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Proc SPIE Int Soc Opt Eng. Author manuscript; available in PMC 2017 August 04. Published in final edited form as: Proc SPIE Int Soc Opt Eng. 2017 February 11; 10137: . doi:10.1117/12.2254626.
Test Suite for Image-Based Motion Estimation of the Brain and Tongue Jordan Ramsey1, Jerry L. Prince2, and Arnold D. Gomez2 1Department
of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, MD, US 21250
Author Manuscript
2Department
of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD,
US 20218
Abstract
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Noninvasive analysis of motion has important uses as qualitative markers for organ function and to validate biomechanical computer simulations relative to experimental observations. Tagged MRI is considered the gold standard for noninvasive tissue motion estimation in the heart, and this has inspired multiple studies focusing on other organs, including the brain under mild acceleration and the tongue during speech. As with other motion estimation approaches, using tagged MRI to measure 3D motion includes several preprocessing steps that affect the quality and accuracy of estimation. Benchmarks, or test suites, are datasets of known geometries and displacements that act as tools to tune tracking parameters or to compare different motion estimation approaches. Because motion estimation was originally developed to study the heart, existing test suites focus on cardiac motion. However, many fundamental differences exist between the heart and other organs, such that parameter tuning (or other optimization) with respect to a cardiac database may not be appropriate. Therefore, the objective of this research was to design and construct motion benchmarks by adopting an “image synthesis” test suite to study brain deformation due to mild rotational accelerations, and a benchmark to model motion of the tongue during speech. To obtain a realistic representation of mechanical behavior, kinematics were obtained from finite-element (FE) models. These results were combined with an approximation of the acquisition process of tagged MRI (including tag generation, slice thickness, and inconsistent motion repetition). To demonstrate an application of the presented methodology, the effect of motion inconsistency on synthetic measurements of head-brain rotation and deformation was evaluated. The results indicated that acquisition inconsistency is roughly proportional to head rotation estimation error. Furthermore, when evaluating non-rigid deformation, the results suggest that inconsistent motion can yield “ghost” shear strains, which are a function of slice acquisition viability as opposed to a true physical deformation.
Keywords Imaging; mechanics; brain; tongue
Send correspondence to Arnold D. Gomez ([email protected]) or Jerry L. Prince ([email protected]).
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1. Introduction
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Understanding tissue deformation patterns is a key factor in both traumatic brain injury research and the study of speech production. Magnetic resonance imaging (MRI) has broad applications in clinical medicine and basic research for visualization of anatomical structures. When MRI is combined with spatial modulation of magnetization (SPAMM),1 artificial sinusoidal patterns or tags on the tissue that enable measurement of deformation across a time series, 3D motion can be recovered from a set of tagged images. These images are generally in the form of stacks of slices acquired in different directions. The acquisition of each slice consists of collecting a 2D array of data in the frequency (Fourier) domain. This process is relatively slow, and only a portion of the array is filled while motion is taking place. The remaining portions require subsequent repetitions of the motion under investigation. If the motion is highly repeatable, such as what is typical in the heart, then the data acquired across multiple repetitions is consistent, and images can be reconstructed with little or no artifacts.1,2 However, such highly repeatable motions are not easily achieved for the tongue during speech nor the brain during mild acceleration, this lack of consistency may cause artifacts to appear in the reconstructed slices. Furthermore, as multiple slices are stacked to reconstruct motion in 3D, subtle variations in movement can have undesirable effects on motion estimation, while not having a noticeable impact over individual slices. To lessen the effects of inconsistency, previous investigations have used strategies to make motion more consistent. In the heart, this includes electrocardiogram triggering and the use of breath holds.1 Researchers studying brain motion under mild acceleration use specialized hardware, and the study of the tongue is aided by a metronome.3,4 However, no technique yields perfect results when the motion under investigation is voluntary. Consequentially, characterizing any effects arising from inconsistency is useful to determine estimation accuracy.3 This study focuses on constructing a realistic test suite for verification of motion estimation techniques in 4D (i.e., a 3D volume and time). The test suite will enable optimization of motion estimation algorithms used in traumatic brain injury and speech production research. This report describes an approach to model acquisition of tagged MRI in the brain and tongue. After describing the contributions of this research in Section 2, the methods for simulating mechanical motion via FE modeling are presented in Section 3.1, and the approach for generating synthetic tagged MRI slices is introduced in Section 3.2. The application, where a simulated acquisition is used to quantify the effect of inconsistency in brain motion estimation is described in Section 4. The overall results, including benchmark verification and the application results, are discussed in Section 5. Finally, some concluding remarks are stated in Section 6.
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2. Contributions This work was inspired by previous work in cardiac motion estimation, where imaging information was obtained in an experimental phantom, and displacements were defined by human observers.5 Unlike the previous work, our approach utilizes synthetic data, which can be readily modified to investigate different types of deformation. This investigation contains key aspects for the accurate construction of synthetic tagged MRI that can be applied,
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without loss of generality, to other types of motion. The stochastic approach for analysis of motion consistency is a step forward in systematic characterization of MRI-based 4D deformation measurements in the brain.
3. Construction of Test Suites for Motion Estimation The general goal of this research is to produce synthetic benchmark data consisting of imaging information (a set of slices) that carry information about a known, 4D deformation field. As a result, the synthetic imaging data can be used as the input for a motion estimation method similar to experimentally acquired images. However, unlike the experimental process, using synthetic images allows direct comparison of the output (a deformation field) to known values. Here, the synthetic slices are constructed by modeling the acquisition of tagged MRI, and the deformation field was obtained from computational mechanics.
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3.1 Simulation of Tagged MRI The first step to generate a group of realistic tagged MRI slices was the generation of SPAMM1,2 or CSPAMM (complementary SPAMM1) tag patterns in a high-resolution image from a healthy volunteer (0.6 mm isotropic resolution in the brain, and 0.8 mm isotropic in the tongue). The patterns were obtained by defining sinusoids with respect to spatial coordinates according to the motion sensitivity of each slice. For example, a slice with sensitivity in the x-direction (horizontal) will have a sinusoidal pattern along the respective direction, which will give the appearance of vertical lines. Figure 1(b) shows a part of two volumes sensitized in the vertical and horizontal directions, which resulted in a grid pattern. The complete tagging simulation resulted in three tagged volumes along the x, y and z directions.
