Diffusion tensor imaging

The Diffusion-weighted magnetic resonance imaging (abbreviated as DW-MRI of English diffusion-weighted magnetic resonance imaging ) is a imaging technique that with the aid of magnetic resonance imaging (MRI), the diffusion motion of water molecules, measuring in body tissue and is spatially resolved. It is used to examine the brain , as the diffusion behavior in the tissue changes characteristically in some diseases of the central nervous system and the directional dependence of the diffusion allows conclusions to be drawn about the course of the large nerve fiber bundles . Like classic MRI, diffusion-weighted imaging is non-invasive : Since the image contrast is achieved solely by means of magnetic field gradients , it does not require the injection of contrast media or the use of ionizing radiation .

The diffusion tensor imaging (abbreviated DTI of English diffusion tensor imaging or DT-MRI of diffusion tensor magnetic resonance imaging ) is a frequently used variant of the DW-MRI, which also detects the directionality of diffusion. For each volume element ( voxel ), it not only determines a single numerical value that can be displayed as a gray value in the sectional image , but also calculates a tensor (specifically: a 3 × 3 matrix ) that describes the three-dimensional diffusion behavior. Such measurements are more time-consuming than conventional MRT recordings and generate larger amounts of data that the radiologist can only interpret through the use of various visualization techniques.

Diffusion imaging emerged in the 1980s. It is now supported by all new MRI devices and has established itself in everyday clinical practice for stroke diagnosis, since the affected brain regions can be recognized earlier in diffusion-weighted images than in classic MRI. Diffusion tensor imaging was developed by Peter J. Basser and Denis Le Bihan in the mid-1990s . Some clinics use them for surgical and radiation planning. In addition, the DT-MRI is used in medical research to study diseases that are associated with changes in white matter (such as Alzheimer's disease or multiple sclerosis ). The further development of diffusion-weighted imaging itself is also a current research subject, for example in the context of the Human Connectome Project .

The DT-MRI enables a reconstruction of nerve tracts in the brain (tractography).

Measurement method

Basics

Diffusion imaging is based on the same physical principles as conventional MRI (see also the main article, magnetic resonance imaging ). It uses the fact that protons have a magnetic moment and align themselves either parallel (low-energy state) or anti-parallel (high-energy state) in an external magnetic field. In equilibrium there is a larger number of protons in the low-energy state, which creates a sum vector parallel to the external field ( paramagnetic effect ). The direction of the external field is called the z-axis in the context of MRI ; perpendicular to this is the xy plane .

The axis of rotation of the protons precesses around the z-axis. The frequency of this movement is proportional to the strength of the external magnetic field and is called the Larmor frequency . A high-frequency electromagnetic wave ("HF pulse") with this frequency stimulates the magnetic moments to change their state ( nuclear magnetic resonance ). As a result, the alignment of the sum vector changes depending on the strength and duration of the pulse, it "flips over". The flipped-over moments initially rotate in phase , so that the sum vector now also has a (rotating) component in the xy plane.

This effect can be observed with a measuring coil that is perpendicular to the xy plane; in it induces the rotating net moment a voltage. If you switch off the HF pulse, the protons return to their state of equilibrium. Due to inhomogeneities in the external field and thermal collisions (“spin-spin interaction”), the phase coherence is also lost and the xy component of the sum vector disappears. To observe the diffusion movement, one has to do a "spatially resolved" NMR experiment, i.e. a field gradient NMR experiment in which the NMR signal frequency is made location-dependent by applying magnetic field gradients and changes in the location of the water molecules through diffusion can be observed.

Diffusion-weighted MRI sequences

Scheme of the Stejskal-Tanner sequence. A diffusion movement along the gradient fields is measured as a weakening of the spin echo (explanations in the article text).

A diffusion-weighted MRT sequence (see scheme) begins with the sum vector first being tilted by 90 ° in the xy plane. The diffusion weighting is done by a briefly switched gradient field that varies the field strength of the external magnetic field in a predetermined direction. In 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 disappears.

