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Virtual Anthropology and Biomechanics

  • Gerhard W. Weber
Living reference work entry

Abstract

The scarcity of fossil hominins imposes the obligation to extract as much information as possible from the few existing remains. Virtual anthropology exploits digital technologies in an interdisciplinary framework to study the morphology of specimens in 3D and 4D. It can contribute to this aim because structures are easily accessible, powerful morphometric analyses can inform about intragroup and between-group form and shape variation, data manipulations and reconstructions become more reproducible, and sample sizes can be increased via sharing of electronic data. The six main areas of virtual anthropology – digitize, expose, compare, reconstruct, materialize, and share – are introduced in this chapter. Biomechanics on the other hand allows inferring certain aspects of function via the study of loadings in structures. Though an efficient formal bridge between those two domains is still missing, there are many overlaps and cross-fertilizations visible, possibly leading into a “virtual functional morphology” to better understand evolutionary adaptations.

Keywords

Finite Element Analysis Rapid Prototype Fetal Alcohol Syndrome Functional Morphology Geometric Morphometrics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Introduction

When the first hominin fossil (later classified as Neanderthal) was found in 1829 by P.C. Schmerling at Engis/Belgium and described by him soon thereafter (1833), there was no such science as paleoanthropology. Not even a proper idea of evolution had been formulated by then, though it was spooking in the head of some enlightened already. This comes as no surprise since the appreciation of human evolution just makes sense if one accepts the changeableness of species and populations – a frightening idea for some against the safe harbor of religious beliefs.

Schmerling recognized that the fossil remains he found were different from what he knew as anatomist and would belong to a “primitive species” (1833, p. 124). Though he was, e.g., impressed by the size of teeth, he had of course no good means to capture size and shape quantitatively to be compared against other populations. T. H. Huxley later used (1863) Engis and the famous calotte from the Neanderthal to argue for Darwin’s ideas. Today, in the second decade of the twenty-first century, we have developed a great many of machines and methods to extract information of all kinds from fossil material so that the approaches of the nineteenth century – describing form mainly qualitatively or adding only a few quantitative measurements – are becoming more rare.

Paleoanthropology tries to settle questions (Henke 2007) like what distinguishes us from our next living relatives, when and where did humans branch off from the other primate tree, which ecological framework enabled the process of becoming human, how many and which hominins were out there, and how did we develop our specific traits like bipedal locomotion or language? The main challenge in our science is that there are only so few sources of evidence available to answer these questions. And even if the number of discovered fossils has increased impressively in the last few decades, we cannot nearly hope to close the gaps in the record or collect representative sample sizes. In the evolutionary sciences, we can only model populations and processes with more or less confidence.

This scarcity of material imposes the obligation to extract as much information as possible from the few existing remains. We have to think hard about experimental designs, methods, and collaborations with other sciences to match this claim. Who would have thought 50 years ago that we would have the complete sequence of the Neanderthal genome (Prüfer et al. 2014) or that the shape of the tiny semicircular canals in the inner ear (Hublin et al. 1996) would suggest a species assignment? If we consider paleoanthropology as a part of the natural sciences (Tattersall and Schwartz 2002), on the other hand we need to follow its rules, i.e., that explanations must come from observations that can be repeated and confirmed by other researchers. This requires eliminating subjective opinions and irreproducible results. Otherwise paleoanthropology is indeed nothing else than a narrative science – a story telling in the sense of Landau (1984). Consequently, we have to walk the thin line between exploiting every possible bit of information stored in a fossil, but not exaggerating its interpretation and keeping in mind the uncertainty that comes attached to our data. Darwin himself recognized the poisonous influence of erroneous data (1871, vol. II, p. 385): “False facts are highly injurious to the progress of science, for they often long endure; but false views, if supported by some evidence, do little harm, as every one takes a salutary pleasure in proving their falseness; ….”

Quantitative data and computer environments offer the advantage that every manipulation becomes obvious, at least it can be made public, if that is the intention. In this sense, virtual anthropology and also biomechanical simulations have the potential to make a step toward reproducibility and, of course, toward sharing ideas and data with the speed of light. This does not guarantee proper investigations. The machines and algorithms will only produce results as intelligent as the researcher has designed the analyses. Critical reflection is important and necessary. T. White put it to the extreme when he said in his Millennium essay (2000, p. 288): “The careerist leaps on each passing technological bandwagon. […] Results can be instant, irreproducible, and irrelevant. When applied without appropriate biological background, they simply muddle fundamental issues in human evolution .” We have indeed to take care that methods and machines are used advisedly and that researchers understand the prerequisites and limits of their use. However, there are enough documents in support of useful applications out there and also White and colleagues later used the toolkit of virtual anthropology to describe and analyze their fossils (e.g., Suwa et al. 2009).

Virtual anthropology (VA) exploits digital technologies and pools experts from different domains such as anthropology, paleontology, primatology, medicine, mathematics, statistics, computer science, and engineering . VA, as the author here defines it, deals mainly with the functional morphology of recent and fossil hominoids. Its methods can, of course, be applied in a much broader sense, e.g., for other primates, mammals, vertebrates and invertebrates, and even for plants or tools. The term “virtual anthropology” was coined in the mid-1990s and first published in 1998 (Weber et al. 1998) when computer power and software became available to work reasonably with digital 3D data – though still at enormous expenses. The term is just one of several (e.g., computer-assisted paleoanthropology; Zollikofer et al. 1998) to mark the onset of a new approach in the field of biological anthropology – performing morphological analysis by means of digital data in a computer environment. Many people have contributed to pioneer this field, e.g., Fleagle and Simons (1982) using computed tomography (CT) to study long bones of an Oligocene primate; Wind (1984) investigating the famous Pithecanthropus IV fossil from Java; G. Conroy and M. Vannier with their first attempt to electronically remove matrix from a fossil scan to investigate the cranial cavity (Conroy and Vannier 1984), and a little later (1987) to determine the dental development of the Taung child; Spoor et al. (1994) revealing inner secrets of the bony labyrinth; and Zollikofer and colleagues (1995) virtually reconstructing Neanderthals and other fossils. The first paleontologist using radiological methods to study hominin fossils, though not digitally, was D. Gorjanovic-Kramberger who published on inner details of the Krapina material (1902) only 7 years after W. Röntgens discovery of X-rays. For a more comprehensive history of the field, see, e.g., Spoor et al. (2000) or Weber and Bookstein (2011a).

In modern paleoanthropology it is beyond any discussion to use the merits of machine power and simulations. But what did we gain after all? Based on the most striking differences to traditional approaches, namely, that virtual copies are used (which derive from digitization processes such as computed tomography or surface scanning , see below) and that these data can easily be analyzed in 3D or 4D within a computer environment, some crucial advantages resulted:
  1. 1.

    The accessibility of the entire structure, including usually hidden features, e.g., the braincase, the sinuses, the dentin of teeth, the medullary cavities of long bones, or the heart including its chambers

     
  2. 2.

    The permanent availability of virtual objects (24/7) on hard drives or servers

     
  3. 3.

    The possibility of obtaining a dense mesh of measurements across the whole geometry for powerful quantitative analyses of form and function

     
  4. 4.

    The great range of options for data handling, statistics, visualization, and data exchange for increasing sample size

     
  5. 5.

