Geometric Morphometric Methods for Bone Reconstruction: The Mandibular Condylar Process of Pico della Mirandola



The issue of reconstructing lost or deformed bone presents an equal challenge in the fields of paleoanthropology, bioarchaeology, forensics, and medicine. Particularly, within the disciplines of orthodontics and surgery, the main goal of reconstruction is to restore or create ex novo the proper form and function. The reconstruction of the mandibular condyle requires restoration of articulation, occlusion, and mastication from the functional side as well as the correct shape of the mandible from the esthetic point of view. Meeting all these demands is still problematic for surgeons. It is unfortunate that the collaboration between anthropologists and medical professionals is still limited. Nowadays, geometric morphometric methods (GMM) are routinely applied in shape analysis and increasingly in the reconstruction of missing data in skeletal material in paleoanthropology. Together with methods for three-dimensional (3D) digital model construction and reverse engineering, these methods could prove to be useful in surgical fields for virtual planning of operations and the production of customized biocompatible scaffolds. In this contribution, we have reconstructed the missing left condylar process of the mandible belonging to a famous Italian humanist of the 15th century, Pico della Mirandola (1463–1494) by means of 3D digital models and GMM, having first compared two methods (a simple reflection of the opposite side and the mathematical–statistical GMM approach) in a complete human mandible on which loss of the left condyle was virtually simulated. Finally, stereolithographic models of Pico's skull were prototyped providing the physical assembly of the bony skull structures with a high fitting accuracy. Anat Rec, 292:1088–1097, 2009. © 2009 Wiley-Liss, Inc.

The problem of reconstruction of fractured, distorted, or missing parts in human skeleton has been given considerable attention in the fields of archaeology, forensic anthropology, and paleoanthropology. As a result, a large amount of knowledge has been amassed to date, including the recent development of the noninvasive computerized methods of virtual reconstruction (Ponce De León and Zollikofer,1999; Recheis et al.,1999a,b; Weber,2001; Neubauer et al.,2004; Gunz,2005; Ulhaas,2007). These methods have enabled reconstruction of distorted or fragmentary hominid fossil for the purposes of their comparative analysis that would be impossible on the incomplete structures (Ponce De León and Zollikofer,1999; Gunz et al.,2004; Neubauer et al.,2004; Gunz,2005). An analogous restoration is also of paramount importance for facilitating historical or forensic investigations with the help of plastic craniofacial reconstruction and skull-photo superimposition for personal identification (Işcan and Helmer,1993; Ghosh and Sinha,2001; Fantini et al.,2005).

Bone reconstruction also presents a fundamental issue in surgical fields. In particular, a reconstruction is frequently carried out for rectification of mandibular defects due to tumors, developmental abnormalities, or trauma (Mehta and Deschler,2004; Young et al.,2007; Madsen et al.,2008). However, the replacement of a mandibular condyle after a resection procedure in cases of ankylosis, degenerative diseases, dysplasia, congenital malformation, or trauma still remains a surgical challenge (Patel and Maisel,2001; Westermark et al.,2006; Pogrel and Schmidt,2007). It is clear, though, that the main goal of surgical intervention is the restoration of the premorbid form and function (Mehta and Deschler,2004; Cunningham et al.,2005). In detail, functional restoration takes into account articulation, occlusion, and mastication, whereas restoration of the original shape is important for esthetic purposes (Fonseca,2000).

The techniques developed in anthropology and paleoanthropology for bone reconstruction could provide a valuable aid for “form and functional restoration” in the medical field. The creation of the three-dimensional (3D) digital models with the help of reverse engineering and geometric morphometric methods (GMM) create the fundamental part of the new field of the “Virtual Anthropology” (Weber,2001). By means of the virtual approach to reconstruction, the problems related to deformation (Ogihara et al.,2006) and missing data could be solved (Gunz et al.,2004; Neubauer et al.,2004; Gunz,2005), at the same time reducing the subjective choices of the operator and increasing reliability and reproducibility of the result (Weber et al.,2001; Fantini et al.,2005; Benazzi et al., 2008).

