Determining the relationship between microscopic anatomy and macroscopic deformation in muscular organs remains one of the signature problems in biomechanics. While it is straightforward to relate structure to function where myofibers are aligned parallel to each other, it is difficult to predict how tissues should deform when their constituting fibers exhibit microscopic crossing or convergence. Such anatomical complexity is, in fact, common in tissues such as the tongue (Sonntag, 1925; Abd-El-Malkek, 1939; Miyawaki, 1974: Barnwell, 1976; Gilbert et al., 1998: Nishikawa et al., 1999; Wedeen et al., 2001), blood vessels (Ostadal et al., 1975), and the heart (Reese et al., 1995; Sanchez-Quintana et al., 1995; Hsu et al., 1998). In each instance, myoarchitectural complexity at the microscopic scale confounds simple predictions of mechanical behavior at the macroscopic scale. The tongue is a particularly intriguing model for study of structure-function relationships since its myoarchitecture contains continuous arrays of crossing fibers, reflecting the structural integration of the extrinsic (possessing external attachment to bony surfaces) and intrinsic (possessing no external attachments) muscle fibers.
The mammalian tongue is a large muscular organ that fills the majority of the oral cavity (Sonntag, 1925). Its phylogenetic origins date back to prehistoric fish, where the tongue first appears as a rudimentary organ (Livingston, 1956), and is a constant feature in vertebrates above this level. In classical terms, the musculature of the tongue is divided into intrinsic muscles, including the superior and inferior longitudinalis, the transversus, and the verticalis muscles, which are wholly contained within the body of the tongue, and the extrinsic muscles, including the genioglossus, the hyoglossus, the styloglossus, and the palatoglossus muscles, which possess bony attachments outside the tongue proper. The tongue rests on a muscular floor composed of the geniohyoid muscle, which runs in the mid-sagittal plane from the mental spine of the mandible to the body of the hyoid bone, and the mylohyoid, which runs from the mylohyoid line of the mandible to the raphe and body of the hyoid bone. While these muscle delineations are readily apparent at the point of extrinsic attachment to bony surfaces, the distinction between the intrinsic and extrinsic musculature breaks down at the point of insertion into the tongue body (Depaul and Abbs, 1996; Mu and Sanders, 1999; Napadow et al., 2001; Takemoto, 2001; Wedeen et al., 2001). In fact, the tongue's myofibers become so extensively interwoven within its body that it may be appropriate to consider the tongue not as a set of anatomically discrete fibers, but as a continuous array of fibers with varying orientations and mechanical properties.
Defining structure-function relationships for the tongue requires knowledge of 3D lingual fiber orientation at both the microscopic and macroscopic scale, and a method capable of translating such anatomical data into the biomechanical realm. Determining 3D myoarchitecture by light microscopy requires meticulous dissection and multislice reconstruction (McLean and Prothero, 1992). The major limitations of this approach stem from the inability of conventional histology to resolve through-plane fiber angle accurately, as well as the difficulty in assembling local orientational data obtained over large spatial scales into a coherent tissue-scale atlas. To address this question, we have examined lingual fiber organization by determining spatially variant water molecule self-diffusivity with diffusion-weighted nuclear magnetic resonance (NMR) imaging (Gilbert et al., 1998; Napadow et al., 2001; Wedeen et al., 2001), a technique that measures molecular diffusion as a function of direction-specific MR signal attenuation. Owing to the fact that maximal diffusion occurs parallel to the axis of most fiber-type cells, diffusion measurements can, in general, be used to derive information regarding 3D fiber orientation in whole tissue.
In the current study, we have employed a variation on the above diffusion-weighted methods, termed diffusion spectrum imaging (DSI), to resolve intravoxel complexity of fiber orientation characteristic for the tongue (Wedeen et al., 2000; Tuch, 2002; Lin et al., 2003; Gilbert et al., 2006). We combined this method with tractography (Basser, 1998), a method defining macroscopic scale geometric associations of fibers on the basis of the similarity of their alignment from one location to another in the tissue. The use of DSI with tractography thus allows us to redefine lingual anatomy in terms of novel macroscopic tract-like structures, which we postulate will provide the structural underpinnings of mechanical function within the body of the tongue.
