- Technical notes
- Open Access
Comparison of diffusion tensor imaging by cardiovascular magnetic resonance and gadolinium enhanced 3D image intensity approaches to investigation of structural anisotropy in explanted rat hearts
- Olivier Bernus†1,
- Aleksandra Radjenovic†2,
- Mark L Trew3,
- Ian J LeGrice3, 4,
- Gregory B Sands3,
- Derek R Magee5,
- Bruce H Smaill3, 4 and
- Stephen H Gilbert6Email author
© Bernus et al.; licensee BioMed Central. 2015
Received: 2 June 2014
Accepted: 11 March 2015
Published: 29 April 2015
Cardiovascular magnetic resonance (CMR) can through the two methods 3D FLASH and diffusion tensor imaging (DTI) give complementary information on the local orientations of cardiomyocytes and their laminar arrays.
Eight explanted rat hearts were perfused with Gd-DTPA contrast agent and fixative and imaged in a 9.4T magnet by two types of acquisition: 3D fast low angle shot (FLASH) imaging, voxels 50 × 50 × 50 μm, and 3D spin echo DTI with monopolar diffusion gradients of 3.6 ms duration at 11.5 ms separation, voxels 200 × 200 × 200 μm. The sensitivity of each approach to imaging parameters was explored.
The FLASH data showed laminar alignments of voxels with high signal, in keeping with the presumed predominance of contrast in the interstices between sheetlets. It was analysed, using structure-tensor (ST) analysis, to determine the most (v 1 ST ), intermediate (v 2 ST ) and least (v 3 ST ) extended orthogonal directions of signal continuity. The DTI data was analysed to determine the most (e 1 DTI ), intermediate (e 2 DTI ) and least (e 3 DTI ) orthogonal eigenvectors of extent of diffusion. The correspondence between the FLASH and DTI methods was measured and appraised. The most extended direction of FLASH signal (v 1 ST ) agreed well with that of diffusion (e 1 DTI ) throughout the left ventricle (representative discrepancy in the septum of 13.3 ± 6.7°: median ± absolute deviation) and both were in keeping with the expected local orientations of the long-axis of cardiomyocytes. However, the orientation of the least directions of FLASH signal continuity (v 3 ST ) and diffusion (e 3 ST ) showed greater discrepancies of up to 27.9 ± 17.4°. Both FLASH (v 3 ST ) and DTI (e 3 DTI ) where compared to directly measured laminar arrays in the FLASH images. For FLASH the discrepancy between the structure-tensor calculated v 3 ST and the directly measured FLASH laminar array normal was of 9 ± 7° for the lateral wall and 7 ± 9° for the septum (median ± inter quartile range), and for DTI the discrepancy between the calculated v 3 DTI and the directly measured FLASH laminar array normal was 22 ± 14° and 61 ± 53.4°. DTI was relatively insensitive to the number of diffusion directions and to time up to 72 hours post fixation, but was moderately affected by b-value (which was scaled by modifying diffusion gradient pulse strength with fixed gradient pulse separation). Optimal DTI parameters were b = 1000 mm/s2 and 12 diffusion directions. FLASH acquisitions were relatively insensitive to the image processing parameters explored.
We show that ST analysis of FLASH is a useful and accurate tool in the measurement of cardiac microstructure. While both FLASH and the DTI approaches appear promising for mapping of the alignments of myocytes throughout myocardium, marked discrepancies between the cross myocyte anisotropies deduced from each method call for consideration of their respective limitations.
Myocyte orientation: mean orientation of aggregated myocytes within a local spatial region
Sheetlet: localized sheet-like aggregations of myocytes ~ 6-cells thick extending as curved branching planes
Sheetlet-interstices: gaps between adjacent sheetlets which exist as potential spaces in vivo and open up on fixation. Collagen structure differs within sheetlets and adjacent to sheetlet interstices, and there is evidence that sheetlet-interstices function as shear layers in vivo 
Myolaminar structure: the combined structure formed by sheetlet and sheetlet-interstices
Isotropic structure: structure with properties (at any point) identical in all directions
Anisotropic structure: structure with properties (at any point) which are different dependent on direction
Orthotropic structure: structure with properties (at any point) which are different and can be described relative to a set of orthogonal perpendicular axes.
Diffusion tensor imaging: CMR of tissue anisotropy involving imaging the directionality and magnitude of water diffusion, which is represented as a mathematical tensor
Structure tensor: an image analysis mathematical tool (operator) which encodes directionality information from a standard image (2D or 3D) into a tensor.
Myocardial structure is important to cardiac electrical and mechanical function and alteration to this structure that accompanies disease can lead to important functional changes . The ventricular myocardium is composed of continuously branching sheetlets of myocytes separated by sheetlet-interstices containing variable amounts of collagen. Importantly to the understanding of myocardial structure and function, it has been demonstrated in a series of studies that three principal orthogonal structural directions are present. These directions are: (i) along the local myocyte axis (m); (ii) perpendicular to the local myocyte axis in the sheetlet plane (s); and (iii) normal to the sheetlet plane (n) - a structural arrangement known as orthotropy [2-7]. It has been shown that myocardial mechanical properties and electrophysiological conductance are different along each axis [2,5,8-10]. The structure of the myocardium at a cellular level has been described in detail elsewhere [6,11]. Briefly, the myocardium consists of stacked branching myolaminae which are generally 4–6 cells (~80 -120 μm) thick [8,12]. The long-axes of the myocytes from which the myolaminae are composed have a regular organization being largely parallel to the epicardial surface and having the classically-described smooth ~120° transmural change in helix angle relative to the circumferential direction [8,13], often described as a helical arrangement. In the rat, myolaminar structure is present throughout the myocardium except in the sub-epicardium [6,11]. Within the myocardium there are regions of abrupt change in laminar orientation, such that the myolaminae have been described as belonging to two populations (reviewed previously ).
