Dentition

This study is based on the complete Hyopsodus skull AMNH 143783 housed at the American Museum of Natural History. The specimen consists in a complete cranium only lacking I1-2 on the left side and C, I3-1 on the right side. The mandible preserves a complete dentition. Its posterior part is broken and the angle, as well as the ascending ramus of the mandible, are missing on both sides. The size of the specimen, intermediate between H. paulus and H. minusculus, and its primitive dental morphology (as described by Flynn [68] ; characters include: absence of molarization of the p4, well developed m1–2 hypoconid, absence of strong preprotocrista on P3–4, absence of strong hypocone on M1–2, absence of strong molar lophodonty) allows referring AMNH 143783 to Hyopsodus lepidus Matthew, 1909. Both a 3D reconstruction of the dentition (Figure S1) and dental measurements (Table S1) are provided in online supporting information. The exact provenance of this specimen remains uncertain, however, the known temporal range of Hyopsodus lepidus is Bridgerian (late Early – early Middle Eocene, [68] ). To our knowledge, this skull has never been figured nor described prior to the present study.
The skull AMNH 143783 was scanned with a high resolution CT-scanner at the American Museum of Natural History. The scans resulted in 1300 slices with dimensions of 990 by 1000 pixels. The slices have a 60.83201 µm thickness and are spaced 60.83201 µm apart; two-dimensional slices were reconstructed from X-rays using Vgstudiomax® (version 1.2; VolumeGraphics GmbH, 2004). The 3D segmentation of bone, endocast and sinuses was performed using Aviso® (VSG); endocast volume has been calculated by surface integration. Measurements were taken with Aviso following the protocol of Macrini [69] , endocast flexure was measured following the protocol of Macrini et al. [14] . Encephalization quotient was calculated both with the equation defined by Jerison [17] and Radinsky [20] : EQ = EV/0.12 (EM)^0.67, and with the equation defined by Eisenberg [39] : EQ = EV/0.055 (EM)^0.74. This latter equation is based on a regression analysis of empirical data from a large sample of extant placental mammal species and confirmed the now widely accepted exponent value of about 0.75 for the scaling of brain size to body size among mammals generally.

Preserved specimens in 70% ethanol were examined for collecting external morphological data. Teeth samples from upper and lower jaws (three lateral teeth from the first series of teeth, right side) were taken and investigated using a stereoscopic microscope. Skin samples measuring 1x1 centimeters were taken from below the first dorsal fin (right side) and analysis of squamation was undertaken using a stereoscopic microscope and Scanning Electron Microscope (SEM) at the Instituto de Biociências, Universidade de São Paulo (IBUSP) and the Electron Microscope Unity, Rhodes University (RU). Terminology for external morphology and colour pattern follows [24 ]. Colouration is described from preserved specimens unless otherwise noted in text. Nomenclature for dentition is according to [25 ]. Terminology for dermal denticles is according to [26 ]. External morphology of the claspers is described following [27 ].

A computer aided design model was created from the CT scan images of the skull of a patient with skeletal class II malocclusion with prognathic maxilla and vertical maxillary excess which were taken at 0.5 mm slice thickness. 3D models of the frontal bone, nasal bone, maxillary bone, zygomatic bone, temporal bone and sphenoid bone were generated individually. Sutures of the craniofacial complex were generated in the model with a width of 0.5 mm [13 ]. Teeth in the maxillary dentition were segmented and modelled individually. The periodontal ligament surrounding the maxillary teeth were modelled with a thickness of 0.2 mm [14 (link)]. DICOM images were generated and converted into STL file format using MIMICS software which were then assembled into a single unit and transferred to ANSYS software (Fig. 1).Fig. 1

Finite element models. a Finite element model with miniplate. b Finite element model with mini-implant

3D model of a Y-type stainless steel miniplate and three mini-screws of dimension 1.5 × 8 mm to be threaded to fix the miniplate to the zygomatic buttress were generated for model 1. For model 2, two separate stainless steel mini-implants of size 1.5 × 8 mm were generated. One was placed in the interradicular space between the premolars at about 3 mm above the cementoenamel junction while the other was placed between the premolar and the molar at about 4 mm from the cementoenamel junction [15 (link)]. The variation in the height of the mini-implants were created in order to deliver a line of force which passes near the center of resistance of the maxillary arch.
Along with the facial bones, a total of five sutures namely the fronto-maxillary suture (FM), zygomatico-maxillary suture (ZM), zygomatico-temporal suture (ZT), zygomatico-frontal suture (ZF) and pterygomaxillary suture (PM) were analysed individually. Apart from the sutures, prime anatomical landmarks such as frontal process, anterior nasal spine, point A, prosthion and maxillary process of zygoma were evaluated separately. The material properties of all structures were assigned as shown in Table 1.Table 1

Material properties

Material	Young’s modulus (MPa)	Poissons’s ratio
Cortical bone	13,700	0.30
Cancellous bone	7930	0.30
Miniplate	103,000	0.33
Miniscrew	10,300	0.33
Suture	68.65	0.40
Tooth	203,000	0.30
Stainless steel	2,059,000	0.30
Periodontal ligament	50.01	0.49

Forces applied were categorized into three levels. (1) 200 g per side, (2) 300 g per side and (3) 500 g per side. The force was applied 45° to the occlusal plane in order to achieve a line of force passing though the centre of resistance of the maxilla which is in the postero-superior aspect of the zygomatico-frontal suture.

Based on the occluding pairs in the posterior teeth (two premolars and two molars), the dentition of each patient was divided into four main occlusal supporting zones. All of the four supporting zones are in contact in class A; one supporting zone is missing in class B, or all of the four supporting zones are absent, but the
anterior region remains intact; and class C has no occlusal contact between the remaining teeth (Figure 1).
This study considered both fully and partially erupted permanent teeth as "present teeth". Moreover, the supernumerary teeth, third molars, pontics of bridge prostheses, and implant-supported superstructures were not counted as the present teeth.