MATERIALS AND METHODS
Diffusion-Weighted Imaging of Tissue Myoarchitecture
MRI has the capacity to image three-dimensional structures in whole tissue nondestructively, a capability obtained by the application of diffusion-weighted imaging methods (Torrey, 1956; Stejskal, 1965; Stejskal and Tanner, 1965; Cory and Galloway, 1990; Moseley et al., 1990; Callaghan, 1993). Diffusion is a physical property, which represents the random translational motion of water molecules in tissue, and is principally affected by the location of diffusional barriers. In muscular tissue, diffusion is greatest along the direction of individual or populations of fibers due to their elongated and cylindrically symmetric geometry. Signal attenuation receives contributions from both intracellular and extracellular fluid; however, the explicit shape of muscle cells ensures that both components induce maximal attenuation along the long axis of the myofiber. As a result of these considerations, diffusion measurements can be used to derive information regarding three-dimensional fiber orientation in situ (Fig. 1). Stejskal and Tanner (1965) solved for the amount of diffusion attenuation due to an applied diffusion weighting gradient of duration δ:
where is called the q-value, γ is the proton gyromagnetic ratio for a water molecule, M is the signal intensity, Δ is the diffusion time, is the diffusion distance, and P̄ is the average probability distribution function of diffusion (PDF). It is also worthwhile to note an additional term, the b-value, which relates to the maximum overall diffusion weighting for a set of diffusion-weighted image acquisitions (Basser et al., 1994):
By combining the signal attenuation obtained from the application of diffusion weighting gradients in multiple directions with standard MRI image acquisition, the amount of diffusion in those directions may be measured for each voxel in the MR image. The voxels may then be reconstructed to constitute 3D representations of the tissue's underlying myoarchitecture.
Diffusion Spectrum Imaging
DSI is a method for determining the average amount of molecular diffusion occurring within any enclosed space, such as the set of myofibers. The goal of DSI is to reconstruct the PDF for diffusion in each voxel. DSI accomplishes this by acquiring a full sampling of diffusion weighting gradient directions and magnitudes, which permits direct reconstruction of the average PDF (Fig. 2) (Wedeen et al., 2000). In this article, we use the term PDF to refer to the observed average distribution obtained from DSI processing of the signal. The use of DSI for imaging lingual fiber populations has been previously described (Gilbert et al., 2006). In brief, during DSI, diffusion-weighted images are acquired for a sphere of q vectors with indexed values in a Cartesian grid in q-space in order to produce a three-dimensional probability distribution. The PDF, , is the inverse Fourier transform of Equation 1:
where F−1 denotes the inverse Fourier transform. The spacing between vectors defines the field of view and the maximum vector defines the resolution of the PDF. The values of are placed in a matrix with indexes given by the indexes of the vectors, and then the 3D inverse discrete Fourier transform is computed, producing the PDF. By measuring the microscopically resolved 3D diffusion function, DSI is able to show complex fiber relationships in terms of the multimodal behavior of the PDF within a macroscopically resolved segment of tissue.
Since the 3D PDF represents a spatial volume, it is necessary to reduce its dimensions to allow visualization and to determine the local maxima of diffusion. The method typically employed in DSI is to integrate radially the PDF by the magnitude of :
where û is a unit vector in the direction of . This produces a probability distribution that is a function of fiber angle and is weighted to better show long diffusion distances. This new data set is termed the orientational distribution function (ODF) and provides a probability distribution for diffusion for a set of directions, regardless of the magnitude of the diffusion. To simplify visualization further, the ODF is normalized by subtracting the smallest magnitude value. The ODF is then plotted with colors corresponding to direction and magnitude, and radii are defined by the values of the ODF. The 3D vector directions of maximum diffusion (and thus muscle fiber directions) in the voxel are then given as a function of the local maxima in the ODF.