Measuring the orientations of these architectural features is important as they have roles in both electrophysiological and biomechanical function in health and disease. Changes in local myocyte orientation and myolaminar sliding (the shearing of adjacent myolaminae over each other) are thought to be the principal mechanisms of ventricular wall thickening in systole [8,9]. During contraction, force is generated along the local myocyte axis, and local myocyte orientation has long been known to influence the spread of myocardial activation , which has recently been shown to be substantially influenced by laminar organization also [2,5]. Knowledge of local myocyte and laminar architecture is therefore important in the understanding of normal cardiac function, in the interpretation of electrical and mechanical studies of cardiac disease in animal models, and, in the long term, may be relevant to the interpretation of clinical cardiac electrophysiology and mechanical recording/imaging. In addition, whole-heart computational modeling of both mechanics and electrophysiology requires detailed structural atlases and Diffusion Tensor Magnetic Resonance Imaging (DTI) is the principal method for generating these geometries [15-17].
Histological validation studies have shown that DTI can be used to measure cardiac local myocyte orientation . Histological validation is experimentally challenging for two reasons: (i) the orthotropic structure of the heart often confuses interpretation of 2-dimensional structural images, and, (ii) the orientation of cardiomyocytes within a local region is an abstract concept where there are no myocardial fibers in the true sense, only myocytes, with multiple branching, and a maximum length of ~120 μm (discussed in ). Indeed this difficulty was recognized by authors of early validation studies . Later, it was proposed that DTI could be used as a 3-dimensional method to measure myocardial laminar orientations [20,21], and fully quantify ventricular myocardial orthotropy. This was an important claim as, if correct, DTI could deliver, from a single imaging experiment, a description of cardiac orthotropy which can be directly used for the computational modeling of cardiac electrophysiology and mechanics. Early validation of DTI laminar structure measurement used non-conventional approaches for the study of tissue architecture (the paper ink blotting of dead tissue) . However, soon after DTI orthotropy measurement was proposed questions and challenges were raised in the literature (from detailed physical studies) about the appropriateness of DTI for measuring laminar orientation (and to a lesser extent local myocyte orientation) [22,23].
A new method for directly imaging myocardial laminar architecture is high-resolution 3D FLASH CMR (previously referred to as high resolution CMR ), which was introduced by  (using T2* contrast). Here the term high-resolution was used with respect to the whole heart geometry and with respect to clinical cardiovascular magnetic resonance (CMR), not with respect to the myocyte/sheetlet dimensions. We recently developed this method further (using Gd-DTPA T1 contrast) and validated it as a means to measure whole ventricular 3D myolaminar architecture . We showed that myolaminar architecture could be imaged and measured using FLASH and that the orientations, obtained using a well-known mathematical operator, the structure tensor (ST), corresponded to histologically measured orientations . This method analyses a tensorial quantity constructed from the structure of the image, very much like the DTI tensor [25-28]. From the mathematics of the ST method, its primary eigenvector is in the direction of maximum image contrast change, and the tertiary eigenvector in the direction of minimum image contrast change. Throughout this manuscript we implement a notation of v 1 ST , v 2 ST and v 3 ST for the ST eigenvectors to simplify the comparison between ST and DTI measurements. In this notation v 1 ST relates to the tertiary ST eigenvector, v 2 ST relates to the intermediate ST eigenvector and v 3 ST relates to the primary ST eigenvector. As the myocardium has an orthotropic structure we hypothesize that the primary eigenvector is the sheetlet normal direction; the secondary eigenvector the sheetlet in-plane direction and the tertiary eigenvector the local myocyte direction.
The aim of this study is to compare the structural measurements from the DTI and ST/FLASH, to demonstrate how both these measures relate to the laminar structure as directly imaged (the laminar structure as revealed by FLASH) and to consider the potential strengths, limitations and applications of these approaches. Our hypothesis is that the myolaminar orientations provided by the FLASH 3D ST would be more accurate and reliable than those measured by DTI, as the primary ST eigenvector (the largest) is calculated from the sheetlet normal direction, and the approach is not subject to the limitations of the DTI model concerning multiple diffusion compartments.
In our analysis we refer to the true orientations of the myocyte, sheetlet-plane and sheetlet normal directions as m, s, and n respectively. When referring to image measured structural orientations and derived structural angles we use the notation for the DTI eigenvectors (e 1 DTI , e 2 DTI , e 3 DTI ) and for the ST derived orthogonal vectors (v 1 ST , v 2 ST , v 3 ST ) until we establish association between the eigenvector and the structural feature. When we refer to the structural feature directly we use the term putative to indicate that this association is not yet confirmed.
Heart preparation and perfusion fixation
Male Wistar rats (N = 8) weighing 220.1 ± 11.2 g were euthanized in accordance with the UK Home Office Animals (Scientific Procedures) Act 1986 with the approval of the UK Home Office and the Local Ethics Committee. Hearts were rapidly dissected, the aorta cannulated and the hearts perfused in Langendorff mode with CMR contrast agent (Gd-DTPA) and fixative for 20 min. Details are given in the Methods Supplement (Additional file 1) and are as described in . The hearts were then removed from the perfusion apparatus and stored 2 hours at 20°C in the contrast/fixative solution before imaging.
