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Show STATE OF THE ART Diffusion Tensor Magnetic Resonance Imaging Vikas Gulani, MD, PhD, and Pia C. Sundgren, MD, PhD Abstract: Molecular diffusion plays an important role in many biologic phenomena. The ability to study diffusion, therefore, is extremely useful in physiology and medicine. MRI offers a non- invasive window to diffusion, particularly water self- diffusion. MRI techniques, which provide diffusion sensitivity or quantitation ( diffusion tensor MRI [ DTI]), have found widespread application in neuroscience and medicine, including the evaluation of stroke, brain development, tumor imaging, and demyelinating disorders. We discuss the tensor nature of diffusion and provide an overview of how DTI offers unique information on tissue organization, water mobility, and disease states, particularly those of neuro- ophthalmologic interest. (/ Neuro- Ophthalmol 2006; 26: 51- 60) Diffusion tensor imaging ( DTI) refers to a set of MRI techniques designed to provide information about water mobility ( diffusion) and tissue micro structure and organization in relation to directionality of diffusion. In general, and particularly in white matter, water mobility is not equal in all directions ( isotropic) but greater in one direction than another. Therefore, diffusion in white matter is described as anisotropic. This anisotropy means that diffusion is characterized, not by a single coefficient, but by a second- order symmetric tensor of six unique elements or diffusivities requiring multiple measurements for complete determination. Once these six diffusion coefficients have been obtained, the degree of mobility of water protons in the system can be determined with an average principal diffusivity The degree of anisotropy of this mobility can be determined by calculating anisotropy indices such as fractional anisotropy ( FA). Anisotropy indices give information about tissue organization, degree of myelination, and water mobility, and serve to complement a traditional anatomic MRI examination ( Fig. 1). While some anatomic information is included in all four images of Figure 1, the Department of Radiology, University of Michigan, Arm Arbor, Michigan. Address correspondence to Pia Maly Sundgren, PhD, MD, Department of Radiology, Room B2A209D, University of Michigan, 1500 East Medical Center Drive, Ann Arbor, MI 48109- 0030; E- mail: sundgren@ umich. edu traditional T2- weighted image contains no information about mobility that the apparent diffusion coefficient ( ADC) map provides. The FA and color- coded FA maps provide information about white matter organization and direction of maximal water mobility. ( For a more detailed introduction to DTI techniques, refer to the Appendix). The structural and organizational information contained in a DTI examination is used as a complement to a traditional anatomic imaging examination. In the short period since its introduction as an experimental technique in 1994, DTI has already been applied to a wide range of clinically relevant areas, including fiber tract mapping, brain maturation, ischemia, demyelinating disease, and tumor imaging. APPLICATIONS OF DIFFUSION TENSOR IMAGING Fiber Tract Mapping Much effort has been exerted in finding single image display schemes for the information within the diffusion tensor, including voxel- wise three- dimensional display forms such as the diffusion ellipsoid ( 1) and various color schemes ( 2). These techniques attempt to incorporate the anisotropy information contained in the eigenvalues and scalar invariants such as FA in the magnitude of the display and the directional information contained in the eigenvectors in the color scheme used ( Fig. 1). Pushing this directionality information one step farther, several groups have accomplished fiber tract mapping using DTI ( 3- 8). The local fiber orientation in each voxel is determined via DTI, and then voxels are connected to each other, starting at a seed point and propagating a tract by mathematically connecting the adjacent voxels based on information gleaned from the magnitude and directionality of diffusion anisotropy. A detailed review of these fiber tracking methods is beyond the scope of this article. An excellent starting point for understanding tractography has been provided by Mori and van Zijl ( 9). These methods provide an unprecedented opportunity to study brain connectivity in vivo. A particularly interesting future possibility is the combination of tractography with blood oxygenation level- dependent ( BOLD) or perfusion- based functional MRI ( fMRI) to J Neuro- Ophthalmol Vol. 