    The increased reproducibility of procedures and measurements, a fundamental requirement of science, as mentioned above

     

It is noteworthy to say that the approach is not restricted to questions in paleoanthropology, though this is the main focus of the current article. Medical applications and comparable studies on living primates have arisen (see below), and tools and artifacts can be analyzed in the same manner (cf. Weber 2013). Talking about fossils, however, needs some extra words on the limitations. Although a fossil appears to be a simple static object, a piece of stone of some specific shape, it may convey a rich variety of data, for instance, with regard to macroanatomy (e.g., the shape of the cranial vault, jaw, or teeth), microanatomy (e.g., the orientation of trabecular structures or the prisms of dental enamel), taphonomy (e.g., the degree of mineralization, the presence of cut marks), individual life history (e.g., traumata and pathologies, incorporated trace elements), or perhaps genetics (ancient DNA from cell mitochondria or nucleus). A virtual fossil currently only contains a small fraction of this information, mostly concerning macroanatomy (and occasionally, depending on the resolution, microanatomy), and probably taphonomy and life history. In the case of volume data, e.g., CT, there is no color or texture information. In the case of surface data, there is information on texture and color together with the digitized surface, but there are no internal structures beneath the surface. Other data channels are missing entirely most often, for instance, a virtual fossil usually does not provide any information on DNA or trace elements. Virtual fossils are thus not intended as a substitute for real fossils. They are useful for specific purposes only: to work on all kinds of aspects with regard to shape and form of the whole structure or its parts. And it is advisable in many cases to look at the original or a premium cast during work since our senses are not well adapted to rely on screen simulations only.

While virtual anthropology was quite an exclusive endeavor in the 1990s, today the demands fall within the feasible range of a medium-cost lab. The most typical infrastructural and personal requirements for a VA lab are fast PCs with multiple core processors; high-end graphics cards (such as those that gamers use); big storage systems (often underestimated in costs); software for image processing, 3D manipulation and visualization, programming, and statistics; and staff to handle all these components. The team would ideally combine people with training in biology, anatomy, mathematics, statistics, programming, physics, and radiology. Devices for data acquisition do not have to be in the same lab or university, but they should be accessible conveniently, as via collaborations.

Virtual anthropology can be divided, with overlaps of course, into six operational areas (Fig. 1):
Fig. 1

The six operational areas of virtual anthropology: Digitize (top left) – an original specimen and its virtual copy (Stw 505). Compare (top middle) – landmarks and curves to capture the shape of a face. Materialize (top right) – upscaled transparent stereolithographic model of an australopithecine tooth (Photo by R. Ginner). Share (bottom left) – example CD-ROM from the digital@rchive of fossil hominoids. Expose (bottom middle) – Magnetic Resonance Tomography, segmented brain, and transparent head. Reconstruct (bottom right) – undeforming parts of an australopithecine skull using reference data (Sts 71, reconstruction by P. Gunz)

  1. 1.

    Digitize – mapping the physical world

     
  2. 2.

    Expose – looking inside

     
  3. 3.

    Compare – using numbers

     
  4. 4.

    Reconstruct – dealing with missing data

     
  5. 5.

    Materialize – back to the real world

     
  6. 6.

    Share – collaboration at the speed of the internet

     

All six are described in detail in a comprehensive textbook of this discipline (Weber and Bookstein 2011a). A summary of each of the six areas will be given below.

Digitize

The conversion of the real objects into virtual ones is obviously the first step in VA. There is a variety of technologies available today, some still sophisticated and costly, others simple in use and cheap. Digital data is a projection of continuous data into the space of integers. The range of numbers used for quantification is therefore limited to a discrete set of values, and the number of elements recorded is limited by the resolution of the sensor. Hence, the first two questions to answer are as follows: (1) Is it enough for the intended purpose (e.g., classification, hypothesis testing, modeling) to capture the surface of the object or is the whole volume of the object needed? (2) Independent of the first question, which resolution is reasonable? In paleoanthropology, many preserved features such as bone and enamel thickness, the cranial sinuses, the enamel-dentin junction of teeth, or the trabecular structures of the pelvis and long bones may carry important information with regard to interpretation of functional morphology and taxonomical assessment. Volume data, i.e., 3D data throughout the whole structure such as CT, is therefore often mandatory. In archaeology or face recognition of living subjects, for instance, surface data would satisfy many applications because the inner composition might be known, as, e.g., with stone tools, or not be part of the investigation. Surface scans can thus be ideal for the sake of saving time and money. Though many, if not most, paleo-questions would involve the inner structures of fossils earlier or later, surface scans can nevertheless be the choice of digitalization because volume data acquisition could simply be not possible for the moment, for instance, in the field or because no permission to transport fossils to the next volume scanner is available.

To scan the whole volume, all kinds of “tomographic” procedures (imaging by sections) are in principle applicable. Computed tomography (CT), a standard medical imaging procedure commonly used for scanning living patients; micro-computed tomography (μ-CT) , an industrial imaging routine to examine materials in very high resolution; or magnetic resonance tomography (MRT), another medical routine to image patients avoiding ionizing radiation, are popular examples. The latter can capture soft tissues very well but hardly delivers usable signals from hard tissues such as bones and teeth. It is used to examine the brain, the heart, the cartilage in joints, and the like in living subjects. Its use for paleoanthropology is limited to very specific problems, predominantly to scan extant primates for comparative purposes (e.g., the relative size of frontal lobes (Semendeferi et al. 1997) or cranial base flexion during ontogeny (Jeffery and Spoor 2002)). In contrast, CT and μ-CT can cope easily with dense and very dense objects like bones, teeth, ivory, antler, shells, and stones. Like any of these tomographic methods, it delivers a stack of 2D images (called “slices”) that are combined to a 3D volume. Images are based on X-ray technology which means that radiation is emitted by a tube, the rays are partly absorbed by the object which is penetrated, and the remaining X-rays are recorded at a detector behind the object. In medical scanners, the object rests at a moving table and the tube-detector system rotates around it. In μ-CT, the object rotates instead which implies the necessity of a rigid fixation at the rotation table to avoid motion artifacts. Since paleoanthropology deals with dead material, the radiation dose is of low interest in both modalities (there might, however, be effects on color and preserved DNA; Paredes et al. 2012; Richards et al. 2012).

Each slice of the volume data consists of small picture elements, like those of any electronic image. While these elements in a 2D photo are called “pixels,” we call elements of 3D volume data “voxels” because they offer a third dimension, a thickness. Voxels carry information about their individual position in the x, y, and z grid of the volume – plus a specific value for their grey value. The inner composition of a scanned object is detected based on the different densities of materials which lead to different grey values of the voxels (a function of the attenuation of the X-rays). If that inner composition is to be expected homogenous, then there is no argument of using a tomographic technology. If, in contrast, different materials or change of material over space can be expected, then it is the appropriate procedure. CT can deliver a resolution of roughly a millimeter down to ~200 μm. Features being smaller cannot be acquired. μ-CT starts somewhere around 100 μm and can go down to 1 μm, depending on the capabilities of the system (e.g., the diameter of the micro-focused X-ray beam, the size of the detector elements) and the applied magnification which again depends on the size of the object and the scanner geometry. Many recording chambers of μ-CTs are limited to relatively small objects (usually only some centimeters in diameter). Only a few machines can handle large objects of the size of a human skull or femur (e.g., VISCOM X8060 II, see www.micro-ct.at). A further increase in contrast quality and resolution is possible with synchrotron tomography which may go down as far as 0.7 μm (Sanchez et al. 2012). However, research times at those facilities are quite in demand and therefore hard to obtain.