Summary of the imaging sequence applied for sensitivity analysis
Start time a
b-value (s /mm 2 )
Scan duration b
DTI Acquisition and Reconstruction
Summary of the notation used for vectors and angles
e 1 DTI , e 2 DTI and e 3 DTI
DTI eigenvector corresponding to the most, intermediate and least extended directions of diffusion
v 1 ST , v 2 ST, v 3 ST
the vector of the most, intermediate and least extended orthogonal directions of FLASH signal, determined by structure-tensor analysis.
eigenvalue (λ) with the subscript indicating the eigenvalue number.
α'v 1 ST and α'e 1 DTI
vector helix angle, used for quantification of the putative myocyte orientation. The vector quantified is identified after α’. The angle is defined in Figure 2.
α''v 1 ST and α''e 1 DTI
vector transverse angle, used for quantification of the putative myocyte orientation.
β'v 3 ST and β'e 3 DTI
vector elevation angle, used for quantification of the putative sheetlet/sheetlet-normal orientation.
β”v 3 ST and β''e 3 DTI
vector transverse angle, used for quantification of the putative sheetlet/sheetlet-normal orientation.
the true myocyte orientation vector.
the true sheetlet (in-plane) vector.
the true sheetlet normal vector. The superscript FI is used in the case of n measured by FLASH/FI.
Structure tensor analysis of high resolution MR images
The following steps were applied to the FLASH images: segmentation, conversion to a stack, boundary smoothing, intensity gradient computation, structure tensor calculation for each voxel, and extraction of principal directions of the structure tensor at each discrete point using eigenanalysis. In detail, the FLASH images were coarsely segmented to remove the ventricular cavity signal using thresholding and semi-automated segmentation in Seg3D (Scientific Computing and Imaging Institute, University of Utah). These FLASH images were then converted to a stack (256 × 256 × 512) of 16-bit images. To avoid undue influence on structural orientation calculations, boundaries at the interface between tissue and non-tissue regions in the CMR images were smoothed as described in . Myostructural orientations were computed from the images by computing intensity gradients with a 3 × 3 × 3 or 5 × 5 × 5 point derivative template  (the derivative template width, DTW). The template was applied to the full 3D image using FFT-based convolution. The structure tensor (the outer product of the intensity gradient vectors) was then computed for each voxel in the 3D image. Structure tensor components at progressive resolution doubling (i.e. 100 μm, 200 μm, 400 μm, etc.) were determined using level 2 or level 4 binomial low-pass filters  to smooth from one level of resolution to the next. The smoothing template width (STW) for these two configurations was 3 and 5 points, respectively. The 200 μm smoothed structure tensor data set (64 × 64 × 128 tensors) was used in order to best match the DTI resolution. The principal directions of the structure tensor at each discrete point were extracted using eigenanalysis. The eigenvector corresponding to the largest magnitude eigenvalue is the least extended orthogonal direction of signal continuity and is therefore the putative sheetlet/laminae normal direction, and for ease of comparison with DTI this vector is denoted by v 3 ST . The eigenvector corresponding to the smallest magnitude structure tensor eigenvalue is the most extended orthogonal direction of signal continuity and is therefore the putative local myocyte-orientation, and for ease of comparison with DTI this vector is denoted by v 1 ST . The eigenvector corresponding to the intermediate magnitude eigenvalue is the intermediate extended orthogonal direction of signal continuity and is therefore the putative sheetlet/laminae in-plane direction, and for ease of comparison with DTI this vector is denoted by v 2 ST . Vectors computed at points lying in non-tissue regions of the image were discarded on the basis of an automated fine-detail 8-bit tissue mask created slice-wise from the segmented images by thresholding intensity values (≤20% intensity) and performing the following sequence of morphological operations: (i) clean (removing isolated foreground pixels); (ii) bridge (connecting pixels separated by one background pixel); (iii) fill (filling isolated background pixels); (iv) open (binary opening); and (v) thicken (adding pixels around the exterior of an object without connecting previously unconnected pixels).
Assignment of the cardiac reference frame
Comparison of structure tensor and diffusion tensor orientations
The ST data was smoothed to the resolution of the DTI data (from 50 μm 256 × 256 × 512 tensors to 200 μm 64 × 64 × 128 tensors). Systematic comparison of the ST and DTI is facilitated as images are in the same CMR frame/position (the hearts were not moved in the scanner between FLASH/ST and DTI). Comparison between different hearts is achieved through the automated approach for finding the left ventricle long-axis and ROI. For each ROI the angles between the eigenvectors and the helix and transverse angles were quantitatively compared.