26, No. 1, 2006 51 Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 Gulani and Sundgren FIG. 1. Normal subject. A. T2- weighted MRI is normal. B. Apparent diffusion coefficient map is normal. C. Fractional anisotropy ( FA) map shows highly directional white matter tracts, including the genu of the corpus collosum ( fat white arrows), the external capsule ( white arrows), and the internal capsule/ corticospi-nal tract ( curved white arrow). D. Color- encoded FA map with the following color assignments: blue for superior- inferior tract orientation, green for anterior- posterior, and red for left- to- right. Fibers with their orientations in other directions are represented by a mixture of colors. Signal intensities reflect FA values. obtain connectivity maps between activated areas of the brain. Promising early work in this direction includes photic stimulation BOLD fMRI experiments in humans showing that fMRI measures of visual system activation correlate with measured FA values for the posterior optic pathways, indicating a connection between function ( fMRI) and underlying structure ( DTI) ( 10). Fiber tracking has also been used to study the alteration in fiber geometry in pathologic processes. For example, it has been shown that the optic radiations in patients with optic neuritis localize more interiorly and more laterally than in control subjects ( 11). Fiber tract mapping also finds application in characterization of white matter tracts that are distorted or destroyed by neoplastic processes, potentially serving as a preoperative, postoperative, and even intra- operative guide to surgical care ( Fig. 2) ( 12). Brain Maturation and Aging While the precise cause of diffusion anisotropy is not definitively known, results from several groups have shown that diffusion anisotropy in white matter is related in part to the water content of the tissue, the degree of myelination of the tissue, and the extent to which the tissue shows macro-organization ( gathering into tightly packed bundles), the latter two factors ostensibly providing barriers to diffusion and allowing preferential diffusion along a given direction ( 13- 20). It is therefore natural to hypothesize that the myelination process can be followed with DTI. It can be shown, for example, that the ADC decreases and the FA increases as human brains myelinate, proceeding from premature to near- term ( 21), as newborns ( 19,20,22- 26), and into childhood until maturation and young adulthood ( 27- 30). There appears to be a decrease in the FA and 52 © 2006 Lippincott Williams & Wilkins Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. Diffusion Tensor Imaging J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 FIG. 2. Fiber tract mapping in glioma. Two sets of fiber tract mapping experiments are superimposed upon each other in a patient with a right temporoparietal glioma from pre- resection and post- resection measurements. The right pyramidal tract shifts dramatically laterally ( arrow) after resection of the tumor. ( Reprinted with permission from Nimsky C, Ganslandt O, Hastreiter P, et al. Preoperative and intraoperative diffusion tensor imaging- based fiber tracking in glioma surgery. Neurosurgery 2005; 56( 1): 130- 8.) ( 12). a concomitant increase in the ADC as adults age ( 31- 34). It is not clear whether this trend reflects a gradual de-myelination or loss of neural density. Some studies suggest that abnormal brain or cognitive development in childhood may manifest as decreased FA values in comparison with age- matched peers ( 21,35). Ischemia and Wallerian Degeneration Reduced oxygen delivery to a region of the brain results in cerebral ischemia. As a result of this ischemia, there is movement of sodium and calcium into the cell, osmotic cellular swelling, and a decrease in the fraction of extracellular water ( 36). These and other changes in the local environment of water molecules can be expected to affect the ADC, and it has long been observed that the ADC is exquisitely sensitive to very early changes in response to ischemia ( 37- 43). However, the precise mechanisms for the observed changes in diffusion during stroke are not yet completely understood. In white matter, there is a potential to miss early changes related to stroke if diffusion sensitivity is applied along a single direction. This is generally avoided by acquisition strategies that sensitize the images to the trace or average ADC or use isotropic diffusion weighting ( 44,45). It has been shown that anisotropy indices do not change as quickly in response to hyperacute ischemia as do the various diffusivity indices ( 46- 