aren't you getting the same it's the
00:19:27
same signal all along sure it is you're
00:19:29
just sampling it multiple times so
00:19:31
you're giving like
00:19:33
256 same signals to this well they're
00:19:36
not the same because this signal is
00:19:38
varying with
00:19:39
time okay okay this is a sine wave so
00:19:42
let's say just in a in the abstract if I
00:19:46
have this sine wave okay let's say it's
00:19:49
playing on an
00:19:51
oscilloscope
00:19:53
and it's playing on an oscilloscope as
00:19:55
just a DOT marching across the screen so
00:20:00
if you come in with your digital camera
00:20:01
and you snap one
00:20:03
picture you're only going to capture
00:20:05
what was happening at that one point in
00:20:07
time you would need multiple samples in
00:20:10
order to be able to recreate
00:20:13
this continuous function is that for
00:20:16
dynamic Imaging or that's for static
00:20:18
Imaging no this is the signal this has
00:20:20
nothing to do with this is static
00:20:22
Imaging because the nature of things is
00:20:25
remember this is the transverse
00:20:27
magnetization inducing a voltage in your
00:20:29
receiver coil so you put the
00:20:32
magnetization starts at rest you tip at
00:20:34
90° and now it is precessing in this
00:20:36
transverse plane and there's a loop of
00:20:39
wire over here each time this goes past
00:20:42
it induces a voltage across that
00:20:44
conductor and as it moves away that
00:20:47
voltage declines to zero and then it
00:20:50
becomes negative and when this comes all
00:20:52
the way back around it becomes positive
00:20:54
again this is the magnetization pressing
00:20:57
at 64 m million times a
00:21:00
second okay so that's just the nature of
00:21:02
the Mr signal yes I'm just not sure how
00:21:04
you derive location based on the
00:21:06
frequency of components okay that's
00:21:08
because we turned on this gradient
00:21:10
magnetic field which meant that the
00:21:13
field strength is
00:21:16
changing from point to point in a linear
00:21:19
fashion lower so first of all just go
00:21:24
back to this frequency is determined by
00:21:29
the net magnetic field strength in the
00:21:31
absence of this gradient magnetic field
00:21:34
everything
00:21:35
sees be not and therefore everything
00:21:39
processes at the same frequency as soon
00:21:41
as we turn on this gradient magnetic
00:21:43
field there is an incremental change in
00:21:47
field strength in B net therefore
00:21:50
there's an incremental change in
00:21:51
frequency so when the 4 transform spits
00:21:54
out a series of frequencies we go back
00:21:57
and we say okay well we know the way
00:21:59
that this gradient was applied and
00:22:01
therefore we can predict the linear
00:22:03
manner in which the frequency should
00:22:04
have lined up and we can put the signal
00:22:06
in the right place is that so it's not
00:22:09
it's not spitting out let's say the
00:22:10
frequencies in the correct
00:22:13
order well it's it's a list of
00:22:16
frequencies so
00:22:19
yeah yeah I mean how how you order them
00:22:22
is up to you it's it's determining what
00:22:24
the components are and then we need to
00:22:26
we can place them in order of ascending
00:22:29
frequency based on the way the gradient
00:22:31
was
00:22:33
applied
00:22:37
okay so any other questions at this
00:22:39
point about frequency
00:22:41
encoding so this is so is everyone
00:22:44
comfortable with localizing this signal
00:22:47
across at least this one dimension of
00:22:48
the image yes
00:22:52
no feel free to shake your head
00:22:56
no okay so now the next
00:23:01
step we said is that if we've already
00:23:04
been able to know right how much signal
00:23:08
comes at each location in this example
00:23:12
left to right so we're already finished
00:23:14
with that
00:23:17
part how is it that we are going to be
00:23:20
able
00:23:21
to tell the location of the signal going
00:23:25
in the next Direction
00:23:28
right and this was where we added a bit
00:23:32
more
00:23:33
complexity right we had started out
00:23:35
before with generating the signal okay
00:23:39
then at some point down here sampling
00:23:42
that signal in the presence of that
00:23:44
frequency en code and
00:23:47
gradients now it turns out actually
00:24:01
so for those of you that may have
00:24:05
noticed this would be the same right
00:24:10
as
00:24:14
acquiring a line of
00:24:17
data with a zero amplitude of the phase
00:24:21
encoding
00:24:22
gradient So based on our discussion of
00:24:25
kpace the signal that we acquire under
00:24:28
this this condition would be written
00:24:30
into
00:24:32
the center of kpace is that clear why
00:24:36