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The second step in the tagged MRI simulation process (Figure 1(c)) consisted of applying simulated organ kinematics to the undeformed tagged volumes in order to generate timevarying sequences. Displacement fields from mechanical simulations (discussed in Section 3.2) were used to deform tagged volumes via 3D spline interpolation. Because displacement information from the simulations was defined at the nodes of the FE mesh, voxel values were interpolated using a given element's shape functions. An inverse isoparametric search was employed to find the element containing each voxel.
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Lastly, note that the volumes used so far have substantially higher resolution than what would normally used in motion estimation3,4—This was necessary to simulate slice thickness via filtering and down-sampling. Slice location, within the high-resolution tagged volumes was defined to reflect typical separation and orientation. Prior to interpolating, intensity values form tagged voxels on to the slices, each of the volumes (including temporal changes) were blurred with a box filter to mimic volumetric averaging according to in-plane slice resolution and thickness. 3.2 Mechanical Simulations Motion in the organs chosen for this investigation can be thought of as two extreme cases: sudden brain acceleration involves relative large bulk motion with relatively small deformations (5% strain or less), while the tongue tends to undergo proportionally small Proc SPIE Int Soc Opt Eng. Author manuscript; available in PMC 2017 August 04.
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bulk motion with large changes in shape. To study variability, brain motion data was assumed to be rigid, but inconsistent across repetitions. The tongue incorporated finite strains and rotations.
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3.2.1 Brain—Although the created motion benchmark was synthetic, its application involves quantification of brain motion estimation error in a realistic acquisition scenario. For this reason, the simulations followed previous research investigating brain motion under mild acceleration3 briefly described as follows: healthy volunteers (in a MRI-compatible motion apparatus) rotate their head towards the left shoulder approximately 26° before encountering a rubber stopper. The stopper causes a mild deceleration that deforms the brain. Because the apparatus is outfitted with a rotational encoder, the imaging trigger is adjusted so that acquisition is initiated just before the stopper. Thus, the total head rotation from the reference state (prior to touching the stopper), including the stopper's deformation, to the resting state on the stopper is approximately 6°. The goal of their experiment is to measure brain deformation.3
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Based on the previous study, the range of rotation of brain images was [0, 6°]. To investigate motion inconsistency, the test suite included different sets of slices with varying degrees of rotation, which was extracted from the encoder data. In particular, 25 rotations were selected based on the maximum amount of rotation after hitting the stopper. These rotation histories (shown in figure 2(a)) were extracted from a larger set of 156 rotations, to achieve a compact set separated by approximately equal (maximum rotation) intervals. For each time history, a total of 15 time steps of 3 tagged directions each were created. Two sets of 11 SPAMM slices of 1.5 mm × 1.5 mm in-plane resolution and 8 mm thickness (one for each orthogonal tagged direction) were constructed in the axial directions, and 7 identical slices were constructed in the remaining tagged direction. Figure 2(b) and 2(c) show synthesized tagged MR images from two different time points. The head and brain were assumed to be rigid. In order to validate the independent rotations, each of the 25 volumetric datasets were registered using 3D affine registration (Optimized Automatic Image Registration method in MIPAV15 7.2.0). Then, the registration result was compared to the data in Figure 2(a)
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3.2.2 Tongue—Non-homogeneous tongue deformations were obtained using a model of the tongue consisting of hexahedral elements divided into 15 regions representative of intersecting tongue muscles as shown in Figure 3 (more details on model geometry and simulations similar to that described here can be found in previous computational studies6, 12). The model included active contraction, to simulate the word “ahgeese” /ә/-/gis/. For simulation purposes, the word was subdivided into /ә/, /gi/ and /s/, and contraction magnitudes were approximated from the literature:7, 8 Activations for /ә/ aimed to place the tongue in the center of the vowel space producing a posterior lower vowel. During /gi/, activations were set to produce a posterior motion of the base of the tongue towards the back of the mouth. Lastly, the activation pattern for /s/ aimed at moving the tip of the tongue forward. The tongue was approximated as a neo-Hookean solid (stiffness coefficients of 0.03 MPa, and 0.01 MPa, and bulk modulus of 30 Mpa), and activations were expressed as a percentage of a maximum contraction of 0.35 Mpa.9, 10 The different mesh regions shown in Figure 3 corresponded to different material domains where active stress was applied in order Proc SPIE Int Soc Opt Eng. Author manuscript; available in PMC 2017 August 04.
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to cause contraction. Simulations were carried out using FEBio a finite element software.11 A total of three sets of orthogonally tagged CSPAMM slices of 2 mm × 2 mm in-plane resolution, and 6 mm thickness were constructed. The simulations were verified via visual inspection to ensure that the resulting motion was similar to previous experimental observations.
4. Experimental Inconsistency and Motion Estimation Error
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These experiments were an application of the brain motion test suite (Sections 3.1, and 3.2.1). Thus, it was necessary to relate the imaging data in the test suite, which consisted of 25 slice sets, each following a specific rotation history (Figure 2(a)), to the actual acquisition process, which consists of assembling a single slice set from motion repetitions following slightly different rotation histories. To this end, synthetic acquisitions were modeled as a stochastic process: during acquisition, each slice was reconstructed by transferring frequency data into an array. However, in this case, the data's source was not the imaging instrument, but was a random selection from the existing imaging data in the test suite. The amount of rotation at each time point was modeled as a normal distribution, where the mean followed a unique rotation history throughout the acquisition, and the variance was a measure of consistency (or inconsistency). For example, if the acquisition had a variance of zero, a slice representing 30 ms in Figure 2(a) (marked with a star) was extracted exclusively from the test suite data at 5.1°. However, a non-zero variance would indicate that the slice was reconstructed from frequency segments selected at random from test suite data as low as 2.8° and as high as 5.7°. Given the test suite's range, the mean time history had a maximum rotation of 4.7, and the variance was assumed to be less than one. Specifically, this experiment looked at five discrete values, 0, 0.25, 0.50, 0.75, or 1° to evaluate different levels of consistency. The result of one simulated acquisition was a randomly combined (RC) slice set of a given variance. The effect of variance in the outcome of motion estimation was investigated using the Monte Carlo approach. A number of RC slices were used to estimate error from rigid and non-rigid motion estimation (below). In each case, error was analyzed across all the estimations from RC slices of the same variance, and the results were expressed as a mean error, and a standard deviation. 4.1 Head Rotation Estimation Error
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The goal of this experiment was to determine how motion consistency, quantified by the variance of an RC slice set, affected rigid estimation of head rotation. To estimate head rotation from the RC slice set, the first time frame was rigidly registered to subsequent frames providing an approximate characterization of the set's rotation time history. Registration was performed using the imregtform method of the affine3d class in MATLAB (2015a). The approximate time history was compared to the reference time history (which provided the mean for all the RC slice reconstruction). Error was defined as the RMS of the residual between these time histories.
