Surface and form analysis

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Surfin’ endocasts: The good and the bad on brain form

Emiliano Bruner and Naomichi Ogihara

Article number: 21.1.1A
Copyright Palaeontological Association, January 2018

Author biographies
Plain-language and multi-lingual abstracts
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Submission: 14 July 2017. Acceptance: 20 December 2017


Digital anatomy and computed morphometrics currently represent basic tools in anthropology, zoology, and paleontology. Despite the user-friendly interfaces of the programs, these methods require a robust expertise in statistics, biomedical imaging, and computer graphics. Geometrical modeling is aimed at normalizing shape variation as to compare forms within a shared reference space. As any other modeling approach, it can be used to test hypotheses or to investigate the structure of sample variation. In both cases, models refer to specific variables and parameters, and they follow numerical criteria that are based on algebraic and conventional rules. If models are interpreted too broadly and confused with the real anatomical elements, conclusions can be seriously biased. This risk can be particularly relevant when dealing with morphometric methods that do not use anatomical references, like sliding landmarks, surface analysis, or voxel-based morphometry. All these techniques are largely employed in craniology, paleoneurology, and evolutionary neuroanatomy. Following these approaches, elements are analyzed as “objects” and not as “anatomical elements,” introducing noise and drawbacks due to the registration processes and to the absence of constraints associated with anatomical boundaries. Downsides can be avoided by interpreting geometric models as specific representations of a set of properties of the original anatomical systems and not as generalized effigy of biological elements.

Emiliano Bruner. Grupo de Paleobiología, Centro Nacional de Investigación sobre la Evolución Humana, Paseo Sierra de Atapuerca 3, 09002 Burgos, Spain. This email address is being protected from spambots. You need JavaScript enabled to view it.
Naomichi Ogihara. Faculty of Science and Technology, Department of Mechanical Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan. This email address is being protected from spambots. You need JavaScript enabled to view it.

Keywords: paleoneurology; morphometrics; shape analysis; surface analysis

Final citation: Bruner, Emiliano and Ogihara, Naomichi. 2018. Surfin’ endocasts: The good and the bad on brain form. Palaeontologia Electronica 21.1.1A: 1-10.

Copyright: January 2018 Palaeontology Association. 
This is an open access article distributed under the terms of Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0), which permits users to copy and redistribute the material in any medium or format, provided it is not used for commercial purposes and the original author and source are credited, with indications if any changes are made.


In the last 20 years, morphometrics has undergone a dramatic development, thanks to computer-based anatomy and statistics. All anatomical fields have been particularly enhanced by such methods and tools, although paleontology (and particularly paleoanthropology) was especially rewarded by the advent of these informatic techniques (Zollikofer and Ponce de León, 2005; Gunz et al., 2009; Weber, 2015). Shape analysis was a major component of such epistemological change, mostly when considering landmark-based approaches, coordinates, superimposition methods, and multivariate statistics (Bookstein, 1991; Rohlf and Marcus, 1993; Adams et al., 2004; Slice, 2007; Mitteroecker and Gunz, 2009). The multivariate analysis of coordinates after spatial superimposition is generally named geometric morphometrics, a field which has experienced a remarkable development in the last two decades (Zelditch et al., 2004). Landmark-based analyses depend on the possibility to localize anatomical points, which must have a set of specific properties. They must have a biological meaning, have a reliable spatial position associated with a finite and punctual location, be present in all the specimens of a sample, be homologous in terms of phylogeny and development, and be associated with stable and rigid anatomical elements. It is apparent that only a limited number of anatomical regions and organs satisfy all these requisites, and it is easy to understand why these methods have been mostly employed to analyze cranial morphology (e.g., Lieberman et al., 2002; Zollikofer and Ponce de León, 2002; Bookstein et al., 2003). Landmark methods were soon also applied to neuroanatomy (Free et al., 2001) and especially to paleoneurology (Bruner et al., 2003; Bruner, 2004), a field that relies on casts of the endocranial cavity in fossil specimens and extinct species to make inferences on brain evolution. Endocranial casts (named “endocasts”) can’t supply information concerning internal brain changes, or aspects other than morphology and macroanatomy, but are useful to evaluate brain size and shape, cortical folding patterns, general brain proportions, and brain-skull spatial relationships (Neubauer, 2014; Bruner, 2015, 2017; Ogihara et al., 2015).