Then you reverse the direction of rotation of the nuclei with a new HF pulse (180 ° pulse) and switch on the same gradient field again. Due to the identical frequency differences when the direction of rotation is reversed, the magnetic moments are now back in phase and a voltage occurs again, the spin echo . However, this is weaker than the signal at the beginning of the sequence because some of the nuclei do not get back into phase - these are especially those that moved in the direction of the gradient field during the measurement. A diffusion movement in this direction is expressed in a weakening of the signal.

As described above, spin-spin interactions also weaken the spin echo; the effects of field inhomogeneities, on the other hand, are eliminated by the measurement sequence. In order to be able to estimate the influence of the diffusion movement, a second recording is necessary for comparison, in which no gradient is switched.

The physical model

To describe the directional dependence of diffusion, the DT-MRI uses the mathematical model of free diffusion, which is described in physics by Fick's laws . In the three-dimensional case, the first is Fick's law

${\displaystyle {\vec {J}}=-D\nabla c.}$

It relates the particle flux density to the concentration gradient . The scalar diffusion coefficient appears as the proportionality factor . In anisotropic media, the diffusion coefficient is direction-dependent and must therefore be replaced by the diffusion tensor in the above equation - a symmetrical 3 × 3 matrix that describes a linear mapping here . ${\displaystyle {\vec {J}}}$ ${\displaystyle \nabla c}$ ${\displaystyle D}$ ${\displaystyle \mathbf {D} }$

Diffusion imaging measures the self-diffusion of water, i.e. the Brownian molecular motion that water molecules constantly carry out due to their thermal energy . This is not associated with a concentration gradient, but forms the physical basis of the process described by Fick's laws and therefore follows the same mathematical model. Strictly speaking, however, the diffusion tensor model described cannot be used in DT-MRI because there is no free diffusion here, but rather the molecular movement is restricted by obstacles at the cellular level. The aim of the method is to draw conclusions about the structure of the tissue in which the water diffuses from the observation of this restriction.

For this reason, instead of diffusion coefficients, one speaks more precisely of an apparent diffusion coefficient (ADC), an "apparent" diffusion coefficient that depends not only on the direction but also on the diffusion length: If you switch the gradient fields at such a short time interval that the Most of the molecules do not encounter any obstacles during this time, the diffusion appears free; if the diffusion time is increased, the movement is restricted and the ADC decreases. In technical applications, this effect is used to determine the pore diameter of microporous substances through measurements with variable diffusion times. In diffusion tensor imaging, the order of magnitude of the cell structures examined is known, so that the diffusion time can be adapted to them. In the practice of DT-MRI, the dependence of the ADC on the diffusion length can therefore be ignored and the term diffusion coefficient often continues to simplify matters.

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 the Stejskal-Tanner equation:

${\displaystyle A({\vec {g}})=A_{0}\cdot e^{-b\,{\vec {g}}^{T}\mathbf {D} {\vec {g}}}.}$

${\displaystyle A({\vec {g}})}$stands for the signal strength under the effect of a gradient field in the direction , is the signal strength of an unweighted measurement and summarizes the measurement parameters. The diffusion tensor describes a positive semidefinite square shape that assigns an ADC to each direction . ${\displaystyle {\vec {g}}}$ ${\displaystyle A_{0}}$ ${\displaystyle b}$ ${\displaystyle \mathbf {D} }$ ${\displaystyle {\vec {g}}}$

${\displaystyle {\vec {g}}}$and are determined before the measurement. and are known after the measurement. Since the symmetrical matrix has six degrees of freedom, in addition to the unweighted at least six diffusion-weighted measurements in different directions are necessary in order to be able to estimate the complete diffusion tensor using the equation. Since the accuracy of the results is limited due to noise and measurement artifacts , the measurements are usually repeated or additional directions are used. The estimation of the tensor is then carried out, for example, using the least square method . ${\displaystyle b}$ ${\displaystyle A({\vec {g}})}$ ${\displaystyle A_{0}}$ ${\displaystyle \mathbf {D} }$

The high number of individual measurements explains the time required for the process, which, depending on the number of slice images, the required accuracy and the field strength of the scanner, is between a few minutes and an hour. Since the procedure is sensitive to external movements, the test person's head is held in place by a frame during this time.