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4.2 Ghost Strains
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The term “Ghost Strains” refers to apparent deformation (measured by strain) that arises as an artifact and not from the system under consideration. The goal in this experiment was to assess the displacement accuracy (per displacement residual magnitude), and ghost strains arising from motion inconsistency, as a function of motion inconsistency variance. By design, the amount of simulated tissue deformation in the test suite was zero. Therefore, any non-zero deformations constituted an erroneous measurement from the motion estimation process.
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The strain measure of interest was shear deformation given its relevance in traumatic brain injury.3 The test suite was constructed based on a rotation about the z-axis (the out-of-the page direction in Figure 2(b)); thus, the largest interslice shears were expected in the xz and yz directions. Because each RC slice set yielded shear strains across a 3D volume, the measurement was simplified as the range within the volume, i.e., the difference between maximum and minimum. Therefore, the strain error metric was extracted from the largest ghost strains in a given volume. Specifically, the range in xz shear strains plus the range in yx shear strains—the total artificial strain error. Non-rigid deformation between the first time frame, and the frame equivalent to t = 20 ms was estimated using 3D implementation of the harmonic phase (HARP) algorithm.2,13,14 In HARP, harmonic phase values from a reference volume converge iteratively towards a deformed configuration. Average harmonic phase residual (across the volumes) was recorded as a metric of HARP convergence (a value of zero indicates perfect convergence). Euler-Lagrange strain values were extracted from the HARP deformation field,1 edge values (the skull) were removed by manual segmentation to avoid edge effects.
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5. Results and Discussion 5.1 Verification of Simulated Benchmarks Registration of the volumetric images in the brain test suite (Sections 3.1 and 3.2.1) were confirmed to agree with rotation time histories to 1° × 10−3 via MIPAV. The small discrepancy was attributed to differences in the center of rotation, and was considered to be negligible since the value was below the resolution of the source rotation data.
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Visual inspection of the tongue test suite suggested that the selected activation patterns yielded deformations similar to experimental observations: The sound /ә/ contains mostly rigid motion from jaw rotation.7 The utterance /gi/ results in elongation of the underside of the tongue, and longitudinal contraction via IL activation.12 The letter /s/ has been shown to depress the tongue which can be accomplished by a contraction in the verticalis muscles, and move the tip of the tongue forward.16 These deformations were accurately transfered to the CSPAMM slices, which show deformation consistent with the FE model (Figure 4). 5.2 Effect of Motion Inconsistency on Rotation Estimation Error and Ghost Shear Strains Figure 5 shows the results of head rotation estimation as a function of motion consistency (measured as variance of randomly combined slice sets). As expected, rotation histories
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approximated using an RC slice set with zero variance accurately follows the reference data (encoder information). In contrast, a RC slice set with a variance of 0.50 (°)2 produces an approximation that deviates from the reference. Error from a total of 100 Monte Carlo iterations (the number needed to achieve consistent results) show that both the average error and its standard deviation increase as a function of RC slice set (acquisition) variance. For example, doubling variance from 0.25 to 0.50 (°)2, results in an increase of approximately 50% in mean error, and a similar increase was observed in the standard deviation. Using the relationship in the same graph suggests that a rotation of 5° would, on average, differ from the reference by 0.2° (or 5%) given an acquisition variance of 0.75 (°)2. In the same circumstances, an error as high as 10% would be likely given the standard deviation in approximation error.
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In terms of non-rigid estimation, the results (Figure 6) suggest that motion consistency (per RC slice set variance) has a direct effect on both displacement residual and total artificial shear strain—both of these quantities increased several times with relatively small changes in variance. For example, doubling the variance from 0.25 to 0.50, results in a 53% increase in error, as well as a 20% increase in total artificial strain. This was not the case with phase residual, which, in total, changed by a small amount (less than 5%) indicating that HARP converged fairly well. Nevertheless, since displacement and strain error increased by much more than 5%, the effectiveness of HARP was hampered fundamentally by variance-driven imaging artifacts rather than lack of convergence. These artifacts created separation between the location on which the motion estimation algorithm converged, and the ideal displacement. Note that no strain was applied in the generation of data for the test suite, and all the apparent measured deformation arose from ghost strains. Although the total artificial strain is a conservative measure of error (associated with the sum of maximum ghost strains), the amount of shear expected in a brain deformation experiment in vivo is relatively low,3 which underscores the need for consistent acquisition or implementation of robust strain estimation techniques.
6. Conclusion
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This research described a framework for creating synthetic benchmark data specifically targeted to deformation analysis of the brain and tongue. The approach for integrating realistic imaging and mechanical simulations applies to different types of motion that can be found in other organs. The focus of the study was generating synthetic data to be used as benchmark; thus, the modeling approach did not concentrate on physical accuracy to the same extent as predictive biomechanical models. However, the simulations of tongue deformation follow basic motion that are patterns present during speech production. This indicates the potential for using the methodology for characterizing motion estimation accuracy in this scenario. A demonstration of accuracy characterization was performed in the brain, where the acquisition process was modeled as a stochastic process. The results show a clear relationship between consistency of motion during acquisition and 4D imagebased motion estimation. The relationship was observed in both, rigid head rotation, and non-rigid brain deformation. In both of these cases, error (as deviations in rotation time history, or artificial “ghost” shear strains) increased as motion become inconsistent. These
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finding underscores the need for consistency or robust estimation of spatiotemporal motion estimation.
