Three-dimensional mandibular kinematics of mastication in the marsupial Didelphis virginiana

Abstract

Didelphis virginiana (the Virginia opossum) is often used as an extant model for understanding feeding behaviour in Mesozoic mammaliaforms, primarily due to their morphological similarities, including an unfused mandibular symphysis and tribosphenic molars. However, the three-dimensional jaw kinematics of opossum chewing have not yet been fully quantified. We used biplanar videofluoroscopy and the X-Ray Reconstruction of Moving Morphology workflow to quantify mandibular kinematics in four wild-caught opossums feeding on hard (almonds) and soft (cheese cubes) foods. These data were used to test hypotheses regarding the importance of roll versus yaw in chewing by early mammals, and the impact of food material properties (FMPs) on jaw kinematics. The magnitude of roll exceeds that of yaw, but both are necessary for tooth-tooth or tooth-food-tooth contact between complex occlusal surfaces. We confirmed the utility of the four vertical kinematic gape cycle phases identified in tetrapods but we further defined two more in order to capture non-vertical kinematics. Statistical tests support the separation of chew cycle phases into two functional groups: occlusal and non-occlusal phases. The separation of slow close into two (occlusal) phases gives quantitative kinematic support for the long-hypothesized multifunctionality of the tribosphenic molar.

This article is part of the theme issue ‘Food processing and nutritional assimilation in animals’.

1. Introduction

Mammalian mastication is characterized by rhythmic chewing sequences driven by central pattern generators in the mesencephalon (i.e. midbrain) and modulated by both sensorimotor cortical control and sensory information from the teeth, tongue and oral mucosa [1–9]. The origin of mastication in therian mammals is associated with the evolution of tribosphenic and tribosphenic-like molariform teeth that are capable of more versatile occlusal functions, a key innovation of crown Mammalia, as well as an unfused mandibular symphysis [10,11]. While the functional morphology of the tribosphenic molar is well-studied, the contribution of an unfused symphysis to the evolution of early mammalian mastication is less well understood.

An unfused mandibular symphysis is the primitive state for the common ancestor of crown Mammalia. The symphyseal joint is held together by a fibrocartilaginous pad and series of transverse and/or oblique ligaments. Multiple extant mammalian lineages (e.g. anthropoid primates, perissodactyls, etc.) have convergently evolved partial to full symphyseal fusion [11–14]. The functional and adaptive significance of a completely fused symphysis has long been debated [14–18] and may well be clade-specific [19–22]. For example, pigs and anthropoid primates have convergently evolved fused symphyses with similar masticatory patterns but show differences in mandibular stress and strain during mastication [23]. Relative to fused mandibular systems, the in vivo mechanics of unfused symphyses during mastication remain poorly understood beyond model species such as Rattus and Oryctolagus [24–26], both of which have highly derived craniomandibular morphology and/or masticatory kinematics relative to generalized stem mammals, and hence are of limited utility for understanding the evolution of symphyseal form–function relationships in early mammals.

Current hypotheses suggest that unfused, ligamentous mandibular symphyses can allow semi-independent movement of the two hemimandibles, facilitating precise occlusion of the molars during mastication. This is argued to be especially beneficial for animals in which precise occlusion requires long-axis rotation (i.e. roll) of the working side hemimandible (same side as food bolus) independent of the balancing side hemimandible [27,28]. Independent hemimandibular motion may also be important in animals with antemolar teeth that lock during occlusion (e.g. taxa with large canines), preventing mediolateral movements of the symphysis [12,18,21,29–31]. In support of these hypotheses, Crompton and Hiiemäe [32–34] reported rotation of hemimandibles about their long axes during the occlusal portion of the mastication cycle in Didelphis virginiana. Similar long-axis rotation movement was also observed in pygmy goats [31], the little brown bat [29], and discussed as the only possible mechanism for tooth occlusion in golden hamsters [35]. Most recently, Bhullar et al. [36] argued that independent rolling of the working side hemimandible is the primary driver of transverse (lateral-to-medial) movement of tribosphenic molars during occlusion in Monodelphis domestica. On the other hand, other workers have suggested that hemimandibular rotation about a superoinferior axis (i.e. yaw) is more important for tribosphenic molar function during mastication in early therians [37,38].

Clarifying the relative magnitudes of roll and yaw of hemimandibles with unfused symphyses requires rigorous quantification of hemimandibular kinematics during individual phases in the entire gape cycle, not just during occlusion (figure 1). Moreover, it requires observations spanning multiple food material properties (FMPs), because FMPs are known to impact mandibular movement during mastication in extant mammals with fused symphyses [39], but their impact on jaw kinematics in animals with unfused symphyses is not well documented.