48). Presumably this phenomenon relates to the lack of disruption of the macro-structure- the myelination and fiber organization- that contributes to the diffusion anisotropy ( 36). In the acute, subacute, and chronic phases following ischemia, significant anisotropy changes have been observed. For example, in the first 24 hours following the reduction of oxygen delivery, there is an acute rise in anisotropy, possibly due to cellular swelling that leads to tighter packing of axons in a bundle ( 49). This packing may result in an increased barrier to transverse diffusion in the affected bundles. As the ischemia progresses, the consequent loss of organizing structure results, as expected, in a drop in diffusion anisotropy ( 50,51). These changes are more marked in white than gray matter, the latter of which does not show marked diffusion anisotropy to begin with. Considerable insight into the pathophysiology of ischemic changes in white matter can be gleaned from diffusion anisotropy experiments. An excellent review of this material has been provided by Sotak ( 36). Wallerian degeneration, or degeneration of axons distal to a focus of injury in the brain, can also be seen with DTI, manifesting as a loss of anisotropy in the involved tracts ( 18,52- 57). Although T2- weighted images show signal alterations in the presence of Wallerian degeneration, DTI methods are more sensitive. Demyelinating Disorders Due to its inherent sensitivity to disruption of barriers to diffusion such as myelin sheaths and tight cell packing, DTI has the potential to complement existing magnetic resonance techniques in the evaluation of demyelinating disorders such as multiple sclerosis ( MS). A number of groups have shown that in comparison to normal- appearing white matter ( NAWM), MS lesions show elevated ADC and diminished anisotropy indices such as FA ( 58- 67), with the anisotropy indices being more sensitive for lesion detection than pure ADC measurement ( 61,63,67). Figure 3 depicts MS lesions imaged at a 3.0 Tesla field strength with disruption of white matter tracts evidenced by FA map abnormalities. Some studies suggest that the degree of diffusion changes correspond to the severity of the demyelinating lesions, which may prove to be of great clinical importance ( 58,67). Acute, enhancing lesions also show larger dif-fusivities and lower FA values than chronic, non- enhancing 53 Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 Gulani and Sundgren FIG. 3. Multiple sclerosis. A. Axial T2- weighted MRI shows two areas of high signal ( arrows). B. Post- contrast axial T1 - weighted MRI shows corresponding non- enhancing " black holes" ( arrows). C. Apparent diffusion coefficient map shows increased diffusivity of the lesions. D. The fractional anisotropy ( FA) is decreased, indicating disruption of the white matter structures. An additional lesion appears in the FA map ( curved arrow) due to slight differences in slice obliquity. lesions. Moreover, DTI shows that NAWM in MS patients has a higher ADC and lower FA than the white matter in normal subjects, suggesting that there is occult damage to white matter in MS that is not seen with other imaging techniques ( 60,65,67). One preliminary study indicates that there may be a correlation between clinical severity of disease ( for example, cognitive impairment in relapsing-remitting MS), and the calculated diffusivities and FA ( 68). Tumor Imaging Conventional MRI has long been the mainstay for evaluating central nervous system ( CNS) tumor morphology and invasiveness. Diffusion imaging has been shown to be useful in helping characterize neoplasm for tumor necrosis, perirumoral edema, and tumor cellularity ( 57,69- 73). It is unclear if measurement of anisotropy adds additional sensitivity in characterizing CNS tumors. Some authors indicate that there is questionable utility for tumor characterization from DTI imaging and calculation of anisotropy indices ( 74- 77). Other recent reports, however, are more encouraging about the possibility of using DTI to characterize tumor infiltration ( 78), differentiation of high-grade from low- grade tumors ( 77), and characterization of peri- tumoral edema ( 77). There is little disagreement, however, that DTI will prove to be useful to evaluate distortion of brain white matter tracts within or adjacent to tumor, potentially altering surgical management. The effect of the neoplasm on the white matter tracts can be depicted by plotting the anisotropy indices or more elegantly by diffusion tractog-raphy ( 12,79- 81) ( Fig. 4). Enhancing lesions that arise on routine follow- up brain MRI at the