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Contrast is the difference between the signals that are measured in the different tissues. We have seen that the signal is proportional to the time derivative of the transverse magnetization. Let us examine how the transverse magnetization depends on the timing parameters of the sequence in case of the simple spin echo described in Chapter 6.2.4.
The timing of the echo, {EQUATION(size="75")}$T_{E}${EQUATION}, affects the signal basically through spin-spin relaxation.
::{EQUATION()}M_{\perp}(t')=M_{\perp}(0^{+})\textrm{e}^{-T_{E}/T_{2}}{EQUATION}::
where {EQUATION(size="75")}$0^{+}${EQUATION} directly refers to the moment after the excitation. (The echo compensates for the phase loss from the static inhomogeneities, thus {EQUATION(size="75")}$T_{2}$
{EQUATION} appears in the formula instead of {EQUATION(size="75")}$T_{2}^{*}${EQUATION})
We have seen that the MR sequences are repeated several times for phase encoding or for optimizing the signal-to-noise ratio. Repetition time {EQUATION(size="75")}$\textrm{T}_{\textrm{R}}${EQUATION}, which is the frequency of the excitation of the magnetization through the spin-grid relaxation, has an effect on the measurable signal. In order to keep things simple, let us assume that the repetition time is long compared to the transverse relaxation {EQUATION(size="75")}$\textrm{T}_{2}${EQUATION}.
{IMG(fileId="349",width="400",imalign="center",align="center",desc="Figure 4.")}{IMG}
Figure 4. shows the sequence of the two-dimensional spin echo experiment. The channels that are depicted are: the radio-frequency (RF) excitation signal, the slice selection gradient {EQUATION(size="75")}$G_{ss}${EQUATION} (the negative line segment that directly follows the RF pulse compensates the defocusing effect of the gradient), the phase encoding gradient {EQUATION(size="75")}$G_{pe}${EQUATION}, the frequency encoding or readout gradient {EQUATION(size="75")}$G_{R}${EQUATION} and the ADC, which refers to the analogue-to-digital converter and which shows the time of data collecting. Due to the phase encoding, the experiment has to be repeated several times with different {EQUATION(size="75")}$G_{pe}${EQUATION} values; this is what the pictogram in the form of a table refers to.
Before the first excitation the magnetization is in equilibrium: it points in the z direction and its magnitude is {EQUATION(size="75")}$\textrm{M}_{0}${EQUATION}. The 90° excitation rotates it completely into the transverse plane. After that, the magnetization develops according to formula (9).
::{EQUATION()}M_{z}(t') & = & (1-\textrm{e}^{-t'/T_{1}})M_{0}{EQUATION}::
::{EQUATION()}M_{\perp}(t') & = & M_{0}\textrm{e}^{-t'/T_{2}}{EQUATION}::
where {EQUATION(size="75")}$t'${EQUATION} the time passed after the last excitation.
