Mandibular movements and their control inHomarus gammarus

Summary The skeletal morphology, musculature and innervation of the mandible of the common lobster,Homarus gammarus, are described as a basis for the functional study included in the two subsequent papers.Although the mandible articulation takes the form of a hinge with movement in a single plane, the musculature of the mandible is complex. The main muscles are similar to those ofAstacus (Schmidt, 1915) but some smaller, previously undescribed muscles were found.As forAstacus (Keim, 1915) andCambarus (Chaudonneret, 1956) the mandibular muscles are innervated by two nerve trunks, the inner and outer mandibular nerves. However, differences occur in the branching of these nerves and the muscles which they innervate.A group of sensory cells associated with the posterior stomach nerve (omn 4) are described. It is suggested that these form a proprioceptive organ associated with the hypodermis overlying the lateral mandible articulation.An interesting group of neurones lying at the confluence of nerve branches from omn 2, omn 3, and omn 4 is described.     

Fibroblast growth factor 10 regulates Meckel's cartilage formation during early mandibular morphogenesis in rats

Fibroblast growth factors (FGF) are pluripotent growth factors that play pivotal roles in the development of various organs. During mandibular organogenesis, Meckel's cartilage, teeth, and mandibular bone differentiate under the control of various FGF. In the present study, we evaluated the role of FGF10 in rat mandibular chondrogenesis and morphogenesis using mandibular organ culture and mandibular cell micromass culture systems. The overexpression of Fgf10 induced by the electroporation of an FGF10 expression vector not only altered the size and shape of Meckel's cartilage, but also upregulated the expression of the cartilage characteristic genes Col2a1 and Sox9 in a mandibular organ culture system. Meckel's cartilage was deformed, and its size was increased when Fgf10 was overexpressed in the lateral area of the mandible. Meanwhile, no effect was found when Fgf10 was overexpressed in the medial portion. In the mandibular cell micromass culture, recombinant FGF10 treatment enhanced chondrogenic differentiation and endogenous ERK (extracellular signal-regulated kinase) phosphorylation in cells derived from the lateral area of the mandible. On the other hand, FGF10 did not have significant effects on mandibular cell proliferation. These results indicate that FGF10 regulates Meckel's cartilage formation during early mandibular morphogenesis by controlling the cell differentiation in the lateral area of the mandibular process in rats.     

The juvenile mandible of<Emphasis Type="Italic">Lufengpithecus</Emphasis>

The juvenile mandible ofLufengpithecus lufengensis (PA869) discovered in 1980 at back to latest Miocene lignite rich deposit in Shihuiba Village, Lufeng County, Yunnan Province in southwest of China is described in this study. The specimen was compared with the juvenile mandibles ofSivapithecus, Australopithecus, earlyHomo and extant great apes. Some characteristics of the juvenile mandible ofLufengpithecus indicate that the proportional relation between the length, the height and the thickness of the mandibular corpus are very similar to those of the adult mandible of same species. This Lufeng juvenile mandible is of a 3–3.5 years old female individual.     

The anatomy and physiology of mouthpart receptors in the lobster,Homarus vulgaris

Summary The lower anterior thorax of the lobster contains a set of three proprioceptors, bilaterally arranged, that monitor the movements of structures in the area, in particular the mandible and the lower oesophagus.These proprioceptors have been named mouthpart receptors 1, 2 and 3 (MPR 1, 2, 3). They form a functional whole, with MPR 1 situated at the front, and MPR's 2, and 3, at the rear, of a single ligament that spans the region between, the anterior border of the lower thorax (at the base of the antennary insertion), and the posterior end of the oesophagus. MPR 1 is composed of 4 or 5 sense cells whose dendrites insert onto a small elastic receptor strand, that itself is attached to the main strand. MPR 2 and 3 also insert on receptor strands that attach at the rear of the main strand, but at somewhat different positions and angles.Physiologically these cells are mechanically sensitive, responding in a variety of ways to stretch and displacement of the main strand. In MPR 1 at least one and sometimes two units fire continuously for long periods at very constant frequency. This frequency is modulated by movement, the frequency either rising or falling depending upon whether the mandible is raised or lowered. Other units are phasic, and velocity sensitive. In MPR 2, and 3, phasic and phaso-tonic units are both present, but few continually firing receptors. MPR 1 seems more affected by mandibular movements, MPR 2 and 3 by oesophageal movements.The possible role of these receptors in the control of mouthpart movements, and the activity of the foregut, is discussed.     

