Investigating muscle coordination patterns with Granger causality analysis in protrusive motion from tagged and diffusion MRI

The human tongue is a multifunctional muscular hydrostat,^1–3 serving critical roles in speech and other lingual behaviors.^4–6 This remarkable muscular hydrostat operates without skeletal support, relying on the coordinated contraction, i.e., muscle shortening along fiber orientations, of multiple sets of muscles aligned in both perpendicular and parallel orientations to the long axis.^1,7 The resulting muscular movement produces successive deformations of the tongue's constant volume,⁸ shaping the vocal tract and generating a diverse array of sounds. The human tongue consists of a number of intrinsic muscles—the transverse (T), verticalis (V), superior longitudinal (SL), and inferior longitudinal (IL) muscles—and extrinsic muscles—the genioglossus (GG), hyoglossus, palatoglossus, and styloglossus muscles—that work together to yield a wide range of tongue movements.^3,9

The muscular hydrostat theory states that the orientation and coordination of these intrinsic and extrinsic muscles, as well as the hydrostatic pressure of the fluid contained within them, enable the tongue to maintain a constant volume while generating movement.¹ As such, any decrease in one dimension is counterbalanced by an increase in another dimension. This is achieved through the contraction and relaxation of various local muscle groups, which cause the tongue to change shape and size.^3,10

The causal relationships among tongue muscles or local muscle groups are crucial for understanding the mechanisms underlying tongue movements during speech or swallowing. There are a few prior studies proposed to investigate the causal relations among tongue muscles or muscle groups. For example, Gilbert et al.¹¹ investigated how the alternation of the T and V muscles during swallowing allows the tongue to translate posteriorly, allowing food to enter the oropharynx. Shinagawa et al.¹² showed that, during protrusion, both the IL and styloglossus muscles stretch anteriorly, lengthen, and align more closely with the resting V-shaped configuration of these muscles, which narrows toward the front. In related developments, Stone et al.¹³ investigated correlations between tongue segments and a few muscles, including the V, T, and GG muscles during speech using tagged MRI and ultrasound. That work identified that these three muscles exhibit strong functional segments and are influenced by phonemic constraints. Woo et al.¹⁰ developed a computational framework using tagged MRI aimed at identifying functional muscle groups within the tongue's local structural elements that operate cohesively and consistently. More recently, Woo et al.¹⁴ further refined the prior work¹⁰ to simultaneously identify common and subject-specific functional muscle groups in a population using tagged MRI.

Understanding the causal predictive relationships among tongue muscles is valuable for a variety of applications, including the development of treatments for speech and swallowing disorders. In addition, understanding the causal predictive relationships among tongue muscles in the context of the muscular hydrostat can also shed light on the biomechanics of movement and muscle coordination in the tongue and other muscular hydrostats more broadly.^15,16 Granger causality analysis¹⁷ is typically the first method used for identifying directed predictive interactions from time-series data. This technique implements a statistical, predictive approach to causality, wherein causes precede and assist in predicting their effects.¹⁸ In this work, we employ Granger causal analysis to investigate the sequential predictive information found in tongue muscle interactions, focusing on five muscles known to contribute to protrusive tongue movements, including the T, V, IL, SL, and GG muscles. We use local strain measurements as input to Granger causal analysis to study their contributions. Our framework is designed to collectively use diffusion MRI and cine/tagged MRI to compute the complex local Lagrangian strain components within the muscle fibers of the tongue during tongue movements. This allows us to assess the geometry of muscle fibers and their motion patterns during tongue activity. These strain measurements are then input to a linear Granger causality model,¹⁷ which facilitates the investigation of pairwise causal predictive interactions among the tongue's internal muscles. While the Granger causality model is not used to determine true causality, analyzing predictive information within time series data with the Granger causality model represents a first step toward understanding the causal relationships among tongue muscle activities.