Interpretation of the diffusion coefficient

In the brain tissue, the mobility of the water molecules is restricted by obstacles such as cell membranes . In particular, in the presence of densely packed nerve fibers , the molecules can move more freely along the elongated axons than across them. The basic assumption when interpreting diffusion tensor data is therefore 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 procedure, which is a few millimeters. The measured signal thus represents an average value over a certain volume, which is only meaningful if the tissue is homogeneous within this area. Therefore only larger nerve fiber bundles can be displayed. The exact mechanisms underlying the observed diffusion behavior have not been conclusively clarified. Based on previous investigations, it is assumed that the directional dependence affects both the molecules inside and those outside the cells and is reinforced by the myelination of nerve fibers, but not caused by it alone.

In muscle fibers too , the diffusion movement has a clear preferred direction. The diffusion tensor model was first tested using measurements on skeletal muscles , since the results are easy to verify here. The structure of the myocardium in mammals, in which the alignment of the individual fibers between the inner and outer wall ( endocardium or epicardium ) rotates by about 140 °, could also be made visible by means of diffusion tensor measurements on prepared hearts. An examination of the beating heart is also possible with specially adapted measurement sequences; However, this is time-consuming and so far (as of 2012) not yet a clinical routine.

Visualization

In DTI slice images, the main direction of diffusion is often represented by colors.

Diffusion ellipsoids allow sections of the data to be shown in detail.

A complete diffusion tensor data set contains more information than a human being could take in from a single image. As a result, a variety of techniques have been developed, each limited to illustrating certain aspects of the data and complementary to one another. Representations of sectional images, tractography and tensor glyphs have become established in practice.

Sectional images

In order to display sectional images, as they are known from traditional MRT, the diffusion tensors are reduced to a gray or color value. Gray values ​​are calculated from the eigenvalues ​​of the diffusion tensor. The average diffusion coefficient and the fractional anisotropy are common . The latter indicates how direction-dependent the diffusion is and is an indicator of the integrity of a fiber bundle. Such images are often evaluated purely visually for diagnostics and enable the diagnosis of strokes, for example. In the context of group studies, statistical differences in these measures are examined, for example a decrease in anisotropy in certain diseases.

In addition, the direction of the greatest diffusion coefficient is often coded as a color value. Each of the three axes is assigned one of the basic colors red, green and blue, which are mixed in the directions in between. Voxels without a clear main direction appear gray (see figure).

Tractography

Techniques that reconstruct the course of larger nerve fiber bundles are referred to as tractography or fiber tracking . For visualization, representations of hypercurrent lines are common, three-dimensional lines whose course follows the direction of the greatest diffusion coefficient. The figure at the beginning of this article shows an example of all the bundles that intersect the median plane . An alternative approach is probabilistic tractography . For each point in the brain, it calculates a probability with which a nerve connection with a given starting area can be assumed on the basis of the data. Such results are less suitable for generating meaningful images, but allow quantitative statements and are therefore used in cognitive research .

The fact that diffusion tensor imaging is currently the only technique that allows a non-invasive visualization of the nerve fiber bundles has contributed significantly to their spread. On the other hand, this makes it difficult to check to what extent the results of common tractography methods correspond to the actual course of the nerve tracts. Initial attempts at validation in animal experiments support the assumption that the main direction of diffusion indicates the alignment of coherent nerve fibers and show similarities between non-invasive tractography and histological examinations carried out after death . Areas in which fiber bundles fan out or cross are only insufficiently covered by the DT-MRI and therefore motivate its further development towards methods with high angular resolution (see below).