Figure 1.

Definitions of gape cycle phases, coordinate systems and kinematic terminology. (a) Movements of right mandible relative to the cranium during a right-sided chew; anterior view at a coronal section through cranium and mandible at the level of upper and lower first molars. Numbers correspond to numbering in (c). (b) Anatomical terminology on a coronal section through cranium and left mandible. (c) Mandibular pitch (blue), yaw (green) and roll (red), and vertical kinematic gape cycle phases. Shade traces are averages ± 1 s.d. normalized to a gape cycle duration of 100%. Numbers correspond to jaw positions in (a). Rotations in this graph are for the right mandible only. (d) Oblique view of mandibular axes, highlighting pitch (blue). In both mandibles negative pitch is jaw depression (opening), and positive pitch is jaw elevation (closing). Black star indicates the location of the coronal section through the first molar in a and b. (e) Posterior view of left and right mandibles and mandibular axes, highlighting roll (red) conventions for left and right mandibles. Positive roll follows the right-hand rule (clockwise in posterior view), corresponding to eversion of right mandibular toothrow and inversion of left mandibular toothrow. Negative roll is the reverse. (f) Superior view of the left and right mandibles and mandibular axes, highlighting yaw (green). Positive yaw is lingual for right mandible and buccal for left; negative yaw is buccal for right mandible and lingual for left. Origin of the cranial coordinate system is midway between the mandibular condyles (see figure 2b). Data from Opossum Li.

In this paper we examine the three-dimensional hemimandibular kinematics of mastication in D. virginiana. Didelphis retains an unfused mandibular symphysis and has tribosphenic molars similar to those of Mesozoic mammals [40–47]. Our objectives are threefold. First, we propose a modification to the traditional four-phase gape cycle model that can better describe movements of hemimandibles with unfused symphyses. This is crucial for future interspecific comparisons of hemimandibular kinematics, as well as perturbation studies. Second, we quantified the relative magnitudes of roll versus yaw during mastication. We predicted that both roll and yaw of jaws would be constant components of tribosphenic molar movement during occlusion. Third, we quantified the effects of FMPs on hemimandibular chewing kinematics using two foods: cheese and almonds. We quantified these effects throughout the gape cycle, not just during occlusion, because hemimandibular kinematics during non-occlusal portions of the gape cycle are important for bolus handling.

2. Material and methods

Bilateral hemimandibular kinematics were recorded in wild-caught D. virginiana using biplanar videofluoroscopy and the XROMM (X-Ray Reconstruction of Moving Morphology) workflow [48–50]. All experiments were approved by the University of Chicago's IACUC (ACUP 72476). Animals were acquired under permits from the Illinois Department of Natural Resources (Wildlife Capture Permit numbers NH19.6055 (2019), NH20.6055 (2020) and W21.6454 (2021)). Animals were housed at the University of Chicago Animal Resource Center.

Experimental subjects were two male and two female wild-caught individuals with intact and fully erupted dentition. There were no obvious gingival wounds or infections, and no cavities exposed the tooth pulp (table 1). Animals were habituated to the experimental foods before data collection. At least two weeks before data collection, each animal was sedated (20–25 mg kg⁻¹ ketamine), intubated and anesthetized (1–4% isoflurane) for surgical placement of 1 mm tantalum bead markers (RSA Biomedical, certified for use in humans; http://www.umrsa.com/umrsa/marker_insertion.php). Two markers were surgically implanted in each of the right and left zygomatic arches of the cranium, and four were implanted in each hemimandible: two in the symphyseal region, one in the anterior border of the ramus at or above the level of the toothrow, and one on the medially inflected angular process of each mandible. All markers were placed through small incisions and pressed firmly into 1 mm diameter holes drilled in the bone with a small hand-held drill. The skin incisions were sutured closed, antibiotics and analgesics administered, and the animals were fully recovered before being returned to their housing cages. All animals fully recovered without incident.

Table 1.

Individuals and food type chew cycle number.

data collection events		number of cycles
individuals	food	total	right working side	left working side	filters (Hz)
opossum Li	almond	75	36	39	30
	cheese	19	14	4	20
opossum Lu	almond	75	41	34	30
	cheese	40	23	17	30
opossum W	almond	33	13	20	20
	cheese	62	42	20	20
opossum A	almond	24	14	20	20

(a) . Data collection

Kinematic data were collected in the University of Chicago XROMM facility. The subjects were fasted 12 h before data collection, before being put into an opaque plastic box (40 cm × 21 cm × 20 cm) positioned next to the image intensifiers and allowed to settle. Food was placed into the box through a small hole at one end; the animal could choose to eat it or not. While the animal chewed, data were collected at 200 Hz, 900 × 900 resolution with radiographic technique of 10 mA and 70–80 kVp. Animals were presented with a single food item and data collected in 10 s bursts until the terminal swallow. Complete feeding sequences could not usually be collected within the 10 s time limit of the x-ray source, but multiple 10 s bursts could be collected with only 1–2 s between. Trials were selected for analysis if all markers were visible in both frames for the majority of the 10 s interval and not occluded by either the position of the animal or the position of the box.