that would be remember the highest
00:24:38
amplitude is in the center so in this
00:24:40
example notice it's missing there's no
00:24:42
phase encoding gradient
00:24:45
here okay now if we change
00:24:49
things
00:24:50
and do this
00:24:53
again with our phase encoding gradient
00:24:56
turned on at some ampl
00:24:59
ude we will so we've acquired right
00:25:02
multiple
00:25:04
samples and then we go back to the
00:25:06
beginning and do this entire thing all
00:25:08
over again everything exactly the same
00:25:11
with one
00:25:12
exception that exception is this phase
00:25:14
encoding gradient and we once again
00:25:17
acquire right multiple
00:25:20
samples and we write those
00:25:23
into let's say our next line in kpace
00:25:29
now how does this allow us to determine
00:25:34
how the signal should be distributed
00:25:35
from top to bottom we know
00:25:39
that in this
00:25:49
case so this is time from left to right
00:25:52
this is just the raw signal that we just
00:25:54
acquired
00:25:56
okay this direction
00:25:59
is
00:26:02
the right the phase encoding step right
00:26:05
it's just the incremental application of
00:26:07
that
00:26:08
gradient so we know based on what we
00:26:10
just discussed a minute ago that we can
00:26:12
for a transform each of these lines
00:26:15
independently and generate something
00:26:17
that looks like this
00:26:31
right the difference here is that this
00:26:34
is now
00:26:36
frequency and this is Phase encoding
00:26:41
steps is everyone clear about this is
00:26:43
exactly what we just did a minute
00:26:48
ago so now if we pick any location left
00:26:53
to right over here
00:27:00
wherever it happens to
00:27:02
be if we pick that location left to
00:27:06
right whether we choose the signal
00:27:09
that's on the black line or the signal
00:27:10
that's on the tan line they both come
00:27:13
from the
00:27:14
same location in our
00:27:19
image which would
00:27:22
be this will be the image
00:27:29
all right which will be at this Left
00:27:32
Right
00:27:37
location oh
00:27:43
okay all right so both of those signals
00:27:46
come from this Left Right location they
00:27:49
also the signal whether it's the black
00:27:52
one or the tan one each represents
00:27:54
signal coming from the entire strip of
00:27:58
tissue in our image from top to
00:28:01
bottom and we have no way of telling how
00:28:04
much of that black signal there comes
00:28:07
from the middle or the bottom or the top
00:28:08
and likewise with the tan
00:28:11
signal
00:28:13
however right because these two gradient
00:28:16
magnetic fields that were applied during
00:28:20
acquisition of each of these signal are
00:28:21
different
00:28:23
amplitudes
00:28:25
right the component
00:28:28
right components of this let's say black
00:28:31
signal all come from someplace along
00:28:34
this
00:28:36
line we don't know exactly where but we
00:28:40
do
00:28:41
know that wherever they are when we turn
00:28:45
on this extra gradient magnetic field
00:28:49
that it causes those spins to excelerate
00:28:52
or decelerate a little bit and therefore
00:28:55
change their phase with respect to other
00:28:57
adjacent and Spins and we know that the
00:29:00
stronger the applied gradient magnetic
00:29:03
field the greater the amount of phase
00:29:05
change that's going to
00:29:07
occur
00:29:10
okay not only that but if we then go
00:29:17
back and look at what's
00:29:21
happening right along that this would be
00:29:24
that top to bottom dimension in our
00:29:26
image is left to right in this graph is
00:29:29
that clear what I mean by
00:29:31
that right no yes no let me let me draw
00:29:35
it again to make it clear okay this top
00:29:39
to bottom dimension in the image is the
00:29:41
phase encoding
00:29:43
Direction
00:29:46
so all I'm doing
00:29:50
is actually know what let's do this
00:30:02
okay so this is the phase encoding
00:30:06
Direction so if we want
00:30:09
to look at what is
00:30:12
happening in terms of location in the
00:30:16
image under each of those gradient
00:30:19
magnetic
00:30:20
fields so what we can
00:30:25
do is draw a graph here
00:30:33
where this
00:30:35
is right the actual spatial dimension of
00:30:38
our
00:30:39
image this is the gradient
00:30:43
strength does this make sense I've
00:30:46
turned this sideways so it parallels the
00:30:48
image that that's all I'm doing okay so
00:30:52
what happens is that at some point along
00:30:55
here is the isocenter of the image
00:30:58
and at some point along here is the zero
00:31:01
strength of the gradient magnetic
00:31:04
field so when we plot what is going
00:31:08
on with that gradient the black line
00:31:12
Looks like
00:31:14
