- Open Access
Diffusion MR tractography of the heart
© Sosnovik et al; licensee BioMed Central Ltd. 2009
- Received: 01 August 2009
- Accepted: 13 November 2009
- Published: 13 November 2009
Histological studies have shown that the myocardium consists of an array of crossing helical fiber tracts. Changes in myocardial fiber architecture occur in ischemic heart disease and heart failure, and can be imaged non-destructively with diffusion-encoded MR. Several diffusion-encoding schemes have been developed, ranging from scalar measurements of mean diffusivity to a 6-dimensional imaging technique known as diffusion spectrum imaging or DSI. The properties of DSI make it particularly suited to the generation of 3-dimensional tractograms of myofiber architecture. In this article we review the physical basis of diffusion-tractography in the myocardium and the attributes of the available techniques, placing particular emphasis on DSI. The application of DSI in ischemic heart disease is reviewed, and the requisites for widespread clinical translation of diffusion MR tractography in the heart are discussed.
- Cardiovascular Magnetic Resonance
- Diffusion Tensor Imaging
- Orientation Distribution Function
- Helix Angle
- Principal Eigenvector
The myocardium can be studied at several spatial scales. New techniques, such as molecular imaging, are providing important insights into cardiac disease at the cellular and subcellular levels [1–3]. At the other end of the spectrum, parameters of regional and whole organ function such as ejection fraction, perfusion, viability and strain are now routinely used in clinical practice [4, 5]. The microstructural organization of the myocardium, however, has been less extensively studied, although changes at this scale could provide important biological insights and a mechanism linking cellular and whole-organ pathology [6–8]. Here we describe our initial ex-vivo experience with a relatively new magnetic resonance (MR) technique, diffusion spectrum MR tractography, capable of imaging myocardial fiber architecture at the microstructural level.
In a series of breakthrough histological studies, Streeter and colleagues demonstrated that cardiomyocytes form tracts with a crossing helical architecture [9, 10]. Myofiber tracts in the subendocardium have a positive or right-handed helix angle, those in the mid-myocardium are circumferential and those in the subepicardium have a negative or left-handed helix angle [9, 10]. These fiber tracts form laminar sheets [11–14], and it is the shear, extension, thickening and radial reorientation of these sheets that allows the myocardium to thicken in systole [12, 15–17]. Changes in scalar indices of diffusion and myofiber anatomy have been documented in a variety of small and large animal models of cardiac disease [18–23], as well as in humans [24–26]. In the majority of these studies, however, fiber anatomy was visualized only at discrete points in the myocardium. In the current article we focus on the use of diffusion-encoded MR to create continuous 3-dimensional tractograms of myocardial fiber architecture. We place particular emphasis on our recent experience in the heart with diffusion spectrum MR tractography . We review the rationale and theoretical basis of MR tractography, its application in animal models of ischemic heart disease, the properties of other diffusion-encoding schemes such as diffusion tensor and q-ball imaging, and the pathway towards clinical translation of MR tractography in the heart.
Diffusion Spectrum MR
Diffusion imaging can be performed at several levels of complexity, ranging from the simple acquisition of a single diffusion-weighted image to the complex but robust acquisition scheme used in diffusion spectrum imaging (DSI) [28, 29]. Diffusion tensor imaging (DTI) and q-ball imaging can be thought of as formalisms that sample diffusion or q-space with an intermediate level of complexity [28, 29]. While complex, DSI is the only technique derived directly from first principles , is hypothesis free [28, 30], broadly generalizable, and is regarded by many (including the authors) as the gold standard diffusion imaging technique [28, 31–33]. In the current implementation of DSI, q-space is sampled with 515 diffusion-encoding vectors or q-vectors, although simulations containing up to 925 q-vectors have been performed . The angular resolution and accuracy of DSI result in large part from the number and distribution of the samples acquired in q-space, analogous to the manner in which the region of support and sample density of k-space influence the spatial resolution and field-of-view of an image.