The animals were fed food items with a range of different material properties. For this study, we analysed data from a relatively soft, deformable food (cheddar cheese) and a brittle food (almonds). Cheddar cheese cubes (2 cm on each side) were chosen to represent a soft substance. Complete, raw shelled California almonds were used as a harder, more brittle substance that had to be broken down before being swallowed (see electronic supplementary material for details). For almond and cheese trials, respectively, the total chew cycle count was 75 and 19 for opossum Li, 75 and 40 for opossum Lu, 33 and 62 for opossum W and 24 for almond (no cheese cycles) for opossum A (see table 1 for working side).

(b) . Data analysis

Marker coordinates were tracked using auto- and manual tracking functions in XMALab version 1.5.5 [49]. Only data where the rigid body three-dimensional error was at or below 0.06 pixels was kept. The rigid body transformations were then low pass filtered (20 or 30 Hz cutoff), exported from XMALab as ‘.csv’ files. Separate data collection events were manually merged in Excel [58], so that multiple sequences could be imported into Maya 2019.3.1 [59] following the XROMM workflow [48–50]. Data were grouped by animal and food type. STL's for each animal were made using CT scans of either the live animal (Vimago L Base version, Epica) or the animal after death (GE Phoenix v|tome|x 240 kv/180 kv scanner). Specimens were scanned with a voxel size of approximately 80 µm at 170 kVp and 130 uA, 1300 projections, averaging of three frames and skipping one.

A rest position for each animal was defined as a time point in data collection when the animal was not feeding, when the symphysis was in the midline, and when gape (pitch) angle was small (see electronic supplementary material, table S1, for rest position values). In each animal, in one frame in which the mandibles were in rest position, we set a midline cranial coordinate system following Orsbon et al. [56] with the origin in the midsagittal plane and level with the top of the two hemimandibular condyles (figure 1 and 2a), and in which both left and right hemimandibular axes systems had the same positive sign. The y-axis (yaw) is oriented superoinferiorly, with superior positive, the x-axis (roll) is oriented anteroposteriorly, with anterior positive, along the midsagittal plane of the cranium, and the z-axis (pitch) is oriented mediolaterally, positive right. All kinematic measurements were made relative to this cranial coordinate system. In Maya, the ‘ORel’ (Output of Relative motion) function was used to measure translations, relative to this midline cranial coordinate system, of the left and right lower first molar talonid basins as well as the superiormost point on the midline of each condyle, midway along mediolateral and anteroposterior lengths (figure 3a1 and a2; see also electronic supplementary material, figures S1–S2).

Figure 2.

Comparison of right mandible kinematics during right chews on cheese and almond by opossum Li. (a) Coronal section through right cranium and mandible showing focal molar features for which translations are presented. Key for kinematic traces: dark solid trajectory lines, average; shaded band, ± 1 s.d. (b) Anterior view of opossum right first lower molar and upper molars. Arrows and descriptions indicate positive rotations for right mandible (cf. figure 1d,e,f) (c) Traces of right working side hemimandibular rotations and m1 talonid basin translations during three complete almond chewing gape cycles. (d–i) The average and ± s.d. rotations and (j–o) the translations of the right working side hemimandible. Traces are measured from the m1 talonid during chewing on almonds and cheese. Thin black vertical lines mark phase transitions. The yellow bar on the right of each graph indicates a two-degree or two-millimeter increment, highlighting different y-axis scales. FC, fast close; SC, slow close; SO, slow open; FO, fast open.

Figure 3.

Right working side almond chew cycles for opossum Li (n = 36). The kinematic data is graphed in three-dimensional space for both right and left condyles (A1, A2, B1, B2) and lower first molars (C1, C2, D1, D2), from both superior (upper box) and anterior (lower box) viewpoints. Condylar and first molar traces are not graphed to scale relative to each other. Coloured dots indicate the position of the molar or condylar point at each phase transition. Gray lines are individual chew cycle traces, while a thick black line on the graph is the average of all shown traces. Dotted lines with an arrow at the end indicate the direction of movement. The reference axis for all traces is the same as all other data presented in this paper. The reference axis is positioned on the base of the cranium, on the basilar part of the occipital and between the mandibular condyles (see figure 2b).