Unfortunately, there is little dialogue between anthropologists and surgeons in this field. The large amount of complete or fragmented skeletal remains with or without pathologies that anthropologists are used to working with can provide for an opportunity to develop methods and to test new composite materials for bone reconstruction. It is especially important given that the new procedures and composite materials, like ceramics, glasses (e.g., Aitasalo et al.,2001; Eppley et al.,2002; Magee et al.,2004), and synthetic polymers (e.g., Chiarini et al.,2004; Wolff et al.,2004), first have to be tested in dead and in living animals before using in patients. Self-evidently, human skeletal remains are better suited to carry out at least the first step of the trials.

In this study, we apply a computerized method of reconstructing missing data to the case of a famous Italian humanist of the 15th century, Pico della Mirandola. We have reconstructed the missing left condylar process of the mandible using virtual models and GMM with the help of geometric information of the well-preserved right hemimandible, having first tested this method on a complete human mandible where the condyle loss was simulated in the virtual environment. The reconstructed portion of the mandible of Pico della Mirandola has been prototyped demonstrating the potential of this approach not only for conservation and valorization purposes but also for development of individual implants that can be used in modern surgery.


The body of Giovanni Pico della Mirandola (1463–1494), an important Italian humanist (Andreolli,1994; Giovio and Caruso,1999), was exhumed from the S. Marco cloister (Florence) in 2007. The overall good preservation of the cranium and mandible, which missed only the left condylar process, provided perfect conditions for virtual reconstruction (Fig. 1a,b).

Figure 1.

(a) Left lateral view of the skull of Pico della Mirandola; (b) 3D digital model of the mandible of Pico della Mirandola.

The skull and mandible were scanned at the radiology department of Ravenna Hospital by means of computed tomography (CT) performed with the Brilliance 64-slice CT scanner (Phillips Medical Systems, Eindhoven, The Netherland) with a slice thickness of 0.9 mm, increment 0.45 mm. Both 3D digital models (the cranium and the mandible) were built using Amira 4.1 software (©Mercury Computer Systems, Chelmsford, MA). The models were achieved semiautomatically by threshold-based segmentation, contour extraction, and surface reconstruction (Fig. 1b).

The validation of the suggested method has been carried out with the help of a computer tomography scan (CT) of a skull of 23-year-old modern human male (Fig. 2a). The data were downloaded from the public space of NESPOS (Neanderthal Studies Professional Online Service) database ( The example dataset was chosen because of the good preservation of the mandible (ID: CT_CSIC_OL1112).

Figure 2.

(a) Frankfurt and midsagittal plane identified on the skull downloaded from NESPOS; (b) in blue the right hemimandible and in red the left hemimandible: the condylar process of the left hemimandible was virtually resected simulating the damage of Pico's mandible; (c) mirror-copy of the right hemimandible (model A) and virtual resection of the condylar process.


The reconstruction procedure was carried out by means of simulating the loss of the left condylar process on the complete mandible dataset. In the IMEdit module of PolyWorks® 10.1 (InnovMetric Software, Québec, Canada), the downloaded skull was oriented in the Frankfurt plane and the midsagittal plane was subsequently constructed (Fig. 2a). The midsagittal plane allowed for the identification of the two hemimandibles (Fig. 2b): the right hemimandible (in blue) and the left hemimandible (in red). Here, the left condylar process of the mandible was marked with the polyline tool to most accurately resemble the damage to Pico's mandible. Afterward, the polyline was used for condylar process resection (Fig. 2b).

Two methods of virtual reconstruction of the missing part were utilized: (1) reflection of the right hemimandible (model A) and replacement of the missing left part by the condylar process extracted from the reflection (Fig. 2c); and (2) the “molding” of model A toward the preserved portion of its left counterpart (model B) with the help of GMM (Gunz et al.,2004; Gunz,2005): the result is a new left hemimandible (model C) (Table 1).

Table 1. List of hemimandible digital models
Model AMirror copy of the right hemimandible
Model BLeft hemimandible after condilar process resection
Model CHemimandible obtained “molding” model A toward model B

For the first reconstruction, model A was superimposed to model B using iterative closest point (ICP), an algorithm that minimizes the distance between two point clouds by the least squares method (Besl and McKay,1992; Zhang,1994). The same polyline used for the resection of the condylar process of model B was projected and fitted onto the surface of model A for extracting its condylar process (Fig. 2c).

