Physics of Image Formation Flashcards
Why is quadrature detection needed in MRI?
A single measurement cannot distinguish between magnetisation precessing above or below the reference frequency. Cos(a)=Cos(-a).
How is quadrature detection achieved?
Measure the signal relative to two axed at 90deg to each other. The real (x) channel shows the magnitude and the imaginary (y) channel shows the direction. The signal is no described in complex notation.
What is the complex notation for an MR signal?
S(r)=M_0.cos{gamma.G(r).r.t}+i.M_0.sin{gamma.G(r).r.t}
What is the exponential notation for an MR signal?
S(r)=M_0.exp(-i.{gamma.G(r).r.t})
What assumption is made about the complex and exponential forms of the signal?
G(r) is time invariant.
How is the exponential notation changed if G(r) is time dependent?
Signal phase, phi, is given by:
phi(t)=int[0-t].(gamma.G(r,t).r.dt)
So:
s(t)=int{M_0(r).exp(-i.gamma.int[0-t]G(r,t).r.dt)}.dr
How does k-space simplify the time-dependent exponential notation?
k=int[0-t’].(gamma.G(r,t).r.dt)
So:
s(k)=int{M_0(r).exp(-ikr)}.dr
How does the sampled signal relate to the proton density?
The sampled signal as a function of k is a direct Fourier Transform of the proton density.
How does the theoretical signal derivation differ from real life signal?
The theoretical equation describes a continuous signal, in reality, we sample discretely and so use the discrete Fourier Transform.
What is the discrete version of k in a constant gradient?
K_n=Sigma[j=0,j=n]{gamm.Gr.j.dt}
Why is it necessary to have a negative gradietn before sampling in k-space?
k=0 is the origin on k-space. if we want to sample negative regions of k-space we need to have a negative k. As k depend on G and t, and t can’t be negative we need a negative gradient.
What is the Nyquist criterion?
To fully realise the data, we must sample at least twice within one cycle of the data.
How is the Field of view related to k-space separation?
Phase accumulation: phi(dt)=gamm.Gx.dt Maximum phase allowed in one dwell time: phi_max=gam.Gx.dt=pi (Nyquist criterion) Rearranging: x= pi/(gamm.Gdt)=pi/dk FOV is2x: FOV = 2*pi/dk
How is the resolution related to the width of k-space?
res = FOV/Np (Np= No. of data points)
res = 2*pi/dk.Np
Np.dk is the width of k-space
What problems arise from the defined frequency range of MRI in the presence of noise and how is it removed?
Noise has a much wider frequency range and so will alias in the image and increase in amplitude.
By filtering any signal before it enters the signal processing to just the MRI frequency range the noise will not alias.
What is the sampling bandwidth?
The frequency separation of magnetisation at the edge of the FOV.
What is the equation for the sampling bandwidth or sweep width?
SW=gamma.G.FOV/2*pi=1/dt
Why can we filter to avoid aliasing in the FE gradient but not the PE gradient?
Not sampling a continuous frequency in PE, we are detecting a pseudo-frequency and so filtering can’t work.
What is the ideal RF pulse for slice selection and what is its associated Fourier Transform?
- Top hat function (square slice) fully excites within the frequency range and no excitation outside.
- Fourier transform is a sinc function (sin(x)/x)
How is the slice selection function created? What two waves are convolved together and what do they each effect?
A carrier sine wave at the Larmor frequency corresponding to the centre of the required slice is amplitude modulated with a sine(x) function that adjusts the slice thickness.
Why is the rewinding gradient needed after the slice selection gradient?
Precession in combined B1 and G field causes dephasing. Need to rewind the phase to compensate for this.
What is the equation for slice thickness?
Ts=(2*pi.BW)/(gamma.G_ss)
How does the RF pulse affect the slice thickness?
Long pulse - Thin slice
Short pulse - Thick slice
Why is impossible to create a perfect top-hat RF pulse?
The sinc function that drives it is an infinite function and must be truncated in the real world.
Truncation alters the frequency spectrum and so the slice is no longer rectangular.