Comparison of structure tensor and diffusion tensor sheetlet orientations to the FLASH isosurface
Cardiac ex vivo contractile state
Summary statistics quantifying ex vivo left ventricle wall thickness and left ventricle chamber diameter with comparison to predicted in vivo values from body mass
Ventricular wall thickness/chamber-diameter measured
Measured thickness in ex vivo FLASH
Predicted in vivo diastolic thickness
Predicted diastolic thickness as percentage of measured
Predicted in vivo systolic thickness
Predicted systolic thickness as percentage of measured
3.0 ± 0.1
1.0 ± 0.0
1.7 ± 0.0
Left ventricular posterior wall
3.5 ± 0.3
1.3 ± 0.0
1.8 ± 0.1
Left ventricular diameter
3.7 ± 0.3
6.2 ± 0.1
3.5 ± 0.0
Laminar structure revealed in FLASH
Quantification myolaminar orientation in ST and DTI
In order to compare whole-heart myolaminar structure measured by ST/FLASH and by DTI the sheetlet-normal angles were visualized on the cardiac volume after long-axis and short–axis cropping of the full image, alongside the FLASH structure (Figure 6A-C; the corresponding sheetlet in-plane angles are visualized in Additional file 3: Figure DS1). To allow direct comparison eigenanalysis was applied to the ST data at the same resolution as the DTI data (64 × 64 × 128 tensors). Additional file 2: Movie 1 and Additional file 4: Movie 2 show animated longitudinal slices of the corresponding FLASH structure and derived angles from a second rat heart. Colored images of sheetlet orientation are widely used in the cardiac structure literature [8,20,32,34,38], and show quantitative information but are challenging to interpret. The images provide limited information about 3D structural complexity and provide no information about the connectivity of spatial scales of laminae. Therefore laminar structure has been directly visualized in a septal transmural ROI, and this is shown together with the ST/FLASH v 3 ST and DTI e 3 DTI , both putative measures of n, in Figure 5.
Comparison of ST and DTI laminar orientation to FI
Summary statistics of voxel-wise comparison of ST/DTI sheetlet normal to FI
b-value (s/mm 2 )
|∠[v 3 ST or e 3 DTI ]n FI | median ± I.Q.R. (°)
First ST and DTI parameter sets
8.7 ± 7.8
22.5 ± 13.8
Second ST and DTI parameter sets
9.1 ± 7.4
24.1 ± 11.9
First ST and DTI parameter sets
7.4 ± 8.7
54.4 ± 47.3
Second ST and DTI parameter sets
8.5 ± 9.7
60.5 ± 53.4
Quantification of the confidence in the sorting of laminar eigenvectors
Direct comparison of ST and DTI laminar orientation
Direct comparison of ST and DTI local myocyte orientation
The comparative deviation angles of distributions of v 1 ST : e 1 DTI ; α’v 1 ST : α’e 1 DTI and α”v 1 ST : α”e 1 DTI are explored in quadrant rose diagrams in Figure 10B (for the septal ROI) and in Additional file 7: Figure DS3B (for the lateral ROI). The distributions for |∠v 1 ST e 1 DTI | are unimodal and narrow in the septal ROI (median ± MAD: 13.3° ± 6.7°) and in the lateral ROI (median ± MAD: 12.6° ± 5.9°). The distributions of |∠α’v 1 ST :α’e 1 DTI | have the same form, being unimodal and narrow in the septal ROI (median ± MAD: 8.5° ± 5.6°) and in the lateral ROI (median ± MAD: 9.1° ± 5.8°). Likewise, the distributions of |∠α”v 1 ST :α”e 1 DTI | also have the same form, being unimodal and narrow in the septal ROI (median ± MAD: 11.5° ± 7.8°) and in the lateral ROI (median ± MAD: 15.6° ± 11.1°). In the septal ROI the distributions of |∠v 1 ST e 1 DTI | (the local myocyte orientation angles) are therefore in contrast to the distributions of |∠v 2 ST e 2 DTI | and |∠v 3 ST e 3 DTI | (and the associated sheetlet and sheetlet normal angles), the latter having greater bias and variation. This pattern is also seen in the lateral ROI in Additional file 7: Figure DS3 and in the anterior and posterior ROI (Additional file 8: Figure DS4), but to a lesser degree.
DTI and ST sensitivity analysis
A series of imaging experiments carried out to explore sensitivity of ST and DTI to imaging parameters are presented in the Digital Supplement (section DTI and ST sensitivity analysis) and in Additional file 10: Figure DS6. We showed that the overall DTI sensitivity to time post fixation is low; to b-value is moderate (with b-value scaled by change in diffusion gradient amplitude with fixed diffusion gradient separation time of Δ = 11.5 ms); and to number of diffusion directions is low. Optimal DTI imaging parameters were b = 1000 mm/s2 and 12 diffusion directions with post-fixation time (up to 72 hours) not being an important factor. ST was not sensitive to image processing parameters in the range explored.
This study compares DTI myolaminar measurement against direct measurement of myolaminar orientation from FLASH of the fixed rat heart. The Digital Supplement (Additional file 1) has further discussion in the sections Discussion of the Results of Other Validation Studies and Eigenvalue Comparison.
The benefits of validating against FLASH
This approach of measuring DTI myolaminar orientation performance and sensitivity referenced to direct measurement in FLASH (the FI method) has several advantages over previously adopted methods. This is discussed in more detail in the Digital Supplement (section Discussion of the results of other validation studies). Our approach has the benefit that: (i) direct comparison of DTI to FI method assumes no cardiac model of local myocyte orientation or of the relationship between local myocyte orientation and myolaminar orientation; and, (ii) no registration is required as FLASH imaging and DTI imaging are carried out sequentially without moving the heart, and using coincident CMR imaging matrices. Unlike all previous methods of validating DTI myolaminar measurements the method we use does not rely on first estimating n through prior knowledge about m. We directly measure the 3D orientation of the laminar normal from images (n FI ) and compare this directly to the putative measure of sheetlet normal orientation e 3 DTI . The rationale for this approach is firstly that it is simple and secondly that it follows directly from the initial description of sheetlets (i.e. from examining images). This simple approach was possible as the 3D myolaminar structure is directly visible and well-defined in the contrast-enhanced FLASH  which is in the same imaging frame as the DTI. Cardiac laminar structure was first described from histological observations, and from using 3D reconstructive methods to show that there was local branching sheetlet structure, which extended in three-dimensions and was divided by sheetlet-interstices, which likewise extended in 3D as a branching network. In this study the sheetlets are defined as the clearly visible local stacked branching structures of low signal intensity in FLASH and correspondingly the sheetlet-interstices are defined as the intermeshed local stacked branching structures of high FLASH signal intensity.
