Diffusion-Weighted (DW) Magnetic Resonance Imaging (MRI) - Essay Example

? Diffusion-Weighted (DW) Magnetic Resonance Imaging (MRI) Table of Contents I. Introduction 3 II. Background on Diffusion 3 III. MRI and Diffusion 4A. How MRI is Sensitized to Diffusion 4 B. Moving and Stationary Spins- Effects 7 C. Diffusion-Weighted Images- Effect of Physiological Motion 9 D. Achievement of Different Diffusion Weightings 11 IV. Diffusion Information- Measurement 11 References 13 I. Introduction This paper discusses diffusion in general, and diffusion in the context of its use in magnetic resonance imaging or MRI. It discusses the use of diffusion in different MRI methods, with a focus on diffusion-weighted MRI. The exploration of diffusion in MRI includes the way MRI is sensitized to diffusion; the effects of spins, both stationary and moving spins; how diffusion-weighted images are affected by physiological motion; the how of the achievement of the various diffusion weightings; and information on diffusion and how those are measured (Hagmann et al. 2006; Mori and Barker 1999, pp. 102-106; Tonarelli 2012; Parker 2004, pp. S176-S178; Everdingen et al. 1998; Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003; Koh and Collins 2007; Le Bihan 2011; Basser and Jones 2002; Battal et al. 2012; De Foer 2010; Luypaert et al. 2001; Williams et al. 1992; Topgaard 2006) II. Background on Diffusion Diffusion on the molecular level is said to be the result of natural Brownian movement, where molecules randomly move through the diffusion medium because of the agitation caused by thermal characteristics of the medium. In all the displacement of the molecules comes up to zero by mean figures, but over time, there are positive probabilities associated with the non-zero movement of a molecule, so that over time, a molecule is said to probably have moved from an initial position at an earlier time. Here the time elapsed corresponds to a correlation with the distance moved, where different fluids acting as diffusion mediums determine the distance as characterized by the diffusion constant for that liquid type. There is a difference between the freely diffusing movement of water molecules, meanwhile, to the diffusion of liquids in the tissues of human beings, so that in human tissues one talks of an ADC, or an apparent diffusion coefficient, to be differentiated from the free diffusion coefficients of liquids outside of human bodies, such as those used to characterize water in containers at certain temperatures. On the other hand, for human tissues, various considerations further come into play, such as differences in the mobility of different fluids in different parts of the body and in different parts of a particular organ, such as the human brain. Boundary conditions also differ for liquids found in different body parts. All these affect the coefficient of diffusion in various ways, with the general observation that the ADC is generally smaller in comparison to the free diffusion coefficients of liquids like water outside of the human body (Luypaert et al. 2001; Roberts and Rowley 2003). Going into diffusion types, meanwhile, there are two, one being isotropic diffusion and the other being anisotropic diffusion. In isotropic diffusion, the rate of diffusion is the same in all directions, and so the resulting diffusion distribution is spherical. In anisotropic diffusion, the diffusion rate depends on where the diffusion is oriented, and there is uneven diffusion in different directions. The distance of the diffusion is orientation-dependent, in other words, and the diffusion distribution is characterized by an ellipsoid (Module 1 2013). III. MRI and Diffusion A. How MRI is Sensitized to Diffusion In a hypothetical case, the typical distribution of displacement of water molecules in such a container is said to follow a bell curve, with majority of the water molecules able to travel only for short distances from their initial location, whereas a few of the water molecules are able to be displaced at further distances from average. For a given initial temperature of the water, moreover, the displacement values are characterized by an appropriate bell-shaped or Gaussian function. A sample Gaussian distribution is given below to illustrate this state of affairs (Hagmann et al. 2006; Mori and Barker 1999, p. 102): Image Source: Hagmann et al. 2006 Extending that single-dimension image into three dimensions, and one sees that in any medium that has uniformity or homogeneity of characteristics the diffusion is characterized by a Gaussian function or distribution. The wideness or the narrowness of that distribution are functions of the molecule type, the diffusion time, and the medium's temperature. The Gaussian function spread, meanwhile, is a function of the variance associated with the medium, with the diffusion coefficient of the medium being a key factor in the determination of the variance, together with the time interval for the diffusion. The variance is proportional to the time it takes for the molecules to diffuse in a medium. In the literature discussing diffusion, there is reference to diffusion and displacement being the same thing (Hagmann et al. 2006; Mori and Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003). Further extending the diffusion discussion to complex structures, such as those found within the human body, and with liquids that are not homogeneous but heterogeneous, the challenge is to find functions to describe the diffusion characteristics of liquids within those complex structures. They are a function of the nature of the enclosing spaces that define the walls of the structures, as well as the nature