Diffusion MRI

The diffusion -weighted magnetic resonance imaging ( DW- MRI of abbreviated English diffusion -weighted magnetic resonance imaging ) is an imaging technique that measures using magnetic resonance imaging (MRI ), diffusion motion of water molecules in body tissues and is spatially resolved. It is used in practice, primarily for the investigation of the brain, since the diffusion behavior in tissues characteristically altered in some diseases of the central nervous system and the directional dependence of diffusion allows conclusions on the course of major nerve fiber bundles. Like the classic diffusion-weighted MRI is non-invasive imaging: As the image contrast is achieved solely by means of magnetic field gradients, it does not require an injection of contrast agents or use of ionizing radiation.

The diffusion tensor imaging ( DTI abbreviated from English- diffusion tensor imaging or DT- MRI of diffusion tensor magnetic resonance imaging ) is a commonly used variant of the DW- MRI, which also captures the directional dependence of diffusion. Per volume element (voxel ) determine not just a single numerical value that can be represented in the sectional view as gray value, but calculates a tensor (specifically, a 3 × 3 matrix ) that describes the three-dimensional diffusion behavior. Such measurements are considerably more time-consuming than conventional MRI scans and generate larger amounts of data that can be interpreted only by the use of various visualization techniques, the radiologist.

Diffusion imaging was developed in the 1980s. Meanwhile, it is supported by all new MRI equipment and has particularly established in clinical practice for stroke diagnosis because the affected brain regions are already much earlier seen in diffusion-weighted images than in classical MRI. The diffusion tensor imaging was developed in the mid 1990s. Some clinics they put a for surgical and radiation planning. In addition, the DT- MRI is used in medical research, particularly for research into diseases that are associated with white matter changes (such as Alzheimer's disease or multiple sclerosis). The development of diffusion-weighted imaging itself is subject of current research, such as under the Human Connectome Project.

• 2.1 sectional images
• 2.2 tractography
• 2.3 Tensor Glyphs

• 3.1 diagnostics
• 3.2 Operation Planning
• 3.3 Research

• 5.1 Improvement of the image quality
• 5.2 increase in the angular resolution
• 5.3 Processing and analysis of data

Measurement methods

Basics

Diffusion imaging is based on the same physical principles as conventional MRI (see also Main article magnetic resonance imaging ). So you use the fact that protons have a magnetic moment and align in an external magnetic field either parallel ( low energy state) or anti-parallel ( high energy state). In equilibrium, there is a slightly larger number of protons in the low-energy state, whereby a sum vector parallel to the external field is created ( paramagnetic effect). The direction of the external field is referred to in the context of MRI as a z-axis; is perpendicular to the xy plane.

The axis of rotation of the protons precess around the z- axis. The frequency of this motion is proportional to the field strength of the external magnetic field and Larmor frequency is called. A high-frequency electromagnetic wave ( " RF pulse " ) with exactly this frequency stimulates the magnetic moments in a change of its state at ( nuclear magnetic resonance). This varies depending on intensity and duration of the pulse, the orientation of the vector sum, he " turns over ". The folded-over first moments rotate in phase, so that the sum vector has now also a (rotating ) component in the x-y plane.

This effect can be observed with a measuring coil, which is perpendicular to the xy plane; in it induces the rotating net moment a voltage. Switched to the RF pulse from the protons return back to its equilibrium state. Due to inhomogeneities in the external field and thermal shocks ( "spin -spin interaction " ) is also the phase coherence and the xy - component of the sum vector loses disappears. To observe the diffusion movement has to be a make " spatially resolved " NMR experiment, ie, a field gradient NMR experiment in which by the application of magnetic field gradient NMR signal frequency is made location-dependent and thus changes in location of the water molecules by diffusion are observed.

Diffusion-weighted MRI sequences

A diffusion-weighted MRI sequence (see scheme) starts with the sum vector is initially tilted by 90 ° in the xy plane. The diffusion weighting is now done by a briefly switched gradient field, which varies the field strength of the external magnetic field in a given direction. Along this direction, the nuclei no longer precess with the same Larmor frequency; they get out of phase and the voltage induced in the measuring coil voltage disappears.

