Folia Morphol. Vol. 80, No. 3, pp. 625–641 DOI: 10.5603/FM.a2020.0149 O R I G I N A L A R T I C L E Copyright © 2021 Via Medica ISSN 0015–5659 eISSN 1644–3284 journals.viamedica.pl Unification of frequentist inference and machine learning for pterygomaxillary morphometrics A. Al-Imam1, 2 , I.T. Abdul-Wahaab1, 3, V.K. Konuri4, A. Sahai5, 6, A.K. Al-Shalchy7, 8 1Department of Anatomy and Cellular Biology, College of Medicine, University of Baghdad, Iraq 2Queen Mary University of London, the United Kingdom 3Department of Radiology, College of Medicine, University of Baghdad, Iraq 4Department of Anatomy, All India Institute of Medical Sciences, Raipur, Chhattisgarh, India 5Dayalbagh Educational Institution, Deemed University, Dayalbagh, Agra, India 6International Federation of Associations of Anatomists, Seattle, United States of America 7Neurosurgical Unit, Department of Surgery, College of Medicine, University of Baghdad, Iraq 8The Royal College of Surgeons, United Kingdom [Received: 17 September 2020; Accepted: 24 November 2020; Early publication date: 30 December 2020] Background: The base of the skull, particularly the pterygomaxillary region, has a sophisticated topography, the morphometry of which interests pathologists, maxillofacial and plastic surgeons. The aim of the study was to conduct ptery- gomaxillary morphometrics and test relevant hypotheses on sexual and laterali- ty-based dimorphism, and causality relationships. Materials and methods: We handled 60 dry skulls of adult Asian males (36.7%) and females (63.3%). We calculated the prime distance D [prime] for the imaginary line from the maxillary tuberosity to the midpoint of the pterygoid process between the upper and the lower part of the pterygomaxillary fissure, as well as the parasagittal D [x-y inclin.] and coronal inclination of D [x-z inclin.] of the same line. We also took other morphometrics concerning the reference point, the maxillary tuberosity. Results: Significant sexual as well as laterality-based dimorphism and bivariate correlations existed. The univariate models could not detect any significant effect of the predictors. On the contrary, summative multivariate tests in congruence with neural networks, detected a significant effect of laterality on D [x-y inclin.] (p-value = 0.066, partial eta squared = 0.030), and the interaction of laterality and sex on D [x-z inclin.] (p-value = 0.050, partial eta squared = 0.034). K-means clustering generated three clusters highlighting the significant classifier effect of D [prime] and its three-dimensional inclination. Conclusions: Although the predictors in our analytics had weak-to-moderate effect size underlining the existence of unknown explanatory factors, it provided novel results on the spatial inclination of the pterygoid process, and reconciled machine learning with non-Bayesian models, the application of which belongs to the realm of oral-maxillofacial surgery. (Folia Morphol 2021; 80, 3: 625–641) Key words: artificial intelligence, cerebral dominance, laterality, masticatory apparatus, osteology, pterygoid process, pterygopalatine fossa, stomatognathic system Address for correspondence: Dr. A. Al-Imam, 2601 Chemin de la Canardière, QC G1J 2G3, Quebec, Canada, tel: +1 (581) 700-0110 [Canada], +964 (0) 771 433 8199 [Iraq], e-mail: [email protected]; [email protected] This article is available in open access under Creative Common Attribution-Non-Commercial-No Derivatives 4.0 International (CC BY-NC-ND 4.0) license, allowing to down- load articles and share them with others as long as they credit the authors and the publisher, but without permission to change them in any way or use them commercially. 625 Folia Morphol., 2021, Vol. 80, No. 3 INTRODUCTION the pterygomaxillary fissure. We shall also estimate The pterygomaxillary region and the maxillary the posterior-superior-medial three-dimensional alveolus are unique from the anatomical and clinical (3D) inclination, i.e., the parasagittal (x-y plane) standpoint and can be affected by several pathologies and the coronal (x-z plane) inclination, of the line [40, 46]. Besides, these regions have peculiar biome- connecting both points. Morphometry will also chanical properties, blood supply, as well as lymphatic include other covariables, including the distance drainage [36]. They neighbour and communicate with from the maxillary tuberosity to the pterygoid ha- some critical areas, including middle cranial fossa, mulus, the greater palatine foramen, the centre of the pterygopalatine fossa, the adjacent part of the the cruciform suture, foramen ovale, and foramen base of the skull, the carotid sheath, the nasopharynx spinosum. We shall implement non-Bayesian sta- and the “danger triangle” of the face [25]. Follow- tistical