The resolution of the data should be generally “good enough for the purpose” (Weber and Bookstein 2011a). While it rarely makes sense for the investigation of the gross geometry of a skull to go down with resolution lower than 200 μm, another scan at 50 μm could still be too coarse for the analysis of tooth wear facets. A good question to start is thus: What is the smallest structure that needs to be detected? And why not digitize everything using μ-CT? Firstly, the accessibility to these machines is still very restricted. They are immobile or, at best, can be transported only with great difficulty. Secondly, mammoth data volumes emerge (e.g., a cranium with 50 μm voxels is roughly 70 GB data), which require high-end computers for their processing. This is where the technical development of computers and storage media still lags, in an affordable price range, behind the possibilities of the technical scan. Thirdly, only small objects can be examined, while crania, jaws, or long bone fragments in many cases do not fit into the recording chamber, with exceptions as mentioned above. For precious objects such as fossils which can undergo an examination perhaps only once, μ-CT is definitely the preferred choice because it delivers data good enough for virtually all purposes and for the middle-term future (even if we have to await technical development to fully use it).

Surface scanning on the other hand does not allow looking even a nanometer below the exterior interface, but, depending on the system used, can digitize the surface in very high resolution too (also in the μm range). Scanners are often based on laser beams or structured light (dark and bright stripes) that are projected over the object. A sensor is measuring the reflected light, respectively the pattern of stripe distortion. Since the geometry of the light/pattern emitting and receiving system is known, the object geometry can be computed by means of triangulation. The acquisition of one such “shot” can be very fast (within seconds). But comparable to photography, it represents only one view. Hence, the object has to be rotated and captured again and again, with overlapping areas. Smart routines in the software will stitch together the different views until the whole object surface is recorded in all dimensions. Data sets are rather small compared to volume data (because the objects are “hollow”), and in some cases also texture/color information can be recorded. This can be an important additional aspect in paleoanthropology – to keep this kind of information in the analysis (which is not possible with any of the tomographic procedures). Surface scanners are easier to transport than CT or μ-CT scanners and a magnitude cheaper. Applications in the field are thus feasible (if there is electric power available). Stereoscopic photography is also an alternative to obtain 3D data from multiple images taken from different views. Recent software packages (e.g., PhotoModeler® http://www.photomodeler.com) assist in calibrating the camera system and identifying overlapping points on images to create a 3D model of the object (Paul et al. 2013).

For scanning bones and fossils, there shaped up a list of do’s and don’ts in practice. For instance, all metal parts (e.g., fixing pins, clips) should be removed from the object to avoid artifacts, the gantry tilt in medical devices should be kept at zero, an appropriate field of view to maximize resolution and the smallest possible slice thickness to minimize the partial volume effect should be chosen, the contrast should be maximized and CT scale overflow artifacts avoided, and the kernel (the convolution filter used for back projection) should be neutral to slightly hard. In any case, the raw data should be kept. New reconstructions can be computed afterward from this source. And after scanning, it is a matter of courtesy to share the data and leave a copy with the institution that hosts the collection of fossils. The brevity of this article does not allow for a discussion in length, but for more technical advice, see, e.g., Spoor et al. (2000); Zollikofer and Ponce de Leon (2005), or Weber and Bookstein (2011a).

Expose

There is nothing to expose with surface data, as mentioned above, because only the visible surface was recorded. Working with tomographic data, the outer and the inner structure can be examined. In contrast to invasive techniques such as histological thin sections or grinding, the advantage is that the object does not have to be destroyed and only has to be touched for transport to a scanner and back. Its interior can be inspected by browsing through the stack of images (like most radiologists still do with their light box examining CT or MRT scans of patients) or by segmenting structures of interest as 3D objects. Segmentation means to separate particular areas of the image from their neighborhood and address them as different logical entities. For instance, the brain in a MRT scan is often segmented from the surrounding liquor, meninges, bones, and muscles to work on its morphology. Paleoanthropologists do the same with the interior of the braincase, the only remainder in fossils to infer speculations about our ancestor’s cognitive capacities. In a dried skull, and often in fossils, the braincase is filled with air which has a different grey value (black) than the bone (white). There are semiautomated algorithms (mostly thresholded region growing) available in many programs (e.g., Amira™, Analyze™) that help labeling the borders between the regions without much manual intervention. The latter is important to approximate the goal of reproducibility, thus avoiding subjective influences. Once this is done for each slice of the volume, there is a new object that is called “virtual endocast ” (Weber et al. 1998). It can be rendered on a computer screen (Fig. 2), where it appears as a “positive” of the formerly hollow cavity. Surface details like imprints of brain convolutions or vessels can be described, and it can be measured, e.g., the cranial capacity (volume). Likewise, other hollow structures can be created as virtual endocasts, for instance, the frontal and the maxillary sinuses or the pulp of a tooth.
Fig. 2

Virtual endocast of the Tyrolean Iceman “Ötzi” which represents the size and shape of the endocranial cavity. The projected X-rays in the background show the actual shrunken brain

Since the brain development is one of the critical issues in human evolution, endocranial endocasts are important sources to compute indices such as the encephalization quotient, which is based on the estimated brain to body size ratio (Martin 1983). Cranial capacity, i.e., the volume of the endocranial cavity, is, however, not equal to the size of the brain but about 10 % less (Holloway et al. 2004). Virtual endocast s were used in many fossil studies to infer an approximate brain volume or other descriptions (Conroy et al. 1998, 2000; Recheis et al. 1999; Falk et al. 2000; Tobias 2001; Prossinger et al. 2003; Bräuer et al. 2004; Carlson et al. 2011; Curnoe et al. 2012) and were also used for modern humans, primates, and vertebrates (Colbert et al. 2005; Rowe et al. 2005; Macrini et al. 2007). Unfortunately, they provide no direct information with regard to the internal structures of the brain, e.g., the number of neurons and their density and histological structure, or about the connectivity between areas of the brain. But beside the mere volume, the full range of the morphometric tool kit (including landmarks, curves, and surfaces, see below) can be used for the quantitative comparison of the internal morphology just as for the outside of skulls. Beside size change, it is mainly changes in the overall proportions of the brain or the proportions of its components such as the size of the frontal cortex and cerebellum (Seidler et al. 1997), or the parietal lobes (Bruner et al. 2003), or the pattern of vascular supply (Neubauer et al. 2004) that inform about hominin evolution. Also the ontogenetic patterns of brain development changed in the course of evolution, which can be studied in fossils and in comparison to extant apes (Neubauer and Hublin 2012).