Free body analysis,beam mechanics,and finite element modeling of the mandible of Alligator mississippiensis

The mechanical behavior of mammalian mandibles is well‐studied, but a comprehensive biomechanical analysis (incorporating detailed muscle architecture, accurate material properties, and three‐dimensional mechanical behavior) of an extant archosaur mandible has never been carried out. This makes it unclear how closely models of extant and extinct archosaur mandibles reflect reality and prevents comparisons of structure–function relationships in mammalian and archosaur mandibles. We tested hypotheses regarding the mechanical behavior of the mandible of Alligator mississippiensis by analyzing reaction forces and bending, shear, and torsional stress regimes in six models of varying complexity. Models included free body analysis using basic lever arm mechanics, 2D and 3D beam models, and three high‐resolution finite element models of the Alligator mandible, incorporating, respectively, isotropic bone without sutures, anisotropic bone with sutures, and anisotropic bone with sutures and contact between the mandible and the pterygoid flange. Compared with the beam models, the Alligator finite element models exhibited less spatial variability in dorsoventral bending and sagittal shear stress, as well as lower peak values for these stresses, suggesting that Alligator mandibular morphology is in part designed to reduce these stresses during biting. However, the Alligator models exhibited greater variability in the distribution of mediolateral and torsional stresses than the beam models. Incorporating anisotropic bone material properties and sutures into the model reduced dorsoventral and torsional stresses within the mandible, but led to elevated mediolateral stresses. These mediolateral stresses were mitigated by the addition of a pterygoid‐mandibular contact, suggesting important contributions from, and trade‐offs between, material properties and external constraints in Alligator mandible design. Our results suggest that beam modeling does not accurately represent the mechanical behavior of the Alligator mandible, including important performance metrics such as magnitude and orientation of reaction forces, and mediolateral bending and torsional stress distributions. J.Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

Determination of expander apparatus displacements and contact pressures on the mucosa using FEM modelling considering mandibular asymmetries

This paper presents a method for prediction of forces and displacements in the expansion screw of a modified mandibular Schwarz appliance and the contact pressure distributions on the mucosa during malocclusions treatment. A 3D finite element biomechanical model of the complete mandible–mucosa–apparatus set was built using computerised tomographic images of a patient's mandible and constructive solid geometry by computer software. An iterative procedure was developed to handle a boundary condition that takes into account the mandibular asymmetries. The results showed asymmetries in the contact pressure distributions that indicated with precision the patient's malocclusion diagnosis. In vivo measurements of contact pressure using piezoelectric sensors agreed with the computational results. It was shown that the left and right ends of the expansion screw move differently with respect to the patient mandible, even though the expansion screw has an opening mechanism to ensure equal stretching at both ends. The contact pressures between the apparatus and the mucosa vary linearly with applied forces, which can simplify the analysis of the biomechanical behaviour of the expander mandible apparatus. The biomechanical modelling proposed in this paper can be a useful tool to improve malocclusions treatment, safely avoiding the use of forces acting on live structures beyond the biological tolerance, which could result in traumatic effects.     

Mandibular ontogeny in the miocene great apeDryopithecus

The type mandible of Dryopithecus fontani,Lartet 1856, has been discovered to be not fully adult. Its development corresponds in dental age to that of a 6-to 8-year-old chimpanzee. Because of its immaturity, a number of seemingly distinctive features of this mandible (some of which resemble hominids) would have been lost with full adulthood. Closed tooth rows, a recurved canine, and a vertical ascending mandibular ramus are related to the age of the specimen. They therefore do not foreshadow hominid characteristics. It is stressed that consideration of individual age is an important factor in interpreting the dentitions of fossil and extant hominoids.     