References
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1. Ibrahim ESH. Myocardial tagging by cardiovascular magnetic resonance: evolution of techniquespulse sequences, analysis algorithms, and applications. J Cardiovasc Magn Reson. 2011 Jul.13:36. [PubMed: 21798021] 2. Osman NF, McVeigh ER. Prince JL Imaging heart motion using harmonic phase MRI. IEEE Trans Med Imaging. 2000 Mar; 19(3):186–202. [PubMed: 10875703] 3. Knutsen AK, Magrath E, McEntee JE, Xing F, Prince JL, Bayly PV, Butman JA, Pham DL. Improved measurement of brain deformation during mild head acceleration using a novel tagged MRI sequence. Journal of Biomechanics. 2014 Jan; 47(14):3475–3481. [PubMed: 25287113] 4. Parthasarathy V, Prince JL, Stone M, Murano EZ, Nessaiver M. Measuring tongue motion from tagged cine-MRI using harmonic phase (HARP) processing. J Acoust Soc Am. 2007 Jan; 121(1): 491–504. [PubMed: 17297803] 5. Gomez-Tobon C, De Craene M, McLeod K, Tautz L, Shi W, Hennemuth A, Prakosa A, Wang H, Carr-White G, Kapetanakis S, Lutz A, Rashce V, Schaeffter T, Butakoff C, Friman O, Mansi T, Sermesant M, Zhuang X, Ourselin S, Peigen HO, Pennec X, Razavi R, Rueckert D, Frangi AF, Rhode KS. Benchmarking framework for myocardial tracking and deformation algorithms: An open access database. Medical Image Analysis. 2013 Jan; 17(6):632–648. [PubMed: 23708255] 6. Fujita S, Dang J, Suzuki, Honda K. A Computational Tongue Model and its Clinical Application. Oral Science International. 2007 Nov; 4(2):97–100. 7. Sanguineti V, Laboissire R, Payan Y. A control model of human tongue movements in speech. Biol Cybern. 1997 Jul; 77(1):11–22. [PubMed: 9309860] 8. Perrier P, Payan Y, Zandipour M, Perkell J. Influences of tongue biomechanics on speech movements during the production of velar stop consonants: a modeling study. J Acoust Soc Am. 2003 Sep; 114(3):1582–99. [PubMed: 14514212] 9. Teran J, Sifakis E, Blemker S, Ng-Thow-Hing V, Lau C, Fedkiw R. Creating and simulating skeletal muscle from the visible human data set. IEEE Trans on Vis and Comp Graphics. 2005; 11(3): 317328. 10. Zajac FE. Muscle and tendon: properties, models, scaling, and applications to biomechanics and motor control. Critical Reviews in Biomed Eng. 1989; 17(4):359–411. 11. Maas SA, Ellis BJ, Ateshian GA, Weiss JA. FEBio: Finite elements for biomechanics. J Biomech Eng. 2011 Jan.134(1) 12. Harandi NM, Woo J, Farazi MR, et al. Subject-specific biomechanical modeling of the oropharynx with application to speech production. IEEE ISBI. 2015 Jul.:1389–1392. 13. Osman NF, Prince JL. Regenerating MR tagged images using harmonic phase (HARP) methods. IEEE Trans Biomed Eng. 2004 Aug; 51(8):1428–33. [PubMed: 15311829] 14. Pan L, Prince JL, Lima JA, Osman NF. Fast tracking of cardiac motion using 3D-HARP. IEEE Trans Biomed Eng. 2005 Aug; 52(8):1425–35. [PubMed: 16119238] 15. McAuliffe MJ, Lalonde FM, McGarry D, Gandler W, Csaky K. Medical Image Processing, Analysis and Visualization in clinical research. IEEE CBMS. 2001 16. Sanders I, Mu L. A three-dimensional atlas of human tongue muscles. Anat Rec (Hoboken). 2013 Jul; 296(7):1102–14. [PubMed: 23650264]
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Tagged MRI simulation. In the brain, the high-resolution undeformed image (a) was synthetically tagged using a SPAMM pattern (b). Deformation fields from mechanical simulations were applied to the tagged volume to impart motion information (c). Simulation of thickness included down-sampling the deformed tagged volume, as well as filtering to recreate spatial averaging (d). In the tongue, the process was identical.
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Head rotation simulation. The rotation histories (a) were obtained from encoder data, and were used to generate synthetic slices at different time points, including t = 0 ms (c) and t = 30 ms (d), which is marked on the rotation history with a star. The test suite consisted of slice sets following all the rotation histories.
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FE model of the tongue. The model's approximate size and shape were similar to the adult human tongue (a). Due to interdigitation, some muscles were represented as shared regions (b,c), which are shown in different colors. Key: T = transverse, V = verticalis, SL = superior longitudinal, IL = inferior longitudinal, SM = surrounding tissue, GG = genioglossus, H = hyoid bone, M = mandible.
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Figure 4.
Simulated tagged MRI slices of tongue motion. Deformation from the FE model (outlined) was used to deform the reference CSPAMM tagged volume (a), according approximated speech utterances, which included: /ә/ (b), /gi/ (c), and /s/ (d). The complete test suite included the images shown and additional slices, which formed 3D slice sets tagged in orthogonal directions.
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Result of the Monte Carlo analysis. In the typical result for two different acquisition variances compared to the reference (encoder data) (a), a higher variance yields less agreement with the true data compared to a lesser value. The relationship between acquisition variance and average error across Monte Carlo iterations suggests that the variance is directly proportional to the mean error (b).
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Effect of motion inconsistency on non-rigid motion estimation. Both, residual magnitude (a), and total artificial strain (b), are quite sensitive to acquisition inconsistency (per RC slice set variance). However, the phase residual increases by a relatively small amount (less than 5%). These relationships indicate that, as variance increased, HARP effectiveness was negatively influenced by image artifacts, rather than lack of convergence.