Any cycles that included stage I transport or swallows [60,61], identified if they were over one and a half times the average chew cycle duration, were excluded from our analyses. Relative translations and rotations of the two hemimandibles were exported from Maya into Matlab version R2020b [62] for analysis. Jaw kinematic data were divided into separate chew cycles using maximum gape, i.e. the most negative value of pitch for a given time frame, using the ‘findpeaks’ function in Matlab [62], and each cycle was assigned to right or left chews using lateral translation data from the right lower m1 talonid basin.

Our initial goal was to quantify kinematics using the four standard gape cycle phases described in the literature (see table 2) [29,33,39,63–66]. To do this we used the ‘findpeaks’ algorithm to identify peaks in the inverted second derivative of pitch (i.e. gape angle) relative to time. That is, the algorithm identifies sudden changes in the rate of gape angle increase or decrease over the course of each chew cycle [39,67,68]. Initially, we expected to identify the four phases as often reported in the literature: fast close (FC), slow close (SC), slow open (SO) and fast open (FO). However, when phase cycle transitions were mapped onto the X, Y and Z coordinate traces at the position of the lower first molar talonid basin (cf. figure 3), it was clear that there were more phase transitions than expected. Furthermore, not all phases were identified in all cycles, so order of occurrence could not be applied to identify a phase within a chew cycle.

Table 2.

Summary of masticatory gape cycle definitions. This table's aim was not to completely catalog all proposed masticatory/chew cycle phases, but to provide an overview of the most commonly used phases in the literature, with a focus on definitions for hemimandibular systems. See Ross & Iriarte-Diaz [51] for a more complete overview. VK phases, vertical kinematic phases; defined by peaks in the second derivative (i.e. change in speed) of pitch. Asterisk, definitions associated with VK phases.

To objectively identify these phase transitions, we used a ‘kmeans’ cluster analysis with group number set to three, and with 500 replicates, to spatially group the phase transitions using the second derivative of gape and time dimensions. The ‘kmeans’ algorithm in the Matlab Statistical Toolbox [62] places three ‘centroids’ at three random points within the two dimensions of the data. The algorithm then calculates the distance of each point from each centroid as the sum of the X and Y values between each centroid and a given point (i.e. ‘city block’ or Manhattan distance algorithm). The optimal clusters are those with the smallest within-group distances for all three groups. The newly grouped phase transitions showed smaller standard deviations relative to the pre-cluster analysis data. When the new phase transition groups were mapped onto the X, Y and Z coordinate traces they clustered spatially (figure 3; electronic supplementary material, figures S1–S2), suggesting that this new sorting method reflects a spatial as well as temporal process. Using the acquired phase transition data, we calculated phase duration for each of the six phases in the gape cycle to test for differences between individuals. Phase durations and transition times were then averaged in raw time, as well as expressed as a percent of cycle duration (0–100). Most of the graphed data is presented as chew cycle percentage. See electronic supplementary material, tables S2 and S3, for phase onset and phase transition statistics of post-cluster analysis data.

To measure the relative contributions of roll and yaw to molar movement during occlusion, we summed the absolute value of roll or yaw over the time frame of the ‘occlusal phase’. As mentioned above, not all phases were identified in every chew cycle. Otherwise, occlusion was defined as from the start of SC1 to the end of SC2.

We tested for the effects of food type on jaw kinematics in each phase of the gape cycle using three-way full factorial ANOVAs, testing for interaction effects (see electronic supplementary material, table S4). The factors were ‘individual’ (random), ‘food type’ (fixed) and ‘chew side’ (fixed). Sex had no effect and so was dropped from the analyses. The dependent variables were magnitudes of m1 translations along, and hemimandibular rotations about, the three orthogonal axes in each phase, and the durations of each phase. The metric for magnitude is curve length, which is calculated as the absolute sum of the hypotenuse of a given translation or rotation (the y-value) over a given time step. If a phase change value was absent, that sample was skipped.

3. Results

All movements described below are for the working side hemimandible unless otherwise stated.

(a) . Fast close 1 (FC1)

FC1 begins at maximum gape (circle 1 in figure 1c; dark blue dots in figure 3), from which the working side hemimandible pitches superiorly (gape decreases, blue traces in figures 1 and 2), and the toothrow inverts (red traces in figures 1 and 2). The working side hemimandible also yaws buccally towards the working side during cheese trials but with minimal yaw during almond trials. Both the toothrow and the condyle of the working side translate laterally during FC1; i.e. the condyle slips laterally as the molar displaces buccally (figure 3 A1,A2).