Previous validation studies have either used a 2D histological method followed by DTI  or DTI followed by a 2D histological method . There are two important limitations in the use of 2D imaging for measuring myolaminar orientation. Due to the limited 2D view of the tissue, and due to sectioning artefact resulting in some cellular separation, it is possible to misinterpret the grain of the local myocyte direction as sheetlet interstices, and hence to measure spurious myolaminae/sheetlet-interstices orientations which have no correspondence to true myolaminae in the native heart (discussed in , ). Secondly, the orientation of myolaminae/sheetlet interstices cannot be directly measured in 2D images, only the intersection angle of the myolaminae/sheetlet-interstices with the section, as discussed in the section (Results of other validation studies) in the Digital Supplement. This seems counterintuitive, as the sheetlet-interstice grain on a 2D section results from the sheetlet-plane. However it is 2D cut through a 3D plane, and by definition it cannot directly give the orientation of the myolaminar plane. The measurement is a line of intersection of the cut section plane, and as such is a non-standard sheetlet angle. A standard sheetlet angle can be obtained by careful alignment of the section plane to a standard cardiac plane, and this allows either β’e 2 DTI or β”e 2 DTI to be measured but not both. A single image of the cut surface of the myocardium gives very limited information on the orientation of the myolaminae below.
Indirect strategies have been developed in order to measure laminar orientation from 2D sections in spite of these two important limitations. The first strategy is to use prior knowledge of local myocyte orientation, for example literature based descriptions or mathematical “rule-based“ models of the local cardiac local myocyte orientation  (rule-based models are myocyte helix and transverse angles determined by simple mathematical functions using the cardiac location as a parameter). The second strategy is to use prior knowledge of cardiac local myocyte/laminar association (the orthotropic model of cardiac structure) in order to reconstruct the sheetlet normal orientation. Both of these strategies are based upon good models of cardiac structure, but these are macroscopic models and are hence approximations of local structure, and their accuracy will vary depending on cardiac location. As such they are not a good method against which to assess DTI.
As FLASH/FI resolves sheetlets and sheetlet-interstices in 3D throughout the myocardium it is an objective basis for comparison of both e 3 DTI and v 3 ST . This comparison shows that DTI performs poorly in measuring laminar orientation when compared to FI in fixed myocardium across the range of DTI imaging parameters investigated. Subsequently we compared DTI and ST determined sheetlet and myocyte orientation with each other directly.
The Limitations of the DTI model
Physical studies have shown theoretical and experimental evidence that the DTI model has shortcomings which may limit its application in the measurement of cardiac orthotropy [22,23,41]. A monoexponential diffusion model is used to analyze the raw signals leading to DTI. This model envisages a single diffusion compartment in each image voxel. Importantly, it has been demonstrated in the ventricular myocardium of ex vivo perfused hearts that there may be more than one diffusion component per voxel (i.e. multiexponential diffusion, with more than one spin compartment) [22,23]. These diffusion components have been classified as a slow component (attributed to compartmentalization of intra- and extracellular (IC/EC) water pools) and a fast component (attributed to diffusion in the vascular space compartment combined with some IC diffusion) . In imaging studies with short diffusion distances (low b-values, i.e. b-value < 1000s/mm2, where the b-value is defined below) the fast-component (vascular/IC) predominates, but this component still influences measurements at higher b-values. Blood vessels generally run parallel to local myocyte directions , and it has been suggested that the summation effect of slow and fast diffusion directions in the standard monoexponential DTI model is not an important practical consideration in the measurement of the local myocyte orientation. Indeed it has been shown that the local myocyte orientations calculated from the fast and slow components of diffusion are similar . However, a consequence of two-component diffusion is that the proposed orthotropic diffusion may be complicated by non-orthotropic fast diffusion which could result in inaccurate measures of laminar orientation. Limitations of the diffusion model have not been addressed to date in direct validation studies of DTI myolaminar orientation measurement [21,40].
b-value, diffusion gradient separation and DTI Imaging protocol used in this study
Sheetlet structure resolved within a voxel by the three methods
DTI and FLASH/ST both represent myocardial structure as a tensor and therefore both methods have inherent limitations in measuring myolaminar architecture in voxels which have 2 or more laminar orientations. The overall myolaminar orientation is simplified to a single laminar normal orientation vector. If a voxel contains two markedly different myolaminar orientations (e.g. sheetlets at 90° to each other, such as sheetlet-normal β” ~ −45° and β” ~ +45°) this will be quantified as a sheetlet-normal vector in a non-physical intermediate orientation (0° for this example case). This limitation is not inherent in the FI method, as a distribution of orientations is obtained for each 200 μm isotropic voxel, however in practice it is necessary to simplify this measure to a single (or small number) of local myolaminar orientations. This limitation of DTI and ST could be addressed by increasing resolution. There are literature reports on DTI in cardiac tissue with up to 100 μm isotropic resolution , but as voxel size is reduced imaging time is increased and SNR falls. The FLASH/ST and FI resolution can be increased by increasing the resolution of the FLASH to ~25 μm near-isotropic  or 25 μm (as used in ). Although some voxels have multiple sheetlet orientations (as shown in Figure 3), this is the minority and it can been seen by comparison with higher-resolution FLASH  that increasing FLASH voxel size does not resolve markedly greater complexity of laminar structure. In  we imaged the rat myocardium at higher FLASH resolution (25 × 25 × 34 μm) resolution and using 40 × histological magnification and the resultant images qualitatively show that increasing FLASH spatial resolution from 50 μm to 25 × 25 × 34 μm yields marginally greater myolaminar branching, and that further increasing resolution to 40 × histological magnification reveals minimal further branching.