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Proc SPIE Int Soc Opt Eng. Author manuscript; available in PMC 2017 August 04. Published in final edited form as: Proc SPIE Int Soc Opt Eng. 2017 February 11; 10137: . doi:10.1117/12.2254626.
Test Suite for Image-Based Motion Estimation of the Brain and Tongue Jordan Ramsey1, Jerry L. Prince2, and Arnold D. Gomez2 1Department
of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, MD, US 21250
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2Department
of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD,
US 20218
Abstract
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Noninvasive analysis of motion has important uses as qualitative markers for organ function and to validate biomechanical computer simulations relative to experimental observations. Tagged MRI is considered the gold standard for noninvasive tissue motion estimation in the heart, and this has inspired multiple studies focusing on other organs, including the brain under mild acceleration and the tongue during speech. As with other motion estimation approaches, using tagged MRI to measure 3D motion includes several preprocessing steps that affect the quality and accuracy of estimation. Benchmarks, or test suites, are datasets of known geometries and displacements that act as tools to tune tracking parameters or to compare different motion estimation approaches. Because motion estimation was originally developed to study the heart, existing test suites focus on cardiac motion. However, many fundamental differences exist between the heart and other organs, such that parameter tuning (or other optimization) with respect to a cardiac database may not be appropriate. Therefore, the objective of this research was to design and construct motion benchmarks by adopting an “image synthesis” test suite to study brain deformation due to mild rotational accelerations, and a benchmark to model motion of the tongue during speech. To obtain a realistic representation of mechanical behavior, kinematics were obtained from finite-element (FE) models. These results were combined with an approximation of the acquisition process of tagged MRI (including tag generation, slice thickness, and inconsistent motion repetition). To demonstrate an application of the presented methodology, the effect of motion inconsistency on synthetic measurements of head-brain rotation and deformation was evaluated. The results indicated that acquisition inconsistency is roughly proportional to head rotation estimation error. Furthermore, when evaluating non-rigid deformation, the results suggest that inconsistent motion can yield “ghost” shear strains, which are a function of slice acquisition viability as opposed to a true physical deformation.
Keywords Imaging; mechanics; brain; tongue
Send correspondence to Arnold D. Gomez ([email protected]) or Jerry L. Prince ([email protected]).
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1. Introduction
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Understanding tissue deformation patterns is a key factor in both traumatic brain injury research and the study of speech production. Magnetic resonance imaging (MRI) has broad applications in clinical medicine and basic research for visualization of anatomical structures. When MRI is combined with spatial modulation of magnetization (SPAMM),1 artificial sinusoidal patterns or tags on the tissue that enable measurement of deformation across a time series, 3D motion can be recovered from a set of tagged images. These images are generally in the form of stacks of slices acquired in different directions. The acquisition of each slice consists of collecting a 2D array of data in the frequency (Fourier) domain. This process is relatively slow, and only a portion of the array is filled while motion is taking place. The remaining portions require subsequent repetitions of the motion under investigation. If the motion is highly repeatable, such as what is typical in the heart, then the data acquired across multiple repetitions is consistent, and images can be reconstructed with little or no artifacts.1,2 However, such highly repeatable motions are not easily achieved for the tongue during speech nor the brain during mild acceleration, this lack of consistency may cause artifacts to appear in the reconstructed slices. Furthermore, as multiple slices are stacked to reconstruct motion in 3D, subtle variations in movement can have undesirable effects on motion estimation, while not having a noticeable impact over individual slices. To lessen the effects of inconsistency, previous investigations have used strategies to make motion more consistent. In the heart, this includes electrocardiogram triggering and the use of breath holds.1 Researchers studying brain motion under mild acceleration use specialized hardware, and the study of the tongue is aided by a metronome.3,4 However, no technique yields perfect results when the motion under investigation is voluntary. Consequentially, characterizing any effects arising from inconsistency is useful to determine estimation accuracy.3 This study focuses on constructing a realistic test suite for verification of motion estimation techniques in 4D (i.e., a 3D volume and time). The test suite will enable optimization of motion estimation algorithms used in traumatic brain injury and speech production research. This report describes an approach to model acquisition of tagged MRI in the brain and tongue. After describing the contributions of this research in Section 2, the methods for simulating mechanical motion via FE modeling are presented in Section 3.1, and the approach for generating synthetic tagged MRI slices is introduced in Section 3.2. The application, where a simulated acquisition is used to quantify the effect of inconsistency in brain motion estimation is described in Section 4. The overall results, including benchmark verification and the application results, are discussed in Section 5. Finally, some concluding remarks are stated in Section 6.
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2. Contributions This work was inspired by previous work in cardiac motion estimation, where imaging information was obtained in an experimental phantom, and displacements were defined by human observers.5 Unlike the previous work, our approach utilizes synthetic data, which can be readily modified to investigate different types of deformation. This investigation contains key aspects for the accurate construction of synthetic tagged MRI that can be applied,
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without loss of generality, to other types of motion. The stochastic approach for analysis of motion consistency is a step forward in systematic characterization of MRI-based 4D deformation measurements in the brain.
3. Construction of Test Suites for Motion Estimation The general goal of this research is to produce synthetic benchmark data consisting of imaging information (a set of slices) that carry information about a known, 4D deformation field. As a result, the synthetic imaging data can be used as the input for a motion estimation method similar to experimentally acquired images. However, unlike the experimental process, using synthetic images allows direct comparison of the output (a deformation field) to known values. Here, the synthetic slices are constructed by modeling the acquisition of tagged MRI, and the deformation field was obtained from computational mechanics.
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3.1 Simulation of Tagged MRI The first step to generate a group of realistic tagged MRI slices was the generation of SPAMM1,2 or CSPAMM (complementary SPAMM1) tag patterns in a high-resolution image from a healthy volunteer (0.6 mm isotropic resolution in the brain, and 0.8 mm isotropic in the tongue). The patterns were obtained by defining sinusoids with respect to spatial coordinates according to the motion sensitivity of each slice. For example, a slice with sensitivity in the x-direction (horizontal) will have a sinusoidal pattern along the respective direction, which will give the appearance of vertical lines. Figure 1(b) shows a part of two volumes sensitized in the vertical and horizontal directions, which resulted in a grid pattern. The complete tagging simulation resulted in three tagged volumes along the x, y and z directions.