of the heterogeneous liquids that are the subject of the diffusion modeling. They are many layers of complexity higher than the simple Gaussian function-defined homogeneous liquid setups that are easier to characterize in terms of their diffusion characteristics, but that complexity is reflected in the functions and density probabilities that are used to enclose and represent them. In the concrete, a practice in MR imaging entails treating the position and the distance traveled by a molecule in a diffusion medium as two sets of three-dimensional factors that together define an image in six dimensions. This needs to be decoded to fit into three dimensions. Here one technique is the switching in the use of the density function for the probability of diffusion with an isosurface, or a function to describe the distribution of orientation, computed from the distribution of the displacement data, known as an orientation distribution function. One way to visualize an orientation distribution function is that of a spherical distribution that has a small deformity, where the radius is equal to adding the density function values for the probability of diffusion for that specific direction (Hagmann et al. 2006; Mori and Barker 1999; Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003). Meanwhile, the mapping of the distribution of the displacement into a magnetic resonance image or MRI is done via the its linking to the measured intensity of the signal in such MR images. The finding that the signal intensity is a function of the presence of spins in the molecules of the dispersing medium when subjected to magnetic fields. The equations to establish this relationship, formulated in 1956 by Torrey, would form the foundation of imaging making use of diffusion methods. In other words, in water for instance, where hydrogen has a spin, the subjecting of the water diffusion medium to magnetic fields is correlated with the waning of the observed intensity of the signals in MR imaging techniques, thereby establishing a link between the characteristic of the diffusing medium molecules and the signal intensity mapping in imaging techniques making use of such introduced magnetic fields. Imaging making use of pulsed gradient spin echo sequences as magnetic fields to which the diffusion medium is subjected is dependent on the insight on the way phase shifts in spins are correlated with diffusion, so that the phase shifts demonstrate themselves as weaker intensity signals in MR imaging methods (Hagmann et al. 2006; Mori and Barker 1999, pp. 102-106; Tonarelli 2012; Parker 2004, pp. S176-S178; Everdingen et al. 1998; Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003; Topgaard 2006). The image below characterizes how MR techniques are able to leverage changes in the phases of the spins of water molecules when subjected to magnetic fields that have been calibrated to be sensitive to such characteristics of the diffusion of those molecules through the medium (Koh and Collins 2007): Image Source: Koh and Collins 2007 This has practical applications in what is considered, for instance, as the least complicated method of diffusion imaging, which are MRI techniques that are weighted for diffusion. In areas where diffusion is limited, for instance, the correlating image density is light, given that the limited displacement results in an intense signal that registers as such in the image. On the other hand, where the diffusion is large, then the technique would show a decrease in the strength of the imaging signal, and such would register as dark in the image. The decreased intensity of the signal for instance corresponds to parts of a man's brain that has had a stroke that are dark in a diffusion-weighted MRI scan, owing to the fact that in those regions that have been affected by the stroke the signal strength is low, because the level of diffusion in the diffusing liquid is low. On the other hand, where the diffusion is unimpeded in those parts of the brain that are unaffected by the stroke, the signal intensity is not diminished in the imaging technique, and so the resulting image areas for those are light, in correlation with the higher signal strength/longer distances of diffusion. This is in gist how MRI methods are sensitized to diffusion (Hagmann et al. 2006; Mori and Barker 1999, pp. 102-106; Tonarelli 2012; Parker 2004, pp. S176-S178; Everdingen et al. 1998; Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003; Koh and Collins 2007; Le Bihan 2011; Basser and Jones 2002; Battal et al. 2012; De Foer 2010; Luypaert et al. 2001; Williams et al. 1992; Topgaard 2006). B. Moving and Stationary Spins- Effects Moving and stationary spin effects and the discussion of these are relevant in the context of how such spins affect the received signal strengths in MR methods, and in the context of how such moving and stationary spins correlate with diffusion rates. Taking a step back, it is important to discuss the mechanics of spin detection and spin phase detection in order to understand how MR utilizes the changes in phase spin observed with the application of magnetic fields to diffusion media. The larger phase spin changes, as discussed earlier, are correlated with larger distances of diffusion observed in human tissues, such as in brain tissues, so that those in turn cause a significant weakening of the received MR image signals in comparison to molecules whose spins are not as phase shifted, in turn indicating less active or shorter diffusion distances. The latter also indicates, as the literature describes, restrictions in diffusion caused by one factor or other. In stroke cases, MR images using diffusion weightings make