The nature of myolaminar structure
There has been ongoing controversy around the presence and nature of cardiac laminar architectural features . Most surprisingly the debate around the presence or absence of laminar structure continues despite strong evidence from numerous imaging modalities. The mounting evidence includes conventional microscopic histology [11,40]; extended volume confocal microscopy [3,6,53]; confocal microscopy after myocardial optical clearing ; scanning electron microscopy , CMR , microCT , phase-contrast synchrotron x-ray imaging , direct myocardial video imaging and photography [11,12] and the orthotropic mechanical material properties of isolated myocardium [2,5,10]. The imaging and analysis in this study provides further evidence of the nature of laminar structure in the fixed heart. Further to  we show that laminar structure is near-universally present throughout the myocardium and that it exists as a highly-branching meshed structure of varying compactness, and is absent in some regions of the compact sub-epicardium. Laminar myocardial architecture was described by LeGrice et al. (1995)  as a branching structure, and in some of the subsequent literature this has been misinterpreted as single unique sheets of structure that have isolated spans across the myocardial wall . This structural form was not proposed in LeGrice et al. (1995)  and indeed if the heart was structured in this way it would be prone to the mechanical separation of these laminae, and could be easily interactively dissected apart along these laminae, neither of which occurs. The 3D images in Figures 3, 4, 5 and 6 and Additional file 2: Movie 1 clearly show that myolaminar structure branches. As such there is no entity which is a single individual myolamina: the structure is orthotropic with preferential directions of sheetlet interstices and matching preferential directions of collagen orientation , but individual myocytes branch across the myolaminae in three-dimensions.
Cardiac ex vivo contractile state
It is inevitable that fixation of hearts before imaging will result in some conformational change, such that the fixed structural state of the heart will not truly match an in vivo contractile state . The fixed hearts are neither in a true physiological systolic or diastolic state.
The application of the FI method
Using the FI method we showed that the quality of the FLASH is adequate to clearly define the sheetlet normal orientation through visualization, and we demonstrated that the ST method was appropriately applied. The raw FLASH images (as shown in Figure 6A and Additional file 2: Movie 1) provide a means of direct visualization and measurement of laminar architecture which can be isosurfaced to measure laminar orientations (Figure 3). A drawback of the FI method is that it is low-throughput and requires interactive segmentation, interactive visualization and interactive optimization of thresholds whereas DTI and ST/FLASH are both high-throughput automated methods. However the strength of the FI method is that each laminar normal orientation measurement had an accompanying 3D visualization of structure which was used to confirm that the method was functioning correctly and that orientation measurements reflected the underlying structure (as shown in Figure 3). The method can be used to measure laminar orientation, but cannot be used to measure local myocyte orientation, as the myocyte long axis is not resolved by the 50 × 50 × 50 μm3 spatial resolution of the FLASH. The reliability of DTI sheetlet orientation measurement (for the range of DTI imaging parameters explored in fixed myocardium, with fixed diffusion gradient separation time of Δ = 11.5 ms) compared to directly measured sheetlets varied depending on cardiac location: in the lateral ventricular wall the deviation angle (|∠e 3 DTI n FI |) was 23 ± 14° (median ± IQR) and in the septal wall deviation angle was 61 ± 53.4°. ST/FLASH is more reliable as in the lateral wall deviation angle was 9 ± 7° and in the septal wall 7 ± 9°. Furthermore, we show erroneous assignment of e 3 DTI and e 2 DTI , in other words where the orientation assigned by DTI to the laminae sheetlet in-plane direction is actually much closer to the true laminar normal orientation. This was explored through assessment of the relative laminar eigenvalue magnitudes (ratios of laminar eigenvalues). DTI showed considerably less accuracy than ST when compared to the FI sheetlet normal orientation in both the lateral and septal ROI. In the septal ROI there was strong evidence of eigenvector missorting as the median difference between the DTI and FI laminar normals was 54.4 ± 47.3° and the deviation angle distribution was bimodal with the larger mode centered on 65° and including 65.1% of the lateral ROI voxels (Figure 7B). An absolute deviation angle of greater than 45° suggests eigenvector misassignment as angles >45° indicate that e 2 DTI is closer to n FI than e 3 DTI (assuming that e 1 DTI is close to the correct local myocyte orientation). The consequences of eigenvector misassignment are substantially deleterious to the accuracy of any imaging method that measures a tensor to encode structure, as the orthogonal system is rotated so as to produce a measure of the laminar-normal as different as possible to the correct values.