For the second reconstruction, a reference template that consisted of four anatomical landmarks and 248 semilandmarks was defined on model A in Viewbox software (dHAL Software, Kifissia, Greece) (Fig. 3).

Figure 3.

(a) Model A with the reference template of landmarks and semilandmarks used for the virtual modelling; (b) four anatomical landmarks (I, infradentale; Cp, coronoid process; L, lingula; Mt, mental tubercle), six curves (Sy, symphysis; Lm, lower mandible margin; Ia, internal alveolar arc; Ea, external alveolar arc; Ra, ramus anterior ridge; Mn, mandibular notch), and curve semilandmarks of the reference template; (c) set of landmarks on model B after minimizing bending energy; (d) three-dimensional digital model of the new left hemimandible (model C) obtained by warping the 252 landmarks of model A into the correspondent landmarks of model B.

Given that only a few anatomical landmarks could be determined on the preserved part, we have chosen to use an excessive amount of curve and surface semilandmarks to achieve the best description of the geometric shape of the complete hemimandible.

In detail, six curves that followed margins of anatomical structures on the hemimandible were marked, and 76 semilandmarks were selected on them (Fig. 3a,b; Table 2). Moreover, further 172 semilandmarks were selected on the surface of model A (Fig. 3a). The algorithm requires constraining sliding semilandmarks by the fixed anatomical landmarks and by curves on the surface (Gunz et al.,2005).

Table 2. List of landmarks and curves identified on the 3D digital models of the hemimandibles
NLandmark nameNCurve nameSmlm counta
  • a

    Semilandmarks identified on the curves.

1Infradentale (I)1Symphysis (Sy)14
2Coronoid process (Cp)2Lower mandible (Lm)25
3Lingula (L)3Internal alveolar arc (Ia)9
4Mental tubercle (Mt)4External alveolar arc (Ea)8
  5Ramus anterior ridge (Ra)10
  6Mandibular notch (Mn)10
   Total semilandmarks on curves76

In the next step, a corresponding set of landmarks and semilandmarks on model B was created with the help of the Viewbox software. Once the four fixed anatomical landmarks were marked on model B, Viewbox automatically estimated the position of the curves. To do so, the program warped subsets of curves from the template into the vicinity of model B with the help of the thin-plate spline (TPS) function computed from the fixed anatomical landmarks (Gunz,2005). Following this step, the position of the curves was manually adjusted by translation and projection onto model B. Using the “Auto All” button Viewbox will automatically locate and digitize all curves semilandmarks that can be located on the curves digitized so far. Finally, using the “Auto Digitize” button, all the other points were loaded to quickly digitize all remaining semilandmarks of the dataset. This is accomplished by doing a TPS warping of the template dataset on the currently digitized dataset, using the landmarks and curves semilandmarks that have already been digitized. As a result of the warping procedure, model B has the same set of landmarks and semilandmarks of the reference template.

After placement of all landmarks and semilandmarks onto model B, the geometrical homology of the semilandmarks' positions was improved by repeatedly sliding them against the complete reference dataset and projecting them onto the preserved surface (Bookstein,1997; Gunz et al.,2005). Curve semilandmarks were constrained to slide along tangent vectors of the curves. The movement along tangent surfaces for surface semilandmarks was constrained by fixed landmarks and curves semilandmarks. The displacement of semilandmarks was first optimized so that the bending energy between the template and the target was minimal. The displaced semilandmarks were then projected back onto the surface of the original (Bookstein,1997; Gunz,2005; Gunz et al.,2005). The procedure was repeated until convergence was achieved. In the course of the sliding, missing semilandmarks were allowed to move without constraints (three degrees of freedom), so that the bending energy of the overall deformation was minimal (Fig. 3c).

