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Magnetic resonance imaging (MRI) is a versatile medical imaging diagnostic tool. MRI produces a map of hydrogen atoms in the body, i.e., uses the magnetic properties of hydrogen and its interaction with both a large external magnetic field and radio waves to produce highly detailed images of the human body. This magnetic field is supplied defines the axis about which protons precess.
The static field direction is also the reference axis for the nutation angle of the protons following the application of radio-frequency (RF) pulses. A range of field strengths is used for imaging. The operation of an MRI system requires the use of several standard electronics components and the process requires a highly trained operator. Quality assurance in MRI reflects the principles of image formation and display that determine the appearance of any medical image. Tests such as resolution, contrast, linearity, and sensitivity are a necessary part of evaluating equipment performance. In some cases, chemical agents can be injected to improve the contrast in the image.
KEYWORDS: MRI; magnetic field; radio-frequency pulse; resolution; contrast; sensivity
Chapter 1 - Basic Concepts to understand the physical phenomenon
1.1 - Introduction
The basic principle of Magnetic Resonance (MR) is the interaction among a foreign magnetic field and a nucleus which has nuclear spin .
To introduce this theme, we think that is useful to do an introduction about atomic structure and the properties of nucleus. With this concepts, is less difficult understand the principles of MR.
1.2 Atomic Structure and Properties
The atomic structure is common in every material. Protons, neutrons and electrons are the main constituents of atoms. Protons have a positive charge and neutrons have no charge; they are in the core of the atom. Electrons have a negative charge and are located in orbitals surrounding the nucleus.
Nuclear spin is also called nuclear spin angular momentum and its value depends on the precise atomic composition. Therefore, physicist must use two properties that identify unequivocally every elements of Periodic Table (PT): atomic number and atomic weight. The atomic number refers the total of protons that are in the nucleus; there aren't two elements with the same atomic number. The atomic weight is defined by the sum of number of protons and the number of neutrons. Are known atoms with the same atomic number but different atomic weight and these atoms are isotopes. 
1.3 Special Properties of atoms used in MR
There are nucleus that can be used for Magnetic Resonance, so in this phenomenon, nucleus must have two important properties: spin and charge.
We can consider that the nucleus is constantly rotating about an axis at a constant velocity. This self-rotation axis is perpendicular to the direction of rotation (Figure 1).
Figure 1.1 A rotating nucleus with a positive charge produces a magnetic field known as the magnetic moment oriented parallel to the axis of rotation (left side of figure). This arrangement is analogous to a bar magnet in which the magnetic field is considered to be oriented from the South to the North Pole (right side)
Source: MRI: Basic Principles and Applications
Analyzing the nature, we found a limited number of values for the spin, i.e., the spin, I, can be quantized to certain discrete values.
These values depend on two factors: the atomic number and atomic weight of the atoms in analysis.
There are three groups of values for I:
Zero (I=0), if the nucleus has an even number atomic weight and an even atomic number; there are no interaction with an external magnetic field so this atoms cannot be studied using MR;
Integral values (e.g. I=1,2,3), if the nucleus has an even atomic weight and an odd atomic number;
Half-integral value (e.g. I=1/2, 3/2, 5/2), if the nucleus an odd atomic weight.
Next table lists the spin for some elements that are usually found in biological systems.
Table 1.1 Spin for Selected Nuclei of Biological Interest
Nuclear spin (I)
Source: Adapted from MRI: Basic Principles and Applications 
1.4 Importance of in MR
The nucleus, that we can consider a single proton, is a natural choice to analyze and study the body with this technique: it has a spin of Â½ and is the most abundant isotope for hydrogen and also, its response to an applied magnetic field in one of the largest found in nature. And still, the human body is composed by tissues that contain water and fat, and these tissues contain this nucleus.
Like we kwon, nucleus which are positively charged have a local magnetic field. This magnetic moment is essential to MR. For understand this property, a bar magnet provides a useful analogy (Figure 1.1) .