Serial homology of the mandible and maxilla in the jumping bristletail Pedetontus unimaculatus Machida, based on external embryology (Hexapoda: Archaeognatha, Machilidae)

The development of the mandible and maxilla is examined with the scanning electron microscope in the Archaeognatha. Serial homology is discussed to elucidate the general construction of the hexapod mandible. The part comparable to the maxillary palp does not develop in the mandible. Thus, the mandible is coxopodal in origin, and not telognathic but coxognathic. The mandible proper is subdivided into two in late embryonic development, and the smaller proximal and larger distal parts are homologized with the maxillary cardo and stipes, respectively, being subcoxal and coxal in nature. The partition into the "mandibular cardo" in which the mandibular monocondyle is formed and the "mandibular stipes" is recognized as a cuticular ridge or the "mandibular basal ridge" in the postembryonic stages including the imaginal. The molar and incisor are comparable in position and homologized with the maxillary lacinia and galea, respectively. The lacinia and galea could be morphologically interpreted as being the endites of the maxillary coxae I and II, respectively, and the molar and incisor might represent the mandibular coxae I and II as their constituents or endites.     

Skeleto‐musculature of the mandible and its function in podocopid ostracodes exemplified by Loxoconcha pulchra (Cytheroidea: Loxoconchidae) and Fabaeformiscandona tyrolensis (Cypridoidea: Candonidae)

A new anatomical interpretation of the skeleto‐musculature of the mandible in podocopid ostracodes is proposed based on ultrastructural observations of Loxoconcha pulchra Ishizaki, 1968 and Fabaeformiscandona tyrolensis (Löffler, 1963). Attachment cells with their numerous microfibers anchor the sclerotized lamella cuticle (chitinous rod) to the outer lamella cuticle via intracuticular fibers. A pan‐shaped structure develops at the attachment area in the outer lamella cuticle and is responsible for the mandibular scar. The sclerotized lamella cuticle is continuous with the dorsal apex of the mandibular coxa, which touches the fulcral point directly without intermediate epidermis. The calcification of the fulcral point starts immediately after ecdysis and this rapid calcification suggests that the fulcral point must play a significant role in functional morphology of podocopid ostracodes. After 3D‐reconstruction of the set of mandibular extrinsic muscles in a podocopid ostracode, we suggest that the fulcral point is a key character for carapace opening by transmitting the force from the mandibular coxa to the valve and at the same time functions as the stable fulcrum for mandibular movement during mastication. J. Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

TGF-beta mediated Dlx5 signaling plays a crucial role in osteo-chondroprogenitor cell lineage determination during mandible development

Transforming growth factor-β (TGF-β) signaling is crucial for mandible development. During its development, the majority of the mandible is formed through intramembranous ossification whereas the proximal region of the mandible undergoes endochondral ossification. Our previous work has shown that TGF-β signaling is required for the proliferation of cranial neural crest (CNC)-derived ectomesenchyme in the mandibular primordium where intramembranous ossification takes place. Here we show that conditional inactivation of Tgfbr2 in CNC cells results in accelerated osteoprogenitor differentiation and perturbed chondrogenesis in the proximal region of the mandible. Specifically, the appearance of chondrocytes in Tgfbr2^fl/fl;Wnt1-Cre mice is delayed and they are smaller in size in the condylar process and completely missing in the angular process. TGF-β signaling controls Sox9 expression in the proximal region, because Sox9 expression is delayed in condylar processes and missing in angular process in Tgfbr2^fl/fl;Wnt1-Cre mice. Moreover, exogenous TGF-β can induce Sox9 expression in the mandibular arch. In the angular processes of Tgfbr2^fl/fl;Wnt1-Cre mice, osteoblast differentiation is accelerated and Dlx5 expression is elevated. Significantly, deletion of Dlx5 in Tgfbr2^fl/fl;Wnt1-Cre mice results in the rescue of cartilage formation in the angular processes. Finally, TGF-β signaling-mediated Scleraxis expression is required for tendonogenesis in the developing skeletal muscle. Thus, CNC-derived cells in the proximal region of mandible have a cell intrinsic requirement for TGF-β signaling.     