Each voxel in a DSI data set has one or more local maxima (the local maxima of the ODF), which defines one or more 3D vectors for each voxel in the set of images. Constructing connections along the vector directions in a vector field is accomplished by determining a set of streamlines. Mathematically, a streamline is defined as the solution of the following differential equation:
where is the streamline, s is a path coordinate along , and is the vector field. Equation 5 demonstrates that the streamline will be tangent to the vector field at all points. Generating streamlines corresponding to a vector field in biological data has been termed tractography (Basser, 1998), since the initial use of this technique was for determining white matter tracts in the brain. Since there can be more than one local maxima per voxel, we have employed a method derived from the theory of generalized streamlines (Daivis and Coelho, 2000). Generalized streamline tractography operates by adding a constraint to the streamlines that a certain angular threshold must be met to establish intervoxel connectivity. If that threshold is met, then the tract will continue into the adjacent voxel. If, however, the threshold is not met, the tract will stop. In the instance where a tract happens on a voxel with two or more vectors that meet the angular threshold criteria, then the tract will continue along the vector of least angular difference compared with itself. In the current work, we employed an angular threshold of < ±17.5° to define tract continuity. The myofiber tract is derived from the principal fiber directions, represented as the directions of maximum diffusion of the ODF, in a set of adjacent voxels. The DSI tracts are displayed using custom software developed using VTK, an open-source 3D visualization tool (http://www.vtk.org/; Fig. 3). To illustrate further the generation of myofiber tracts in actual tissue, we show in Figure 4 a characteristic set of fiber tracts from a mid-sagittal slice of the bovine tongue, in which the myofiber tracts and the underlying DSI ODFs, from which the tracts are derived, are displayed in the same image. The myofiber tracts so identified do not necessarily correspond to conventional anatomical entities, such as fiber bundles or fascicles. In the current context, the tract is a macroscopic representation of multiple fibers or bundles within a segment of tissue that share similar orientation. To quantify tract angle, tract position is determined at two consecutive points along the tract, thus dividing the tract up into segments. The x, y, and z coordinates of each segment are subtracted and divided by the length of the segment, thus identifying the segment's 3D orientation. These segment orientations are colored based on direction and then represented on a spherical graph, with graph center being (0, 0, 0).
Image Acquisition Protocol
Imaging was performed with a Siemens Allegra 3T scanner on eight ex vivo cow tongues obtained from Blood Farms (West Groton, MA). Whole specimens were refrigerated and scanned within 24 hr of harvest. The imaging protocol employed a diffusion gradient sampling scheme, which consisted of a keyhole Cartesian acquisition to include q-space values lying on a Cartesian grid for a total of 515 sampling points. Typical image matrix sizes were 64 × 64 × 25 with voxel resolutions of 2.8–4 mm3. The b-values used were in the range of 5,500–8,500 s/mm2.
The images shown in this article are representative of those obtained from a set of adult bovine tongues (n = 8 tongues). For ease of visualization, the DSI tractography images display only those tracts passing through a designated plane. Thus, we show only a subset of all the tracts in a given data set in each image. The color-coding is the same in all images, regardless of the slice orientation, and is depicted as follows: green indicates tracts in the anterior-posterior direction (longitudinal orientation of the tissue), blue indicates the side-to-side direction (transverse orientation of the tissue), and red indicates the superior-inferior direction (vertical direction of the tissue).
Figure 5 depicts the myofiber populations passing through a mid-sagittal plane from opposite lateral perspectives. Since the tracts represent only the tracts passing through a mid-sagittal plane, the lateral portions of the tongue, and the associated fiber tracts, are largely cut away. Owing to the fact that the tracts were obtained directly from DSI data, they are a statistical representation of the set of similarly aligned fibers across multiple voxels. While these tracts tend to correlate well with several classically defined extrinsic and intrinsic muscles, the tracts also display novel attributes of the tissue geometry. The individual tract depicts a unique population of myofibers, independent of their point of origin (i.e., extrinsic vs. intrinsic), which is defined at the macroscopic (or tissue) scale by the similarity of their alignment. In general, the longitudinal sheath fibers are depicted as long tracts (shown in green) sandwiching the lingual core. The lingual core is most distinct in the anterior portion of the tissue, but in fact persists into the posterior portion of the tissue as well. The lingual core is comprised of distinct transversus tracts (shown in blue) and vertically oriented tracts (shown in red). Notably, one cannot distinguish if these vertically oriented tracts correspond in fact to the verticalis or to vertically aligned genioglossus myofibers. There is a set of large midline fiber tracts, which fan out radially from a medial connection on the mandible bone into the core of the tongue, likely to correspond to the genioglossus fibers, and which merge with the vertically aligned tracts. In addition, there is separate vertically aligned set of fiber tracts, which originates at a posterior medial connection on the hyoid bone, and then courses laterally and vertically, and finally merges with lateral longitudinal fibers. These latter myofibers are likely to correlate with the hyoglossus. We demonstrate in Figure 6 an obliquely oriented image in which the superior aspect of the longitudinalis is removed, demonstrating the relationship between the laterally located longitudinally oriented sheath fibers (green), the transversely oriented transversus fibers, and the vertically oriented fibers (red and orange) comprised by the verticalis and genioglossus.