When a strong magnetic field is applied in tissue, the protons line up their spins with the direction of the magnetic field in a manner similar to a compass needle aligned with the earth's magnetic field.
If the patient is placed in a magnetic field , the individual protons begin to rotate perpendicular to the magnetic field, so its axis of rotation is parallel to .
The protons that have spin aligned with the magnetic field have slightly less energy than protons with spin opposing the magnetic field. A photon with energy equal to the energy difference between the two states can boost protons from the lower to the higher energy state. In mechanical model, the frequency of the radio wave that interacts in resonance is given by the Larmor equation:
In the quantum mechanical model, the energy of the photon is given by the equation ,
This equation permits a calculation of the photon energy required to cause transitions between law high energy states.
Knowing the Larmor frequency, we can use it to predict the frequency of precession of a proton in a magnetic field. When one wave has a frequency that matches the precession of protons in a magnetic field, it is said to be in "resonance" . Appropriate frequencies are in the FM radio portion of the electromagnetic spectrum .
When a radio wave is applied to a tissue at the Resonance Frequency (RF), the bulk magnetization precesses at the Larmor Frequency. The angle of precession is determined by the intensity of the ratio wave and the amount of time over which it is applied.
When the RF pulse is applied, the spins are brought into synchrony, and the individual nuclear magnetic moments reinforce each other to produce a strong bulk magnetic moment.
1.5 Relaxation Processes: T1,T2 e T2*
When the radio wave is turned off, the signal come-down. This decay is the result of the return of protons to the state that existed before the radio wave was applied. This return is called by relaxation of protons. There are three basic processes that are observed on the MR signal.
The first relation process involves a return of the protons to their original alignment with the static magnetic field. This process called longitudinal or spin -lattice relaxation, is characterized by a time constant T1. The term spin-lattice refers to the interaction of the protons (spins) with their surroundings. This interaction causes a net release of energy to the surroundings as the protons returns to the lower energy state of alignment.
The other relaxation process is a loss of synchrony of precession among the protons. Before a radio wave is applied, the precessional orientation of the protons is random. The application of a radio wave brings the protons into synchronous precession, or "in phase". When the radio wave is switched off, the protons begin to interact with their neighbors and give up energy in random collisions. In so doing, they revert to a state of random phase. As the protons revert to random orientation, the bulk signal decreases because the magnetic moments tend to cancel each other. This process is called transverse or spin-spin relaxation and is characterized by a time constant T2 .
Finally, disturbances in magnetic field (magnetic susceptibility) increase the rate of spin coherence T2 relaxation and this process is characterized by a time constant T2*. Inhomogeneities in the field cause some protons to spin at slightly different frequencies so they lose coherence faster and T2* decay can change .
In a patient undergoing MRI, both longitudinal and transverse relaxation processes occur at the same time. The transverse (T2) relaxation time is always shorter than the longitudinal (T1) relaxation time. That is, magnetic moments diphase faster than they move into alignment with the static magnetic field.
Figure 1.2 A: Two relaxation processes in a sample of nuclear spins. A1: Longitudinal relaxation occurs as the spins return to alignement with the static magnetic field, B0.A2: Transverse relaxation occurs as the spins preccess "out of phase" B: spin-spin relaxation diagramed in the rotating frame of reference. B1: Magnetic moment of the sample is aligned with the magnetic field. B2: Immediately after an RF pulse, the magnetic moment of the sample can be represented by a single vector. B3: As the magnetization vector begins to break up or dephase as a result of localized nonuniformities in the applied field, components of the vector begin to fan out in the xy plane. B4: when there are an equal number of the components in all directions in the xy plane, the components cancel one another and the MR signal disappears. B5: As time passes, the cone representing the precessing but dephased magnetic moment continues to arrow because of spin-lattice relaxation. B1: Finally the magnetic moment once again is realigned with the applied field
Source: Medical Imaging Physics
"For typical biological materials, T1, may be on the order of several hundred milliseconds while T2 is a few tens of miliseconds" 
Table 1.2 Relaxation times (Mean Â±SD) in Miliseconds for Various Tissues at 1 Tesla Static Magnetic Field Strength (42.6 MHz)
732 Â± 132
47 Â± 13
423 Â± 93
43 Â± 14
589 Â± 159
58 Â± 24
241 Â± 68
84 Â± 36
813 Â± 138
101 Â± 13
683 Â± 116
92 Â± 22
Source: Medical Imaging Physics
Relaxation of the MR signal is characterized by exponential expressions analogous to those used to describe radioactive decay and absorption of photons .