Additional mandibles of Rangwapithecus gordoni,an early Miocene catarrhine from the Tinderet localities of Western Kenya

Two catarrhine mandibles and five isolated teeth have been discovered from Early Miocene localities in Western Kenya. One mandible comes from the well‐known locality of Songhor whereas the other is from a newly discovered locality, Lower Kapurtay, located near Songhor. The mandibles both can clearly be assigned to the species Rangwapithecus gordoni based on molar morphology, which is unique among Early Miocene catarrhines. The isolated specimens can be assigned to Rangwapithecus based on their similarities in morphology to the homologues preserved in the two mandibles. These specimens provide important new information about the dentognathic morphology of Rangwapithecus, which is described in detail. The mandible from Songhor (KNM‐SO 22228) represents the first definitive female mandible of Rangwapithecus. The Lower Kapurtay mandible (KNM‐KT 31234) appears to be male but is much smaller than another recently described male mandible of this species (KNM‐SO 17500) and the type maxilla (KNM‐SO 700). These specimens enable a reassessment of the attributions of all other mandibles and isolated lower teeth of Rangwapithecus, and we present a complete hypodigm of the mandibular and lower dental material for the species. Finally, we provide some additions to the diagnosis of Rangwapithecus gordoni based on previously unknown morphology. Am J Phys Anthropol 153:341–352, 2014. © 2013 Wiley Periodicals, Inc.     

Predictive functional ANOVA models for longitudinal analysis of mandibular shape changes

In this paper, we introduce a Bayesian statistical model for the analysis of functional data observed at several time points. Examples of such data include the Michigan growth study where we wish to characterize the shape changes of human mandible profiles. The form of the mandible is often used by clinicians as an aid in predicting the mandibular growth. However, whereas many studies have demonstrated the changes in size that may occur during the period of pubertal growth spurt, shape changes have been less well investigated. Considering a group of subjects presenting normal occlusion, in this paper we thus describe a Bayesian functional ANOVA model that provides information about where and when the shape changes of the mandible occur during different stages of development. The model is developed by defining the notion of predictive process models for Gaussian process (GP) distributions used as priors over the random functional effects. We show that the predictive approach is computationally appealing and that it is useful to analyze multivariate functional data with unequally spaced observations that differ among subjects and times. Graphical posterior summaries show that our model is able to provide a biological interpretation of the morphometric findings and that they comprehensively describe the shape changes of the human mandible profiles. Compared with classical cephalometric analysis, this paper represents a significant methodological advance for the study of mandibular shape changes in two dimensions.     

A comparative study of incisor procumbency and mandibular morphology in vampire bats

The three species of vampire bats (Phyllostomidae: Desmodontinae), Desmodus rotundus, Diaemus youngi, and Diphylla ecaudata, are the only mammals that obtain all nutrition from vertebrate blood (sanguinivory). Because of the unique challenges of this dietary niche, vampire bats possess a suite of behavioral, physiological, and morphological specializations. Morphological specializations include a dentition characterized by small, bladelike, non‐occlusive cheek teeth, large canines, and extremely large, procumbent, sickle‐shaped upper central incisors. The tips of these incisors rest in cuplike pits in the mandible behind the lower incisors (mandibular pits). Here, we use microCT scanning and high‐resolution radiography to describe the morphology of the mandible and anterior dentition in vampire bats, focusing on the relationship between symphyseal fusion, mandibular pit size, incisor size, and procumbency. In Desmodus and Diaemus, highly procumbent upper incisors are associated with relatively small mandibular pits, an unfused mandibular symphysis with substantial bony interdigitations linking the dentaries, and a diastema between the lower central incisors that helps to facilitate the lapping of blood from a wound. In Diphylla, less procumbent upper incisors are associated with relatively large mandibular pits, a completely fused mandibular symphysis, and a continuous lower toothrow lacking a central diastema. We hypothesize that symphyseal morphology and the presence or absence of the diastema are associated with the angle of upper incisor procumbency and mandibular pit development, and that spatial constraints influence the morphology of the symphysis. Finally, this morphological variation suggests that Diphylla utilizes a different feeding strategy as compared to Desmodus and Diaemus, possibly resulting from the functional demands of specialization on avian, rather than mammalian, blood. J. Morphol., 2010. © 2010 Wiley‐Liss, Inc.     