inference and machine learning models to ing a posterior maxillary molar tooth extraction, the test three hypotheses. The first two will examine the management routinely involves dental prostheses and potential sexual dimorphism and laterality-based implants. The implant site may require bone graft- differences in connection with our morphome- ing techniques that involve the maxillary tuberosity try. The third hypothesis will attempt to explore and the pterygoid process of the sphenoid bone, to patterns of causations and the interaction effect ensure an implant that closely resembles the nor- among different explanatory factors with a par- mal anatomy and attains biomechanical stability [2]. ticular interest in explaining the variables affecting The clinical applications for studies on morphome- the 3D inclination of the pterygoid process relative try and pathologies affecting the pterygomaxillary to the maxillary tuberosity. We will also discuss junction are valuable for traumatology physicians, the relevant evolutionary lines of the skull, clinical oral and maxillofacial surgeons, plastic surgeons and applications in oral and maxillofacial surgery, as dentists [2, 11]. well as reporting anecdotal pathologies of interest. The configuration of the skull is mainly deter- Following a pragmatic review of the literature, we mined by the development of the brain and the confirm that our study is first of its kind regarding masticatory apparatus and the relationships between its objective and methodology. the brain capsule and the latter [26]. In mammals, We opine that the present study is novel for five the cranial cavity grows with the enlargement of reasons. Firstly, our study is the only one in the litera- the brain and approaches the nasal cavity [14]. In ture to address the spatial inclination of the pterygoid humans, the nasal cavity altogether with the facial process in relation to the maxillary tuberosity within part of the skull, moves under the braincase, not only the Asian population. Secondly, we are approaching because of the evolutionary expansion of cerebral our research question using an unprecedented meth- hemispheres but also due to the reduction of the odology, in anatomical sciences, by implementing and masticatory apparatus [27]. These features distin- contrasting classical non-Bayesian statistics versus guish the human skull from the skulls of the lowest machine learning techniques. Thirdly, we implement- mammals as well as anthropoid apes [13]. In animals, ed several models of regression analytics, multivariate the sphenoid bone forms as the result of the fusion tests, and neural networks to attempt finding the of several bones that coexist independently [34]. It, model that best describe and explain the pterygomax- therefore, develops as a mixed bone from several illary morphometrics of interest. Fourthly, we argue paired and unpaired foci of ossification merging at that this robust approach in analysing data is external- the time of birth into three parts, which, in turn, fuse ly valid and replicable by other researchers, thereby, to form a single bone by the end of the first year of serving as a foundation of future research within the neonatal life [30]. discipline of anatomical and morphological scienc- The primary objective of the current study is to es. Finally, we are analysing our research question and measure several morphometric parameters for the study objectives not only from an anatomical sciences pterygomaxillary region, considering various ana- perspective but also from the viewpoint of evolution- tomical landmarks. Morphometry will principally ary biology and comparative anatomy, which renders include measuring the distance from the maxillary our research genuinely interdisciplinary, combining tuberosity to the midpoint of the pterygoid process aspects of human anatomy, vertebrates’ evolution, located between the upper and the lower part of data science, and artificial intelligence. 626 A. Al-Imam et al., Pterygomaxillary morphometrics MATERIALS AND METHODS recorded the distance from the maxillary tuberosity Ethics and code of conduct, the osteology to the pterygoid hamulus (D [hamulus]), the greater sample, morphometry and tools palatine foramen (D [greater palatine foramen]), the The study was conducted following the stand- centre of the cruciform suture (D [cruciform suture]), ard protocol of Ethics and Scientific Committee of foramen ovale (D [ovale]), and foramen spinosum the College of Medicine (study protocol 155-19 on (D [spinosum]). We used Neoteck aluminium digital 29 December 2019), the declaration of Helsinki by angle finder protractor and a digital protractor ap- World Medical Association, the European Union (EU) plication (Toolbox pro v5.4.0), which is