site of a previously identified and treated primary intracranial neoplasm present an important diagnostic dilemma. MRI cannot reliably discriminate tumor recurrence or progression from the inflammatory or 54 © 2006 Lippincott Williams & Wilkins Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. Diffusion Tensor Imaging J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 FIG. 4. Glioblastoma. A. Axial T2- weighted MRI shows left paraventricular high signal. B. Post- contrast T1 - weighted MRI shows an enhancing lesion in the same area. C. Apparent diffusion coefficient map shows slightly high signal, indicating decreased average diffusivity. D. Fractional anisotropy ( FA) map shows displacement and possibly partial destruction of the white matter structures, as indicated by decreased FA values in the region. necrotic changes resulting from radiation ( 82). Whereas radiation injury may exhibit telltale morphologic changes, such as a " soap bubble" pattern ( 83), or a necrosis metabolic pattern as measured by magnetic resonance spectroscopy ( 84,85), these indicators are not entirely specific. In a recent preliminary study evaluating new contrast-enhancing lesions in patients previously treated for brain neoplasm, ( 86) substantial differences between recurrent neoplasm and radiation injury could be demonstrated when measuring FA and FA ratios ( ratio of FA in the lesion to the FA on the contralateral side). Higher FA values and significantly higher FA ratios were found in NAWM outside the boundaries of peri- lesional edema in patients with radiation injury compared with those with recurrent tumor. One explanation for the difference is that in recurrent tumor, the affected white matter tracts are less well- organized resulting in a more marked decrease in anisotropy than that observed in tracts affected by radiation damage. This explanation is supported by a previous study where it has been shown that tumor can be distinguished from peri- rumoral vasogenic edema using DTI ( 77). Trauma Traumatic brain injury and its effect on the measured diffusion tensor is as yet an understudied topic in radiology. Focal brain injuries such as hematomas and contusions are well characterized by a combination of CT and traditional MRI. Less well- characterized by traditional imaging methods is diffuse axonal injury ( DAI), thought to occur in shear injury as a result of abrupt deceleration or abnormal rotation of brain tissue and the subsequent frictional effects of unequally rigid tissues sliding against each other. The effect on white matter tracts is that of stretching of axons and distortion or even disruption of white matter tracts. Case 55 Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 Gulani and Sundgren reports and early studies indicate that DTI holds considerable promise in helping delineate the location and extent of DAI, potentially serving as an adjunct to T2- weighted imaging, which allows sensitive detection of DAI due to the susceptibility artifacts produced by hemoglobin and breakdown products in microhemorrhages ( 87- 91). DTI studies indicate that FA decreases in DAI, reflecting the disruption of underlying tissue organization. The extent of DTI abnormality correlates with clinical markers such as the Glasgow Coma Scale ( 89,90). FUTURE DIRECTIONS In the little over ten years since the introduction of the technique, DTI has quickly gone from a technical innovation to an important scientific and clinical tool. Applications of the technique include fiber tracking and determination of connectivity between different areas of the brain, evaluation of white matter maturation, and imaging of ischemia, myelination disorders such as MS, neoplasms, and traumatic brain injuries. Further applications are almost inevitable as research continues to help make the technique more robust and easier to apply, and as more scientists and clinicians gain an understanding of DTI and the information about structure and function that it can provide. Also, further technical innovations in resolution of fiber directions and crossing fibers will also allow the imaging of subtle white matter and fiber tract pathology. APPENDIX Diffusion Imaging Mathematical descriptions of the macroscopic and microscopic consequences of diffusion phenomena were originally provided by Fick and Einstein, respectively ( 92,93). Diffusion can be described as the process of transport of matter due to the random motion of molecules in a given medium ( 94). When the diffusing substance and the medium are the same, the measured coefficients are referred to as self- diffusion coefficients. While MRI