use of the shorter phase shifts in the diffusing medium to indicate areas that have been affected by the stroke, owing to restrictions in the diffusion, in contrast to freely diffusing fluids in other parts of the brain that have not been affected by the stroke. Those latter areas are darker in comparison to the lighter regions of the stroke-affected regions, where the signal intensity has been dimmed by the larger phase shifts associated with more restricted diffusion. On the other hand, it is clear that where the movement of the spins is rapid, then the application of the gradients to sensitize diffusion in MR setups results in a greater phase shift for those moving spins, whereas the opposite is true for stationary spins. For totally stationary spins, there is no movement at all associated for those molecules under observation in the MR image, meaning that diffusion is totally halted, and the diffusing medium is stagnant or blocked. These would show in the image as areas that are significantly lighter. On the other hand, for spins that are rapidly moving, the indication is that those areas are characterized by rapid diffusion, more pronounced phase shifts, and therefore a greater attenuation in the signal intensity received by the MR imaging (Hagmann et al. 2006; Mori and Barker 1999, pp. 102-106; Tonarelli 2012; Parker 2004, pp. S176-S178; Everdingen et al. 1998; Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003; Koh and Collins 2007; Le Bihan 2011; Basser and Jones 2002; Battal et al. 2012; De Foer 2010; Luypaert et al. 2001; Williams et al. 1992; Topgaard 2006). Another way to look at stationary and moving spins is in the context of how the application of magnetic fields to water, for instance, results in the generation of spins. The movement of water in diffusion, both natural and in the biological processes within the human body, impact the intensity of the received signals from the magnetic fields that are generated from the spins. In MR imaging, those differences in spin movements are what makes up the differences in the observed images that are captured. The movement of the spins are what accounts for the fluctuations in the signal intensities that are recorded (Le Bihan et al. 2006). C. Diffusion-Weighted Images- Effect of Physiological Motion Gradient magnetic pulses are limited by the hardware that are used to produce them and the hardware that are used to detect and to make sense of the resulting signals coming out of the target specimens. One cure for this is to use strong gradient pulses, but due to the limitations in hardware, this is not always possible. Moreover, physiological motion can attenuate the problems of strong gradient pulses too, because greater sensitivities in the signalling and reading of the gradient pulses results in larger aberrations caused by inadvertent motion, as in the case of the physiological motion of the samples being MRI'd. The greater the sensitivity of the diffusion-weighted MRI techniques, the greater the sensitivity too to motion of the physiological kind, and the greater the opportunity to introduce noise into the resulting images. Where bodies move, for instance, the observation is that spins phases also move in large amounts, and the shifts in phases are correlated with the strength of the gradient pulses too. The large aberrations in the shifts in phases register as large diffusions or rapid rates of diffusion in the samples being observed. In the case of human body parts samples., such as the brain, large head movements can eschew readings for spin shifts, and so can contribute to erroneous imaging of the areas being imaged. The observation is that there is no observed difference in the resulting ADC and the attenuation of the signal strength where the displacement in the movement of the physiology occurs in one direction only. There is a shift of phase in the signal, but the signal strength remains the same, and the image is unperturbed in general. On the other hand, it may be that even relatively slight physiological motion in different directions can result in large and unpredictable swings in the readings for the phase changes, and so the images that result from reading the results of the pulsed gradients application. The motion is erratic physiologically, which translates to the creation of all kinds of distortions and ghosts in the resulting MRI image. Physiological motion effects are typified by the blurred MRI images below, containing ghost images alongside the main image, or else they result in the distortions in the received signals and the corresponding images as well (Le Bihan et al. 2006, pp. 480-482): Image Source: Le Bihan et al. 2006, p. 481 To sum up, in diffusion-weighted images, the introduction of physiological motion introduces errors into the resulting images, to the extent that the finer the precision of the two gradient pulses and the components to read the differences in the received signal intensity from those, the greater too are the potential errors introduced by the physiological motion, especially where the motion is unpredictable both in duration and in direction (Le Bihan et al. 2006; Cercignani and Horsefield 2001). The utilization of one shot EPI has the impact of reducing the effect. The EPI is characterized by the swiftness of the technique. The image acquisition times for this technique can be in the vicinity of just 100 ms. The use of EPI likewise confers several advantages, including that the sequence lends itself to repeated playing over. This enables for the directionally-universal application of the gradients of diffusion, which in turn has the potential to improve the accuracy of the measurement. There