Imagen de resonancia magnética

http://www.cis.rit.edu/htbooks/mri/inside.htmMagnetic resonance imaging, G.A. WRIGHT IEEE SIGNAL PROCESSING

MAGAZINE pp:56-66 JANUARY 1997

MRI Timeline1946 MR phenomenon - Bloch & Purcell1952 Nobel Prize - Bloch & Purcell1950 NMR developed as analytical tool196019701972 Computerized Tomography1973 Backprojection MRI - Lauterbur1975 Fourier Imaging - Ernst1977 Echo-planar imaging - Mansfield1980 FT MRI demonstrated - Edelstein1986 Gradient Echo Imaging NMR Microscope1987 MR Angiography - Dumoulin1991 Nobel Prize - Ernst1992 Functional MRI1994 Hyperpolarized 129Xe Imaging2003 Nobel Prize - Lauterbur & Mansfield

Modelos de scanners

Algunas bobinas de GE

Doty coils

Tomographic imaging

Magnetic resonance started out as a tomographic imaging modality for producing NMR images of a slice through the human body.

Magnetic resonance imaging is based on the absorption and emission of energy in the radio frequency range of the electromagnetic spectrum.

Many scientists were taught that you can not image objects smaller than the wavelength of the energy being used to image.

MRI gets around this limitation by producing images based on spatial variations in the phase and frequency of the radio frequency energy being absorbed and emitted by the imaged object.

Microscopic Property Responsible for MRI

The human body is primarily fat and water.

Fat and water have many hydrogen atoms which make the human body approximately 63% hydrogen atoms.

Hydrogen nuclei have an NMR signal.

For these reasons magnetic resonance imaging primarily images the NMR signal from the hydrogen nuclei.

The proton possesses a property called spin which:

1. can be thought of as a small magnetic field, and 2. will cause the nucleus to produce an NMR signal.

Basic physics

Magnetic resonance imaging, G.A. WRIGHT IEEE SIGNAL PROCESSING MAGAZINE pp:56-66 JANUARY 1997

The relevant property of the proton is its spin, I, anda simple classical picture of spin is a charge distribution inthe nucleus rotating around an axis collinear with I.

The resulting current has an associated dipole magnetic moment, , collinear with I, and the quantum mechanical relationship between the two is where h is Planck’s constant and y is the gyromagnetic ratio.

For protons, y/2n = 42.6 MHz/T.

In a single-volume element corresponding to a pixel in anMR image, there are many protons, each with an associateddipole magnetic moment, and the net magnetization,

M = Mx j+ Myi + Mzk,

of the volume element is the vector sum of theindividual dipole moments, where i, j, and k are unit vectorsalong the x, y , and z axes, respectively.

In the absence of a magnetic field, the spatial orientation of each dipole moment is random and M = 0.

This situation is changed by a static magnetic field, Bo =Bok.

This field induces magnetic moments to align them-selves in its direction, partially overcoming thermal randomization

so that, in equilibrium, the net magnetization,

M =M0k, represents a small fraction (determined from theBoltzmann distribution) of times the total number ofprotons.

While the fraction is small, the total number of contributing protons is very large at approximately 10'' dipoles in a S mm3 volume.

Equilibrium is not achieved instantaneously. Rather, from the time the static field is turned on, M grows from zero toward its equilibrium value M, along the z axis; that is,

where T1 is the longitudinal relaxation time. This equationexpresses the dynamical behavior of the component of the netmagnetization Mz along the longitudinal (z) axis.

The component of the net magnetization, Mxy, which liesin the transverse plane orthogonal to the longitudinal axis,undergoes completely different dynamics. Mxy, often referred to as the transverse magnetization, can be described by acomplex quantity

where Thiscomponentprecesses about Bo, i.e., The precession frequency

is proportional to B, and is referred to as the Larmor frequency(Fig. 1 b). This relation holds at the level of individualdipoles as well, so that

Accompanying any rotating dipole magnetic moment is aradiated electromagnetic signal circularly polarized about theaxis of precession; this is the signal detected in MRI.

The usual receiver is a coil, resonant at 0 , whose axis lies in thetransverse plane-as Mxy, precesses, it induces an electromotiveforce (emf) in the coil.

If Bo induces a collinear equilibriummagnetization M, how can we produce precessingmagnetization orthogonal to Bo?

The answer is to apply asecond, time-varying magnetic field that lies in the planetransverse to Bo

This field rotates about the static field direction k at radian frequency 0

If we then place ourselves in a frame of reference (x'y'z) that also rotates at radian frequency 0, this second field appears stationary.