provides the ability to study a number of chemicals and nuclei, diffusion MRI is most commonly used to study the self- diffusion of water. The sensitivity of the nuclear magnetic resonance ( NMR) signal to the effects of diffusion has been known since very shortly following the discovery of NMR. This effect has long been used to measure diffusion coefficients ( 95- 97). By the mid- 1980s, NMR techniques and analysis had been applied to imaging to obtain pixel- wise ADC maps ( 98- 102). Most modern diffusion imaging techniques rely on variations of bipolar pulsed field gradient methods ( 97) to obtain diffusion sensitivity. In these sequences, two magnetic field gradients are applied sequentially to de- phase and then re- phase spins or protons. Any spins that have moved in the interval between the two gradients do not " feel" the same magnetic field as during the first gradient, and thus they do not get re- phased, resulting in a net loss of spin coherence. This results in a quantifiable loss in the MRI signal, which can be related to the ADC. In the simplest case, with spin- echo MRI and considering for the moment only a single diffusion coefficient per voxel, it can be shown that the signal and the ADC are related as follows: S = S0e- bD [ 1] where S is the measured signal, S0 the signal in absence of the gradients, and D is the ADC. The b or so- called b- factor in this equation is a function of the gradient strength G, duration 8, and time separation A between the gradient pulses. The b- factor must be calculated for each sequence, which can be non- trivial when the diffusion gradients interact with the imaging gradients in a complicated fashion. For the simple case where imaging gradients and the resultant cross terms in the b- factor calculations are ignored b = y2G2 § 2( D- W3), where 7 is a physical constant, the gyromagnetic ratio. D can be determined from Equation 1 if at least two images are acquired with different diffusion weightings ( and thus different b- factors). It also becomes evident from this equation that any movement of spins during the diffusion time A will result in MRI signal loss. Thus diffusion MRI is sensitive to all motion of molecules during the sequence, and not just purely diffusive motion. Moreover, the observed diffusion coefficients in tissues reflect diffusion in several compartments ( extracellular and intracellular, intranuclear, mitochondrial, etc.) which may all have different diffusivities if one could resolve them. It is for these reasons that the diffusion coefficient and tensor as measured with MRI are called the apparent diffusion coefficient ( ADC) and apparent diffusion tensor ( ADT), respectively. The Diffusion Tensor In an environment where the barriers to diffusion are identical in all directions, diffusion is considered isotropic. This is the case, for example, in a cup of water, where even if molecules are allowed to diffuse for relatively long times, they are unlikely to encounter a barrier to diffusion such that movement in one direction would be favored over any other. In such situations, the diffusion coefficients in all directions are the same, hence the term isotropic diffusion. For isotropic cases, measurement of a single scalar coefficient suffices to completely characterize the system. However, the diffusivity of a substance cannot always be assumed identical in all directions. Diffusion coefficients can be relatively large in one direction, and small in 56 © 2006 Lippincott Williams & Wilkins Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. Diffusion Tensor Imaging J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 another. For medical applications, this is the case for example in white matter, muscle, cartilage, and in the lens of the eye ( 103- 109). In such settings, diffusion is said to be anisotropic, reflecting the non- equal diffusivities in various directions. Diffusion is more generally characterized by a second order tensor, or a matrix of nine coefficients: D Ax D DXy D D D. Dxz Dyz D. - [ 2a] This implies that nine diffusivities would have to be determined to measure the tensor. However, the diffusion tensor is symmetric, meaning that Dxy = Dyx, Dxz = Dzx, and D^ = Dzy. Thus, only six diffusivities need to be determined. When the axes of the measurement system coincide exactly with the axes of the fiber or object being studied, the off- diagonal elements of the tensor ( i. e., Dxy, Dxz, and Dyz) become zero, and the measured diagonal diffusivites A*. Dyy, and Dzz are termed the principal diffusivities, often annotated Dn, D22, and Dn or X7, X2, and X5, as given by Eq [ 2b]: D prin A, 