We showed that under the imaging parameter ranges explored in fixed myocardium there are greater grounds for sorting between the ST laminar eigenvectors than the DTI laminar eigenvectors. This was anticipated as: (i) ST is, from first principles, a method highly appropriate to quantifying laminar architecture in images where that structure is clearly visible on simple inspection; (ii) underlying myocardial diffusion has previously been shown to be complex, and the DTI model has limitations for describing this diffusion. We do not show that eigenvalue differences are insufficient to allow laminar measurement, but we show that there is little difference between the magnitudes of sheetlet eigenvalues and sheetlet-normal eigenvalues, and that e 3 DTI is not close to n FI . The small difference between sheetlet eigenvalues and sheetlet-normal eigenvalues is a further indicator that DTI is a suboptimal measure of laminar orientation in fixed myocardium. This is further discussed in the Digital Supplement (section Eigenvalue Comparison).
Direct comparison of DTI and ST measured myolaminar structure
The ST sheetlet angle and sheetlet normal angle maps largely recapitulate features described in the literature ([20,32,38,40,58,59] and discussed elsewhere ), and orientations can be seen to correspond to the FLASH image in Figure 6 and Additional file 4: Movie 2. We showed qualitatively and quantitatively that the degree of agreement between e 3 DTI and v 3 ST differed from region to region, and overall there was poor agreement. Likewise we showed qualitatively and quantitatively that the degree of agreement between e 2 DTI and v 2 ST differed from region to region, and overall there was poor agreement (worse than for the equivalent normal orientations). In this way we showed that the fixed-myocardium DTI secondary and tertiary eigenvector orientations are influenced by the underlying laminar architecture, but the assignment of these vectors to either orientation is not robust, and varies depending on cardiac location.
Comparison between ST and FI
There is good agreement between the ST quantified laminar normal orientation and the FI quantified normal orientation (mean ± SD deviation 12.8° ± 13.2 for the combined equatorial ROI for STW = 3, DTW = 3). The mechanisms responsible for the systematic deviation between ST and the FI method based on FLASH have not been determined but it is likely associated with differences in the methodology used in the FI method to ST. ST is a tensor method so is influenced by the optimal orthotropic description of local contrast change (optimal fit of an orthogonal set of vectors with v 3 ST in the direction normal to contrast change), v 2 ST in the plane of local consistent contrast, and v 1 ST in the direction of minimum contrast change. The FI method is only influenced by the local normal. It was noted that there was some eigenvalue misassignment in ST compared to FI. The probable reason for this is that unlike FI and DTI, in which just a single 200 × 200 × 200 μm3 voxel influences the local measured myolaminar normal orientation, in ST neighboring voxels also influence the tensor calculation (as discussed in detail in the Sensitivity Analysis section below). For at DTW = 3 each structure tensor component in the 200 × 200 × 200 μm3 representation has worked with intensities gathered from an effective 9 × 9 × 9 template at the original 50 μm resolution, i.e. around 450 × 450 × 450 μm3. However, the principal data weighting is at the center of that template. This will have minimal consequences when myolaminar structure is spatially conserved, but in regions of high-spatial change in laminar orientation then the neighbor influence will result in a different measure of laminar structure from ST/FLASH and from FI/FLASH.
Comparison between DTI and ST local myocyte orientation
We showed that the ST myocyte α’ angle displays the familiar transmural rotation, observed circumferentially in the short-axis slice, and in the long-axis cuts. This myocyte helix angle has long been known from gross dissection, histology, and DTI  [8,60]. The myocyte transverse angle (α”) is generally described as closely following the left ventricle-short axis tangent orientation (i.e. this angle is ~0°). In Figure 6C α” deviates from this description as it has negative values, approaching −45° in the lateral sub-endocardium. These DTI images are not novel as many previous studies have measured and visualized the e 1 DTI in this manner. However, the accompanying v 1 ST images are novel and are striking in the degree of similarity between α’ and α” of v 1 ST and of e 1 DTI . This has not previously been demonstrated. Despite disagreement between e 3 DTI and v 3 ST and e 2 DTI and v 2 ST , there is remarkably good agreement between e 1 DTI and v 1 ST . Our finding that DTI measures m well, but s and n poorly in fixed myocardium is consistent with the findings and conclusions of others [22,23], who found DTI reliable for measuring local myocyte orientation, but provided evidence that it was less reliable for measuring myolaminar orientation. The finding that ST measures m can seem counterintuitive as myocytes are not resolved by FLASH at 50 × 50 × 50 μm3 resolution as they have the approximate dimensions of 10 × 10 × 100 μm3 . Indeed it is not possible to image whole rat hearts with conventional CMR imaging systems at sufficient resolution to be able to resolve individual myocytes. A resolution in the order of 3.5 × 3.5 × 3.5 μm3 would be required with good contrast and SNR, which is possible in small tissue blocks using phase-contrast synchrotron x-ray imaging  and is also obtainable in small volume MRI microscopy imaging  but not at the scale of the rat heart. Also, the small blood vessels cannot be discerned in the 50 μm isotropic resolution FLASH voxels (Figures 3, 4, 5, 6 and Additional file 2: Movie 1 and ). ST of the 50 × 50 × 50 μm3 FLASH data therefore depends on the tissue laminarity and orthotropy to measure the local myocyte orientation, and not myocyte orientation or blood vessel orientation. Given that ST is sensitive for measuring the image contrast changes associated with laminar orientation , then, if cardiac structure is genuinely close to orthotropic, it follows that v 1 ST will be an accurate measure of local myocyte orientation. We show that v 1 ST is a good approximation to the classically reported local myocyte orientation , and this provides further support for the orthotropic model of ventricular structure. We show that global myocyte orientation measured by DTI is well matched with the global myocyte orientation measured by ST. This is evidence which supports the use of DTI in measuring the local myocyte orientation.