Staying with the brain for a moment longer, there are of course applications of the VA action “expose” to extant humans as well, reaching far into medicine. The fetal alcohol syndrome, for instance, leaves its traces in the connecting structure between the hemispheres, the corpus callosum. With the use of MRT scans and semilandmarks along its midline, researchers (Bookstein et al. 2006) could clearly show a specific geometric signal indicating brain damage in this class of birth defect that is triggered by alcohol abuse during pregnancy. The method is even used in American courtrooms to detect this damage in the brains of certain convicted murders at risk of a death sentence. Virtual endocast s of recent humans have also been used to illustrate the effects of a new surgical intervention to relief intracranial pressure in cases of severe brain edema. “Posterior-hinged circular craniotomy” (Traxler et al. 2002) is applied when conventional therapy and trepanation fails. The whole calotte is cut, with the only exception of a small region at the occiput to protect the vital blood drainage via the sagittal sinus. But the gain in volume at a certain degree of frontal elevation of the calotte is almost impossible to measure on a patient while it is quite simple by means of virtual endocasts where this elevation can be simulated on the computer and volume increase be measured and correlated with skull shape and other factors such as sex.

Coming back to paleoanthropology, “ electronic preparation” of specimens is another important domain of VA. A form of interest in many fossils is not or only partly accessible because it is covered by some foreign material, sometimes called “matrix” or “encrustation.” The foreign material must be removed without jeopardizing the surface of the object any more than necessary. Physical preparation is a manual procedure that requires highly trained and experienced staff with good eyesight and steady hands. Miniature chisels, air hammers, sandblasters, and the like are used to remove the matrix bit by bit. Nevertheless, there is a considerable element of risk because the matrix could be excised too deeply, destroying actual fossil bone. Good preparators avoid such errors by working very slowly. Still, internal features like sinuses or cranial cavities are impossible to uncover.

Electronic preparation, in contrast, is based on volume data (surface data do not inform about internal characteristics) which allows access at any point of the object. For fossils, these are typically CT or μ-CT scans. If the fossilized bone displays a distinctly different range of grey values (density) than the matrix does, the removal of the foreign material is a fairly straightforward job. The material properties of matrix vary, however, widely, as do the difficulties associated with their virtual removal. But one overwhelming advantage of computer-based methods is immediately evident: the original specimen is not impaired. There is no “undo” command for operations on physical objects.

In difficult cases, there is overlap in grey values (density) between fossilized bone and matrix or the matrix is heterogeneous, as when gravels and grains of rock are embedded in calcareous sand. Sophisticated filtering might be necessary during segmentation to find a clear boundary between bone and matrix. Such filters to enhance the boundaries may involve a single application of a Sobel, Laplace, Low Pass or other filter (Weber and Bookstein 2011a), or even a fine-tuned sequence of many filters (e.g., Prossinger et al. 2003). Morphological filtering is another routine to support the separation of logically different units by breaking up tiny bridges that may be left over after region-growing procedures or to smooth the results. There is a huge literature out there about digital image processing, which is not related to VA specific tasks, but very helpful to consult (e.g., Gonzalez and Woods 2008; O’Gorman et al. 2008; Yoo 2004).

Compare

Morphological studies involve the need to capture the shape and form of objects and to compare individuals or samples to each other. Typical questions that arise are the following: How does the average form look like? How does form vary in a population around this average? How are two groups differing from each other? What might be the functional meaning of such form differences? In VA, the aim is to treat the shape and form of specimens or groups by means of numbers, which ideally consider the whole form under investigation rather than “atomizing” it by describing countless separate traits (e.g., occipital bun, high parietal boss, low cranium, projecting midface) by words or by characterizing form by a restricted and unrelated set of measurements. This brings along some advantages. The numbers help limiting subjectivity as far as possible. Considering the whole form at once avoids treating the skull as a set of features that could not actually be independent. And using computing power and memory facilitates the comparison of hundreds of “traits” (actually then the whole form at once) from hundreds of individuals simultaneously (see, e.g., Gunz et al. 2009a). The human mind is not able to keep an overview over such large data sets and tends to overlook facts and introduce its opinions. Paleoanthropology is probably not a bad example for this inherent imperfection of the human analogous computing mode (which has admittedly great advantages otherwise, see below).

VA uses machines to do the computing of powerful statistics, not to interpret them meaningfully. This is still the domain of the researcher in front of the machine (with his/her integrative brain, a feature that machines are still very bad in simulating). Nevertheless, this way offers a step toward more reproducible results, a fundamental claim of any natural science. There are several different techniques to quantify shape and form, for instance, outline approaches such as elliptic Fourier analysis (EFA, Kuhl and Giardina 1982) capturing closed contours quite well and not being dependent of evenly spaced points or equal number of points across specimens, or Euclidean distance matrix analysis (EDMA, Lele and Richtsmeier 1991) based on distances between landmarks and thus well suitable for sufficiently large sets of caliper measurements. Another approach is called “geometric morphometrics (GM) ” which uses multivariate statistics based on 3D coordinate data. Avoiding distances and angles (which have some specific disadvantageous statistical properties such as introducing artifactual covariance structures (Rohlf 1999) and biased mean estimates (Rohlf 2003; Slice 2005)) and orientation problems, GM retains all geometric information contained within the data. A combination of outline and landmark-based approaches would be desirable in some cases (Baylac and Friess 2005). There are of course many pros and cons for the individual approaches. The space of this review article does by far not allow for a detailed discussion; however, some references are suggested to form an opinion (e.g., Bookstein 1991; Rohlf and Marcus 1993; Bookstein 1996; Dryden and Mardia 1998; Lele and Richtsmeier 2001; Slice 2005; Weber and Bookstein 2011a).

Comparisons of biological forms have to be kept under the control of biological theory: the rule of homology (comparing like to like). GM utilizes a particular formal technique, that of landmark/semilandmark points, which enforces this rule. Landmarks are specific points on a form or image of a form located according to some rule. There are several types of landmarks corresponding to the method how they are identified. For instance, they can be located at the crossing of bony sutures or at extreme points of curvature or along ridges (see landmark types I–VI in Weber and Bookstein 2011a). Central to the GM approach are some key elements such as generalized procrustes analysis (GPA; Gower 1975; Marcus et al. 1996), principal component analysis (PCA), and thin plate spline warping (TPS; Bookstein 1978, 1991) that lead to representations of form by size along with shape coordinates and visualization not only of single forms but also of comparisons via the deformation grids that illustrate and formalize shape differences between geometrical objects. Moreover, the way data are represented allows the scientist to compute means and variances of groups at the same time that differences between two specimens or mean configurations are visualized as deformation grids. Importantly, size can be kept in or otherwise be eliminated from the analysis (the message to remember is form is shape and size).