The 180° pulse converts the longitudinal magnetization into its opposite: {EQUATION(size="75")}$M_{z}(\tau^{+})=-M_{z}(\tau^{-})${EQUATION}. According to our assumption the transversal component decays before the end of the cycle, so before the second 90° excitation only the longitudinal magnetization is present, the magnitude of which is
::{EQUATION()}M_{z}(T_{R}^{-}) & = & -M_{0}(1-\textrm{e}^{-\tau/T_{1}})\textrm{e}^{-(T_{R}-\tau)/T_{1}}+M_{0}(1-\textrm{e}^{-(T_{R}-\tau)/T_{1}})\\ & = & M_{0}(1-2e^{-(T_{R}-\tau)/T_{1}}+e^{-T_{R}/T_{1}}){EQUATION}::
This is rotated into the transverse plane by the second excitation, thus the magnetization that determines the measurable signal is
::{EQUATION()}M_{\perp}(T_{E}) & = & M_{0}(1-2e^{-(T_{R}-\tau)/T_{1}}+e^{-T_{R}/T_{1}})e^{-T_{E}/T_{2}}{EQUATION}::
The longitudinal component is built up in the same way as it is after the first excitation, thus its amplitude does not change during the subsequent repetitions. Assuming a homogeneous case, the signal can be written in the following simple form:
::{EQUATION()}S=\varrho_{0}(1-2e^{-(T_{R}-\tau)/T_{1}}+e^{-T_{R}/T_{1}})e^{-T_{E}/T_{2}}{EQUATION}::
The amplitude of the signal is basically affected by the ratio of the relaxation time {EQUATION(size="75")}$T_{1}${EQUATION} to the repetition time {EQUATION(size="75")}$T_{R}${EQUATION}, and the ratio of the relaxation time {EQUATION(size="75")}$T_{2}${EQUATION} to the echo time {EQUATION(size="75")}$T_{E}${EQUATION}. Three limiting cases are worth examining:
#__{EQUATION(size="75")}$T_{1}${EQUATION}-weighted imaging:__ the echo time is short compared to the typical relaxation time {EQUATION(size="75")}$T_{2}${EQUATION} of all tissues that are to be imaged, then the exponential factor is around 1 and the spin-spin relaxation affects the image to a lesser extent. Meanwhile, if {EQUATION(size="75")}$T_{R}${EQUATION} is in the order of magnitude of the spin-grid relaxation time of the tissues to be imaged, then typically {EQUATION(size="75")}$T_{R}\gg\tau${EQUATION}, the formula can be simplified and the image will be determined by {EQUATION(size="75")}$T_{R}/T_{1}${EQUATION} This is called a {EQUATION(size="75")}$T_{1}${EQUATION}-weighted image.
#__{EQUATION(size="75")}$T_{2}${EQUATION}-weighted imaging:__ if the repetition time {EQUATION(size="75")}$T_{R}${EQUATION} is long compared to all spin-grid relaxations, the corresponding exponents can be neglected and the signal will not be dependent on {EQUATION(size="75")}$T_{1}${EQUATION}. Meanwhile, if the echo time {EQUATION(size="75")}$T_{E}${EQUATION} is in the order of magnitude of the transverse relaxations, the image will be determined by the difference between them, and a so-called {EQUATION(size="75")}$T_{2}${EQUATION}-weighted image is obtained.
{img fileId="353,352,351" width="150"}
::Figure 5.::
Figure 5. shows coronal skull images with different contrasts. The image on the left is a {EQUATION(size="75")}$T_{1}${EQUATION} -weighted image, the one in the middle is a {EQUATION(size="75")}$T_{2}${EQUATION} -weighted image, while the one on the right is a proton density weighted image. The purpose of the different contrast mechanisms is not only the separation of the brain tissues (gray and white matter (GM and WM) and the cerebrospinal fluid (CSF)), but also the identification of different pathological conditions.
#__Spin density weighted imaging:__ if the repetition time {EQUATION(size="75")} $T_{R}${EQUATION} is long compared to all spin-grid relaxations the corresponding exponents can be neglected and the signal will not be dependent on {EQUATION(size="75")}$T_{1}${EQUATION}. Meanwhile, if the echo time {EQUATION(size="75")}$T_{E}${EQUATION} is short compared to all transverse relaxations, then the image will basically be determined by the inhomogeneity of the spin density {EQUATION(size="75")}$\varrho_{0}${EQUATION}.
By changing the timing parameters of the sequence, the measurable signal will be determined by different physical properties, which thus dominate the contrast of the image. It can also be seen that the regions of different contrast have blurred boundaries. The phrasing that a parameter “is in the order of magnitude of the relaxation times” is diffuse, since the relaxation times often encompass several orders of magnitude (bone: 150 ms / 350 μs, GM: 920 ms / 100 ms , WM: 780 ms / 90 ms, CSF: 4300 ms / 2200 ms). Due to different practical considerations (typically the duration of the examination) it is often impossible to aspire to clear contrasts.
The three cases described above are only the simplest contrast mechanisms. Further physical quantities – such as the rate of diffusion, the full diffusion tensor, the flows, and the physical deformation – can be imaged with more complex sequences.