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The second step in the tagged MRI simulation process (Figure 1(c)) consisted of applying simulated organ kinematics to the undeformed tagged volumes in order to generate timevarying sequences. Displacement fields from mechanical simulations (discussed in Section 3.2) were used to deform tagged volumes via 3D spline interpolation. Because displacement information from the simulations was defined at the nodes of the FE mesh, voxel values were interpolated using a given element's shape functions. An inverse isoparametric search was employed to find the element containing each voxel.
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Lastly, note that the volumes used so far have substantially higher resolution than what would normally used in motion estimation3,4—This was necessary to simulate slice thickness via filtering and down-sampling. Slice location, within the high-resolution tagged volumes was defined to reflect typical separation and orientation. Prior to interpolating, intensity values form tagged voxels on to the slices, each of the volumes (including temporal changes) were blurred with a box filter to mimic volumetric averaging according to in-plane slice resolution and thickness. 3.2 Mechanical Simulations Motion in the organs chosen for this investigation can be thought of as two extreme cases: sudden brain acceleration involves relative large bulk motion with relatively small deformations (5% strain or less), while the tongue tends to undergo proportionally small Proc SPIE Int Soc Opt Eng. Author manuscript; available in PMC 2017 August 04.
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bulk motion with large changes in shape. To study variability, brain motion data was assumed to be rigid, but inconsistent across repetitions. The tongue incorporated finite strains and rotations.
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3.2.1 Brain—Although the created motion benchmark was synthetic, its application involves quantification of brain motion estimation error in a realistic acquisition scenario. For this reason, the simulations followed previous research investigating brain motion under mild acceleration3 briefly described as follows: healthy volunteers (in a MRI-compatible motion apparatus) rotate their head towards the left shoulder approximately 26° before encountering a rubber stopper. The stopper causes a mild deceleration that deforms the brain. Because the apparatus is outfitted with a rotational encoder, the imaging trigger is adjusted so that acquisition is initiated just before the stopper. Thus, the total head rotation from the reference state (prior to touching the stopper), including the stopper's deformation, to the resting state on the stopper is approximately 6°. The goal of their experiment is to measure brain deformation.3
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Based on the previous study, the range of rotation of brain images was [0, 6°]. To investigate motion inconsistency, the test suite included different sets of slices with varying degrees of rotation, which was extracted from the encoder data. In particular, 25 rotations were selected based on the maximum amount of rotation after hitting the stopper. These rotation histories (shown in figure 2(a)) were extracted from a larger set of 156 rotations, to achieve a compact set separated by approximately equal (maximum rotation) intervals. For each time history, a total of 15 time steps of 3 tagged directions each were created. Two sets of 11 SPAMM slices of 1.5 mm × 1.5 mm in-plane resolution and 8 mm thickness (one for each orthogonal tagged direction) were constructed in the axial directions, and 7 identical slices were constructed in the remaining tagged direction. Figure 2(b) and 2(c) show synthesized tagged MR images from two different time points. The head and brain were assumed to be rigid. In order to validate the independent rotations, each of the 25 volumetric datasets were registered using 3D affine registration (Optimized Automatic Image Registration method in MIPAV15 7.2.0). Then, the registration result was compared to the data in Figure 2(a)
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3.2.2 Tongue—Non-homogeneous tongue deformations were obtained using a model of the tongue consisting of hexahedral elements divided into 15 regions representative of intersecting tongue muscles as shown in Figure 3 (more details on model geometry and simulations similar to that described here can be found in previous computational studies6, 12). The model included active contraction, to simulate the word “ahgeese” /ә/-/gis/. For simulation purposes, the word was subdivided into /ә/, /gi/ and /s/, and contraction magnitudes were approximated from the literature:7, 8 Activations for /ә/ aimed to place the tongue in the center of the vowel space producing a posterior lower vowel. During /gi/, activations were set to produce a posterior motion of the base of the tongue towards the back of the mouth. Lastly, the activation pattern for /s/ aimed at moving the tip of the tongue forward. The tongue was approximated as a neo-Hookean solid (stiffness coefficients of 0.03 MPa, and 0.01 MPa, and bulk modulus of 30 Mpa), and activations were expressed as a percentage of a maximum contraction of 0.35 Mpa.9, 10 The different mesh regions shown in Figure 3 corresponded to different material domains where active stress was applied in order Proc SPIE Int Soc Opt Eng. Author manuscript; available in PMC 2017 August 04.
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to cause contraction. Simulations were carried out using FEBio a finite element software.11 A total of three sets of orthogonally tagged CSPAMM slices of 2 mm × 2 mm in-plane resolution, and 6 mm thickness were constructed. The simulations were verified via visual inspection to ensure that the resulting motion was similar to previous experimental observations.
4. Experimental Inconsistency and Motion Estimation Error
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These experiments were an application of the brain motion test suite (Sections 3.1, and 3.2.1). Thus, it was necessary to relate the imaging data in the test suite, which consisted of 25 slice sets, each following a specific rotation history (Figure 2(a)), to the actual acquisition process, which consists of assembling a single slice set from motion repetitions following slightly different rotation histories. To this end, synthetic acquisitions were modeled as a stochastic process: during acquisition, each slice was reconstructed by transferring frequency data into an array. However, in this case, the data's source was not the imaging instrument, but was a random selection from the existing imaging data in the test suite. The amount of rotation at each time point was modeled as a normal distribution, where the mean followed a unique rotation history throughout the acquisition, and the variance was a measure of consistency (or inconsistency). For example, if the acquisition had a variance of zero, a slice representing 30 ms in Figure 2(a) (marked with a star) was extracted exclusively from the test suite data at 5.1°. However, a non-zero variance would indicate that the slice was reconstructed from frequency segments selected at random from test suite data as low as 2.8° and as high as 5.7°. Given the test suite's range, the mean time history had a maximum rotation of 4.7, and the variance was assumed to be less than one. Specifically, this experiment looked at five discrete values, 0, 0.25, 0.50, 0.75, or 1° to evaluate different levels of consistency. The result of one simulated acquisition was a randomly combined (RC) slice set of a given variance. The effect of variance in the outcome of motion estimation was investigated using the Monte Carlo approach. A number of RC slices were used to estimate error from rigid and non-rigid motion estimation (below). In each case, error was analyzed across all the estimations from RC slices of the same variance, and the results were expressed as a mean error, and a standard deviation. 4.1 Head Rotation Estimation Error
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The goal of this experiment was to determine how motion consistency, quantified by the variance of an RC slice set, affected rigid estimation of head rotation. To estimate head rotation from the RC slice set, the first time frame was rigidly registered to subsequent frames providing an approximate characterization of the set's rotation time history. Registration was performed using the imregtform method of the affine3d class in MATLAB (2015a). The approximate time history was compared to the reference time history (which provided the mean for all the RC slice reconstruction). Error was defined as the RMS of the residual between these time histories.