Classic landmarks have a long tradition in anthropology (for a comprehensive list see, e.g., Martin 1914), but they are rare on many structures, for instance, on the braincase, where obviously whole regions on the frontal, parietal, occipital, and temporal bone offer no landmarks. The same problem applies to many other structures, also in the viscerocranium, on most of the postcranial skeleton, on the teeth, and of course on the face and body of living humans. The GM machinery allows identifying the so-called semilandmarks on curves and surfaces. These points are geometrically homologous (Bookstein 1989; Gunz et al. 2005) and can capture previously unattended regions. The 3D model of the human cranium provided here (Fig. 3) shows 25 classic landmarks like those that are usually applied to “caliper” studies and 824 semilandmarks on curves (temporal line, zygomatic arch, orbita, alveolar rim of the maxilla) and surfaces that capture previously unattended regions. The semilandmark approach obviously considers more information and thus can support more sophisticated statements about shape and form differences between groups or individuals. However, these semilandmarks cannot be identified in the physical world, rather they have to be constructed following certain principals that can only be followed in the virtual world. In practice, semilandmarks (sLM) are identified on one template specimen (any from the sample to start with) and then projected to the other specimens in the sample. After this step, they need to be “slid” (curve sLM have 1° of freedom, surface sLM have 2° of freedom, free points have 3° of freedom). Semilandmarks are matched between specimens under control of some global energy term, such as the bending energy of the thin plate spline. After this first round, the template specimen is replaced by the new Procrustes average configuration, and the process repeated until no changes appear. The number of semilandmarks needs to be sufficient to capture the spatial nature of variation or covariation that will emerge from multivariate analysis of these shape coordinates (Weber and Bookstein 2011a).
Fig. 3

Rendered 3D model of human cranium with 25 classical landmarks (biologically homologous measuring points) as dark spheres and 824 semilandmarks (geometrically homologous measuring points) as bright spheres. Almost the complete geometry of the cranium can be captured with this method

What works well with skulls and bones also works with stones and artifacts, soft tissues, or even cars. Particularly, the last years have seen the applications of geometric morphometrics in the context of quantitative analysis of lithic assemblages, for instance, using landmark/semilandmark approaches (Lycett et al. 2010; Archer and Braun 2010; Buchanan and Collard 2010) or surface areas (Lin et al. 2010). GM is widely used to characterize facial shape and its asymmetries and relations to other tissues (e.g., Fink et al. 2005; Bugaighis et al. 2010; Pflüger et al. 2012; Meindl et al. 2012; Kustár et al. 2013), and even the shape of “car faces” was associated with trait attribution (Windhager et al. 2012).

The common problem of all these applications of GM is that they need a fairly rich theoretical background before they can be used properly and that programming knowledge is often necessary to translate theory into results. In the early 2000s, mathematical packages such as Mathematica™ (Wolfram Research) or Matlab™ (MathWorks) had to be used to write routines that perform generalized procrustes analysis or thin plate spline warping. Not every good biologist is necessarily a good programmer, thus the application of GM often stranded for practical reasons. While the development of new algorithms inevitably needs the interdisciplinary action (a core domain of VA) between biologists, mathematicians/statisticians, and software engineers, the application of established procedures became meanwhile easier with some software solutions that did not reach the standard of commercial products but are “usable for the accustomed user.” Morphologika (https://sites.google.com/site/hymsfme/downloadmorphologica) was one of the first such solutions that could process 2D and 3D data and handle GPA, PCA, regression, and warping. Morpheus (http://www.morphometrics.org/) by Dennis Slice, Viewbox (http://www.dhal.com/viewboxindex.htm) by Demetrios Halazonetis, the suite of tps programs (http://life.bio.sunysb.edu/ee/rohlf/software.html) by James Rohlf, and edgewarp (http://brainmap.stat.washington.edu/edgewarp/, restricted to Linux) by Bill Green offer access to some or almost all GM routines to a varying degree. In an attempt to spread knowledge among young European scientists and to establish VA-related infrastructure, the EU-funded project EVAN (European Virtual Anthropology Network) has developed and released the EVAN Toolbox (ET; http://www.evan-society.org/node/23, Fig. 4). Beside for research purposes, ET has turned out to be a fairly good teaching tool so that the issues of GPA, PCA, TPS, group mean comparisons, regression, reflected relabeling, or the analysis of asymmetry (Mardia et al. 2000) lose some of their frightening flavor during practical application with real data. Programming is not necessary because all operations can be put together in visual programming networks, just as modules that are connected by lines.
Fig. 4

Screenshots of the EVAN Toolbox. Mean shapes can be warped between sexes (top left); Procrustes distances are exported into a spreadsheet for further computation (top right); principal component analysis of shape for modern humans, chimps, and orangutans is shown for the first two relative warps (bottom right); a typical visual programming network to operate analyses (bottom left)

Independent of which software and methodological approach is used, it seems most important for advances in quantitative morphology to train young people on a broad scale to use these techniques of the twenty-first century.

Reconstruct

Reconstruction in virtual anthropology refers to the form and shape of biological objects, while in archaeology it refers to the form and shape of artifacts or buildings. Whenever the present form of an object fails to correspond with its supposed original form, reconstruction might be needed. Taphonomic processes, but also damage during excavation or manipulation, can lead to four principal kinds of disturbances of a form (Weber and Bookstein 2011a). All of these apply similarly to archaeological objects:
  1. 1.

    An object can be broken, but (almost) all pieces are preserved. This is called a type 1 disturbance, e.g., a broken cranium, even if it consists of many pieces, which can be fully restored using glue.

     
  2. 2.

    Whenever parts of an objects are missing, it is called a type 2 disturbance, e.g., a humerus that is basically intact but missing its head.

     
  3. 3.

    An object can be deformed. That is a type 3 disturbance, e.g., a fossilized pelvis that shows plastic deformations due to million-year-long pressure of the overlaying rocks.

     
  4. 4.

    An object can be intact but not be directly accessible because it is covered by a foreign material. This type 4 disturbance was mentioned above in the context of electronic preparation, e.g., a finger bone that is embedded in calcareous sands.

     

Of course, all kinds of combinations of these disturbances may exist, and in fact, we rarely find one alone (e.g., there is often broken & missing, broken & covered, missing & deformed & covered, etc.). We speak of reconstruction when a disturbance has been recognized and corrected (Weber and Bookstein 2011a). The types of disturbances introduced above help thinking about the varieties of reconstruction problems that one will face during the process. Single types 1 and 4 problems can have unique solutions, at least in principle (there are only very limited degrees of freedom to put together a complete 3D puzzle, and e-preparation can eliminate matrix in many cases entirely). For most type 2 problems, there is no unique solution, and the same is true for type 3 problems (except for those where the deformation forces are known or one half of a symmetric structure is unaffected and can be mirrored). This is because the form of missing or deformed parts has to be estimated which involves data about undisturbed forms of the same group of objects and assumptions.

A reconstruction can therefore never duplicate the original. It can approximate it. The role of VA in reconstruction is to make the various manipulations reproducible, ergo to involve numbers in the process as far as possible. Biological forms follow constraints, for instance, laws of physics such as gravity, material strength, and load; they respond to the mechanisms of evolution such as the selection of environmentally favorable traits, and anatomical modules develop in concert (integration). The numerous genetic, developmental, and functional factors applying to the form of biological objects enable us to reduce the “degrees of freedom,” the uncertainties, for a reconstruction. However, there is also a lot of interindividual variation in a group, another principle of evolution. For instance, the form of an upper jaw (maxilla) is of course known in principle for modern humans, but each human has a slightly different form which is determined by genetic and environmental factors. Bone remodeling happens during the whole life. A maxilla’s form is depending on the inherited skull form, the individual loadings (related to muscles and diet), the preservation and position of teeth (e.g., some might be lost, some inclined forward or backward), or other behavioral aspects (e.g., teeth might be used as tool or clenched during the night). In biology, we can thus reconstruct most parts only based on a reference data set (a sample of similar organisms) and with a particular likelihood. In contrast, if a portion of a ceramic vase is missing, it could be relatively easy to recreate its initial form because it would follow a pretty strict rule of a smooth surface (especially if done with a potter’s wheel). With fossils, it becomes actually more difficult because the reference sample might be small or even absent. In those cases, reconstruction resorts to the closest sample available – a compromise.