The q-vectors used to sample q-space in a DSI experiment vary in both their strength (b-value) and spatial orientation, sampling q-space in a dense 3D lattice. The b-value of a q-vector is proportional to the product of the square of the gradient strength and the diffusion time interval. (b ~ q2Δ, where q = γδG and γ is the gyromagnetic ratio, δ is the gradient duration, G is the gradient strength and Δ is the diffusion time interval). The b-value in a diffusion-encoded acquisition is in some ways analogous to the degree of velocity encoding (venc) used during phase contrast imaging. Higher b-values increase the resolution of the diffusion spectrum, and are thus desirable. However, an excessively high b-value can reduce image signal-to-noise ratio (SNR) severely, and an optimal balance between these two competing factors must thus be struck [31, 33]. B-values greater than 10,000 s/mm2 have been used both in-vivo and ex-vivo in the brain and myocardium [27, 30, 33].
In a DSI acquisition, each voxel in the spatial (x, y, z) domain of an image has its own 3D q-space associated with it. DSI images are thus 6-dimensional in which the 3 dimensions of q-space are superimposed on the 3 dimensions of image space [28, 30]. Q-space is sampled in a DSI experiment by applying a B0 gradient field (q-vector) along a specific spatial orientation. The duration and intensity of the applied field (b-value) determines the length of the q-vector relative to the origin of q-space, while the vector direction is determined by the spatial orientation of the applied gradients. The resulting signal intensity determines the coefficient for that value of Q in each voxel. A 3D image with 96 × 96 × 96 voxels will thus have greater than 8 × 105 q-space datasets, with each dataset containing 515 coefficients.
The merits and limitations of other diffusion-encoding schemes (q-ball imaging, spherical deconvolution, diffusion tensor imaging) will be discussed in detail later in the article. These techniques sample q-space less fully than DSI, enforce a diffusivity model (Funk transform, spherical harmonics, tensor) on the sampled data and degeneralize DSI to some degree. The simplest of these models that still includes directional information is DTI, but this differs however from DSI in several important ways: With DSI each distinct fiber population in a voxel is represented by a unique local maximum in the PDF/ODF [30, 37, 38]. As described below, however, the principal eigenvector of a diffusion tensor reflects the average direction of myofiber orientation in the voxel . In addition, while the spatial resolution of DTI is determined by/identical to the resolution of the image, the 6-dimensional nature of DSI provides subvoxel resolution, determined by the resolution of the ODF . The attributes of DSI are thus inherently suited to the generation of 3D tractograms of myocardial fiber architecture.
DSI Tractography of the Myocardium
DSI tractograms can be visualized as projection images or as tomographic reconstructions of the 3D dataset. Tomographic representation involves the selection of a plane in the 3D field, the thickness of which is defined by the user. Only those myofibers that intersect the plane are shown in the reconstructed image (figures 4 and 5). The density of fibers in the myocardium, however, can make projection images and even tomographic reconstructions complex to interpret. Spherical or discoid regions-of-interest (ROIs) can thus be defined to visualize only those fiber tracts intersecting the ROI (figures 3 and 6). As shown in figure 6, myofiber tracts in the subendocardium and subepicardium form half-turns of a spiral but have orthogonal helix angles. Fibers in the subendocardium of the lateral wall track from the posterior-base to the anterior apex, while those in the subepicardium track from the anterior-base to the posterior apex .
Diffusion Tensor MR (DTI)
Diagonalization of the diffusion tensor rotates its axes out of the laboratory frame (x, y, z) and along the eigenvectors of the tensor, which reflect the diffusion properties of the tissue in the voxel (figure 10) [28, 29]. The principal or largest eigenvector, designated λ1, describes the direction of diffusion along the long axis of the myofibers in the voxel, the second largest eigenvector the direction of the myofiber sheets and the third eigenvector the direction normal to the myofibers [14, 16, 35]. Several important scalar parameters, such as mean diffusivity and fractional anisotropy, can be derived from the eigenvalues associated with these eigenvectors [28, 29]. Studies in animals and humans have shown that both mean diffusivity and fractional anisotropy change significantly in infarcted and healing myocardium [18–26].