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4.2 Ghost Strains
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The term “Ghost Strains” refers to apparent deformation (measured by strain) that arises as an artifact and not from the system under consideration. The goal in this experiment was to assess the displacement accuracy (per displacement residual magnitude), and ghost strains arising from motion inconsistency, as a function of motion inconsistency variance. By design, the amount of simulated tissue deformation in the test suite was zero. Therefore, any non-zero deformations constituted an erroneous measurement from the motion estimation process.
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The strain measure of interest was shear deformation given its relevance in traumatic brain injury.3 The test suite was constructed based on a rotation about the z-axis (the out-of-the page direction in Figure 2(b)); thus, the largest interslice shears were expected in the xz and yz directions. Because each RC slice set yielded shear strains across a 3D volume, the measurement was simplified as the range within the volume, i.e., the difference between maximum and minimum. Therefore, the strain error metric was extracted from the largest ghost strains in a given volume. Specifically, the range in xz shear strains plus the range in yx shear strains—the total artificial strain error. Non-rigid deformation between the first time frame, and the frame equivalent to t = 20 ms was estimated using 3D implementation of the harmonic phase (HARP) algorithm.2,13,14 In HARP, harmonic phase values from a reference volume converge iteratively towards a deformed configuration. Average harmonic phase residual (across the volumes) was recorded as a metric of HARP convergence (a value of zero indicates perfect convergence). Euler-Lagrange strain values were extracted from the HARP deformation field,1 edge values (the skull) were removed by manual segmentation to avoid edge effects.
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5. Results and Discussion 5.1 Verification of Simulated Benchmarks Registration of the volumetric images in the brain test suite (Sections 3.1 and 3.2.1) were confirmed to agree with rotation time histories to 1° × 10−3 via MIPAV. The small discrepancy was attributed to differences in the center of rotation, and was considered to be negligible since the value was below the resolution of the source rotation data.
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Visual inspection of the tongue test suite suggested that the selected activation patterns yielded deformations similar to experimental observations: The sound /ә/ contains mostly rigid motion from jaw rotation.7 The utterance /gi/ results in elongation of the underside of the tongue, and longitudinal contraction via IL activation.12 The letter /s/ has been shown to depress the tongue which can be accomplished by a contraction in the verticalis muscles, and move the tip of the tongue forward.16 These deformations were accurately transfered to the CSPAMM slices, which show deformation consistent with the FE model (Figure 4). 5.2 Effect of Motion Inconsistency on Rotation Estimation Error and Ghost Shear Strains Figure 5 shows the results of head rotation estimation as a function of motion consistency (measured as variance of randomly combined slice sets). As expected, rotation histories
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approximated using an RC slice set with zero variance accurately follows the reference data (encoder information). In contrast, a RC slice set with a variance of 0.50 (°)2 produces an approximation that deviates from the reference. Error from a total of 100 Monte Carlo iterations (the number needed to achieve consistent results) show that both the average error and its standard deviation increase as a function of RC slice set (acquisition) variance. For example, doubling variance from 0.25 to 0.50 (°)2, results in an increase of approximately 50% in mean error, and a similar increase was observed in the standard deviation. Using the relationship in the same graph suggests that a rotation of 5° would, on average, differ from the reference by 0.2° (or 5%) given an acquisition variance of 0.75 (°)2. In the same circumstances, an error as high as 10% would be likely given the standard deviation in approximation error.
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In terms of non-rigid estimation, the results (Figure 6) suggest that motion consistency (per RC slice set variance) has a direct effect on both displacement residual and total artificial shear strain—both of these quantities increased several times with relatively small changes in variance. For example, doubling the variance from 0.25 to 0.50, results in a 53% increase in error, as well as a 20% increase in total artificial strain. This was not the case with phase residual, which, in total, changed by a small amount (less than 5%) indicating that HARP converged fairly well. Nevertheless, since displacement and strain error increased by much more than 5%, the effectiveness of HARP was hampered fundamentally by variance-driven imaging artifacts rather than lack of convergence. These artifacts created separation between the location on which the motion estimation algorithm converged, and the ideal displacement. Note that no strain was applied in the generation of data for the test suite, and all the apparent measured deformation arose from ghost strains. Although the total artificial strain is a conservative measure of error (associated with the sum of maximum ghost strains), the amount of shear expected in a brain deformation experiment in vivo is relatively low,3 which underscores the need for consistent acquisition or implementation of robust strain estimation techniques.
6. Conclusion
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This research described a framework for creating synthetic benchmark data specifically targeted to deformation analysis of the brain and tongue. The approach for integrating realistic imaging and mechanical simulations applies to different types of motion that can be found in other organs. The focus of the study was generating synthetic data to be used as benchmark; thus, the modeling approach did not concentrate on physical accuracy to the same extent as predictive biomechanical models. However, the simulations of tongue deformation follow basic motion that are patterns present during speech production. This indicates the potential for using the methodology for characterizing motion estimation accuracy in this scenario. A demonstration of accuracy characterization was performed in the brain, where the acquisition process was modeled as a stochastic process. The results show a clear relationship between consistency of motion during acquisition and 4D imagebased motion estimation. The relationship was observed in both, rigid head rotation, and non-rigid brain deformation. In both of these cases, error (as deviations in rotation time history, or artificial “ghost” shear strains) increased as motion become inconsistent. These
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finding underscores the need for consistency or robust estimation of spatiotemporal motion estimation.