sfigure1Many surveys have been using geometric morphometrics to analyze brain morphology (e.g., Bruner et al., 2010, 2014; Gómez-Robles et al., 2013, 2014), but the elusive brain form is particularly void of fixed anatomical references, a limitation which seriously hampers a comprehensive analysis of its shape variations (Gómez-Robles et al., 2018; Pereira-Pedro and Bruner, 2018). The brain is made of soft tissues, and hence it lacks its “own form”. Its geometry is the result of an inner pressure exerted by blood, and an external tension exerted by the connective tissues attached to the cranial bones. The main macroscopical elements of the cortex are folds, which display an outstanding variation among individuals, which present blurred surfaces and boundaries, and whose associations in terms of functions, ontogeny, or morphogenesis are not known (Van Essen and Dierker, 2007). Because of these limitations, many surveys in evolutionary neuroanatomy have employed a different perspective, trying to escape the conceptual constraints of “anatomical landmarks” (Figure 1).

A first advance was achieved by introducing the so-called “sliding landmarks” (see Bookstein, 1997; Gunz et al., 2005; Perez et al., 2006; Gunz and Mitteroecker, 2013; Ogihara et al. 2014). In this case, landmarks are positioned evenly along a surface or curve, and then superimposed minimizing some algebraic criterion such as spatial distance (Procrustes distance) or spatial deformation (Bending Energy) among corresponding points, allowing their tangential displacement (“sliding”) constrained by the neighboring elements. The introduction of sliding landmarks notably enhanced the geometric morphometric toolkit, with crucial applications in paleoneurology (Neubauer et al., 2009, 2010; Gunz et al., 2010; Ponce de León et al., 2016). A second advance was based not on landmarks but on surfaces, by comparing the overall geometry of 3D objects using different criteria, registration procedures, and numerical approaches (e.g., Specht et al., 2007; Durrleman et al., 2012; Beaudet et al., 2016; Dupej et al., 2018). Sliding landmarks and surface analysis allow a finer geometric modeling of the anatomical forms, extending the resolution and applicability of form morphometrics, mostly in those fields (like paleoneurology) in which the anatomical elements are particularly void of consistent spatial references.

Nonetheless, the mathematics behind these computed approaches is indeed complex and extensive, requiring many operational passages and numerical transformations. This is not a problem when the final results are interpreted as the output of a numerical modeling that is a numerical simulation, which represents some qualities of the original anatomical system (position, spatial relationships etc.) according to specific algebraic procedures. Conversely, it may generate important bias when interpreting these models as a true corresponding representation of the real anatomical elements. Frequently, in the name of fluency, the term “endocranial cast” or “brain spatial model” is substituted for “brain”, and this may lead to stringent statements or generalized conclusions, which tend to confound the rough numerical results with a strict anatomical meaning.


Analyses that are not based on homologous landmarks have two main limitations. The first one regards the amount of algebraic transformation required for these kinds of techniques. Any step is based on registration passages and algorithms, which implies a large chain of crucial methodological choices. The final result is an “ordination” of the original variables (coordinates), which should grant a proper correspondence between forms and areas, but which is sensitive to many operational issues. For example, when dealing with sliding landmarks, different sliding criteria can give different results (Bruner and Bastir, 2009), and attention must be paid when deciding between the available operational alternatives. Procrustes distances are influenced by local variation, while bending energy is responsive to more global changes (Gunz and Mitteroecker, 2013). Every registration procedure can be biased by an uneven distribution of the differences and/or uneven distribution of landmarks (Richtsmeier et al., 2002), but in these cases the risks are even larger, because of the lack of strict anatomical correspondences between spatial units (landmarks or pixels) and their supposed anatomical background. Therefore, when we introduce additional transformations, we are introducing more operational steps within the chain of numerical adjustments, increasing the separation between the rough data and their final synthetic representations. For surface analyses this chain is definitely much larger than for sliding landmarks, and the list of steps which are sensitive to possible biases, errors, or numerical constraints, is much longer. Only a very small percentage of morphometricians (and an even lower percentage of journal readers in general) are competent in all the aspects required to control this dense mathematical background, and hence capable of a full and critical comprehension of the numerical adjustments involved. This limitation is even more significant when considering that in the current scientific literature, the description of such methods is more and more relegated to secondary supplementary online materials, and often ignored by the general readership. All this methodological development has empowered analytical capacity, but it has also incremented pitfalls and drawbacks, which require caution and a constant technological verification from the community.