Then, it returns to a new RF pulse to the direction of rotation of the cores (180 ° pulse ), and again on the same gradient field. Due to the identical frequency differences in the reverse direction, the magnetic moments come again in phase and there is again a voltage on the spin-echo. This is, however, weaker than the signal at the beginning of the sequence, since a part of the cores does not come back into phase - These are in particular those that have moved during the measurement in the direction of the gradient field. A diffusion movement in this direction is thus manifested in an attenuation of the signal.

As described above also weaken spin -spin interactions, the spin echo off; the effects of field inhomogeneities, however, be eliminated by the measurement sequence. In order to estimate the influence of the diffusion motion, therefore, a second receptacle is necessary for comparison in which no gradient is switched.

The physical model

To describe the dependency of the diffusion direction, the DT- MRI makes use of the mathematical model of the floating diffusion, which is described in physics by the Fick's laws. In the three-dimensional case is the first Fick's law

It represents the particle current density J in relation to the concentration gradient. When this occurs the proportionality scalar diffusion coefficient D on. In anisotropic media, the diffusion coefficient depends on the direction and must therefore be replaced by the diffusion tensor D in the above equation - a symmetric 3 × 3 matrix, which describes a linear map here.

Diffusion imaging measures the self-diffusion of water, that is run continuously Brownian motion, the water molecules due to their thermal energy. It is not associated with a concentration gradient, but it forms the physical basis of the process described by Fick's law and hence follows the same mathematical model. Nevertheless, the described diffusion tensor model is, strictly speaking, in DT - MRI did not apply because here no free diffusion is present, but the molecular motion is restricted by barriers at the cellular level. The aim of the procedure is to draw conclusions from the observation of this limitation conclusions about the structure of the tissue in which diffuses the water.

For this reason is referred to instead of the diffusion coefficient in more detail by an apparent diffusion coefficient (ADC ), an "apparent " diffusion coefficient, which depends not only on the direction, but also by the diffusion length: Switch to the gradient in such a short time interval that the majority of the molecules during this time encountering any obstacle, the diffusion appears free; increasing the diffusion time, shows the restriction of the movement of the ADC decreases. In technical applications one uses this effect to be determined by measurements with a variable diffusion time the pore diameter of the microporous materials. In the diffusion tensor imaging, the magnitude of the tested cell structures is known, so that the diffusion time can be adjusted to them. In practice, the DT- MRI can therefore ignore the dependence of the ADC of the diffusion length, and often continues to speak simplification of diffusion coefficients.

Calculation of the diffusion tensor

The central equation of diffusion tensor imaging describes the attenuation of the measurement signal as a function of the measurement parameters and the diffusion tensor. It is called Stejskal -Tanner equation:

A ( g) stands for the signal strength under the effect of a gradient in the direction of g, the signal strength measurement and an unweighted b summarizes the measured parameters together. The diffusion tensor D now describes a positive semidefinite quadratic form g assigns to each direction of an ADC.

G and b are determined before the measurement. A ( g) and are known by the measurement. Since the symmetric matrix D has six degrees of freedom, in addition to the un-weighted least six diffusion-weighted measurements in various directions necessary to appreciate the full by means of the equation can Diffusion. Since the accuracy of the results is limited due to noise and measurement artifacts, the measurements are usually repeated or used additional directions. The estimation of the tensor is then, for example, by the least squares method.

The high number of individual measurements explained the expenditure of time, which varies according to the number of cross-sectional images, required accuracy and field strength of the scanner from several minutes to an hour. Since the method is very sensitive to external movements of the head of the test person is fixed during this period by a frame.

Interpretation of the diffusion coefficient

In brain tissue, the mobility of water molecules is restricted by barriers such as cell membranes. In particular, the molecules can in the presence of densely packed nerve fibers unimpeded along the elongated axons move as across them. The basic assumption in the interpretation of diffusion tensor data, therefore, is that the direction of the greatest diffusion coefficient reflects the course of the nerve fibers.

Such an interpretation must take into account that the axons with a diameter in the micrometer range are well below the resolution of the method, which is a few millimeters. Thus, the measured signal represents an average over a certain volume, which is only meaningful when the tissue is homogeneous within this area. Therefore, only larger nerve fiber bundles can be represented. The exact mechanisms underlying the observed diffusion behavior based are not yet fully understood. Due to the recent studies, it is believed that the enhanced directionality both molecules inside and outside the cells, and that relates to the myelination of nerve fibers, but will not be caused solely.