Tensor glyphs

In the visualization, glyphs are geometric bodies whose shape and orientation convey the desired information. They offer the possibility of fully representing the information contained in a diffusion tensor. In this case, however, only a section of the data can be shown, as glyphs must be of a certain size and must not cover each other in order to remain recognizable. The most common tensor glyphs are ellipsoids , whose semi-axes are scaled with the strength of the diffusion in the respective direction; the longest semi-axis therefore points in the direction of the strongest diffusion. If the diffusion coefficient is roughly the same in all directions, the diffusion ellipsoid resembles a sphere (see illustration).

Applications

Diagnosis

A frequent use of diffusion-weighted MRI is stroke diagnostics. The affected brain tissue often shows lower diffusion coefficients than the healthy surroundings after just a few minutes. This effect is attributed to the fact that after failure of the sodium-potassium pumps in the damaged area, extracellular fluid flows into the cells, where its diffusion movement is subject to greater restrictions.

The infarct is only visible later in conventional MRI images, in some cases only after 8 to 12 hours. This difference is clinically significant, as thrombolysis therapy usually only makes sense within 3 to 4.5 hours after the onset of the infarction.

Operation planning

In the case of surgical interventions in the brain and the irradiation of brain tumors , it is important to preserve the nerve tracts as much as possible, as their injury usually leads to permanent functional failures. Diffusion tensor imaging can help to determine the position of the nerves in advance and to take it into account when planning surgery or radiation therapy. Since the brain deforms during the procedure, it can be useful to interrupt an operation in order to record again.

Diffusion tensor imaging also provides information on whether a tumor has already penetrated a nerve tract and in some cases can support 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 here is mostly on changes in the mean diffusion coefficient ( mean diffusivity ) and fractional anisotropy , the latter often being interpreted as an indicator of the integrity of nerve fibers.

For example, it could be shown that normal aging processes are associated with a significant decrease in fractional anisotropy and an increase in mean diffusivity. Changes in the DT-MRI can also be detected in many neurological and psychiatric diseases, including multiple sclerosis , epilepsy , Alzheimer's disease , schizophrenia and HIV encephalopathy . Many studies based on diffusion imaging address the question of which brain regions are particularly affected. Diffusion tensor imaging is also used here to complement functional magnetic resonance tomography .

Neuroscience also uses probabilistic tractography methods that provide information about nerve connections between certain brain areas. This allows the thalamus to be further subdivided, although it appears as a uniform structure in conventional magnetic resonance imaging.

A special focus is on current variants of diffusion imaging in the Human Connectome Project , the aim of which is to investigate the natural variability of the healthy human connectome . As part of this program, which was funded with a total of almost 40 million US dollars between 2010 and 2015, the results of diffusion imaging are correlated with genetic analyzes and cognitive abilities , among other things .

Historical development

As early as 1965, the chemist Edward O. Stejskal and his doctoral student John E. Tanner described how a briefly switched gradient field in nuclear magnetic resonance experiments can be used to measure the diffusion movement of hydrogen nuclei. Both the basic measurement sequence for diffusion imaging and the formula that makes it possible to calculate the diffusion coefficient from the attenuation of the spin echo are named after them.

In the 1970s , Paul Christian Lauterbur and Peter Mansfield created the possibility of using magnetic resonance imaging for imaging with spatially resolved magnetic resonance tomography . In 1985, the neuroradiologist Denis LeBihan introduced the diffusion measurement method developed by Stejskal and Tanner into MRI. In collaboration with LeBihan, the engineering scientist Peter J. Basser finally proposed the diffusion tensor as a model in 1994. It takes into account the directional dependence of the diffusion coefficient and thus allows conclusions to be drawn about the course of large nerve tracts. Since around the year 2000, various research groups have been developing more complex variants of diffusion imaging that require a large number of measurements and / or particularly strong diffusion weighting. A large number of new models have been proposed for this data, none of which has so far (as of 2011) experienced a distribution comparable to the diffusion tensor.