sfigure2A second limit is inherent to this kind of data. Both approaches (most of all surface analyses) rely on geometric correspondence and not on anatomical correspondence. Geometric correspondence is a good criterion to analyze a 3D object, but implicitly it cannot provide information on anatomical boundaries and proportions. That is, the object is analyzed as “an object”, and not as “a skull” or as “a brain”. Of course, this is true for whatever registration approach (Richtsmeier et al., 2002), but in the case of surfaces or outlines the model is further disconnected from local features of the anatomical system. Spatial variations of the object are then “spread” over the whole surface, and this involves two main consequences. First, there will be a loss of information, because the absence of specific anatomical boundaries will hide local differences (Figure 2). Namely, if we analyze the morphology of distinct anatomical areas together, the final results will depend on an admixture of independent factors, ignoring the respective contributions of the different parts. This is a limitation, but not a bias, when opportunely taken into consideration. The same uncertainty can be observed any time one analyzes pooled variables (including size or volumes) of different anatomical districts. For example, dealing with traditional volumetric comparisons, Semendeferi and Damasio (2000) found a proportional variation of the parieto-occipital cortical block among apes, including humans. They analyzed together the parietal and occipital lobes because of difficulties in separating the two districts, and then properly limited their conclusions to the parieto-occipital block. Nonetheless, many papers subsequently citing that study inappropriately mentioned that allometric analyses had demonstrated constant proportions in the parietal “and” in the occipital lobes. The fact that humans have a reduced primary visual cortex (De Sousa et al., 2010) suggests that the lack of change in the overall parieto-occipital proportions might be instead a hybrid result of increase of the parietal cortex and decrease of the occipital one. A pooled analysis of the parieto-occipital block masks the distinct contributions of the two elements. When dealing with shape instead of volume, the examples can be far more complex and subtle.

sfigure3The second consequence of grouping different elements in morphometric surveys may be more influent, mostly when dealing with shape analysis and registration procedures: without boundaries, shape variation will be equally distributed through the whole spatial model, loading (and smoothing) local changes onto global changes, and artificially displacing the form differences (Figure 3). Namely, a change associated with a specific anatomical element or area will be interpreted as a more extensive and less pronounced morphological variation. In these cases, we have a loss of information but we also have a biased result, which wrongly assumes that all parts have equally contributed to the phenotypic differences. If we are only considering the covariation structure, this effect is less relevant, because the main target is to localize correlations and associations between coordinates, ordering the overall variation according to these hidden rules (Bruner, 2018). But then, when mapping these patterns on graphical anatomical models for visual purposes (as is usually done in geometric morphometrics or surface analysis), the result may be seriously misleading if interpreted too strictly. This is a generalization of the so-called “Pinocchio effect” (Walker, 2000; Klingenberg, 2013), that can bias the final conclusions of a study when semi-landmarks and surface analysis are applied without taking into account the existence of actual anatomical boundaries, particularly on an “object” (the brain) which has an extremely complex topological organization (Glasser et al., 2016).


When distinct parts have different effects on the overall morphological difference, if they are analyzed together their relative contribution cannot be ruled out. Their influences can be artificially mixed, and different phenotypic processes can be confounded if local contributions cannot be properly taken into account. These consequences are proportional to the extent of the lack of anatomical boundaries. Namely, they will be more misleading in cases with few anatomical landmarks and many semi-landmarks, and even extreme in surface analyses, which are generally based almost only on surface matching.

Such limitations of course should not be used to reject the contribution of these morphometric tools, which probably represent one of the major advances in this field in recent years. Quantitative outputs, like warping grids, color maps, or complex dendrograms, are but visual representations of mathematical relationships, as evidenced according to specific algebraic criteria. Thus, those outputs (which are but numerical results) should not be confused with a specific biological effect, or with a specific hypothesis. Instead, those outputs should be used to support or to reject some preceding hypothesis, which must be based on multiple and independent evidence. In absence of a specific hypothesis, geometric modeling is also useful to investigate and “explore” the multivariate structure of a given anatomical variation (Bruner, 2018). However, in this case, conclusions must be based on the actual signal associated with the numerical modeling. That is, results must be interpreted within their methodological constraints, avoiding generalized inferences that go beyond the actual range of the study. A bunch of pixels or a covariance matrix are digital and numerical representations of some properties of a brain, and should not be confounded with the brain itself.