The geometry of several of these fiber tracts may be accentuated by electing to use alternative planes of reference. In Figure 7A, we show in more detail the fiber tracts traversing a horizontal reference plane in order to emphasize the varying angles exhibited by the verticalis and vertically oriented genioglossus as they project to the superior surface of the tissue. The longitudinal sheath of the tongue is still visible in green, but in this view, mainly the lateral tracts are present and the inferior and superior populations have been cut away. A small population of longitudinally oriented fiber tracts is observed to enter posteriorly and superiorly, coursing lateral to the apparent hyoglossus fiber tracts, and finally interdigitating with longitudinal fiber tracts. These fiber tracts may correlate with the styloglossus fibers, although this association is more difficult to discern without the presence of the surrounding muscular anatomy. In Figure 7B, we depict the lingual fiber tracts also from the perspective of a horizontal reference plane, but orient the image so that the superior longitudinally oriented fiber tracts are cut away, displaying the crossing fiber tracts of the lingual core. We demonstrate in this image the variation in the merging and crossing of vertically oriented and transversely oriented bundles of fibers, shown in red and blue, respectively, as a function of anterior-posterior position.
The corresponding vertically aligned and transversely aligned fiber tracts in the anterior and posterior lingual core are shown in a representative set of axial slices in Figure 8. Figure 8A represents an anterior axial slice (thickness ∼ 2 cm). The longitudinal sheath is shown as green fibers surrounding the core and oriented out of the page. The transversus fibers are shown in blue and the verticalis as red. Interestingly, the transversely aligned fibers tend to be localized to the more superior region. In addition, the vertically aligned fibers are separated into two lateral populations with slightly oblique orientations toward the superior midline. Figure 8B represents a representative posterior slice, and demonstrates a set of posteriorly oriented (green) fiber tracts in the midline, likely to be the posterior genioglossus tracts, as well the longitudinally oriented sheath tracts, and superiorly located vertically and transversely aligned fibers. Distinct vertically aligned fiber tracts, likely to be the hyoglossus, are shown laterally in the most posterior axial image. We demonstrate (Fig. 8C) the fiber tract angles from Figure 8A quantitatively on a 3D scatter plot. This method allows us to depict the variation of tract angles on an x-y-z coordinate system, with y corresponding to the longitudinal direction, z to the vertical direction, and x to the transverse direction. The green-red-blue color scheme, employed in the above images, was continued in this graph. As predicted, there is a distinct population of tracts aligned in the longitudinal direction clustered around origin of the graph (0, ±1, 0), and populations orthogonal to each other aligned in the vertical and transverse directions. The minimal degree of overlap between these populations of fiber tracts indicates that these tracts are aligned in the segment of the tissue in an explicitly orthogonal configuration. The fiber tract angles derived from Figure 8B are shown quantitatively in Figure 8D. It should be noted that there is considerably more overlap of tract angle in this case (posterior tongue) as compared to Figure 8C (anterior tongue). This is consistent with the fact that fiber tracts align more closely in an orthogonal manner in the anterior tongue, thus resulting in more apparent angular separation, as compared to the more complex angular relationships present in the posterior tongue.
The study of lingual anatomy poses a classical dilemma: How is it possible to relate the tissue's highly complex myoarchitecture with the multitude of possible deformations occurring during physiological motion? The extent to which lingual deformation corresponds to its underlying myoarchitecture has offered both the opportunity and the challenge to explore fundamental concepts of structure and function. We present here a novel approach, DSI with tractography, for visualizing the complex myoarchitecture of the mammalian tongue, which depicts muscular organization, not as individual myofibers but as macroscopically resolved myofiber tracts, representing similarly aligned myofiber populations. The length and orientation of an individual myofiber tract are in turn dictated by the extent (in voxels) over which myofiber orientational similarity exists in the tissue. We propose that these macroscopically defined myofiber tracts constitute a structural template, which dictates the direction of local tissue shortening during deformation. Whole tissue deformation, resulting from the net effect of such local shortening events, thus comprises the physiological basis for purposeful motion.