(b) . Fast close 2 (FC2)

FC2 begins when there is a change in pitch velocity before the working side molars near occlusion (red dots in figure 3). In practice, this requires identifying SC1 first and then checking for an additional peak in the second derivative of pitch. When FC2 is not present, FC1 transitions directly to SC1. The transition from FC1 to FC2 often marks the lateral most position of the lower first molar on the working side (figure 2n and o; see also ‘mediolateral movement’ graphs in electronic supplementary material, figures S3–S9). The working side mandible continues to invert and yaw buccally during FC2 as the hemimandibles continue to pitch upward. The working side first molar translates anteriorly by a few mm (figure 3 C1). As the working side mandible nears minimum pitch and begins to move back toward the midline, it decelerates again, indicating the start of SC.

(c) . Slow close 1 (SC1)

The hemimandibles continue to pitch superiorly, but at a much slower rate than in FC1 (circle 3 in figure 1c; yellow dots in figure 3). Raw fluoroscopic images and reconstructions in Maya both show molar cusps interdigitating—intercuspation—suggesting that tooth-tooth or tooth-food-tooth contact has begun. At approximately the beginning of SC1, the toothrow reverses its direction of roll from inversion to eversion, and yaw reverses from the buccal to the lingual direction (figure 2n and o). The first molar and condyle both translate medially during SC1 (figure 3 A1 to B2, yellow to purple dots).

(d) . Slow close 2 (SC2)

At the start of SC2 (circle 4 in figure 1c; purple dots in figure 3), the toothrow continues to evert and yaw continues in the lingual direction. During this phase, roll reverses from eversion to inversion and yaw reverses direction from lingual to buccal (figure 2d–g). Pitch and all three translational dimensions exhibit very little change.

(e) . Slow open (SO)

SO (circle 5 in figure 1c; green dots in figure 3) is the longest phase, taking up roughly 30–40% of the chew cycle (figure 2, ‘SO’ in d-o). The mandible pitches down as the mouth opens (negative pitch). After the start of slow open, roll reverses from inversion to eversion of the toothrow and yaw reverses from buccal to lingual. There is sometimes a second reversal of both roll and yaw approximately halfway through phase in which roll reverses from eversion to inversion and yaw reverses from lingual to buccal. The molar translates inferiorly and slightly posteriorly as the teeth come out of occlusion. Mediolateral translation at m1 is variable and might move first medial and then lateral, or exhibit the opposite behaviour (figure 4n and o). This mediolateral movement can be seen in the three-dimensional trace data (figure 3: purple dots to green dots). There is a slight posteriorly directed translation of the molar, consistent with the widening of gape at slow open.

Figure 4.

Absolute magnitude of roll (red) and yaw (green), anteroposterior (yellow) and mediolateral (blue) translation in different phases of the gape cycle during chewing on two food types. Cheese data includes opossums Li, Lu, and W. Almond data includes A, Li, Lu, and W. Data were calculated as the absolute sum of the length of the line (i.e. the tangent) at each time step for each dimension over the two different time periods. (a) Orientation diagram showing anterior view of a coronal section through cranium and mandible at the level of upper and lower first molars. Axis in the upper diagram is for conception of rotational dimensions only. TX, translation along x-axis (anteroposterior); TZ, translation along z-axis (mediolateral). (b–i) The slow close 1 phase of a chew cycle was considered to be the onset of slow close 1 to the beginning of slow close 2; red, roll; green, yaw. (j–q) The slow close 2 phase of the chew cycle is from the onset of slow close 2 to the onset of fast open; blue, mediolateral translation; yellow, antero-posterior translation. All stacked bar graphs have error bars ± 1 standard deviation from the mean. Outliers were calculated as any value that was more than three scaled absolute deviations from the mean.

(f) . Fast open (FO)

At the onset of fast open (circle 6 in figure 1c; light blue points in figure 3), pitch speed increases. Roll is variable, and the toothrow may invert or evert. There is a slight amount of yaw in the lingual direction that reverses approximately halfway through the phase. The hemimandible at m1 translates posteriorly, consistent with increasing pitch about an axis near the condyle. Mediolateral movement is variable. The onset of fast open clusters closely in three-dimensional space when compared to the other non-occlusal cycles (FC1 and FC2). This is more evident in the almond chew cycles (electronic supplementary material, figure S1). Effects of food type on hemimandible kinematics are discussed below.