Apart from a proper interpretation of the results, shape analysis in neuroanatomy and paleoneurology should be improved at least in three ways. First, anatomical and homologous landmarks should be included in landmark-based approaches, so as to “anchor” variation according to local changes of real anatomical elements. Second, more information on folding schemes and cortical biology is necessary. The noticeable individual variation of the cortical surface and the lack of a proper knowledge on its functional meaning often hamper a reliable use of cortical landmarks. Cortical variations could be the result of geometrical relationships (Hofman, 2014), connectivity patterns (Van Essen, 1997), and biomechanical constraints (Tallinen et al., 2016). In any case, the scarce information available on variations and the mechanisms of cortical folding is still limiting the application of shape analysis in many brain districts. Third, most of all in paleoneurology, more information on the spatial and morphogenetic relationships between skull and brain can surely add to provide more robust neuroanatomical inferences on extinct species (Pearce et al., 2013; Kobayashi et al., 2014a; Kochiyama et al., 2018). The spatial relationships between brain and braincase can reveal some useful correlations between soft and hard tissues, and quantify the degree of association and reliability between cranial and cortical areas (Kobayashi et al., 2014b; Bruner et al., 2015).

As further cautionary note, it is worth noting that many brain and cranial anatomical traits display a remarkable intra-specific variation, and at the same time minor or subtle inter-specific mean differences. Therefore, large samples are generally required to provide consistent numerical results, able to identify and test, with a proper statistical power, group similarities, or, conversely, distinct patterns. Such large samples, in general, are not available when working with the human fossil record. Accordingly, analyses based on few individuals (or even single specimens) can be central in some cases, but should not be regarded as conclusive.

A final note concerns the use of registration approaches and surface-based analyses to compare brain volumes and parcellations in different groups or subjects, according to standardized atlases and spatial references (Van Essen and Dierker, 2007). While in morphometrics, algorithms and deformation fields are generally used to reveal differences, when working with brain mapping the same numerical transformations are used to eliminate differences, registering the specimens within a shared space (Ashburner and Friston, 2000). Rigid and non-rigid transformations are used to minimize the differences among individuals, so making them comparable within the same system of coordinates. Such transformation is necessary to deal with the considerable inter-individual anatomical and functional variability associated with brain anatomy. In this case, two limitations must be taken into account. The first one is once more associated with the reliability of the large chain of numerical transformation used in these kinds of approaches. Results will depend on the algorithms employed, on the template used as a reference, and on a large set of constraints introduced in the registration process. Therefore, results will be “true” only according to those specific operational and numerical criteria, and are sensitive to many possible bias and mistakes (Gronenschild et al., 2012). The second limitation is due to the principles behind the registration procedures that, in general, are based on spatial information and not on anatomical information. For example, the widely used voxel-based morphometry is a voxel-to-voxel statistic of the grayscale values after registration of brain images within the same spatial framework. This technique is extremely useful to compare global differences in terms of quantitative signals (the proportions and spatial distribution of the grayscale values), but the correspondence between the original and registered morphology is lost. In fact, registration deforms the original images by shrinking and expanding local topology. This normalization, essential to perform population-based mapping and cortical cartography, represents a bias when the final target is a morphometric (form and shape) analysis of the brain districts. All these limitations are part of the method, and they are perfectly acknowledged in the general outlines of these techniques (see Ashburner and Friston, 2000, 2001; Van Essen and Dierker, 2007). Nonetheless, they are often neglected in many specific surveys, when dealing with specific case-studies or with more heuristic explorations.

All these techniques represent a real revolution in neuroanatomy and morphometrics. Nevertheless, such analytical power can introduce major bias when it is not used properly. The more the power, the more the effect can be influential. And, of course, a methodology is not necessarily good or conclusive simply because it is complex or pioneering. Most of these analytical tools and procedures are based on very large operational chains made of assumptions, criteria, and technological devices, which cannot be properly described or verified in every published paper. In all these cases, methods largely rely on citations and previous literature, so requiring a sort of trust and reliance on their efficiency. Caution is required, and competence is the only warranty we have to exploit the exceptional potentialities of these tools, reducing the drawbacks of their limitations.


We are grateful to M. Bastir, A. Gómez-Robles, P. Gunz, A. Beaudet, J. Dupej, O. Kondo and H. Amano for the many debates and collaborations on the topics discussed in this article. This paper has been designed within the Grant-in-Aid for Scientific Research on Innovative Areas “Replacement of Neanderthals by Modern Humans: Testing Evolutionary Models of Learning” from the Japanese Ministry of Education, Culture, Sports, Science, and Technology (#22101006). EB is funded by the Spanish Government (CGL2015-65387-C3-3-P).


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