DSI resolves morphologically complex myoarchitecture by obtaining the average molecular diffusion function within a region of tissue and depicting it as the probability that a given water molecule will undergo direction-specific motion within a given period of time. The degree of diffusivity in a particular direction is dictated largely by the presence of physical barriers to diffusion, such as cell membranes and cytoskeletal fiber elements. The net diffusion in a tissue sample is represented as an ensemble PDF for the complete array of displacements in that region of tissue. The PDF for a given diffusion data set is specifically based on the Fourier relationship between the PDF and the diffusion signal for the spin echo obtained at various gradient strengths. Complete DSI acquisitions are assembled by fully sampling q-space, where q-space is a formalism that represents diffusion weighting as a function of the strength and direction of the magnetic field gradient applied during the MRI experiment (Wedeen et al., 2000, 2001; Tuch, 2002). This is in contrast to other diffusion weighting gradient sampling schemes, which sample only on a segment (or surface) of q-space by acquiring images based on only a limited sample of gradient strengths or directions (Basser et al., 1994; Basser, 1998; Napadow et al., 2001; Tuch, 2002). For purposes of visualization, the full 3D PDF may be converted to an ODF, which collapses the data to better display the directions of maximum diffusion. By this conversion, there are a finite number of directions in which the 3D diffusion function is sampled, which translates into the maximum possible angular resolution. Since one local point minima must separate two local maxima, the maximum possible angular resolution is within the noise threshold found in the reconstructed 3D diffusion function. Since most the crossing fibers observed in the tongue have orthogonal relationships to each other, this does not generally constitute a limitation of the ODF method. In the less common instance where fibers merge or diverge within a given voxel, i.e., possess small angular relationships, the precise angular relationship may be difficult to distinguish by observing the diffusion functions or ODFs alone, and it is the angular coherence between adjacent voxels that is important.
Tractography is a means for relating the angular coherence between voxels and relating the orientations obtained from the tissue diffusion microenvironment to the overall tissue macroenvironment. The logical underpinnings for tractography come from a desire to connect orientations, in a very similar manner to which streamlines connect vector fields in order to view trajectories in those fields. For example, a charged particle moving in a complicated magnetic field can be viewed as a streamline, thus providing a macroscale picture by knowing only the various microscale environments that particles might encounter. The goal is similar in the case of tractography, with the principal difference being that intervoxel angle similarity is also a driving factor in determining the trajectory that a tract may take. The tractography algorithm is constructed such that the tract takes the path of minimum angular difference. Consequently, the tract will stop if the angular difference between adjacent voxels is too high. Similarly, if the voxel contains two or more compatible paths, the tract will take that of the least angular difference. The exact minimum angular difference may vary with the tract construction algorithm. In the current work, we chose a minimum angular difference, which provided a reasonable depiction of the predicted macroscale myofiber relationships. This condition will, however, be systematically studied in future work in order to determine its discriminant value in determining myoarchitecture in this and other tissues.
These tracts may be considered the macroscopic representation of the population(s) of aligned myofibers within the imaged segment of tissue. Through the use of DSI with tractography, we have created a novel multiscalar metric for depicting complex myofiber populations, which represents at the same time microscopic and macroscopic myofiber orientation. In doing so, we have confirmed a number of previous notions of lingual myoarchitecture and demonstrated several novel concepts.
One, the lingual core consists of orthogonally related transversus and verticalis fibers, whose associated tracts span the distance between the superior and interior longitudinalis fibers. This property was exhibited by the distinct angular differences shown by the tract oriented longitudinally, transversely, and vertically. Differences also exist in the broad pattern of alignment exhibited by these tracts. For example, the transversus tracts are arrayed in a parallel configuration, principally in the superior portion of the tissue, whereas the verticalis tracts are configured in a way that separates into right and left tracts. The functional consequences of the latter configuration are at this point unknown.