We performed the next step of reconstruction, that is, warping of the 3D surface from model A onto the landmarks and semilandmarks of model B in Amira 4.1® software. To do so, the complete sets of landmarks and semilandmarks coordinates for model A and model B after sliding were imported into Amira 4.1® software. Then, all of the 252 landmarks and semilandmarks of model A were transformed into the corresponding landmarks and semilandmarks for model B, whereas the surface of the reference hemimandible was automatically warped, so as to minimize the bending energy of the according transformation. This procedure was performed with the help of the Bookstein transformation mode in Amira 4.1® software based on the TPS method (Bookstein,1997). Bookstein mode guarantees that all landmarks are transformed exactly to their corresponding points, and the nearest neighbor interpolation is used for resampling the final model. As a result of the TPS warping, a third model that was morphologically and morphometrically similar to model B (named model C) was obtained (Fig. 3d; Table 1).

To obtain a 3D model of the missing condylar process, model B was subtracted from model C with the help of the Boolean operation in the IMedit module of the PolyWorks® software. Finally, refinement editing operations, such as filling holes and deleting abnormal faces, were applied to the overall geometry of the 3D model of the condylar process.

A test of the match between the reconstructed condylar processes (obtained from model A and from model C) and model B was performed through the superimposition of the extracted reconstructions to the original left condylar process (Fig. 4a,c) using an ICP algorithm. Moreover, the extent to which reconstructions resembled the original left condylar process was measured by deviation analysis. The procedure was performed with the help of IMInspect module of PolyWorks® 10.1. IMInspect computes the shortest point-to-surface distance of the data points of the reconstructions to the original left condylar process surface displaying the result by means of an error color scale (Fig. 4b,d).

Figure 4.

(a) In red the portion of the condylar process virtually resected from model A and fitted onto model B; (b) deviation analysis between the condylar process of model A and model B: anterior side on the left and posterior side on the right; (c) in red the portion of the condylar process virtually resected from model C and fitted onto model B; (d) deviation analysis between the condylar process of model C and model B: anterior side on the left and posterior side on the right.


The experimental attempt of reconstructing the missing left condylar process by means of reflecting the right hemimandible (model A) was not successful (Fig. 4a,b). Specifically, the extracted condylar process did not fit perfectly well to the break line on the incomplete left hemimandible (model B) (Fig. 4a). The superimposition of the reconstructed and the original condylar process yielded differences ranging between −1.5 and 2.0 mm. (Fig. 4b). In detail, the posterior surface of the condyle and the neck deviated more than 1 mm negatively, as did the area on the anterior surface of the fragment just below the condyle. At the same time, the inferior break area at the anterior side deviated more than 1 mm in the positive direction, giving an impression of global differences in shape between the reconstruction by reflection and the original condyle.

The alternative solution after warping (model C) yielded a better outcome both at the fit with model B (Fig. 4c) and at the superimposition with the original left condyle and the neck (Fig. 4d). Here, most deviations between the two surface areas range ±0.5 mm except for the area on the anterior side below the condyle, which goes up to −1.5 mm in deviation. It is necessary to note that the top of the articulated surface of the mandibular condyle showed similar deviation in both reconstructions, which reached up to +1.5 mm. This suggests that the exact shape of the lost condyle would be difficult to predict given the remaining portion of the left hemimandible.

The aforementioned test demonstrated that prediction of the missing condylar process shape with the help of warping the reflected complete hemimandible onto the remains of the left hemimandible provides the best reconstruction results. Therefore, the decision was made to use this procedure for reconstruction of the left condylar process of Pico's mandible. The exact procedure of reflection of the complete right hemimandible, and the creation of the complete dataset of landmarks and semilandmarks on it was used. It was followed by finding fixed anatomical landmarks and curves on the remains of the left hemimandible with the subsequent warping of the complete semilandmark dataset onto them. Next, iterative sliding and projection of semilandmarks, followed by warping of the surface of the complete right hemimandible's reflection onto the reconstructed complete landmark and semilandmark dataset of the left hemimandible was performed. To verify the correspondence between the reconstruction after warping and the original left hemimandible, the two digital models were superimposed. The deviations between the two surface areas range ±0.5 mm (Fig. 5a). As mentioned earlier, the final reconstruction of the left condyle was obtained by Boolean subtraction of the original left hemimandible from the reconstruction (Fig. 5b,c).

Figure 5.