The advantage of using VA in reconstruction is that reference data and assumptions have to be made explicit. There is no mumbo jumbo of the expert who pulls out a reconstruction of the hat like a rabbit. Everything is based on measurements and explicit statements can be made, e.g., which kind of reference data was used or which geometric constraint (e.g., bilateral symmetry) was applied. In lucky cases, the task may boil down to limit the 6° of freedom (three to translate, three to rotate) to possibly zero when putting pieces together or to apply a priori knowledge about the form (e.g., smoothness of curvature, radial or bilateral symmetry) during estimation of missing parts.

In opposite to a physical reconstruction, a virtual one is not depending on sources of irritation such as gravity, glue, or having only one trial. This is one of the reasons why they appeared already very early in the history of VA (Kalvin et al. 1995; Zollikofer et al. 1995; Thompson and Illerhaus 1998). Absolute control over fragment translations and rotations can be achieved with many software packages, particularly in the CAD (computer aided design) domain, that also support the process with aiding constructions such as B-splines or NURBS (non-uniform rational B-splines). Aside from a highly controlled merging of pieces on the screen (already an important improvement) and including occasionally mirroring of pieces, as we see it frequently in anatomical reconstructions (Zollikofer et al. 2005; Ryan et al. 2008), some other technology introduced under “compare” can be used for estimating missing or deformed parts (i.e., types 2 and 3 problems).

Thin plate spline interpolation (Neubauer et al. 2004; Gunz et al. 2009b; Grine et al. 2010; Weber and Bookstein 2011a; Senck et al. 2013) can be applied for geometric reconstruction. It uses a map of landmarks and semilandmarks from a complete specimen (the “reference”) and whatever is left on the specimen to be reconstructed (the “target”). It is a deformation of the reference that is computed to match the location of the corresponding points on the target while filling in the rest of the information. Noteworthy, this is not a simple “copy and paste” action, rather it takes the preserved morphology of the target into account and adapts the missing parts, which are filled in from the template. Applications range from fossil reconstructions (Gunz et al. 2009b; Benazzi et al. 2011a, 2013a) to the preoperative implant planning for large skull defects (Heuzé et al. 2008). There is, however, a caveat of TPS-based reconstruction: it should not be used when it is an extrapolation – when the region being reconstructed extends substantially beyond the limits of the region present in the target (i.e., do not reconstruct the face if just the braincase is preserved). Nevertheless, it works particularly well to reconstruct smooth surfaces, such as the neurocranium, when coordinate-based landmarks and semilandmarks are sampled densely. Alternatively, a reference database can be used to drive reconstructions via multivariate regressions, which rely on the covariation among the observable coordinates (Gunz et al. 2009b; cf. Neeser et al. 2009). However, the sample has to be sufficiently large to increase the certainty of estimates – a demand that is rarely met in paleoanthropology. TPS in contrast just needs one reference specimen but the result is entirely depending on it. Whenever more than one reference specimen is available, multiple reconstructions can be computed to assess their range of possible variation (Gunz et al. 2009b; Benazzi et al. 2011a; Weber and Bookstein 2011a) or the sample average can be computed and used for the TPS warping (Senck et al. 2013).

In a science that is highly depending on reconstructed forms on the one hand (be it for morphological comparison or just for museum display) but which has only a few intact templates to offer on the other, we naturally have to make compromises. In some cases, even a composite fossil (Kalvin et al. 1995) might be a solution to make a further step in a heuristic process. Strait et al. (2009), for instance, have used a fairly complete but edentulous cranium of Australopithecus africanus (Sts 5) and a fairly complete dentition of another member of this taxon (Sts 52) to be able to simulate loadings on the cranium during different modes of bite. Though both specimens were in a similar dental stage and the preserved tooth roots of Sts 5 were matched with the teeth of Sts 52, the reconstruction would certainly deviate within limits from the original appearance of Sts 5 in its lifetime. However, these deviations could be regarded small enough to be accepted in a situation where a more persuasive solution is impossible (at least until a complete and undeformed cranium with dentition is unearthed and accessible).

Materialize

There are two sources for appraising morphology in classical anthropology, original specimens and their casts, and there are two in virtual anthropology, digital copies on the screen and rapid prototyping models deriving from these copies (Fig. 5).
Fig. 5

The Upper Paleolithic cranium of Mladeč 1 as (a) original, (b) traditional cast, (c) virtual specimen on the computer screen, and (d) rapid prototyping model (With permission of the Natural History Museum Vienna)

For teaching and training purposes, as well as for permanent museum display, real models can be more desirable media to create knowledge than virtual ones. In any case they are essential when there is no computer available. But also for the researcher, real models provide a substantial aid to understand three-dimensional relationships of spatially complex structures. Architects are certainly among the best trained people with regard to spatial imagination, but in practice many of them still build real models of constructions to appraise complex interactions of structures. There is a German word called “begreifen” which not by accident means both “to touch” and “to understand.”

Rapid prototyping (RP) technology was realized in the 1980s to facilitate quick and relatively cheap manufacturing of industrial prototypes. The idea is to have something real in hand that was initially created in a computer environment, a newly designed telephone before mass production, an implant to train with before surgery, a downscaled model of an airplane to be tested in the wind tunnel, and the like. The principle behind all kinds of different RP techniques out there is to build an object layer by layer with small elements. This is actually a very ancient idea looking at the Great Pyramids of Giza that are constructed the same way, layers of stones over layers of stones. The great advantage of the relatively slow layer-wise approach is that even hollow spaces and undercuts can be built which is not possible with other techniques, e.g., with CNC (computer numerical control) machinery.

Stereolithography (STL) was one of the first and still is one of the most advanced procedures which allow producing accurate models down to a resolution of ~0.1 mm. The STL data generated during preparation derive from 3D volume or surface data, e.g., CT or surface scans, or constructed surfaces like CAD objects, or a reconstructed fossil. They serve to control a mobile mirror that directs an ultraviolet (UV) laser beam in accordance with the layer geometry. Where the UV laser beam comes into contact with a photosensitive liquid acrylate or epoxide resin, it hardens. Then the part is lowered deeper – by the thickness of one layer – into the liquid polymer bath. The surface must be leveled initially by a recoating system and then the next layer is hardened. This process continues automatically until the production of the 3D part has been completed. Supporting constructions permit the fabrication of “overhanging” parts that would otherwise float away before they are connected to the structures above.

Other methods use powders rather than liquids (e.g., Z-printing, laser sintering) or meltable plastics (e.g., fused deposition modeling) applied through heating nozzles, comparable to what a printer does with ink. There can be huge differences in the price, the speed, and in the quality of models (see Weber and Bookstein 2011a for an overview). A decision with regard to the planned application is thus needed – cheap, accurate, enduring, fast, transparent, and multicolor are some of the options to be considered.

Whatever the choice of method is, any type of RP model has some advantages over casts in the following respects:
  1. 1.

    There is no mold that is aging (of course the model itself will age, but it can be reproduced to 100 %), only the digital data has to be kept save.

     
  2. 2.

    There is no contact to the original object, only contactless scanning is required, a big issue in many cases of fragile and brittle specimens with porous surfaces.

     
  3. 3.