Ontogenetic relationships between cranium and mandible in coyotes and hyenas

Developing animals must resolve the conflicting demands of survival and growth, ensuring that they can function as infants or juveniles while developing toward their adult form. In the case of the mammalian skull, the cranium and mandible must maintain functional integrity to meet the feeding needs of a juvenile even as the relationship between parts must change to meet the demands imposed on adults. We examine growth and development of the cranium and mandible, using a unique ontogenetic series of known‐age coyotes (Canis latrans), analyzing ontogenetic changes in the shapes of each part, and the relationship between them, relative to key life‐history events. Both cranial and mandibular development conform to general mammalian patterns, but each also exhibits temporally and spatially localized maturational transformations, yielding a complex relationship between growth and development of each part as well as complex patterns of synchronous growth and asynchronous development between parts. One major difference between cranium and mandible is that the cranium changes dramatically in both size and shape over ontogeny, whereas the mandible undergoes only modest shape change. Cranium and mandible are synchronous in growth, reaching adult size at the same life‐history stage; growth and development are synchronous for the cranium but not for the mandible. This synchrony of growth between cranium and mandible, and asynchrony of mandibular development, is also characteristic of a highly specialized carnivore, the spotted hyena (Crocuta crocuta), but coyotes have a much less protracted development, being handicapped relative to adults for a much shorter time. Morphological development does not predict life‐history events in these two carnivores, which is contrary to what has been reported for two rodent species. The changes seen in skull shape in successive life‐history stages suggest that adult functional demands cannot be satisfied by the morphology characterizing earlier life‐history stages. J. Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

Dietary correlates of temporomandibular joint morphology in the great apes

Behavioral observations of great apes have consistently identified differences in feeding behavior among species, and these differences have been linked to variation in masticatory form. As the point at which the mandible and cranium articulate, the temporomandibular joint (TMJ) is an important component of the masticatory apparatus. Forces are transmitted between the mandible and cranium via the TMJ, and this joint helps govern mandibular range of motion. This study examined the extent to which TMJ form covaries with feeding behavior in the great apes by testing a series of biomechanical hypotheses relating to specific components of joint shape using linear measurements extracted from three‐dimensional coordinate data. Results of these analyses found that taxa differ significantly in TMJ shape, particularly in the mandibular fossa. Chimpanzees have relatively more anteroposteriorly elongated joint surfaces, whereas gorillas tend to have relatively anteroposteriorly compressed joints. Orangutans were most commonly intermediate in form between Pan and Gorilla, perhaps reflecting a trade‐off between jaw gape and load resistance capabilities. Importantly, much of the observed variation among taxa reflects differences in morphologies that facilitate gape over force production. These data therefore continue to emphasize the unclear relationship between mandibular loading and bony morphology, but highlight the need for further data regarding food material properties, jaw gape, and ingestive/food processing behaviors. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

Anatomy and phylogenetic value of the mandibular and coronoid canals and their associated foramina in proboscideans (Mammalia)

Characters associated with the mandibular canal are differently distributed amongst proboscidean lineages and provide useful information on the systematics and relationships of proboscideans. The aim of this paper is to describe the pattern of the mandibular canal and its associated foramina in proboscideans in order to fully appreciate the extent of interspecific variation of these structures within the group and to discuss its systematic and phylogenetic value. Outgroup comparison indicates that the condition presented by the basal proboscidean Phosphatherium is morphotypic for proboscideans. Primitive proboscidean characters are: the low position of the mandibular foramen, and its crescent‐shaped outline, the occurrence of a coronoid foramen (canal), the occurrence of two lateral mental foramina, the posterior one at the level of (or slightly behind) the posterior margin of the symphysis, the anterior one in a more distal position, the absence of a medial mental foramen (MMF), the mandibular canal set just below the tooth row. The occurrence of a single lateral mental foramen may represent a shared derived character of Daouitherium, Numidotherium, and Barytherium. A unique derived feature of the Elephantinae mandible is the occurrence of a medial mental foramen on the medial side of the incisive part of the mandible. MMFs have never been observed in other proboscideans excluding elephantines. The very high frequency of MMFs observed in Mammuthus meridionalis–Mammuthus trogontherii–Mammuthus primigenius (>93 per cent of the studied specimens) could be considered a synapomorphy of this group. © 2010 The Linnean Society of London, Zoological Journal of the Linnean Society, 2011, 161 , 391–413.     