The principal eigenvector of the tensor can be used to estimate the average direction and helix angle of the myofibers in a voxel [14, 35]. A reduction in right-handed (subendocardial) fibers and an increase in left-handed (subepicardial) fibers has been noted in animals and patients with myocardial infarction [22, 25]. While of substantial value, several significant limitations of DTI impact cardiac tractography and merit discussion. DTI tractography can only resolve one fiber population, described by the principal eigenvector, in a given voxel. Moreover, the principal eigenvector is a composite measure of mean diffusion in the voxel. If a voxel contains more than one fiber population the principal eigenvector will represent the average direction of diffusion in the voxel, which may actually not be an accurate representation of the fibers in the voxel [28, 39, 44]. In the context of tractography, DTI thus reduces the information contained in the PDF into a single average value, the principal eigenvector. DTI can thus be viewed conceptually as a linear approximation of the displacement spectrum.
The principal eigenvectors in adjacent voxels can be connected using several algorithms to form streamlines of fiber tracts (figure 10) [39, 44]. DTI tractograms, however, are limited in both angular and spatial resolution and are susceptible to a degree of bias and uncertainty introduced by the undersampling of q-space [39, 44]. Because only one average fiber population per voxel can be resolved with DTI, it is unable to detect complex and converging fiber anatomy [33, 38]. The lower number of seed points produced with DTI also leads to smaller and less complete tractography datasets than DSI. In theory, depending on the number of fiber populations per voxel, dramatic improvements in the spatial resolution of DTI could produce a tractographic dataset similar to DSI. In practice, however, this cannot be done because DTI acquisitions are already highly SNR constrained due to the phase dispersion induced by the diffusion-encoding gradients. A simple isotropic doubling of the resolution of a DTI acquisition, for instance, would require 64 signal averages to maintain SNR. DTI acquisitions with near microscopic resolution would thus require prohibitively long scan times even ex-vivo to maintain adequate SNR. The longer readout duration of these ultra-high resolution scans would also increase the TE and thus reduce SNR even further. The parameters of a diffusion-encoded acquisition, particularly in-vivo, are thus frequently dominated by the need to achieve adequate SNR, as discussed below.
In-Vivo Diffusion Imaging
Diffusion, strain and velocity encoded MR are all displacement encoding techniques that rely on the presence of a residual phase following the application of equal and opposite gradients. The spatial scale of the displacement due to diffusion, however, is far lower and requires significant modifications to be made in the acquisition scheme and/or the strength of the applied gradients. Diffusion encoded acquisitions are usually performed with single-shot readouts such as EPI (echoplanar MRI) or HASTE (half Fourier acquired single shot turbo spin echo) , ensuring all lines of k-space have the same phase. Multishot diffusion imaging has been performed but requires a scheme to detect and correct random shot-to-shot phase changes produced by motion and the diffusion-encoding gradients . The incorporation of diffusion encoding in to a HASTE sequence violates the CPMG condition since δ, and hence the time between the 90° and the first 180° refocusing pulse, is significantly greater than half the time between successive 180° refocusing pulses in the readout. This causes phase cancellation between echoes and poor image quality. Experimental techniques have been developed to address phase incoherence in diffusion-encoded HASTE, but many of these eliminate 50% of the signal (either even or odd echoes) and thus suffer from low SNR . Despite the potential for susceptibility, chemical shift and ghosting artifacts to occur, the vast majority of diffusion-encoded acquisitions are thus performed with single-shot EPI.