We acquired both cine/tagged MRI and diffusion MRI from a healthy, male, non-native speaker of English, whose first language does not have the/ə/sound, at the ages of 33 and 42, respectively. For cine/tagged MRI, the participant performed tongue protrusion and a simple speech task, “asa,” while following a metronome sound as an auditory guide during the tasks. The protrusion task required the participant to extend the tongue maximally for a duration of 1 s, synchronized with a metronome-like auditory cue. To acquire a single slice, 2 or 3 repetitions were necessary, resulting in over 20 repetitions for each orientation. Cine/tagged MRI datasets were collected on a Siemens 3.0 T Tim Trio system with a 12-channel head coil and 4-channel neck coil during the protrusion and the simple speech task. The image sequence was obtained at a rate of 26 frames per second with a temporal resolution of 36 ms, which was synchronized with the participant's responses. It is worth noting that both the cine and tagged MR images were acquired within the same spatiotemporal coordinate system. A diffusion MRI dataset was acquired on a Siemens 3.0 T Skyra system with 64 head and neck coils using a single-shot echo-planar imaging readout. The MR imaging parameters incorporated diffusion weighting across a spectrum of 64 distinct gradient vector directions, utilizing a b value of 500 s/mm². The time to echo was 51 ms, the time to repetition was 4800 ms, and the flip angle was 20°. Notably, the in-plane resolution was set at 2 × 2 mm², while maintaining a consistent 2 mm slice thickness. We reconstruct diffusion tensor and visualize the muscle fibers using Trackvis.¹⁹ 

To obtain the tracking results of the tongue during the tasks, we create tongue segmentation masks over time after creating super-resolution volumes from three orthogonal orientations from cine MRI.^20,21 We then use a previously developed phase-based tracking method⁸ to precisely track every voxel within the tongue from tagged MRI. In brief, we first generate high-density 2D slices from sparsely acquired tagged MRI slices using cubic B-spline interpolation, thereby ensuring a comprehensive coverage of all three orientations. Next, a harmonic phase filter is applied to the interpolated data, yielding three harmonic phase volumes. Finally, we use a modified iLogDemons algorithm²² to identify accurate correspondences across time frames for accurate tracking of the motion of the tongue during both protrusion and the speech task. The resulting method yields incompressible motion fields that effectively capture the dynamic motion of every voxel within the tongue.

Our framework to compute Granger causality of internal tongue muscles consists of multiple steps, as shown in Fig. 1. First, in order to localize the five muscles in the diffusion MRI space, we perform diffeomorphic registration between the whole tongue segmentation masks of the previously constructed high-resolution atlas^3,9 and the B0 image in diffusion MRI. Specifically, the use of tongue masks as a reference for diffeomorphic registration²³ facilitates the transfer of the atlas labels originally delineated in high-resolution atlas by a domain expert to the corresponding diffusion MRI space. Of note, this was an automatic registration process, and we did not need manual correction, since the registration was very accurate, as visually assessed.

Third, as a prerequisite to the application of the Granger causality test, it is necessary that the statistical properties of the time series remain stationary. We achieve this stationarity through the application of a differencing function, which is then validated via the Augmented Dickey-Fuller test.²⁶ 

Our imaging data, along with the motion fields and derived displacement and strains along fiber orientations, are presented alongside a Granger causality diagram for both the protrusion and speech task in Figs. 3 and 4, respectively.

In protrusion, the tongue uses second-order deformation, characterized by fairly uniform stretching. The significant relationships among almost all the muscles indicate a unified focus in creating forward thrust. In particular, our findings pertaining to strain patterns over time and pairwise causal relationships align with the muscular hydrostat theory. Analysis of the fiber strain values over time shows three functional groupings: (1) GG, V, and SL; (2) IL; and (3) T. Specifically, the GG, V, and SL muscles experience similar patterns of muscle shortening from the beginning to time frame 13, followed by muscle lengthening in subsequent time frames. In contrast, the length of the T muscle remains relatively constant, serving to resist and balance forces in the left-right direction, consistent with its role as an anchor in the context of the tongue as a muscular hydrostat. Analysis of the Granger causality diagram further reveals that GG is observed to Granger cause V and SL, indicating that GG is precedent in time compared with other muscles, followed by the IL and T muscles during the protrusion task. The T muscle does not shorten or lengthen in the direction of action. Therefore, our data show that, in this protocol, the T muscle acts as an anchoring muscle, stiffening the core of the tongue. It functions as part of a hydrostatic system. In contrast, muscles oriented in the longitudinal direction do shorten and lengthen, enabling movement and performing work.