4. ANOVA results

There are no food effects on jaw kinematics independent of individual effects; i.e. all food type effects are individual specific (see electronic supplementary material, table S4; only factors where the ‘Probability > F’ is less than 0.005 are reported). During FC1 there are significant interaction effects between food type, individual and chew side on roll and the associated ML translation of the m1, and there are significant individual effects on pitch and yaw magnitudes. During FC2 there are significant interaction effects between food type and individual on pitch magnitudes, as well as interactions between individual and chew side on vertical displacement of the m1 and the associated pitch rotation. During SC1 there are significant interactions between food type and individual on vertical translation of the m1 translation, and significant interactions between food type, individual and chew side on ML translation of the m1. There are also individual effects on phase duration of SC1, as well as significant interaction effects of individual and chew side on vertical translation of the m1 and the associated pitch rotation. Neither food type nor any of the other factors significantly impact jaw kinematics during SC2. During SO there is a significant interaction effect of food type and individual interaction on AP translation of the m1. The duration of FO is significantly affected by individual effects, as is the magnitude of yaw rotation; yaw rotation during FO is also significantly impacted by interactions between food type, individual and chew side.

In sum, food type, individual difference and chew side have three-way interaction effects, and these together have an impact on: roll and mediolateral m1 translation during FC1, mediolateral m1 translation during SC1, and yaw during FO. Food type and individual interaction effects together have an impact on pitch during FC2 and SC1, vertical translation of m1 during SC1, and on anteroposterior m1 translation during SO. Food type does not impact jaw kinematics during SC2.

(a) . Comparing yaw and roll

We compared the magnitude of roll and yaw for both slow close 1 and slow close 2 in four of the six measures, leaving out pitch and superoinferior translation (figure 4). Roll (red bars) is consistently larger in magnitude than yaw (green bars) during SC1 and SC2 (see electronic supplementary material, tables S5 and S6 for two-way t-tests) when the means are statistically differentiable. There is a great deal of variability (i.e. large standard deviations) in the means of both cheese and almond trials for all individuals. Consistent with the ANOVA results, a change in magnitude between SC1 and SC2 for roll, yaw, mediolateral translation and superoinferior translation was dependent upon a combination of food type, individual and chew side. Translational changes were more often different in magnitude between SC1 and SC2 than rotations, with the notable exception of cheese in the mediolateral dimension (z-axis translation), which was not statistically differentiable between SC1 and SC2. During SC1, translational movement of the right or left first lower molar talonid basin (figure 4, two rightmost columns) shows that anteroposterior translations (yellow bars) were greater than mediolateral translations (blue bars), again, with large standard deviations. During SC2 of almond trials (figure 4l–m), there is very little translational movement. During cheese trials (figure 4p–q), the amount of movement was, on average, about the same as SC1.

5. Discussion

(a) . Phase identification and jaw movements during mastication

Hemimandibular kinematics during mastication are more complex and varied than previously reported. The standard four vertical kinematic phases of the gape cycle (FC, SC, SO, FO) do not fully capture the complexity of hemimandibular kinematics in opossums. Further, contrary to Bhullar et al. [36], food type does significantly impact hemimandibular jaw kinematics during chewing, but only in interaction with other factors (chew side and individual). The way that food type impacts jaw kinematics varies between individuals and chew sides.

FC initially proved to be a difficult phase to define objectively because it appeared to often overlap with the beginning of SC. That is, the mandible sometimes showed multiple sharp changes in velocity when only one was expected. This additional acceleration was often approximately midway between maximum gape and the onset of slow close, and thus obviously not part of the occlusal phases. We performed a cluster analysis, constraining the identified points to be clustered to those between the beginning of FC1 and SC2. This cluster analysis successfully distinguishes between phases that contain a subphase transition from those that do not. During the fast close phases, the lower molars rotate from an everted to inverted orientation or they are inverted for all of fast close, as in figure 2e.

SC subdivisions did not require a cluster analysis, as there was always a clear division between SC1 and 2 when we used the second derivative of pitch as the metric for division. Yaw and roll are not consistent indicators of this phase change. Instead, yaw reverses direction from buccal to lingual halfway through SC1. This reversal of yaw mid SC1 is initially counterintuitive, as the translation data show both the condyle and lower first molar moving lingually during SC1 (figure 3 A2 and C2). These paradoxical results are possible because the hemimandible is more mobile caudally (at the condyle) than rostrally (symphysis). Mobility of the symphyseal region is limited by the occlusion of the upper and lower canines and by ligamentous attachments and so cannot move as freely as the mandibular condyle [33,69,70]. Thus, during SC1 lingual translation of the condyle is larger than lingual translation of the symphyseal region, resulting in negative yaw during the second half of SC1, even though the toothrow is translating lingually.