In muscle fibers, the diffusion motion on a clear preferred direction. Thus, the diffusion tensor model was first tested by means of measurements on skeletal muscles, because the results are easy to verify here. Also, the structure of the heart muscle of mammals in which rotates the orientation of the individual fibers between the inner and outer wall ( endocardium and epicardium ) to about 140 °, could be visualized on prepared hearts by diffusion tensor measurements. With specially adapted measuring sequences also an investigation of the beating heart is possible; this is costly and so far (as of 2012) no clinical routine.

Visualization

A complete diffusion tensor data set contains more information than humans might by a single figure. Therefore, a variety of techniques have been developed which are limited thereon, respectively, to illustrate certain aspects of the data and complement each other. Established in practice, have representations of cross-sectional images, tractography, and tensor glyphs.

Sectional images

For the preparation of cross-sectional images, as they are known from the traditional MRI, the diffusion tensor can be reduced to a gray or color value. Gray values ​​are calculated from the eigenvalues ​​of the diffusion tensor. Are usual, especially the average diffusion coefficient and the Fractional anisotropy. The latter indicates how the direction depends on the diffusion and is an indicator of the integrity of a fiber bundle. Such images are often evaluated by purely visual means for the diagnosis and allow, for example, the diagnosis of stroke. In the context of group studies beyond statistical differences in these dimensions are examined, for example, a decrease in the anisotropy of certain diseases.

In addition, the direction of the greatest diffusion coefficient is often coded as a color value. Here, each of the three axes is assigned one of the primary colors red, green and blue which are mixed at intermediate directions. Voxels with no clear main direction appear gray ( see figure).

Tractography

As tractography or fiber tracking methods are referred to reconstruct the course of major nerve fiber bundles. To visualize this respect are representations of hyper Streamline common three-dimensional lines, during which the direction of greatest diffusion coefficient follows. The picture at the beginning of this article shows an example of all the bundles that intersect the median plane. An alternative approach is the probabilistic tractography; they calculated for each point in the brain a chance with the data on the basis of a nerve connection can be assumed with a given output area. Such results are less suitable for the production of meaningful pictures, but allow quantitative statements and therefore apply in the cognitive research use.

The fact that diffusion tensor imaging is the only method currently which allows a non- invasive imaging of the nerve fiber bundles, has contributed to its spread. On the other hand, it is because its difficult to check how consistent the results of current tractography method with the actual course of the nerve pathways. However, initial attempts at validation in animal experiments support the hypothesis that the main direction of the diffusion orientation coherent nerve fibers displays and exhibit similarities between noninvasive tractography and carried out after the death of histological examinations after. Areas where fiber bundle fan out or tick is barely recorded by DT - MRI is very inadequate and therefore motivate their further development into methods with high angular resolution ( see below).

Tensor Glyphs

As glyphs geometric bodies are referred to convey the shape and orientation of the desired information in the visualization. They offer the ability to fully represent the information contained in a diffusion tensor. However, only a portion of the data can be shown in this case, since glyphs must have a certain size and must not cover to remain recognizable. The most common tensor glyphs are ellipsoids whose semi-axes are scaled with the strength of diffusion in each direction; So the longest semi-axis points in the direction of the strongest diffusion. If the diffusion coefficient in all directions about the same, so similar to the diffusion ellipsoid a sphere ( see figure).

Applications

Diagnostics

A common application of diffusion-weighted MRI is the stroke diagnosis. The affected brain tissue often has after a few minutes lower diffusion coefficient than the healthy environment. This effect is attributed to the fact that after the failure of the sodium-potassium pump flows in the damaged area of ​​extracellular fluid into the cells, where their diffusion motion is subject to greater restrictions.

In conventional MRI images of the infarct is only clearly visible later, in some cases only after 8 to 12 hours. This difference is clinically significant because thrombolytic therapy is usually only useful within 3 to 4.5 hours after onset of infarction.

Surgical planning

In surgical procedures in the brain and the irradiation of brain tumors, it is important to get the nerves as much as possible, since their injury usually leads to permanent functional deficits. Diffusion tensor imaging can help determine in advance the location of the nerve and to consider in the operation or treatment planning it. Since the brain is deformed during the intervention, it may be useful to interrupt an operation to make a re-recording.

