**1. Introduction**

The structural and functional asymmetries of the human brain have been extensively studied in the fields of medicine and biology, especially as they relate to handedness and cognitive function [1–9]. The morphological characteristics of the brain surface are pressed into the inner cranium and may be visualized on endocasts, which are casts of the interior portion of a cranium [10,11]. Previous studies have demonstrated that the left and right hemispheres of human endocasts are usually asymmetrical in shape [12]. It is worth mentioning that asymmetries are divided into three categories: directional asymmetry, anti-symmetry, and fluctuating asymmetry [13,14]. The most concerning asymmetry pattern is directional asymmetry, characterized by a consistent directional bias within a population [13,15]. "Anti-symmetry" represents the reverse pattern (direction) of the population's directional asymmetry and is restricted to a small portion of the population. The third type of asymmetry is "fluctuating asymmetry", which means the asymmetry pattern of a character is diverse without a particular direction in a population [15].

A local impression on the internal surface of a skull, resulting from a protrusion of one brain hemisphere relative to the other, has been referred to as "petalia" and may be visible on endocasts [7]. Left occipito-petalias have been frequently associated with right frontopetalias, whereas the directional asymmetries of parieto-petalias and temporo-petalias are inconsistent in different research [16,17]. Petalial asymmetries have been demonstrated to exist in a wide variety of hominids [3,12,15,18,19]. The particular petalia asymmetry pattern

**Citation:** Lin, S.; Zhao, Y.; Xing, S. Asymmetry of Endocast Surface Shape in Modern Humans Based on Diffeomorphic Surface Matching. *Symmetry* **2022**, *14*, 1459. https:// doi.org/10.3390/sym14071459

Academic Editors: Sebastian Ocklenburg and Jan Awrejcewicz

Received: 29 May 2022 Accepted: 9 July 2022 Published: 17 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

with a right-frontal and left-occipital bias, commonly recognized in modern humans and fossil hominins, is considered to be associated with handedness [2,19–22]. Previous studies have also shown that petalial asymmetries differ between males and females, with males having slightly stronger right-frontal and left-occipital lateralization [1,2].

In many cases, protrusions of brain hemispheres are associated with lobar asymmetries. Previous investigations have revealed that the right frontal lobe and the left occipital lobe are frequently wider than the opposite hemisphere in modern humans and grea<sup>t</sup> apes [7,12,23]. Indeed, a prominent geometric distortion of the hemispheres, known as Yakovlevian anticlockwise torque, is frequently observed in human brains and endocasts [7,24]. Specifically, the Yakovlevian anticlockwise torque includes the left-occipital and right-frontal petalias, with the left occipital lobe extending across the midline over the right and wider/larger right frontal and left occipital regions [22]. More recently, endocasts of the genus *Homo* have revealed that the right hemisphere often has a greater surface area than the left, while the right parieto-temporal lobe and the left occipital lobe have larger surface areas than their contralateral regions [4]. In addition, the asymmetries of the cerebellum and temporal lobe have also attracted attention, though relatively little is known about what their structural asymmetries may reflect [25].

The study of the brain lateralization associated with language was one of the most profound discoveries for neurobiology and linguistics. The leftward asymmetry of Broca's area, as a motor speech area, including the pars triangularis and pars opercularis of the inferior frontal gyrus, was first identified by Broca in 1861 [26]. Functional magnetic resonance imaging (fMRI) studies have provided more evidence for the specialization of the left hemisphere for language [5,27]. Broca's area is referred to as Broca's cap on an endocast, representing a "protrusion of the orbital portion of the inferior frontal gyrus" [28]. Since the emergence of genus *Homo*, it is generally accepted that the left Broca's cap is larger and more prominent than the right [29–31]. Recently, a landmark-based quantitative study of the asymmetry of the third frontal convolution in endocasts suggested that the left Broca's cap of modern humans, although smaller in size, is more globular and better defined than the right side [32]. Wernicke's area is responsible for language comprehension and mainly includes the posterior portion of the superior temporal gyrus and middle temporal gyrus, as well as the inferior parietal lobule, which includes the angular gyrus and supramarginal gyrus [24]. Due to the lack of homologous anatomical markers, Wernicke's area is not well defined on endocast surfaces and displays an unclear pattern of asymmetry [5,33–35]. Generally, though, the planum temporale (the main cortical area of Wernicke's area) is larger on the left hemisphere than on the right [36–38].

As mentioned above, most of the work on the asymmetry of endocasts has been focused on the degree of anterior or posterior protrusion, the lateralization of some regions associated with speech (e.g., Broca's cap), or the relative width and area of frontal and occipital lobes [39]. Moreover, previous research usually compared the human endocast with that of grea<sup>t</sup> apes or other primates to reveal a shared directional asymmetry pattern or a particular characteristic rather than conduct a global comparison of the entire brain surface [3,12,32,40]. The breadth of endocast asymmetry patterns within modern humans remains unclear.

Due to methodological limitations, it is difficult to comprehensively quantify the asymmetry of an endocast's entire surface. Previous studies typically relied on morphological descriptions, linear measurements, and geometric morphometrics [41–44]. The development of a landmark-free surface deformation method, diffeomorphic surface matching (DSM), provides interesting research opportunities for evaluating morpho-architectural variation on endocasts [45–47]. Compared with geometric morphometrics, DSM does not rely on the definitions of landmarks and semi-landmarks to capture the shape of the whole anatomical structure and can dynamically display the shape variation among different specimens [45–47]. Analytic results based on DSM indicate that endocasts of *Australopithecus africanus* (Sts 5 and Sts 60) display a more elongated frontal bec and a substantially less elevated parietal area, different from those of genus *Homo* [46]. Visualizations of sulcal patterns have contributed

more information to taxonomic identification in Old World monkeys [45]. Additionally, this deformation-based approach has been applied to dental materials and the vestibular apparatus [48,49]. However, no studies focusing on the morphological asymmetry of endocasts in modern humans have ye<sup>t</sup> used this landmark-free method.

In the present study, 58 endocasts of archaeological modern Chinese crania were virtually reconstructed with high-resolution computed tomography and three-dimensional virtual technology. Landmark-free diffeomorphic surface matching analysis was performed to quantify and visualize the shape variation of the endocasts. We aim to quantify individual variation in the asymmetry of the endocast surface shape and analyze the variation of asymmetry patterns between the left and right hemispheres within the modern human population, as well as tentatively discuss the correlations between the structural and functional asymmetry of human brains.

## **2. Materials and Methods**