    Most biological objects feature hollow structures and undercuts which are no problem to be realized with RP. To access them, models can be built as separate parts, e.g., a skull with removable calotte to enable inspection of the cranial cavity.

     
  4. 4.

    Models can be up- or downscaled (e.g., 25 %-sized “pocket replicas” of skulls or a 400 %-sized model of trabeculi in a cut of the femoral neck).

     

Of course, there are drawbacks of RP procedures as well: Some of them are rather expensive (a stereolithography of a skull can cost more than € 1,000). However, there is a growing market of desktop 3D printers that permit production of models in a very low price range (some machines are cheaper than a STL model). The other important drawback is the limited resolution of RP models, somewhere in the 100 μm range. It depends on the incoming data, which in the case of medical CT is even lower (typically 200–500 μm), and the characteristics of the RP procedure itself. On account of their layered structure, the aliasing effect (jagged surface) of all RP models can be recognized – a smooth surface can be achieved only by intensive reworking. Recent developments can improve resolution considerably by a combination of micro-computed tomography and micro-stereolithography. The size of objects is limited, but a layer thickness of less than 25 μm is possible. A first application to a fossil object (lower molar of an Australopithecus afarensis) is described in Weber and Bookstein (2011a, p. 321).

The usefulness of rapid prototyping models has been amply argued over the years. The first stereolithographic model in anthropology was by the way done on the Tyrolean Iceman “Ötzi” to get access to the skull of the precious mummy (Seidler et al. 1992; zur Nedden et al. 1994). The full potential for anthropological application turned out soon thereafter (e.g., Hjalgrim et al. 1995; Zollikofer et al. 1995; Seidler et al. 1997; Recheis et al. 1999; Ponce de Leon and Zollikofer 1999; Weber et al. 2001; Kimbel et al. 2004). In the medical field, RP models are used as well since the early 1990s, particularly for implant planning (e.g., Klein et al. 1992; Anderl et al. 1994; Yau et al. 1995). There is thus a considerable overlap in techniques used in paleoanthropology and surgery planning, which opens possibilities for collaborations and jobs for (paleo)anthropologists.

Share

Speaking of collaboration, most contemporaries have recognized that scientific progress can be advanced by sharing methods and data resources. Studying biological and evolutionary questions, it is of the essence to talk about intragroup and between-group variation. There is one very simple guideline coming from statistics: The larger the samples are the sharper is our picture with regard to variation and differences. With the introduction of the Internet, some sciences saw a progressively increasing behavior of sharing information. Open access journals are meanwhile widespread, and data archives were and are created in any field of research. Probably the most consequent application is found in genetics, where the human sequences and meta-information are published as a matter of course (e.g., http://www.ncbi.nlm.nih.gov/gene, http://www.genecards.org/). Paleoanthropology, however, is a field where the idea of sharing data for the sake of creating knowledge is still not pervasively accepted. The first electronic archive of hominin fossils was created in 1999 (http://www.virtual-anthropology.com/3d_data/3d-archive), and the idea of an opening – “glasnost in paleoanthropology” – was expressed soon after the Millennium (Weber 2001). The paleo community saw reviews and conferences on the topic (Gibbons 2002; Soares 2003; Delson et al. 2007; Kullmer 2008; Mafart 2008), and some further archives were established (e.g., NESPOS, EVAN-Society, ORSA, DigiMorph, Paleoanthportal, RHOI, AHOB, Visible Human Server). However, researchers and curators remained reluctant (Weber and Bookstein 2011b). The digital@rchive of fossil hominoids is still the largest database providing access to a significant number of very important hominin fossils without restrictions.

Beyond doubt, there are a lot of difficult questions involved in this problem, for instance, how to protect the legitimate interests of the discoverers who often invested considerable amounts of time and money, in some cases even risking their life in the field, to make their findings. How should large funding agencies and journals act to enforce publication of data, rules that are somewhere hidden in the fine print? It seems reasonable to allocate sufficient time for the discoverers to work on their specimens. Yet, there are large numbers of fossils that are not accessible, even decades after their discovery. As mentioned at the beginning, it is a quite essential claim in science that results can be checked by others, particularly if a new taxon is described and established. As a consequence, there is thus a reasonable demand that at least electronic data from specimens should be accessible after a publication, or, if nothing is published, after a certain number of years.

Gene sequences of humans are accessible because they represent our common evolutionary heritage and an important resource to gain further knowledge for the benefit of all. When a fossil is discovered, it is usually owned by the country from which it originates. The fossil is then carefully stored in a national institution such as a natural history museum and administered by the local curator who acts as the representative of the owner (which is the country but not the curator). Although it is alright that the country has this exclusive control over its property, there is another obligation associated with the curation – to grant access to all researchers who have a reasonable research question and the capacity to answer it. A hominin fossil contains data about our common evolutionary heritage, as well as genes do. Restriction of access to data cannot be found on the list of privileges associated with ownership. In other words, fossils may be owned, but they may not be copyrighted.

Data itself can have diverse characteristics which are associated to the mode of measurement and to the user’s context. It is necessary to reflect these qualities of data because they are relevant for access policies and structuring data archives . For instance, when a data archive is to be established for paleoanthropological purposes, a number of researchers will probably be interested in data from hominids, e.g., a CT scan of an Australopithecus skull or a chimpanzee thigh bone. These data can be called “source data” because they were mainly acquired by a machine (e.g., CT, μ-CT, surface scanner) and are thus much less biased by any intellectual treatment of colleagues than another kind of data that can be called “derived data.” The latter would be, for instance, coordinate measurements of landmarks or a virtual reconstruction because these tasks involve an observer’s perception and include individual interpretation. It is a fundamental issue for access rights on the one hand and for further application of data on the other to be aware of this history. An anthropologist will ultimately also want to make use of the geochronologists’, paleontologists’, or pathologists’ data archives in order to acquire another sort of data, “contextual data” pertaining to the specimen under examination. Electronic archives have to be structured according to these needs.

In the first place, clear access policies are necessary; it is secondary what they actually are. A minimum standard could be that museums and other organizations accommodating valuable material in their collections make accessible list of specimens and statements as regards curation and access policies. A recently upcoming attitude of a “data embargo” continuing over many years after fossils have been scanned by some researchers should also be condemned because it does not lead to an opening and the protection of specimens but just to other data syndicates preventing access and to the desire for re-scanning.

Biomechanical Analysis of Biological Objects

The mechanics of organismal structures can be studied in various ways, including physical and mathematical models (Demes and Creel 1988; Spencer and Demes 1993), in vivo and in vitro experimentation (Hylander 1979; Ravosa et al. 2000; Daegling and Hotzman 2003; Wang and Dechow 2006), and, since the availability of adequate computer technology, computer-based simulations (Sellers and Crompton 2004; Koolstra and Van Eijden 2005; Rayfield 2005; Ross 2005; Dumont et al. 2009; Strait et al. 2009, 2010, 2013; Kupczik et al. 2009; Wroe et al. 2010; Benazzi et al. 2011b; Gröning et al. 2011; O’Higgins et al. 2012). One approach to study how mechanical systems such as the musculoskeletal apparatus move under the influence of forces is Multibody Dynamics Analysis (Curtis et al. 2008, 2013; Fitton et al. 2012; O’Higgins et al. 2012). Finite element analysis (FEA) , another engineering technique, has been particularly widely applied in clinical and evolutionary biomechanics because it allows exploring how objects of complex geometries respond to external loads. It has thus the potential to test biomechanical hypotheses in functional morphology. Models are created by capturing the geometry (obviously one of the major inputs and an important link to VA), assigning material properties, specifying simulated forces, and imposing constraints. Models have to be validated, comparing results with in vivo or in vitro experimental data, and can be altered to examine the consequences of changes to input parameters. The output of FEA is quantitative too and mostly relates to stress, which is a measure of the amount of force per unit area; to strain, which is a measure of deformation representing the relative displacement between units in the material body; and to strain energy, which is the net potential energy stored in a solid that has been deformed by forces.