is a high likelihood of shearing of the images when EPI sequencing is used for diffusion imaging purposes, and this hinges on the direction of the gradients. Such shearing can be removed through the registration of the acquired images making use of the gradients of diffusion versus those images that have been generated without the use of gradients of diffusion. Moreover, where eddy currents exist, there is the possibility of the generation of distortions. Such distortions manifest in shearing that occurs in the direction of the phase encoding. On the other hand, there is a greater level of complexity in the artifacts of distortion generated in imaging via the use of diffusion tensors (mres7007; module 3 2013) D. Achievement of Different Diffusion Weightings The different diffusion weightings are achieved via accounting for the differences in the attenuation of the received signal intensities from the spinning hydrogen ions in the water molecules as the result of the application of magnetic fields and gradient fields, and the attenuation in particular of the received signal intensity arising from the differences in the shifts in phases from the moving spins. The larger the distance traveled, the larger the phase shifts, and the larger the attenuation or the decrease in the signal intensity. By applying gradient fields along the three axes in a three-dimensional mapping of the signal intensities, and by reading the various levels of received signal intensities/or signal attenuations that result, one is able to come up with the different diffusion weightings necessary to produce an image. It is noted that where the direction of the gradient fields are directed to a certain axis, the signals are subjected to attenuation likewise along that axis, and so the resulting diffusion weightings are arrived at for that axis. In mappings where it is necessary to achieve diffusion weightings for all three axes, it is then necessary to be able to apply gradient pulses along the three axes, to be able to attenuate the signal intensities along all those axes and determine the diffusion rates for the molecules in three dimensions. It is worthwhile to note too, that taking a step back, the differences in the readings for the two gradient pulses used to determine signal attenuation and diffusion rates and distances achieved is what allows for the measurement of those metrics. It is the application of the gradient magnetic pulses and the measurement of attenuation of signal intensities along the axes of interest that allow for the determination of the diffusion weightings (Tonarelli 2012; Hagmann et al. 2006; Mori and Barker 1999). IV. Diffusion Information- Measurement As discussed above, the measurement of the diffusion information rests on the discovered attenuation of the signal intensity received in MR methods when it comes to water molecules diffusing and subjected to strong magnetic fields. That the attenuation in the signals corresponds to the rate of diffusion or the distance that has been traveled by the water molecules after a given amount of time is what makes all of this possible. From a spin point of view, on the other hand, the differences phases observed as water molecule hydrogen ions are spinning and move through the diffusion medium are observed to correlate with the rate of their movement and the distance that they have traveled in particular. Moreover, it is the shifts in phases that cause the attenuation in the signal intensity. In other words, where the spins are mobile, the signal intensity is reduced in proportion to the rate of its movement or conversely the distance that it has traveled through that diffusion medium. The measurement of the signal intensity attenuation is a proxy measure of the rate of the diffusion, and all of this fits in nicely into the theory that has been made possible by the mathematical models that have pinned the exact relationships among spin, strength of signals recorded in MR methods, and the rate of diffusion or rate of travel of diffusing molecules in a medium. In modern diffusion MRI methods, this measurement is achieved via the use of timed gradient pulses, with the differences in time between the two pulses providing the timing within which to measure the changes in spin, and therefore the distance traveled and the rate of movement of the molecules being observed to produce the MRI images (Hagmann et al. 2006; Mori and Barker 1999, pp. 102-106; Tonarelli 2012; Parker 2004, pp. S176-S178; Everdingen et al. 1998; Barker 1999; Maas 2005; Le Bihan et al. 2006; Yablonskiy et al. 2003; Koh and Collins 2007; Le Bihan 2011; Basser and Jones 2002; Battal et al. 2012; De Foer 2010; Luypaert et al. 2001; Williams et al. 1992; Topgaard 2006). References Basser, P. and Jones, D. 2002. Diffusion-tensor MRI: theory, experimental design and data analysis- a technical review. NMR Biomed 15. [Online]. Available at: https://www.physast.uga.edu/uploads/phys4510_zhao/review_DTI_theory.pdf [Accessed 11 April2013] Battal, B. et al. 2012. 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Available at: http://www.cewebsource.com/coursePDFs/DW-MRIIschemicStroke.pdf [Accessed 11 April2013] Topgaard, D. 2006. Probing biological tissue microstructure with magnetic resonance diffusion techniques. Current Opinion in Colloid & Interface Science 11. Williams, D. et al. 1992. Magnetic resonance imaging of perfusion using spin inversion of arterial water. Proc. Natl. Acad. Sci 89. Yablonskiy, D. et al.. 2003. Statistical Model for Diffusion Attenuated MR Signal. Magnetic Resonance in Medicine 50. [Online]. Available at: http://bayes.wustl.edu/glb/StatModel.pdf [Accessed 11 April2013] Read More