In the speech task “asa,” the utterance was selected because it begins with a neutral tongue position, followed by a primarily forward movement (i.e., protrusive motion). In this study, we do not consider any speech patterns beyond this specific motion. More specifically, the tongue uses higher-order (local) deformations to shape and position the tip for/s/frication. GG and SL work together to elevate the tip by simultaneously shortening the upper surface (SL) and creating a local bend behind the tip (GG) to support tip elevation. In particular, similar to the protrusion task, analysis of the fiber strain values reveals the same muscle groups: (1) GG, V, and SL; (2) IL; and (3) T. GG plays a significant role in this task as well, predicting the behavior of other muscles, as shown in the Granger causality diagram. The T muscle is affected similarly to the protrusion task, being influenced last. We can observe that the action of GG on T is mediated by SL and IL, indicating an indirect relationship between SL, IL, and T. Both tasks clearly demonstrate that the protrusive action begins longitudinally before transitioning to a transverse movement, where the transverse action serves as a stabilizer. Figure 4(C) shows fewer links between muscles, particularly for SL, compared to Fig. 3(C). During protrusion, SL is tightly linked to V, and Granger causality predicts IL. In “asa,” these relationships disappear, consistent with SL having a very specific goal: to elevate the tongue tip.

In this work, we developed a computational framework with Granger causality to identify sequential and predictive information present among tongue muscles using cine/tagged and diffusion MRI data. Our experimental results, carried out with two types of protrusive movements, suggest sequential muscle coordination patterns; that is, the GG muscle initiates the entire motion, followed by three muscles (IL, SL, and V) ending with the T muscle. To the best of our knowledge, this is the first attempt at carrying out the analysis of the Granger causal model on Lagrangian strains over the course of protrusive tongue movements. To achieve our goal, we utilized a suite of previously developed, well-established techniques, including the tongue MR imaging, image analysis, and motion tracking.

Our results demonstrate that our framework provided not just the theory of muscle hydrostate but also predictive information present in sequence among tongue muscles through Granger causality analysis, which would have been difficult to obtain otherwise. While muscular hydrostats reveal conservation laws rather than temporal sequence or prediction, our Granger causality analysis adds an additional layer to investigate sequential muscle coordination patterns during both protrusion and the simple speech task. Of note, since Granger causality analysis cannot capture true causal relationships, its interpretation leans more toward predictive power. In the context of analysis of Granger causality, it is possible for both time series to Granger cause each other. This does not imply a circular causality, but rather reflects that there may be mutual predictive information between the two time series. This can occur in situations where there are mutual influences between the strain values. For example, in the protrusion task, bidirectional relationships appear between GG and V, as well as between SL and V. In the “asa” task, bidirectional relationships appear between GG and V.

Based on the current research findings, there are a few aspects worthy of deeper exploration in future studies. First, our analysis was limited to two tasks performed by a single healthy participant. Consequently, our findings may be specific to this individual and may not generalize to broader populations. In future studies, we will investigate Granger causal relationships in more complex tasks and across various control or patient populations. Second, in the present work, we specifically examined four intrinsic muscles along with the GG muscle, which are crucial for tongue protrusion. The absence of other muscles in our analysis is partly due to the challenges associated with interpreting the roles of extrinsic muscles using linear Granger causality. These extrinsic muscles, along with the intrinsic muscles involved in the present work, would have more complex interactions and influences that are difficult to capture with our current methodology. Future research will aim to incorporate additional muscles, such as the hyoglossus, palatoglossus, and styloglossus, using more advanced techniques to provide a more comprehensive understanding of lingual articulation. Third, since the tongue muscles are interdigitated with each other, there are confounding factors affecting the analysis. We will develop more advanced techniques to disambiguate the complex relationships among tongue muscles.

Our work can have broader clinical and technical implications. First, in speech or swallowing therapy, our framework can be utilized to aid in developing better therapeutic or rehabilitative regimens. Specifically, if specific causal relationships are identified that are disrupted in individuals with speech or swallowing impairments, this may lead to the development of targeted therapies that can help restore normal tongue function. Second, our framework can be used to inform or corroborate biomechanical simulation designs, accurately reflecting the anatomy and physiology of the tongue during tongue movements.

This work was supported by National Institutes of Health R01DC018511, R01DC014717, and R01CA133015.

The authors have no conflicts to disclose.

The Institutional Review Board at the University of Maryland, Baltimore and Massachusetts General Hospital approved this study. The participant in this study signed the written informed consent with HIPAA compliance.

The data that support the findings of this study are available from the corresponding author upon reasonable request.