this okay all that means is that no
00:31:17
matter where we are along this dimension
00:31:19
of the image we see Zero gradient
00:31:22
strength guess I should maybe I should
00:31:24
have done that in Black huh
00:31:34
whereas the tan
00:31:39
line Looks something like that where you
00:31:43
are along this dimension of the image
00:31:46
there is going depending on where you
00:31:47
are there is going to be a different
00:31:48
amount of gradient
00:31:50
strength okay the zero gradient doesn't
00:31:53
cause any def
00:31:55
phasing the one represented by the tan
00:31:59
line does cause some incremental amount
00:32:01
of Def
00:32:02
phasing if we make a comparison between
00:32:06
the amount of Def phasing that occurs
00:32:09
when we acquire a signal under the black
00:32:13
gradient and compare that to the amount
00:32:16
of Def phasing that occurs under the tan
00:32:19
gradient you can see that the amount of
00:32:22
change in gradient strength grows as you
00:32:26
get farther away from the ISO center of
00:32:28
the magnet so if you're the component of
00:32:32
this signal that's sitting right at the
00:32:34
isocenter it's right in the middle of
00:32:36
the image right over here right whether
00:32:40
we have this extra gradient on or not
00:32:42
it's all the same thing there's no net
00:32:45
amount of Def phasing all right if
00:32:47
you're farther away from the isocenter
00:32:49
and as you get increasingly farther away
00:32:52
then the amount of change in phase and
00:32:55
therefore as we heard before change in
00:32:57
actual signal intensity is going to
00:33:00
grow so we now have collected these two
00:33:04
signals each with a different amount of
00:33:09
phase information conferred on the
00:33:13
signal and if we now make a comparison
00:33:16
between phase at this location and this
00:33:20
location right that is going to vary
00:33:23
depending on location along this
00:33:26
dimension in the image if we have enough
00:33:32
samples right each of
00:33:35
these right acquired at a
00:33:38
different gradient
00:33:41
strength we can take all of those
00:33:44
samples and using the 4A transform we
00:33:48
can
00:33:49
derive right how much signal amplitude
00:33:53
belongs to small amounts of phase change
00:33:56
and how much signal amplitude belongs to
00:33:59
large amounts of phase change those
00:34:01
small amounts of phase change correlate
00:34:03
with close to the iso Center and large
00:34:06
amounts of phase change correlate with
00:34:08
far from the isocenter and they line up
00:34:11
in a linear pattern so by having
00:34:14
multiple samples here we essentially
00:34:16
then just ask the
00:34:20
question we say if we for you transform
00:34:23
in this
00:34:25
direction what we are looking for now
00:34:27
instead of a series of frequencies and
00:34:31
how much amplitude goes with those
00:34:33
frequencies we are looking for a series
00:34:36
of amounts of phase change or you could
00:34:39
think it of it almost as rates of change
00:34:42
of phase when you're farther from
00:34:44
isocenter phase is changing more rapidly
00:34:47
from one gradient to the next when
00:34:50
you're close to isocenter phase is
00:34:52
changing more slowly from one gradient
00:34:54
to the next that rate of change of phase
00:34:56
essentially is a velocity or a frequency
00:34:58
it's the same type of information that
00:35:01
you would extract from the 4 transform
00:35:04
explicitly at
00:35:05
frequency so the for transform will give
00:35:08
us a list of pieces of signal
00:35:11
amplitude each of them assigned to some
00:35:15
Delta phase and that allows us to
00:35:19
localize our signal in this third
00:35:24
dimension is that clearer
00:35:28
yes
00:35:29
no questions about
00:35:35
this not good when there are no
00:35:37
questions why can't they just turn on
00:35:39
both those gradient the frequency and
00:35:41
the phase encoding gradient at the same
00:35:43
time just do it in one shot okay why
00:35:48
not that wasn't a rhetorical
00:35:51
question but you know the answer well
00:35:54
why
00:35:55
not maybe you're right why can't you do
00:36:02
that oh they add up together so that's
00:36:05
one issue first of all if they're on at
00:36:06
the same time you essentially have a
00:36:09
single oblique gradient magnetic field
00:36:12
okay well that's one issue but there's
00:36:15
another reason why it's a
00:36:20
problem when would you turn them
00:36:25
on well you said you would turn both on
00:36:28
at the same time oh you have to pulse it
00:36:31
with the with the B1 or with the RF or
00:36:36
whatever what you need is multiple
00:36:41
samples okay if you're going to use the
00:36:43
fora