Slow close 2 was the most surprising phase division in our data. Neither yaw nor roll reverses direction at the onset of SC2, but both rotational dimensions reverse during SC2 when translational movement is negligible (compare figure 2d–g with j–o). How is it possible for roll and yaw to both simultaneously reverse direction despite almost no translational movement? We propose that the mandible is rotating around an axis that passes through the condyle and the first molar, an axis of rotation that is oblique to the axes defining both roll and yaw. This rotation resembles that described by Bramble's bifulcral model [71], allowing the ‘rocking’ motion of the lower molar as it occludes with the upper molars in the absence of translational movement (see figure 1a and c, SC1–2). Similar observations have been reported by Bhullar et al. [36]. Again, these motions are possible because the hemimandibles are semi-decoupled from one another, allowing the working side mandible to pivot around the M1 talonid, thus there is little translation during SC2 at the first molar. When the teeth are visualized separate from the rest of the lower jaw, it looks like the ‘grinding’ motion predicted by early researchers of tribosphenic dentition [72,73] and reported by Bhullar et al. [36] for Monodelphis.

These observations have important implications for tribosphenic molar function as well as hemimandibular movement. We observed that the condyles, molar occlusal surfaces and symphysis are constantly moving. However, division of these kinematics into phases is possible based on significant changes in velocities of rotations and/or translations. These changes in velocity often mark significant changes in sensorimotor events—tooth-food contact, end of opening, start of closing—many of which are known to be associated with changes in neural activity [74]. Electromyographic (EMG) and strain gauge data are needed to ascertain the degree to which muscles of mastication are actively controlling this mandibular rotation, and the degree to which it is caused by reaction forces at teeth and condyles. The reversal of roll from eversion to inversion at the start of SC1 is likely due to the addition of reaction forces from the teeth or food to a mandible being pulled medially by masticatory muscles: i.e. we hypothesize that both the vertical slowing of the mandible and the change in roll direction at the start of SC1 are not due to changing muscles activity, but to interaction with the food and upper dentition. The occlusal surfaces of the molars are, at least in part, acting as ‘guides’ for specific, highly replicable and precise occlusal movements, as predicted by previous descriptions of mastication and tribosphenic molars [32]. The absence of food type effects on jaw kinematics during SC2 suggests that occlusal morphology and tooth neurofeedback may be especially important for kinematic control during this phase.

Slow open is the phase in which the tongue engages with the bolus in order to reposition it for the next chew cycle [9]. In this study, during slow open there is a distinctive ‘jerking movement’ towards the midline which can be seen in the translational data during slow open (see figure 3), prompting suggestions to divide slow open into two phases [9]. This movement may be correlated with tongue, hyoid, masseter and internal pterygoid muscle activity seen in EMG studies of opossum mastication [75,76]. In this study, pitch never shows a sharp change in speed during slow open. Thus, by this paper's definition of phase change, there was no evidence for a consistent phase transition within slow open.

At the beginning of FO, the mandible is on the working side (figures 2 and 3) or at the midline. Depending on the individual, the mandible will either move toward the working or balancing side at maximum gape, consistent with the ANOVA results for yaw during FO (see below).

(b) . Kinematic variation and food type

Thexton & Hiiemäe [76] found that timing and magnitude of EMG activity of masticatory muscles in Didelphis was far less variable during chewing on a soft and uniform food than on a harder, more heterogeneous food. Our data show the opposite pattern in the kinematics, with more kinematic variability in the soft cheese cycles than almond cycles (figure 2). Without simultaneous measurement of both muscle activity and jaw kinematics, explanations for these results must be tentative. However, the current data suggest that variability in jaw kinematics during chewing soft food is due to greater variation in joint and/or bite reaction forces than in muscle forces.

(c) . Yaw versus roll

There is ongoing debate about the relative importance of yaw and roll of the hemimandibles during mastication in early mammals. Bhullar et al. [36,77] assert that because roll is greater than yaw during occlusion, roll is more critical for tribosphenic molar function and overall chewing performance among ancestral therians. Grossnickle [37,38] instead asserts that yaw is more prominent in stem cladotherian chewing kinematics on the basis of comparative lever-mechanic analyses. It is important to remember that quantification of hemimandibular or mandibular kinematics using roll, yaw and pitch angles involves projection of a single rotational movement about a moving axis—the finite helical axis—onto arbitrary anatomical axes. This is a common approach in XROMM studies of mammal feeding [36,78,79] and is the approach we took for this paper. However, whether comparisons of relative magnitudes of rotations about these arbitrary axes provide meaningful insight into the mechanical factors driving evolution of mammalian feeding remains to be determined. We argue that given both roll and yaw are universally present in Monodelphis and Didelphis chewing cycles, both kinematic phenomena are necessary for hemimandibular function. This should also be true for stem mammaliaforms. It is not obvious to us why the smaller magnitudes of yaw make them less important than roll. An interesting analogy to consider is that of eye movements. Highly precise vergence movements and small-magnitude saccades are just as important as large-magnitude saccades or large smooth pursuit movements.