The diffusion tensor imaging also provides information on whether a tumor has already penetrated a nerve tract and can help in some cases, the assessment of whether an operation is at all promising.

Research

Diffusion tensor imaging is increasingly used as a research tool in medical and cognitive science studies. The focus of interest here are mostly changes in the mean diffusion coefficient (mean diffusivity ) and the Fractional anisotropy, the latter is often interpreted as an indicator of the integrity of nerve fibers.

So could some be shown that normal aging processes associated with a significant decrease in Fractional anisotropy and an increase in mean diffusivity. Even with many neurological and psychiatric diseases, including multiple sclerosis, epilepsy, Alzheimer's disease, schizophrenia and HIV encephalopathy, changes in DT - MRI can be detected. Many studies based on diffusion imaging go primarily by the question of which brain regions are particularly affected. Diffusion tensor imaging is here sometimes also used complementary to functional magnetic resonance imaging.

Neuroscience also uses probabilistic tractography methods that provide evidence of nerve connections between certain brain areas. This allows, among other things, the thalamus continues to be broken, even though it appears as a uniform structure in the conventional magnetic resonance imaging.

A special emphasis is current variants of diffusion imaging in the Human Connectome Project, whose goal is to investigate the natural variability of the healthy human Konnektoms. As part of this during the years 2010 to 2015, a total of nearly 40 million U.S. dollars funded program, the results of diffusion imaging are correlated, among other genetic testing and cognitive abilities.

Historical development

The chemist Edward O. Stejskal and his graduate student John E. Tanner described in 1965 how a briefly switched gradient field can be exploited in nuclear magnetic resonance experiments to measure the diffusive motion of hydrogen nuclei. After them, both the basic measurement for the diffusion imaging sequence named, and the formula which allows to calculate the attenuation of the spin echo to the diffusion coefficient.

Only in the 1970s created Paul Christian Lauterbur and Peter Mansfield with the spatially resolved magnetic resonance imaging the possibility of using magnetic resonance imaging. In 1985, the neuroradiologist Denis Lebihan one developed by Stejskal and Tanner method for diffusion measurements in the MRI. In collaboration with the engineer Lebihan scientist Peter J. Basser finally struck in 1994 diffusion tensor as a model before. It takes into account the directional dependence of the diffusion coefficient and thus allows conclusions on the course of major nerves. Since about 2000, several research groups develop more elaborate variants of diffusion imaging, which require a large number of measurements and / or a particularly strong diffusion weighting. For this data, a number of new models has been proposed, of which so far (as of 2011), none experienced a similar distribution to the diffusion tensor.

Development of the process

Improving the image quality

Diffusion-weighted MRI measurements often provide only a limited picture quality. The over traditional MRI higher susceptibility to interference is due to the measurement procedure described above: Since the diffusion movement expresses itself in a weakening of the measured signal, this is more influenced by the noise of the measuring apparatus. For this reason, there is little progress towards a higher spatial resolution of the method, as smaller volume elements provide a correspondingly weaker output signal. In addition, one needs a large number of individual measurements and therefore usually uses time-saving measurement sequences, such as the echo planar imaging in order to keep the total costs and the burden on the patient justifiable. These sequences most often lead to artifacts.

These problems are encountered both by post-processing of the measured data in the computer, so that the faults can be corrected to some extent. The radiological research will also look for new MRI sequences that are less prone to error.

Increase in the angular resolution

The diffusion tensor model describes the diffusion behavior within a voxel only approximately correct when the diffusion has a single main direction. Thus, it comes in voxels where nerves cross each other or fan out to its limits. Therefore, approaches have been developed in recent years to make very many (60 or more) different directions diffusion- weighted images to capture complex diffusion behavior better. Such methods are referred to by the abbreviation HARDI (High Angular Resolution Diffusion Imaging, " Diffusion imaging with high angular resolution ").

Processing and analysis of data

Also, the methods by which the data of diffusion imaging for medical studies are further processed and evaluated, are currently (as of 2011) still active subject of research. Early studies used some very simple methods of image registration to compare data derived from the diffusion measurements over larger groups of subjects across. This has proven to be problematic since it is difficult to bring the anatomical structures of different individuals perfectly to cover and may cause deviations in misleading and contradictory study results. In addition to improved algorithms for registration, therefore, methods for the statistical analysis are being developed that are less sensitive to registration errors.