Tractography of stationary structures such as the brain and the myocardium ex-vivo can be performed with a Stejskal-Tanner diffusion encoded sequence [28, 29, 34]. In practice, however, diffusion-encoded imaging of the brain is frequently performed with a twice refocused spin echo sequence to limit the effects of eddy currents on image quality . The diffusion-encoding gradients in the Stejskal-Tanner sequence are placed on either side of a 180° refocusing pulse [28, 29, 34], which refocuses the diffusion-encoded signal at the echo time of the spin echo EPI readout (figure 11A). The use of this sequence in the heart in-vivo, however, is precluded by motion. A stimulated echo approach has thus been developed to overcome this (figure 11B) : Three 90° radiofrequency (RF) excitation pulses are applied within two successive RR intervals. The first and third excitation pulses have identical trigger delays from the onset of the successive R-waves and are both followed by unipolar diffusion encoding gradients. The second 90 degree RF pulse is placed a duration of TE/2 from the first, and effectively flips the transverse magnetization back into the longitudinal plane, where it is subject to R1 decay but not to R2* decay and motion induced phase change. The diffusion sensitivity of the sequence is determined by the physical displacement of water between the onset of the first and second unipolar diffusion encoding gradients. Diffusion sensitization thus continues to occur while the magnetization produced by the first excitation pulse is stored and protected in the longitudinal axis during a period known as the mixing time (TM). The application of the third 90-degree RF pulse and the second unipolar gradient produce a diffusion-encoded stimulated echo that has adequate diffusion sensitization and is largely free of motion related artifacts .
Several caveats of this approach, however, need to be considered. Diffusion imaging is frequently signal-to-noise (SNR) constrained and a stimulated echo EPI sequence has half the SNR of a spin-echo EPI readout. In addition, the delay between the R wave and the first and third RF pulses needs to be carefully selected to eliminate the effects of myocardial strain on the diffusion measurements . Diffusion measurements (particularly the second and third eigenvectors) with this technique may thus be optimally made only at certain "sweet spots" in the cardiac cycle, for instance at midsystole, where the strain effects become negligible . To overcome this limitation myocardial strain data can be acquired with the diffusion MR data and be used to retrospectively correct the diffusion measurements [48, 49]. A strain-insensitive stimulated echo sequence has also been developed and uses a pair of bipolar diffusion-encoding gradients, rather than unipolar diffusion-encoding gradients (figure 11C) . Diffusion encoding with this sequence, however, occurs only during the duration of the 2 pairs of diffusion encoding gradients, which are insensitive to first order motion terms (flow compensated) . While this sequence is strain-insensitive and can be performed at any stage of the cardiac cycle, the gradient duration required for adequate diffusion encoding (b-values) significantly lengthens the TE and reduces SNR.
The stimulated echo approaches described above have been successfully used to perform DTI in patients in-vivo [24–26], but on a limited scale in a few centers of expertise. More widespread clinical performance of DSI tractography in the heart will require several technical and scientific advances to be made. Gradient technology on whole body MR scanners will need to be improved by at least a factor of 2. The potential of improved gradient performance was demonstrated recently by Gamper and colleagues on an 3 Tesla clinical system equipped with an 87 mT/m gradient . The strength of this gradient allowed a spin-echo EPI readout to be used, avoiding the SNR penalty of a stimulated echo approach. A pair of bipolar diffusion encoding gradients was placed on either side of a 180° refocusing pulse in a flow-compensated modification of the Stejskal-Tanner approach (figure 11D) . While the use of this approach does impose certain constraints, it overcomes several factors impeding the performance of diffusion tractography in-vivo. Clinical translation will also require improved techniques for whole-heart imaging to be developed. The development of multi-element arrays, including a recently developed 128-element cardiac array , has the potential to facilitate the acquisition of volumetric whole-heart datasets in a single breathold. In addition, improvements in radiofrequency and navigator technology will also facilitate the acquisition of volumetric diffusion encoded data of the heart in-vivo .
Q-Space Sampling In-Vivo
Several q-space sampling schemes have been proposed for tractography of the brain in-vivo [30, 31, 55, 56]. The optimal q-space sampling scheme for in-vivo tractography of the heart, however, needs to be considered in the context of the SNR and motion-imposed constraints specific to the heart. Nevertheless, the experience in the brain with different q-space sampling schemes remains highly relevant to in-vivo tractography of the myocardium and worthy of discussion. Diffusion tractography in the brain is SNR constrained [39, 44]. Thus, even if only 6 independent diffusion encoding vectors are applied in order to perform DTI tractography, several signal averages need to be performed to achieve adequate SNR. This, however, is being less frequently done . Rather than averaging data produced by the same diffusion-encoding vector several times, the scan time is used to acquire data in more than 6 directions [44, 57–59]. The improvement in SNR, which is dependent on the total number of acquisitions, is similar with the two approaches. However, the accuracy of the data derived from the tensor is improved when a greater number of directions are sampled [57–59].