It was observed that for both DTI and ST α” did not have a simple circumferential pattern, but rather had high negative values in the anterio-lateral myocardium (blue in Figure 6C and Figure 13). This pattern closely follows that reported for normal rat heart DTI in the literature . It is likely largely a result of the cylindrical coordinate system used, which is based on a centroid optimized on the whole heart, rather than an individual slice and is a known source of error in α” , but it may to some degree be due to true variation of α”.
Here the term high-resolution is applied to FLASH CMR in the context of the whole heart geometry and with respect to clinical CMR, not with respect to the myocyte/sheetlet dimensions. The current study investigates conventional DTI on 200 μm isotropic voxels and b-values of 1000 s/mm2, with 6 or 12 gradient directions. Other Diffusion imaging models and approaches (such as High Angular Resolution Diffusion Imaging (HARDI) ) may perform better than DTI, and have the potential to provide greater sub-voxel information on sheetlet orientation. As DTI and FLASH both take several hours to perform imaging experiments are separated in time. However, the similarity between DTI and ST/FLASH determined local myocyte-orientations indicate that changes in structure between imaging experiments has been minimal. Both DTI and ST/FLASH produce a tensor which describes orthogonal cardiac structure. It is therefore implicit that in using these measures we take a starting assumption that myocardial structure is approximately orthotropic, and this has been demonstrated to be the case in the bulk of the ventricular myocardium . The cylindrical coordinate system has greatest accuracy near the left ventricle equator, and has reduced accuracy approaching the left ventricle apex and base. The FI method as implemented in this study depends upon a manually optimized local tissue threshold.
This study explores DTI and FLASH in fixed myocardium perfused with gadolinium (Gadopentetate Dimeglumine). Many DTI studies have explored structure in fixed ex vivo cardiac tissue [20,32,38,40,58,60,64,65] and the findings in this study are relevant to the interpretation of past and future imaging of fixed myocardium. It is known that fixation results in structural changes including shrinkage and the opening up of sheetlet-interstices . It is not known if sheetlet-interstices open equally on fixation and therefore the performance of FLASH, ST/CMR and DTI may differ when applied to in vivo or when applied to ex vivo physiologically perfused tissue, and the absolute values of sheetlet orientations may not reflect in vivo values. The high spatial resolution FLASH imaging requires ~18 hrs to image a rat heart and therefore requires cardiac fixation. As discussed in the section ‘b-value, diffusion gradient separation and DTI Imaging protocol used in this study’ above, fixation shortens myocardial T2 and therefore imposes short DTI TE and diffusion gradient pulse separation (Δ) compared to parameter ranges possible in unfixed myocardium. A consequence is that more accurate measurement of sheetlet orientation may be possible in unfixed myocardium than can be achieved in fixed myocardium. Therefore our conclusions on the accuracy of DTI sheetlet orientation measurement cannot be extrapolated to DTI in unfixed or in vivo myocardium.
DTI and ST both produce tensors whose eigenvectors correspond to a greater-or-lesser degree with the cardiac orthotropic structural axes. DTI and ST predict globally similar myocyte orientations, and this evidence supports using DTI to measure local myocyte orientation. DTI produces smoother local myocyte orientation maps and is faster for imaging local myocyte orientation but with appropriate regularization, ST is likely to be useful for this purpose also. In fixed myocardium ST is a better measure of myolaminar orientation than DTI over the parameter ranges explored. The reliability of DTI sheetlet orientation measurement compared to directly measured sheetlets was low or markedly low depending on cardiac location and we showed that poor DTI performance over this parameter range could be a consequence of poor laminar eigenvector assignment. Sensitivity analysis showed that overall DTI sensitivity to time post fixation is low, to b-value is moderate (with fixed diffusion gradient separation time of Δ = 11.5 ms), and to number of diffusion directions is low. Optimal DTI imaging parameters were b = 1000 mm/s2 and 12 diffusion-directions with time post fixation up to 72 hours not being an important factor. ST was not sensitive to image processing parameters. FLASH and ST requires more time (~1 day) compared to DTI (~3 hours). However, FLASH directly resolves myolaminae and FLASH/ST more accurately quantifies the orientation of these structures. We conclude that the FLASH/ST framework is reliable, robust and the preferred option for myolaminar measurement in fixed myocardium. DTI has an important role for local myocyte orientation measurement, and a method could be developed for combining the optimal characteristics of ST and of DTI. The methods developed and assessed in this study will be useful in future development and refinement of diffusion CMR of cardiac structure, both in vivo and ex vivo. Future studies are required to quantify the accuracy of structural orientation measurement by DTI in unfixed myocardium (either in vivo or with ex vivo perfused hearts) against direct 3D imaging measurements.
The authors acknowledge David Benoist at L'Institut de rythmologie et modélisation cardiaque (LIRYC), Bordeaux, France for help with the contrast perfusion fixation method.
Supported in part by grants from the Medical Research Council (G0701785, S.H. Gilbert), the EU FP7 Marie Curie Program PIEF-GA-2010-275261 (S.H. Gilbert), the European Society of Cardiology - European Association of Cardiovascular Imaging Research Grant (2014, S. H. Gilbert) and IRSES-GA-2013-317767. This work was also supported by a grant from the Agence Nationale de la Recherche through the program ”Investissements d’Avenir” (ANR-10-IAHU04-LIRYC).
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