Moreover, any magnetizationcomponent orthogonal to B0, no longer appears to rotateabout Bo. Instead, in this rotating frame, M appears to precessabout the "stationary" field B1, alone with radian frequency.

One can therefore choose the duration of B1, so thatM is rotated into the transverse plane.

The corresponding B1 waveform is called a 90" excitation pulse

The signal from Mxy will eventually decay.

•Part of this decay is the result of the drive to thermal equilibrium where M is brought parallel to Bo, as described earlier.

•Over time, the vector sum, M, decreases in magnitude since the individual dipole moments no longer add constructively.

The associated decay is characterized by an exponential with time constant T2*

the loss of transverse magnetization due to dephasing can be recovered to some extent by inducing a spin echo.

Specifically, let the dipole moments evolve for a time after excitation. At this time apply another B1 field along y' to rotate the dipole moments 180" around B1. This occurs in a time that is very short compared to .

This pulse effectively negates the phase of the individual dipole moments that have developed relative to the axis of rotation of the refocusing pulse. Assuming the precession frequencies of the individual dipole moments remain unchanged then at a time ,, after the spin-echo or 180" pulse, the original contributions of the individual dipoles refocus (Fig. 2a). Hence, at a time TE = 2 after the excitation, the net magnetization is the same as it was just after excitation.

If one applies a periodically spaced train of such 180" pulses following a single excitation, one observes that the envelope defined by at each echo time steadily decays (Fig. 2b).

This irreversible signal loss is often modeled by an exponential decay with time constant T2. the transverse relaxation time:

Before the experiment can he repeated with another excitationpulse, sufficient time must elapse to re-establish equilibriummagnetization along k.

As indicated in Eq. (l), a sequence repetition time, TR, of several Tls is necessary for full recovery of equilibrium magnetization, Mo, along Mz, between excitations.

Bloch equation

Imaging, contrast and noise

Imaging: spatial resoltion of the signal

Two-step process: (i) exciting the magnetization into the transverse plane

over a spatially restricted region, and

(ii) encoding spatial location of the signal during data acquisition.

Spatially Selective Excitation

The usual goal in spatially selective excitation is to tip magnetization in a thin spatial slice or section along the z axis, into the transverse plane. Conceptually, this is accomplished by first causing the Larmor frequency to vary linearly in one spatial dimension,

and then, while holding the field constant, applying a radiofrequency (RF) excitation pulse crafted to contain significant energy only over a limited range of temporal frequencies (BW) corresponding to the Larmor frequencies in the slice.

To a first approximation, the amplitude of the componentat each frequency in the excitation signal determines theflip angle of the protons resonating at that frequency.

If the temporal Fourier transform of the pulse has arectangular distribution about 0, a rectangular distributionof spins around zo is tipped away from the z axis over a spatial extent

For small tip angles we can solve the Bloch equations explicitly to get the spatial distribution of Mxy following an RF pulse, B1(t), in the presence of a magnetic field gradient of amplitude Gz:

Assume that all the magnetization initiallylies along the z axis. Under these conditions, a rectangularslice profile is achieved if

Image Formation Through S p a t i a l Frequency Encoding

The Imaging Equation

Once one has isolated a volume of interest using selectiveexcitation, the volume can be imaged by manipulating theprecession frequency (determined by the Larmor relation), and hence the phase of Mxy. For example, introduce a linear magnetic field gradient, Gx, in the x direction so that

each dipole now contributes a signal at a frequency proportional to its x-axis coordinate.

In principle, by performing a Fourier transform on the receivedsignal, one can determine Mxy as a function of x.

An equivalent point of view follows from observing that eachdipole contributes a signal with a phase that depends linearlyon its x-axis coordinate and time.

Thus, the signal as a whole samples the spatial Fourier transform of the image along the kx spatial frequency axis, with the sampled location moving along this axis linearly with time.

A more general viewpoint can be developed mathematicallyfrom the Bloch equation.Using spatially selective excitation only protons ina thin slice at z = zo are tipped into the transverse plane so that

Let the magnetic field after excitation be

Assume is relatively constant during data acquisition (i.e. acquisition duration << Tl,T2,T2*); and let the time at the center of the acquisition be tacq. During acquisition

The signal received, S(t), is the integral of this signal overthe xy plane.

If this signal is demodulated by 0 then the resulting basebandsignal, Se(kx(t), ky(t)), is the 2D spatial Fourier transform of

at spatial frequency coordinates kx(t) and ky(t).

One chooses Gx(t) and Gy(t) so that, over the full data acquisition, the 2D frequency domain is adequately sampled and the desired image can be reconstructed as the inverse Fourier transform of the acquired data.