Further development of the process

Image quality improvement

Diffusion-weighted MRT measurements often only offer limited image quality. The higher susceptibility to interference compared to traditional MRI can be explained by the measurement method described above: Since the diffusion movement is expressed in a weakening of the measured signal, this is more strongly influenced by the noise of the measuring apparatus. For this reason there is hardly any progress towards a higher spatial resolution of the method, since smaller volume elements offer a correspondingly weaker output signal. In addition, a large number of individual measurements are required and therefore mostly time-saving measurement sequences such as echo planar imaging are used in order to keep the overall effort and stress on the patient justifiable. However, these sequences often lead to artifacts.

These problems are countered, on the one hand, by reprocessing the measurement data in the computer, whereby the disturbances can be partially corrected. Radiological research is also looking for new MRI sequences that are less prone to error.

Increase in angular resolution

The diffusion tensor model describes the diffusion behavior within a voxel only approximately correctly if the diffusion has a single main direction. It therefore reaches its limits in voxels in which nerve pathways cross or fan out. In recent years, approaches have therefore been developed to take diffusion-weighted recordings in very many (60 and more) different directions in order to be able to better record complex diffusion behavior. Such procedures are known by the abbreviation HARDI ( High Angular Resolution Diffusion Imaging , "Diffusion imaging with high angular resolution").

Processing and evaluation of the data

The methods with which the diffusion imaging data are further processed and evaluated for medical studies are currently (as of 2011) the subject of research. Early studies sometimes used very simple methods of image registration in order to compare measurements derived from the diffusion data across larger groups of test subjects. This has been found to be problematic as it is difficult to perfectly align the anatomical structures of different individuals and deviations can lead to misleading and contradicting study results. In addition to improved algorithms for registration, methods for statistical evaluation are currently being developed that are less sensitive to registration errors.

literature

• Derek K. Jones (Ed.): Diffusion MRI: Theory, Methods, and Applications . Oxford University Press, 2011. ISBN 978-0-19-536977-9 English-language textbook that, in contributions from international experts, covers physical and biological principles, measurement methods, algorithmic evaluation, applications, current research topics and historical backgrounds.
• Bernhard Preim , Dirk Bartz : Visualization in Medicine . Morgan Kaufmann, 2007. ISBN 978-0-12-370596-9 English-language specialist book. Covered in Chapter 18 Measurement, Processing, Visualization, and Interpretation of Diffusion Tensor Data.
• Charles D. Hansen, Christopher R. Johnson (Eds.): Visualization Handbook . Academic Press, 2004. ISBN 978-0-12-387582-2 English-language specialist book. Chapter 16 covers the visual preparation of diffusion tensor data.
• Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H: Diffusion Tensor Imaging: Concepts and Applications . In: Journal of Magnetic Resonance Imaging . 2001, p. 534–546 (English, Diffusion Tensor Imaging: Concepts and Applications ( Memento from October 19, 2013 in the Internet Archive ) [PDF; 696 kB ; retrieved on June 22, 2016] Review article in specialist journal).
• Joachim Weickert, Hans Hagen (Eds.): Visualization and Processing of Tensor Fields . Springer, Berlin 2006. ISBN 3-540-25032-8 English-language specialist book for the visualization and processing of tensor data, with a clear focus on DT-MRI.
• On the trail of the secrets of the brain. in: Doctors Week. Vienna 16.2002, No. 27. ISSN  1862-7137 Generally understandable overview of the procedure, German.