Two, while the tracts associated with the genioglossus muscle are notable for their fan-like projection to the superior surface in the mid-sagital tongue, the vertically oriented segment of the genioglossus and the verticalis tracts per se are largely indistinguishable from each other on the basis of orientation. This suggests that in addition to the merging of microscopic anatomy, there may be a merging of mechanical function in the vertical orientation. Local fiber tract orientation may thus constitute a more appropriate determinant of local mechanical function in complex tissues than the function of one discrete muscle or another.
Three, based solely on its myoarchitecture, the tongue segregates itself into the anterior tongue, which is comprised almost completely of intrinsic fibers aligned along the principal axes, and the posterior tongue, which embodies the intrinsic fibers but incorporates fibers that originate externally, i.e., genioglossus, styloglossus, hyoglossus, and palatoglossus. It is noteworthy that the anterior tongue is capable of a vast array of displacements along with the institution of variable stiffening. Such properties are important both in speech and in the accommodation of a large array of bolus types. In contrast, the posterior tongue possesses a more limited repertoire of mechanical functions, yet is capable of exerting greater force to achieve certain physiological goals, such as bolus propulsion during swallowing.
The existence of overlapping and variably aligned fiber tracts supports the conceptualization of the tongue as a continuum of muscular elements. From a mechanical perspective, the tongue is believed to fall into a class of organs known as a muscular hydrostat, an organ whose musculature both creates motion and supplies the skeletal support for that motion (Kier and Smith, 1985; Smith and Kier, 1989; Napadow et al., 1999, 2002). Such organs characteristically are isovolemic, i.e., maintain their volume while undergoing various changes of shape and form, and are composed of complex fiber arrays aligned at angles orthogonal to the direction of deformation. Such fiber arrangements comprise the structural underpinnings for hydrostatic deformation and therefore are fundamental in the generation of lingual force. By definition, all hydrostats possess fibers parallel and perpendicular to the organ's long axis, but differ regarding the relative position and geometry of the perpendicular fibers. For example, muscular hydrostats that principally perform bending motions tend to have longitudinal fibers farther away from the longitudinal axis. An example of this phenomenon is the snake, which typically flicks its chemoreceptor-laden organ to sense its prey (de Groot et al., 2004). The fibers of the elephant trunk, on the other hand, are organized in a spiral fashion about the central longitudinal axis, thereby maximizing the ability of the organ to perform the twisting needed for grasping arboreal vegetation (Endo et al., 2001). The tentacle of the squid, which is most structurally similar to the mammalian tongue, has a core region of transverse fibers surrounded by a longitudinal sheath (Friel and Wainwright, 1998). The presence of structural complexity, both in terms of crossing myofibers (single voxel scale) and variably aligned myofiber tracts (multivoxel scale), as shown in this report, may be seen as an anatomical prerequisite for hydrostatic deformation.
Based on the above considerations, we postulate that these 3D aligned tracts provide a reference configuration, or mechanical template, on which deformation preferentially occurs. In this manner, it should be possible to conceive of the principal directions of contraction in a complex tissue, such as the tongue, by a superposition of tissue shortening in the directions of the indicated fiber tracts. In turn, this should allow an explicit conceptualization of macroscale mechanical function from the net microscale anatomical data set. Despite the many degrees of freedom embodied by the tongue and the large number of compatible contractions, it should be feasible to project deformed configurations from the myoarchitecture specified by DSI tractography. Several limitations of this technique should, however, be acknowledged. Since fundamentally DSI resolves fiber orientation through a determination of principal directions of diffusion, certain microscopic complexity seen at the resolution of conventional light microscopy will be missed. Whether this level of resolution is significant in terms of understanding tissue mechanics has not been determined. Furthermore, it is uncertain whether DSI tractography, at the level of angular resolution shown in this report, will be feasible in vivo due the required imaging time and the deleterious effects of gross motion on image integrity. An alternative approach, albeit with less angular precision, may be to derive intervoxel tracts based on voxel-specific principal fiber direction with high-resolution DTI.
In conclusion, we have employed a novel method, DSI tractography, for determining the orientation of variably aligned myofiber populations in the mammalian tongue. The delineation of myofiber tracts in the tongue allows us to compile a macroscale anatomic model, which can be explicitly related via the diffusion function to microscopic anatomy. We postulate that the definition of locally aligned fiber populations constitutes a measure of mechanical continuity and forms a structural template on which region-specific contractions occur under physiological conditions.