FEA is a deterministic process, i.e., the outputs of two simulations using different parameters (varying geometry, material properties, force, constraints) will always lead to different results. The problem with FEA is that there is no method to compare them in a statistical sense, e.g., how different are the results between two group average models compared to within group variation? As discussed above, geometric morphometrics can deliver a group mean configuration or a warped intermediate geometry. It can also inform about shape and form variation within groups or between groups and it can provide reconstructed input forms for biomechanics in a more reproducible way than traditional procedures can do. Nevertheless, whatever the inputs of FEA are, the outputs are most often colored images (Fig. 6) that can just be compared visually. While one observer might interpret the differences in stress and strain between models as being “almost similar,” another might exclaim how different they are. The discrepancy between the mathematical physics of elastic theory, essential for mechanics, and the quite different mathematics used in shape analysis – respectively a missing mathematical bridge between them – is a major problem in biomechanical analysis of biological forms (Weber et al. 2011). A theoretical solution was published recently (Bookstein 2012), but has not yet been tested with real data. Other attempts were undertaken to make FEA results comparable between specimens and groups. However, strain frequency plots, e.g., used in a recent publication (Parr et al. 2012), cannot relate strains to the actual location (instead they just provide a summed picture of appearing strains), and landmark point strains cannot be based on semilandmarks for the mentioned mathematically incompatible differential equations. Others (Strait et al. 2009; O’Higgins et al. 2010; Wroe et al. 2010; Cox et al. 2011; Gröning et al. 2011) relied on visual comparisons between strain plots, or have tried to infer the mean of, e.g., appearing maximum and minimum principal strains, or invoked profiles along a structure of such. However, these measures only provide very scant pictures of the whole structure or sometimes involve subjective judgments. Displacement plots (O’Higgins et al. 2010; Gröning et al. 2011) again only carry information on the direction of displacements but cannot inform about the quantity of work to impose particular simulated strains.
Fig. 6

Maximum principal stress distribution observed in FEA when a human molar is loaded onto occlusal contact areas (maximum intercuspation) detected by the occlusal fingerprint analysis. First row, occlusal view; second row, distolingual view. Note the high tensile stresses along the fissures (dark areas) (From Benazzi et al. 2011b)

Despite the still absent formalism to join geometry and biomechanics effectively, it can still be a step forward to simulate stresses and strains in a form. The loadings appearing on human teeth during chewing are, for instance, not well known. Recent studies (Benazzi et al. 2011b, 2013b) combining FEA and occlusal fingerprint analysis (a technique to determine actual movements from wear signals of the teeth, Kullmer et al. 2009) could show that high tensile stresses appear particularly along the fissures of the occlusal surface when realistic loading scenarios were applied (Fig. 6). Even if no big samples can be statistically compared so far, the simulations reveal important aspects that have not been considered yet, e.g., the mechanical consequences of filling fissures for protection against caries, a common dental practice. Other studies showed that the pattern of strain distribution during biting could be relatively conservative within species, regardless the actual magnitudes (Smith et al. 2014), or that certain facial geometries are not well adapted to produce high bite forces due to occurring distractive joint reaction forces (Ledogar et al. 2014). In many of those biomechanical studies, VA methods are a vital component, e.g., to virtually reconstruct a fossil form prior to FE model creation or to determine a limited set of extreme group forms to be modeled then in the FE process. Biomechanics is not part of VA but the cross-fertilizations are manifold, and innovations resulting from this combination are considerable.

Conclusion: Virtual Functional Morphology

Morphology deals with the study of shape and form of organisms and their parts. Functional morphology is the study of the relationship between the structure and the function of an organism’s parts. Functional morphology is concerned with explaining how body structures such as bones, teeth, muscles, or tendons relate to different behaviors, including locomotion, feeding, defense, and reproduction. It integrates concepts from anatomy, mechanics, evolution, and development. The idea of “form follows function” in biology is an old one, for instance, expressed by Georges Cuvier (1769–1832) in his “conditions d’existence” (roughly speaking, Cuvier argued that all organismal parts that we see are already optimized toward their functional demands, otherwise the animal would not subsist). Although we have learned in the meantime that shape and form may deviate from this strong canon (genetics and theory of evolution had not been discovered at Cuvier’s time), we recognize the importance of the relationship between form and function. Functional morphology is thus a fundamental approach to studying biology on a macro-level with the goal of understanding how shape and size might affect function or what the function of a structure might be at all (Rohen 2007; Lucas 2004). Such knowledge is important for developing an integrated view on biological form in the light of its function and, last but not least, it is essential to relate the phenotype with the genotype.

If we just look at the masticatory apparatus, which is certainly a key to studies in hominin evolution, the kind of unresolved fundamental questions in biology and medicine that touch closely paleoanthropology are, for instance:
  • How does variation of skull shape relate to variation of mechanical loadings? At this point, we have no good data whether there is a tight relationship or not. We also do not know how the entity of a skull might compensate in one part for deficiencies in another.

  • How far can geometry deviate from the mean shape to meet a given functional demand? The surviving members of a taxon were all successful despite their individual shape variation. How would a chimp, or australopithecine, or Neanderthal, or modern human with a shape outside the 99 % sample confidence interval cope with default mechanical stresses?

  • Which particular feeding behavior (which is strongly related to ecology) would make the skull shape unsuccessful? Can we predict a skull shape that would fail – given a certain behavior?

  • How do the shape and mechanics of the teeth (e.g., relative cusp size, cusp relief) relate to the biomechanics of the entire skull? Can we describe patterns that make particular configurations (e.g., larger/smaller teeth, flat/high relief, protruding/retracted faces) more favorable combinations?

  • What were the biomechanical consequences of the evolutionary form changes of the human skull, e.g., when jaws became smaller, the braincase grew bigger, and cranial base flexion increased?

  • Depending on the result of the former question, what then could have been the feeding strategies that favored those changes, and how do they fit to what we know about related paleoecology?

We have still great difficulties to understand our evolutionary adaptations, and we do not base the treatment of patients on thorough knowledge of function in dependence of form in the field of dentistry, orthodontics, or craniofacial surgery. However, a growing number of publications are documenting a substantial progress in the development of methods, software packages, computer power, and awareness of the technologies for each field separately. Many pieces of the puzzle are already there since Schmerling discovered Engis and Darwin put evolutionary theory in place. A “virtual functional morphology” that integrates shape and form analysis with biomechanics and also considers developmental pathways controlled by genes is the next step forward for systems biology and evolutionary sciences.

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of AnthropologyUniversity of ViennaWienAustria

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