1.6 Relaxation times (T1 and T2) for biological materials
Biological materials may be characterized to some degree by their T1 and T2 values. However, there are several difficulties. For example, the exact values are not a range of values for T1 and T2.; the temperature of a sample also influences relaxation.
The rate of interaction among spins and their surroundings determines the rate at which the spins in a higher energy state dissipate energy to their surroundings. Molecules in a sample are in constant motion and rotate with frequencies that range from zero up to a maximum value determined by the temperature. Any magnetic moment is influenced by the rotation of nearby magnetic moments. Spins may change energy states from parallel to antiparallel alignment (T1), and they may also move out of phase with other spins (T2) as a result of these interactions.
Longitudinal relaxation T1 has been shown to vary magnetic field strength. Since magnetic field strength, along with the gyromagnetic ratio, determines the resonance frequency for a nucleus, T1 may be expressed as a function of resonance frequency. "For a wide range of tissues, T1for hydrogen can be approximated as
Where T1 is in milliseconds, is the resonance frequency in hertz, and the parameters and vary with tissue type over a Range and . The transverse relaxation time T2 has been found to be independent of resonance frequency (magnetic field strange)" .
The properties of a material that give rise to observed values of T1 and T2 are complex. However, a theory of the contribution of molecular motion to relaxation was suggest by Bloembergem et al. in 1948. An important characteristic of this theory is the correlation time of molecules. Molecules in liquids and semisolids are free to rotate. The rate at which they rotate is the rotational frequency. The inverse of rotational frequency is the rotational period, also called the correlation time . Molecules that rotate more slowly have a greater probability of interacting with their neighbors. In such materials, relaxation can occur more rapidly, and the relaxation time constant is smaller. For T2 relaxation, the prediction is straight-forward; a longer correlation time implies a faster transverse relaxation (short T2). For T1, however, there is a resonance phenomenon to consider. Molecules rotating at Larmor frequency maximize their rate of interaction with their neighbors, just as the interaction of radio waves with magnetic moments is maximized at the Larmor frequency. Thus a material having a correlation time that happens to coincide with the inverse of the Larmor frequency being used for MRI yields the minimum T1. Materials having smaller or larger values of correlation time have a larger T1. Furthermore, T1 depends on the Larmor frequency and increase as the magnetic field strength is increase. T2 is relatively unaffected by changes in resonance frequency and is therefore independent of field strength.
Chapter 2 - Creating an MR image
2.1 Spin eco
The imaging involves a succession of impulses that emphasize the parameters that most interest us. One of the sequences corresponds to the sequential repetition of a pulse of 90 Â° followed by a number of 180 Â°. In this sequence, , is the time between impulse of 180 Â° and two consecutive pulses of 90 Â°.
2.2 Signal strength
The signal strength is all the more intense the higher the density proton,
I Î± n (4)
The signal intensity depends on T2, according to the expression,
The signal intensity depends on T1, according to the expression,
Thus, the measured signal depends on the proton density, relaxation time spin / spin and relaxation time spin/lattice.
This form shows how to manipulate the contrast of images, emphasizing the features you want. When two tissues have close relaxation time but different protons densities, we use short intervals between two impulses of 180° (TE) and long intervals between two impulses of 90°. In this case the way to separate the tissue it is primarily for proton density.