Web links

Commons : Diffusion Tensor Imaging  - collection of images, videos, and audio files

• Information from the Center for Imaging in Neuroscience ( Brain Imaging Center , Frankfurt) on how the DT-MRI works
• Press release of the National Institutes of Health (2000) on the possibilities of the DT-MRI (English)

Individual evidence

1. ^ Christian Beaulieu: The basis of anisotropic water diffusion in the nervous system - a technical review. In: NMR in Biomedicine 2002, 15: 435-455.
2. ^ PJ Basser, J. Mattiello, D. LeBihan: Estimation of the effective self-diffusion tensor from the NMR spin echo. In: Journal of Magnetic Resonance. Series B. San Diego Cal 103.1994, 247-254. ISSN  1064-1866
3. ↑ Sonia Nielles-Vallespin, Choukri Mekkaoui u. a .: In vivo diffusion tensor MRI of the human heart: Reproducibility of breath-hold and navigator-based approaches. In: Magnetic Resonance in Medicine. 70, 2013, p. 454, doi : 10.1002 / mrm.24488 .
4. ↑ S. Pajevic, C. Pierpaoli: Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data. Application to white matter fiber tract mapping in the human brain. In: Magnetic Resonance in Medicine. New York 42.1999, 3, 526-540. ISSN  0740-3194
5. ^ S. Mori, BJ Crain, VP Chacko, PCM van Zijl: Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. In: Annals of Neurology , 45 (2): 265-269, 1999
6. ↑ PJ Basser, S. Pajevic, C. Pierpaoli, J. Duda, A. Aldroubi: In vivo fiber tractography using DT-MRI data. In: Magnetic Resonance in Medicine. New York 44.2000,625-632. ISSN  0740-3194
7. ↑ TEJ Behrens, MW Woolrich, M. Jenkinson, H. Johansen-Berg, RG Nunes, S. Clare, PM Matthews, JM Brady, SM Smith: Characterization and Propagation of Uncertainty in Diffusion-Weighted MR Imaging. In: Magnetic Resonance in Medicine. 50: 1077-1088, 2003.
8. ↑ C.-P. Lin, W.-YI Tseng, H.-C. Cheng, J.-H. Chen: Validation of diffusion tensor magnetic resonance axonal fiber imaging with registered manganese-enhanced optic tracts. In: NeuroImage , 14 (5): 1035-1047, 2001.
9. ↑ J. Dauguet, S. Peled, V. Berezovskii, T. Delzescaux, SK Warfield, R. Born, C.-F. Westin: 3D histological reconstruction of fiber tracts and direct comparison with diffusion tensor MRI tractography. In: Medical Image Computing and Computer-Assisted Intervention , pp. 109–116, Springer, 2006.
10. ↑ K.-O. Lövblad, H.-J. Laubach, AE Baird, F. Curtin, G. Schlaug, RR Edelman, S. Warach: Clinical Experience with Diffusion-Weighted MR in Patients with Acute Stroke. In: American Journal of Neuroradiology. Oak Brook Ill 1998/19, 1061-1066. ISSN  0195-6108
11. ↑ W. Hacke et al .: Trombolysis with Alteplase 3 to 4.5 Hours after Acute Ischemic Stroke. In The New England Journal of Medicine , 359, 2008, 1317.
12. ^ E. V. Sullivan and A. Pfefferbaum: Diffusion Tensor Imaging in Aging and Age-Related Neurodegenerative Disorders. Chapter 38 in D. K. Jones (Ed.): Diffusion MRI: Theory, Methods, and Applications. Oxford University Press, 2011.
13. ↑ TEJ Behrens, H. Johansen-Berg u. a .: Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging. In: Nature Neuroscience . New York 6.2003,7, 750-757. ISSN  1097-6256
14. ^ EO Stejskal, JE Tanner: Spin Diffusion Measurements - Spin echoes in the presence of a time-dependent field gradient. In: Journal of Chemical Physics. Melville 42.1965, 288-292. ISSN  0021-9606
15. ↑ SM Smith, M. Jenkinson, H. Johansen-Berg, D. Rueckert, TE Nichols, CE Mackay, KE Watkins, O. Ciccarelli, MZ Cader, PM Matthews, TEJ Behrens: Tract-based spatial statistics: Voxelwise analysis of multi -subject diffusion data. In: NeuroImage. 31 (4): 1487-1505, 2006.

This article was added to the list of excellent articles on November 20, 2006 in this version .