References
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1. Ibrahim ESH. Myocardial tagging by cardiovascular magnetic resonance: evolution of techniquespulse sequences, analysis algorithms, and applications. J Cardiovasc Magn Reson. 2011 Jul.13:36. [PubMed: 21798021] 2. Osman NF, McVeigh ER. Prince JL Imaging heart motion using harmonic phase MRI. IEEE Trans Med Imaging. 2000 Mar; 19(3):186–202. [PubMed: 10875703] 3. Knutsen AK, Magrath E, McEntee JE, Xing F, Prince JL, Bayly PV, Butman JA, Pham DL. Improved measurement of brain deformation during mild head acceleration using a novel tagged MRI sequence. Journal of Biomechanics. 2014 Jan; 47(14):3475–3481. [PubMed: 25287113] 4. Parthasarathy V, Prince JL, Stone M, Murano EZ, Nessaiver M. Measuring tongue motion from tagged cine-MRI using harmonic phase (HARP) processing. J Acoust Soc Am. 2007 Jan; 121(1): 491–504. [PubMed: 17297803] 5. Gomez-Tobon C, De Craene M, McLeod K, Tautz L, Shi W, Hennemuth A, Prakosa A, Wang H, Carr-White G, Kapetanakis S, Lutz A, Rashce V, Schaeffter T, Butakoff C, Friman O, Mansi T, Sermesant M, Zhuang X, Ourselin S, Peigen HO, Pennec X, Razavi R, Rueckert D, Frangi AF, Rhode KS. Benchmarking framework for myocardial tracking and deformation algorithms: An open access database. Medical Image Analysis. 2013 Jan; 17(6):632–648. [PubMed: 23708255] 6. Fujita S, Dang J, Suzuki, Honda K. A Computational Tongue Model and its Clinical Application. Oral Science International. 2007 Nov; 4(2):97–100. 7. Sanguineti V, Laboissire R, Payan Y. A control model of human tongue movements in speech. Biol Cybern. 1997 Jul; 77(1):11–22. [PubMed: 9309860] 8. Perrier P, Payan Y, Zandipour M, Perkell J. Influences of tongue biomechanics on speech movements during the production of velar stop consonants: a modeling study. J Acoust Soc Am. 2003 Sep; 114(3):1582–99. [PubMed: 14514212] 9. Teran J, Sifakis E, Blemker S, Ng-Thow-Hing V, Lau C, Fedkiw R. Creating and simulating skeletal muscle from the visible human data set. IEEE Trans on Vis and Comp Graphics. 2005; 11(3): 317328. 10. Zajac FE. Muscle and tendon: properties, models, scaling, and applications to biomechanics and motor control. Critical Reviews in Biomed Eng. 1989; 17(4):359–411. 11. Maas SA, Ellis BJ, Ateshian GA, Weiss JA. FEBio: Finite elements for biomechanics. J Biomech Eng. 2011 Jan.134(1) 12. Harandi NM, Woo J, Farazi MR, et al. Subject-specific biomechanical modeling of the oropharynx with application to speech production. IEEE ISBI. 2015 Jul.:1389–1392. 13. Osman NF, Prince JL. Regenerating MR tagged images using harmonic phase (HARP) methods. IEEE Trans Biomed Eng. 2004 Aug; 51(8):1428–33. [PubMed: 15311829] 14. Pan L, Prince JL, Lima JA, Osman NF. Fast tracking of cardiac motion using 3D-HARP. IEEE Trans Biomed Eng. 2005 Aug; 52(8):1425–35. [PubMed: 16119238] 15. McAuliffe MJ, Lalonde FM, McGarry D, Gandler W, Csaky K. Medical Image Processing, Analysis and Visualization in clinical research. IEEE CBMS. 2001 16. Sanders I, Mu L. A three-dimensional atlas of human tongue muscles. Anat Rec (Hoboken). 2013 Jul; 296(7):1102–14. [PubMed: 23650264]
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Author Manuscript Figure 1.
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Tagged MRI simulation. In the brain, the high-resolution undeformed image (a) was synthetically tagged using a SPAMM pattern (b). Deformation fields from mechanical simulations were applied to the tagged volume to impart motion information (c). Simulation of thickness included down-sampling the deformed tagged volume, as well as filtering to recreate spatial averaging (d). In the tongue, the process was identical.
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Head rotation simulation. The rotation histories (a) were obtained from encoder data, and were used to generate synthetic slices at different time points, including t = 0 ms (c) and t = 30 ms (d), which is marked on the rotation history with a star. The test suite consisted of slice sets following all the rotation histories.
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Author Manuscript Figure 3.
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FE model of the tongue. The model's approximate size and shape were similar to the adult human tongue (a). Due to interdigitation, some muscles were represented as shared regions (b,c), which are shown in different colors. Key: T = transverse, V = verticalis, SL = superior longitudinal, IL = inferior longitudinal, SM = surrounding tissue, GG = genioglossus, H = hyoid bone, M = mandible.
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Figure 4.
Simulated tagged MRI slices of tongue motion. Deformation from the FE model (outlined) was used to deform the reference CSPAMM tagged volume (a), according approximated speech utterances, which included: /ә/ (b), /gi/ (c), and /s/ (d). The complete test suite included the images shown and additional slices, which formed 3D slice sets tagged in orthogonal directions.
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Result of the Monte Carlo analysis. In the typical result for two different acquisition variances compared to the reference (encoder data) (a), a higher variance yields less agreement with the true data compared to a lesser value. The relationship between acquisition variance and average error across Monte Carlo iterations suggests that the variance is directly proportional to the mean error (b).
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Effect of motion inconsistency on non-rigid motion estimation. Both, residual magnitude (a), and total artificial strain (b), are quite sensitive to acquisition inconsistency (per RC slice set variance). However, the phase residual increases by a relatively small amount (less than 5%). These relationships indicate that, as variance increased, HARP effectiveness was negatively influenced by image artifacts, rather than lack of convergence.
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