2.3 Magnetic Field Gradients
The mechanism to distinguish the various points of a tissue involves applying a gradient field in place of the static magnetic field. By applying a magnetic field gradient in a certain direction, the spins will start to rotate at different velocities and thus the frequencyof the radiation measured will be different for each portion of the perpendicular .
Figure 2.1 A craniocaudal "gradient" or change in the magnetic field along the craniocaudal axis allows receiver coils to be "turned in" to a slice
2.4 Gradients for imaging
It is also necessary to know the mechanism for associating a signal to a position and then the construction of the image. To measure the transverse magnetization we have access to three parameters: proton density, T1 and T2.
Figure 2.2 Notation system of axis used.
It begins by introducing a second field gradient z, i.e., the static magnetic field to which the individual subject adds to small fields of different intensity according to z. These conditions the protons of hydrogen atoms in each purchase a plane perpendicular to the z axis, a certain frequency. This implies that, when applied to an RF field with a specific frequency, it acts only on the spins that process with this frequency. That is, only a few spins are responsible for the magnetization of the tissue.
Knowing this mechanism, the portion of tissue is established from the range of frequencies contained in the RF pulse. However, there is a practical difficulty in setting limits in the range of frequencies present in the RF pulse. Thus, the option is to leave a neutral piece of tissue over which it obtained information .
Afterwards, apply a second gradient on y direction, spins that were in phase acquire different frequencies. When this gradient stops spins start to rotate with the same velocities but each portion of tissue is out of phase. For the three-dimensional information is used a gradient field on x-axis using different frequencies to each point.
Chapter 3 - Instrumentation
3.1 - Introduction
The instrumentations used on MRI is one of the most important aspects in this technique. The machines that can be found on the market have different capabilities and features which make difficult to compare and evaluate objectively. The main differences are in the software provided by the manufacturer, since the hardware components are common to all systems.
The major components that compose the system are the computer and image processing systems, a magnet system, a gradient system, a radiofrequency system and a data acquisition system.
Figure 3.1 - MRI scanner cutaway
3.2 - Computer and image processing system
Actually for produce the MRI image we need has a minimum of two computers, the main or host computer controls the user interface software, which enables the operator to control all functions of the scanner. The user is able to select or modify the parameters, and the images can be displayed or recorded on a film or other media, one or more hard disks are used to store the patient images immediately following reconstruction. The image processor is controlled by the second computer, these perform the Fourier transformations or other processing of detected data, and all the processes carried out by the processor are controlled by software provided by the manufacturer. "This image processors used in the MRI system are capable of performing the Fourier transformation for a 256 x 256 matrix in less than 50 milliseconds" .
For the operator input its necessary a console, which may be attached to the main computer or may have direct access to the reconstructed images. Each console has a keyboard and one or more monitors for displaying images and text information. Sometimes, other viewing stations may be completely detached from the primary computer system and access the image data through a network connection.
Most MRI systems are incorporated with a facility's computer network. This allows transferences directly from MRI host computer to another computer in a remote location than using removable data storage (e.g., film or CD-ROM). The interconnections between the computers are normally one of two connection types, Ethernet or through a dial-up or cable modem. On this type of information sharing it's, the computers must be a common format for writing the data if it is to be interpreted correctly. One format that becomes the industry standard for facilitating image and medical data transfer is now as DICOM, which stands for Digital Imaging and Communications in Medicine. It is a result of a join committee of American College of Radiology and the National Electrical Manufactures Association (ACR-NEMA).  Programs for reading DICOM-format images are available at no cost and others available for free. The DICOM standard has features that control the communication relationship between systems, this is critical to ensure confidentiality of patient information according to Brown, Mark A et al.
Figure 3.2 - Diagram of the main electronic components of an MRI system. The functions of the various components are described in the text
Source: Medical Imaging Physics
3.3 - Magnet System
Any component of the MRI scanner is so important and expensive as the magnet. "Magnets are usually categorized as low-, medium-, or high-field systems. Magnets are also characterized by the metal used in composition" . Most magnets are of the superconducting type, this one's use niobium-titanium alloy wire immersed in liquid helium.