Roll and yaw magnitudes show different correlations between occlusal versus non-occlusal phases of the cycle. During the occlusal phases of the chew cycle, neither roll nor yaw magnitudes are affected by food type, working side, individual or any combination of the three. By contrast, roll and yaw magnitudes in non-occlusal phases (FC1, FC2, SO and FO), are affected by these factors. Roll magnitudes are affected by all three factors during FC1, pitch and roll are affected by individual and food type during SO, and yawed affected by individual, and by interactions between all three factors during FO. This suggests that roll and yaw are important for food bolus manipulation during non-occlusal phases. Successful food breakdown likely depends just as much on detection of bolus properties during non-occlusal phases, and on positioning of the bolus prior to occlusion, as it does on mechanics of occlusion itself.

The ANOVA results at the first molar also suggest a bimodal neurofeedback system during mastication. Phase durations (the last two rows in electronic supplementary material, table S4) are significant for part of the occlusal portion of the chew cycle (SC2), while translations and rotations (rows 2–3 and 11–15 in electronic supplementary material, table S4) are significant for the non-occlusal phases of the chew cycle. We hypothesize that jaw kinematics during the occlusal phases are constrained by occlusal morphology and controlled by periodontal ligament afferent feedback, which reflected in the timing of phases, whereas jaw kinematics during non-occlusal phases are more strongly affected by food material property effects on tongue kinematics. Many intrinsic and extrinsic tongue muscles work against the hemimandibles to move food particles and liquids around the mouth. The reaction forces from the tongue muscles result in predicable translations and rotations of the hemimandible.

6. Conclusion

In this paper we analysed the hemimandibular jaw kinematics of four individuals of D. virginiana and found that two of the four traditional vertical gape cycle phases (FC and SC), when identified by the second derivative of pitch (gape), could be further subdivided. FC is divided into FC1 and FC2 when there is an extra change in speed between FC and SC. SC is divided into SC1 and SC2 when there is an extra change in speed between SC and SO. SC2 has very little movement in the translational dimensions, relative to SC1, as the working side mandible pivots around the M1 trigonid. When we examined the relative importance of roll and yaw, we found that the magnitude of roll was consistently 2–3 times greater than that of yaw but roll and yaw are both universally present in chewing cycles and hence likely to be necessary components of hemimandibular movements. We note that both components showed a wide range of cycle-to-cycle variation. ANOVAs showed that neither roll nor yaw is affected by food type, working side, individual, or any combination of the three during the occlusal portions of the cycle (SC1 and SC2). Roll during FC1 shows three-way interaction effects, roll during SO shows food type effects, and yaw during FO shows both individual and for three-way interaction effects. Food material properties only show effects for SI translation at the condyle and roll, both during SO, the phase when the compacted and broken apart food particles are gathered by the tongue in preparation for a swallow, repositioning on the working side toothrow, or a combination of the two. Otherwise, food type only shows effects on chew cycle phases as an interaction effect with both individual and side. Phase duration only shows effects of individual (three-way interaction effects) during SC2. These results support the hypothesis that there are sensory and functional divisions between the occlusal (timing) and non-occlusal (bolus manipulation) phases of the chew cycle in this tribosphenic and hemimandibular system.

Ethics

All experiments were approved by University of Chicago's IACUC (ACUP 72476). Animals were acquired under permits from the Illinois Department of Natural Resources (Wildlife Capture Permit numbers NH19.6055 (2019), NH20.6055 (2020), and W21.6454 (2021)). Animals were housed at the University of Chicago Animal Resource Center.

Data accessibility

Data and MatLab scripts are available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.qrfj6q5n9 [80].

The data are provided in electronic supplementary material [81].

Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors' contributions

K.S.: conceptualization, formal analysis, investigation, methodology, software, visualization, writing—original draft, writing—review and editing; Z.L.: conceptualization, funding acquisition, resources, supervision, validation, writing—review and editing; P.L.: data curation, investigation, methodology, writing—review and editing; S.O.: data curation, investigation, methodology, writing—review and editing; C.R.: conceptualization, data curation, funding acquisition, investigation, methodology, project administration, resources, supervision, validation, visualization, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

Funding for the UChicago XROMM Facility was provided by National Science Foundation Major Research Instrumentation Grants (grant nos MRI 1338036 and 1626552).