A voxel containing n individual myofiber populations will have 3n degrees of freedom, and likely require up to 6n independent q-vectors to fully resolve diffusion in the voxel. Whether the application of greater than 6n q-vectors would be desirable would depend in large part on the SNR of the data. The application of additional q-vectors would consume time but on the other hand increase the SNR of the image and also potentially de-alias the PDF/ODF. The more densely q-space is sampled the larger the PDF/ODF becomes, reducing the potential for aliasing. (This is analogous to increasing the FOV of an image to reduce aliasing in the spatial domain.) The approach favored by many, including ourselves, is thus to sample q-space as densely as possible within the limitations imposed by acquisition time, patient tolerance and the pulse sequence considerations discussed above.
Several high angular resolution diffusion imaging (HARDI) techniques have been developed that sample q-space more densely than DTI, but less so than DSI [55, 56, 60]. All of these techniques are based on certain hypotheses and assumptions, but are easier to implement in-vivo than DSI and may be well suited to imaging of the myocardium under certain scenarios. Q-ball imaging for instance involves the use of q-vectors that all have an identical and fairly large b-value [28, 56, 60]. Rather than sampling a 3D lattice in q-space, the technique samples the surface of a sphere with a given radius in q-space. The technique is simpler and more rapid than DSI but assumes that the selected b-value is optimal for the detection of all fiber or nerve tracts in the tissue, which may not always be the case. In normal myocardium the myofiber tracts have reasonably similar lengths and morphology (figure 6) and q-ball imaging may perform very well in this scenario. Infarcted myocardium, however, much like the brain has a highly heterogeneous population of myofibers, which may not all be detected optimally at the selected b-value. (A useful analogy to consider is the use of a single preset velocity encoding gradient to image several hemodynamic jets, despite large potential variations in the velocities of these jets). Nevertheless, q-ball imaging maintains many of the attributes of DSI, is easier to implement clinically and has the potential to be of significant value in the myocardium.
Validation of DSI Tractography.
Known Anatomical Features
Wedeen et al 
Crossing nerve tracts (optic chiasm, brainstem and others)
Gilbert et al 
Core of crossing fiber tracts
Sosnovik et al 
Array of crossing helical myofibers
Lin et al 
Schmahmann et al 
Gaige et al 
Sosnovik et al 
The potential of diffusion-tractography, and in particular DSI tractography, to resolve microstructural fiber anatomy in the heart has been demonstrated in several studies ex-vivo. At present, hardware limitations on most clinical scanners constitute the principal impediment to the clinical translation of diffusion tractography in the heart. Progress in the field will thus be rapidly accelerated by the widespread introduction of clinical scanners with gradients greater than 80 mT/m. Advances in RF technology, multi-element arrays, navigators and parallel acquisition schemes will also facilitate the clinical translation of more advanced q-space acquisition schemes. Clinical translation of this promising technology, however, will be a major challenge, requiring an excellent level of collaboration between engineers, industry and physicians. Diffusion tractography does not involve ionizing radiation or exogenous contrast media, and poses no risk to the patient. The technique images the myocardium at the microstructural scale and provides information that is highly complementary to that provided by other modalities and imaging techniques. Diffusion tractography of the myocardium expands the breadth and scope of cardiovascular magnetic resonance and has the potential to become an extremely powerful tool in both the research and clinical settings.
This study was supported in part by the following grant from the National Institutes of Health: DES (R01 HL093038 and K08 HL079984), VJW (RO1 MH64044), and (NCRR P41RR14075) to the Martinos Center for Biomedical Imaging.
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