The design of the magnet can affect the homogeneity or uniformity of the magnetic field. Magnets which are large-bore solenoidal generally have the best homogeneity over the largest volume. For express magnetic field homogeneity usually is used ppm relative to the main field over a certain distance, this values are measured at various locations inside the magnet and used to calculate the field variation.
"Field homogeny is an important factor for consider when evaluating an MRI system, as inadequate homogeneity can cause problems with fat saturation or even general imaging." 
3.4 - Gradient System
The gradient coils produce the gradients in the, magnetic field, which is used to localize the tissue signals. The gradients are used one each in the directions x, y and z, these three are necessary to produce the orthogonal fields variation required for imaging. During the performance of assessing gradient system performance, there four important aspects: maximum gradient strength, rise time or slew rate, duty cycle, ant techniques for eddy current compensation. For the gradient measure are used or as the units of calculation, with typical maximum gradient strengths for the current state-of-the art MRI system being . 
The effective gradient is also a quantifier used to describe maximum gradient amplitudes. This is the vector sum of all three gradients when applied during the scan:
The gradient coils produce the gradients in the magnetic field. The creation of the desired gradient is responsibility of the configuration the coils. The horizontal bore superconducting magnet is the most common configuration used.
3.5 - Radio Frequency System
To excite the protons its necessary a radio frequency (RF) transmitter which generate and broadcast the RF pulses. This transmitter it's composed by four main components: a frequency synthesizer, the digital envelope of RF frequencies, a high power amplifier, and a coil or antenna.
The frequency synthesizer has three main functions, one of these is the production of the center carrier frequency for the RF pulse. It also provides the master clock for the measurement hard-ware during the scan, and controls the relative phase of the RF pulse.
The production of sufficient power from the frequency synthesizer signal to excite the protons is one responsibility of RF power amplifier. The amplifier may be solid state or a tube type.
For the storage of the range or bandwidth of frequencies it's necessary the RF enveloped which is stored as a discrete envelope or function. It is mixed with the carrier frequency prior to amplification to produce an amplitude- or phase-modulated pulse centered at the desired frequency. For some scanners, the final frequency is produced exclusively by the frequency synthesizer, whereas for other scanners, the RF envelope is modulated to incorporate a frequency offset into the pulse, according to Brown, Mark A et al.
The transmitter coil is the last component of the RF system, all MR measures needs an antenna or transmitter coil to broadcast the RF pulses. This transmitter don't have a defined size or shape, the only requirement that must be met they generate an effective field perpendicular to
Although MR is considered a relatively safe imaging technique, the absorbed RF power generates heat inside the patient. Manufactures are required by the governing regulatory organizations [Food and Drug Administration (FDA), International Electrotechnical Commission (IES), etc.] to monitor the RF power absorbed by the patient so that excessive patient heating does not occur in the both the excited tissue volume (localized) and the entire patient, according to Brown, Mark A et al.
Chapter 4 - Applications
The clinical applications of MRI images are very different according to the specify characteristics of the human body. For a better understanding here are some examples of how these are useful in diagnosis and characterization of several diseases.
One of the most important areas where the RMI images are indispensable is the neurology. As can be observed in the figure (x) these images have the advantage of discern the anatomic differences and by that indentify some diseases.
Figure 4.1 - Sagittal image of the head
The abdomen is also a region where MRI images are widely used for
observe any injury or change of structure resulting in a wonderful clarity of all
Figure 4.2 Image of the abdomen.
On the bone structure, MRI does not reveal more information than the TAC. Nevertheless, in tumor studies MRI can be a big help, since it allows, usually, in tumor studies, a great contrast between the normal, tumor and all the other human tissues.
Figure 4.3 - Image of bone and skeletal muscle.