00:36:45
transform to generate your result you
00:36:49
need to provide it with multiple
00:36:52
samples so when we're sampling the
00:36:55
signal using the frequency encoding
00:36:57
gradient we have the opportunity to
00:36:59
acquire multiple samples of that signal
00:37:02
over
00:37:03
time all right but where do the multiple
00:37:07
samples come from with the phase
00:37:08
encoding
00:37:10
gradient see if we just turned it on
00:37:13
over here it would essentially just be
00:37:15
frequency encoding along a compound
00:37:18
oblique but the other issue is that we
00:37:20
need to have multiple the reason why we
00:37:22
have to iterate this again and again and
00:37:24
again is be because we need multiple
00:37:27
discret
00:37:29
samples that have this phase information
00:37:32
in them and the way it's set up now
00:37:35
since we're already doing our sampling
00:37:37
on the frequency encoding Direction
00:37:38
during signal
00:37:40
acquisition we essentially have to
00:37:43
encode that entire signal exactly the
00:37:45
same way so it's only one sample as far
00:37:49
as phase encoding goes and that's the
00:37:51
reason we have to go back and do this
00:37:52
again because we need to have these
00:37:55
multiple discret samples there really
00:37:57
there's no way around having to do this
00:38:00
again and again so for each time to
00:38:02
repetition we're doing all of these
00:38:05
frequency en coding and then we're going
00:38:07
back and doing all the phase encoding no
00:38:10
for each repetition this is what we're
00:38:12
doing so each repetition contains both
00:38:16
phase encoding and frequency encoding
00:38:20
but in sequence not in parallel okay
00:38:24
okay so each time we repeat this we are
00:38:29
frequency encoding because we need our
00:38:31
signal always to be encoded in both
00:38:34
directions if we only encoded it once in
00:38:37
One Direction then we did everything
00:38:39
again encoding it in the other direction
00:38:41
then we would never be able to put the
00:38:43
two pieces of information together so
00:38:45
every line that we fill up here is
00:38:48
encoded both in the frequency and phase
00:38:51
directions right just in the frequency
00:38:54
Direction it's encoded in its entirety
00:38:59
every time we sample
00:39:01
it so we have our multiple samples
00:39:05
acquired every time we fill in one row
00:39:07
of kpace but when we fill in a single
00:39:10
row of kpace all we have is a single
00:39:16
sample as far as phase encoding is
00:39:19
concerned so when we repeat this again
00:39:22
we change the phase encoding gradient in
00:39:25
order to acquire another sample with
00:39:28
respect to phase encoding our frequency
00:39:31
encoding stays exactly the
00:39:34
same
00:39:36
yes I have a question on the pH anding
00:39:40
it's represented Cas so I think I
00:39:43
understand this like the central signal
00:39:46
intensity with regards to time why you
00:39:48
have a peak of the sple but don't
00:39:51
understand why you have a central
00:39:54
intensity pH and Direction okay so if
00:39:58
I'm turning on a phase encoding gradient
00:40:00
anytime I do that at any amplitude it
00:40:04
will mean that adjacent
00:40:07
spins or non-adjacent spins for that
00:40:09
matter will see different amounts of
00:40:11
gradient strength and therefore we'll
00:40:13
process at different frequencies and
00:40:14
we'll def phase that def phasing means
00:40:17
there's less trans net transverse
00:40:20
magnetization and less
00:40:21
signal okay if the gradient magnetic
00:40:24
field is stronger
00:40:27
the difference in processional frequency
00:40:30
between those two spins will be greater
00:40:33
because they're seeing a greater
00:40:34
difference in net field strength so
00:40:36
there will be a greater amount of Def
00:40:38
phasing so the steeper the gradient the
00:40:41
greater amount of Def phasing and
00:40:42
therefore the less
00:40:45
signal amplitude that is
00:40:48
lost so each of these rows in kpace is
00:40:52
acquired under a unique strength or
00:40:54
slope of that phase encoding gradient is
00:40:57
it it gradually increasing so it's
00:40:59
incremented and it is laid out so that
00:41:02
the weakest gradients are in the center
00:41:05
and the strongest are at the periphery
00:41:08
yes now it might be reordered
00:41:10
differently in some special applications
00:41:13
but as far as we're concerned at this
00:41:14
point they are incrementally ordered so
00:41:17
that the weakest gradients are at the
00:41:19
center and the strongest gradients are
00:41:22
placed at the peradi you have less phase
00:41:25
less def phasing def phasing
00:41:29
yes
00:41:31
mhm okay