Functional and morphological correlates of mandibular symphyseal form in a living human sample

Variation in recent human mandibular form is often thought to reflect differences in masticatory behavior associated with variation in food preparation and subsistence strategies. Nevertheless, while mandibular variation in some human comparisons appear to reflect differences in functional loading, other comparisons indicate that this relationship is not universal. This suggests that morphological variation in the mandible is influenced by other factors that may obscure the effects of loading on mandibular form. It is likely that highly strained mandibular regions, including the corpus, are influenced by well‐established patterns of lower facial skeletal integration. As such, it is unclear to what degree mandibular form reflects localized stresses incurred during mastication vs. a larger set of correlated features that may influence bone distribution patterns. In this study, we examine the relationship between mandibular symphyseal bone distribution (i.e., second moments of area, cortical bone area) and masticatory force production (i.e., in vivo maximal bite force magnitude and estimated symphyseal bending forces) along with lower facial shape variation in a sample of n = 20 living human male subjects. Our results indicate that while some aspects of symphyseal form (e.g., wishboning resistance) are significantly correlated with estimates of symphyseal bending force magnitude, others (i.e., vertical bending resistance) are more closely tied to variation in lower facial shape. This suggests that while the symphysis reflects variation in some variables related to functional loading, the complex and multifactorial influences on symphyseal form underscores the importance of exercising caution when inferring function from the mandible especially in narrow taxonomic comparisons. Am J Phys Anthropol 153:387–396, 2014. © 2013 Wiley Periodicals, Inc.     

Relationships between bone mass and micro-architecture at the mandible and iliac bone in edentulous subjects: a dual X-ray absorptiometry, computerised tomography and microcomputed tomography study

doi: 10.1111/j.1741‐2358.2011.00527.x Relationships between bone mass and micro‐architecture at the mandible and iliac bone in edentulous subjects: a dual X‐ray absorptiometry, computerised tomography and microcomputed tomography study Objectives: To compare bone volume, bone mineral density, cortical thickness and bone micro‐architecture in a series of paired mandibular and iliac bone samples analysed by various imagery techniques to see whether relationships exist between the various techniques and between mandibular and iliac bone. Materials and methods: Bone samples from the mandible and ilium were harvested in 20 cadavers and analysed by dual energy X‐ray absorptiometry (DXA), computerised tomography (CT) on a conventional hospital machine and microCT. Results: Significant correlations were found between Hounsfield density obtained by CT, and bone mass determined by microCT but not with DXA values. Cortical thickness measurements were well correlated between CT and microCT. No relationships were found between mandibular and iliac bone, when considering mineral density, cortical thickness, bone volume or micro‐architecture. Conclusion: In clinical practice, CT remains the most appropriate routine means for bone qualitative and quantitative evaluation at the mandible. In this ex vivo study, these results confirm that mandibular bone status does not reflect the axial skeletal one and assist in the placement of implants with dental prostheses in old or osteoporotic patients.     

Sensory innervation monitoring movement and position in the mandibular stylets of the aphid, Brevicoryne brassicae

The sensory innervation of the mandibular stylets of the aphid Brevicoryne brassicae (L.) has been examined by electron microscopy. Two groups of sensory neurones are present in the mandible. Each has two neurones, one with a short dendrite extending into the base of the mandible and ending in the base and another with a long microtubular process which extends 500 m? down to the distal tip of the mandible. The two neurones are enclosed by an ensheathing cell comparable to the trichogen cell enveloping the group of neurones innervating pegs and hairs. This ensheathing cell is supported by extensive electron-dense filaments to form a scolopale and is embedded in the mass of stylet-forming cells at the base of the mandible. The inner segments of the dendrites are anchored to the ensheathing cell by desmosome junctions. Desmosome junctions also bind the microtubular outer segments of the short and long dendrite to each other. There is no evidence of a dendritic sheath enclosing the distal portion of the short dendrite which ends while still in the extracellular space within the ensheathing cell. The microtubular process of the long dendrite extends down the lumen of the mandible enclosed by a close-fitting extracellular sheath which penetrates and is attached to the cuticular wall of the mandible tip. Distally this sheath is thickened on one side. Deflection of the mandible would therefore deform the dendritic membrane asymmetrically because the thin walls of the sheath would bend more than the thick walls. This would exert an unequal mechanical strain on the dendritic membrane which could result in depolarization in response to deflection in a particular direction. The arrangement of the dendrites and their sheaths within the mandible is such that deflection to the right would distort one dendrite in the same way as deflection to the left would distort the other.