0 0 0 A2 0 0 0 A3 [ 2b] Of course, in the general case, the measurement and principal axes of diffusion do not coincide for most fibers. In such a case, these principal diffusivities which are also called the eigenvalues of the diffusion tensor, along with the eigenvectors of the system ( defining the directions of the principal diffusivities), can be calculated from the measured tensor by a simple mathematical transformation relating the measured tensor ( Equation [ 2a]) to the principal diffusivities ( Equation [ 2b]. Basser et al ( 1,110) provided the seminal work depicting the measurement of the ADT with MRI. Starting with the mathematical expressions for the description of magnetization in the presence of spin diffusion ( 96), they derived the expressions necessary to calculate the various terms of D ( or ADT) from an MRI experiment. They showed that where ly = y Gtdt' IGjdt'dt [ 3] [ 4] Here, the indices i andy represent the measurement axes ( 1, 2, and 3 being x, y, and z, respectively). G, and G, thus represent the applied diffusion gradients in various directions. Equation 3 bears obvious resemblance to Equation 1, the case for measuring a single diffusion coefficient. However, all six unique diffusivities must be accounted for, and thus Equation 3 implies that at least seven images must be acquired to completely determine the seven variables in this equation ( S0 and the six unique diffusivities). Obviously, the calculation of the b- matrix as per Equation 3 is considerably more complex than that of b- factors for a unidirectional experiment, and care must be taken to account for the interaction between the various diffusion and imaging gradients. Data interpretation in DTI can be difficult. The information contained in the six diffusivities of the measured tensor or in the eigenvalues and eigenvectors of the system has to be displayed, and the information contained within the datasets further extracted. DTI reveals much architectural information about the various fiber tracts being studied. Scalar invariants are calculated from the measured diffusivities obtained from a DTI experiment and are not dependant on gradient directions and their relationship to the subject. Several such invariants, which are easy to conceptualize and display, have been used in DTI. These quantities are useful in that they provide structural information about the diffusion system, and along with the eigenvalues and eigenvectors of the system, are independent of the measurement axes across data sets. The diffusion trace ( Tr( D)) is calculated as follows: rr( D)= A1+ A2+ A3 [ 5] The trace, or mean diffusivity (( X) = Tr/ 3) gives information about the overall mobility of water molecules in the environment being studied. Several scalar invariants have been suggested to give information about diffusion anisot-ropy The most commonly used of these quantities are FA and relative anisotropy ( RA), which are calculated as follows: FA = { jl^ v11- v': y: v: \ v ' / v v ~ j-^^ [ 6] ' 3/ 2[( Ai - ( A)) + ( A2 - ( A)) + ( A3 -< A » ] A^+ A^+ Aa2 '( Ai-< A » 2 + ( A2-< A » 2 + ( A3 - < A » 2 RA = f VV> '" " [ 7] FA and RA are similar in that both quantitate the degree of diffusion anisotropy in the tensor. FA ranges from 0 ( completely isotropic) to 1 ( completely anisotropic diffusion), while RA ranges from 0 to - J2. FA and RA maps are often depicted for DTI data, as they, along with the ( X), offer computationally and conceptually the simplest yet quantitative insight into diffusion anisotropy in the system. Another frequently encountered measure of anisotropy, ACT, is not shown here but is closely related to RA. As a rough guide to the reader, we provide parameters used for a typical clinical ADT experiment and the 57 Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited. J Neuro- Ophthalmol, Vol. 26, No. 1, 2006 Gulani and Sundgren quantitative information that is often extracted from it. A routine ADT examination at our institution consists of collecting single- shot echoplanar imaging ( EPI) with diffusion weighting in 10 directions ( including b = 0), a field of view of 32 cm encoded with a 160 X 120 matrix, and 2 signal averages. Since the EPI images are collected as single shots, the imaging time is small (- five minutes including sequence setup time), though the images must be post-processed to obtain the diffusivity and anisotropy information. This latter process also usually requires a few minutes, though it can be more time consuming, especially if quantitative data about given lesions are to be obtained and analyzed. 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