(a) Color coding differences between the reconstruction and the original left hemimandible: deviation range is ±0.5 mm; (b) the original left hemimandible with assembled the reconstructed condylar process (black color); (c) the condylar process was isolated by means of a Boolean subtraction between the original left hemimandible and the reconstruction.

The reconstruction of the left condyle was virtually joined with the damaged left hemimandible (Fig. 5b) and fitted to the cranium of Pico della Mirandola (Fig. 6). The test was performed in IMedit module of PolyWorks 10.1®. First, the cranium was oriented in the Frankfurt plane. Then, using the manual alignment options, the mandible with the reconstructed part was translated until the condyles were in the glenoid cavities and the right teeth (lower first molar, upper second premolar, and upper first molar) were in a correct occlusal relationship. A dynamic orientation process was used to arrive at the best possible alignment of the mandible and the cranium.

Figure 6.

In black the reconstructed condylar process: (a) frontal and perspective view of Pico's skull; (b) basal view of Pico' skull in which both the condyles are positioned in the respective glenoid cavities; (c, d) perspective views of the left lateral side of Pico's skull.

As underlined in Fig. 6b, both the condyles fit well in the glenoid fossa. The left reconstructed condyle is correctly positioned within the boundaries of the articular surface and is well proportioned to the size of the left glenoid fossa (Fig. 6b–d).

After the previous virtual validation between the cranium and the restored mandible, the three elements (cranium, mandible, and the condylar process) were fabricated by a rapid prototyping system (Fig. 7). Rapid prototyping is a method of manufacturing in which physical models are built up layer-by-layer in an additive process. This type of technology allows the construction of physical models characterized by geometric complexity, such as skulls, which cannot be achieved through conventional subtractive processes by removing material from an original starting block. The three physical models were generated by stereolithography (SLA) with a SLA 7000 (3D-Systems).

Figure 7.

Physical models of Pico's left condyle (a) mandible (b) and skull (c: frontal view; (d: left lateral view; (e: detail of the left condyle from posterolateral view) prototyped by SLA 7000 (3D-Systems). The left condyle was built from a transparent orange colorable SL material.

It allows for the creation of prototypes by the addition of subsequent layers in 0.1 mm thickness of Renshape SL 7570 photopolymers (a rigid material, with a high flexural strength and excellent clarity). The cranium (Fig. 7c,d) and the mandible (Fig. 7b) were built colorless, whereas the condyle (Fig. 7a) was built from a transparent orange colorable SL material to emphasize the difference of the reconstructed part.

After some manual finishing of the three plastic models, all prototyped elements were assembled demonstrating a perfect fit (Fig. 7c–e).


In this study, we have applied methods of geometric morphometrics to the reconstruction of the complete shape of the mandible belonging to Pico della Mirandola, the Italian humanist of the 15th century. These methods have supplied good results for missing data reconstruction in the area of palaeoanthropology (Gunz et al.,2004; Neubauer et al.,2004; Gunz et al.,2005) and have now demonstrated their potentiality in history and forensics. The 3D physical model of the mandible and cranium has been prototyped to facilitate the restoration of facial features, thus providing an excellent example of the valorization of the skeletal remains.

A foreseeable successful influence of the virtual approach and GMM can also be recognized in surgical fields. For example, Cunningham et al. (2005) highlighted the usefulness of the 3D models fabricated from SLA for planning reconstructive surgical operations. These models present the possibility to carry out not only surgical simulation but also provide a template for modification of bone plates and for the manufacture of implants. Furthermore, it is possible to create custom-made implants using SLA-generated models from materials that are biocompatible and exhibit osteoconduction and induction characteristics (Wong et al.,2002; Perez-Arjona et al.,2003; Cunningham et al.,2005; Bártolo and Bidanda,2008). In this way, undercuts and internal cavities that reproduce anatomical shapes can be created (Wong et al.,2002; Bártolo and Bidanda,2008). Therefore, it is likely that custom-made implants will be preferred in the future because they are more similar to the healthy original bone, they would create less danger of attrition and destruction of adjoining surfaces, and they would be esthetically sound.

For this reason, we stress the reproducibility of mandible reconstruction with the help of the presented methods. Here, the complete right hemimandible was sufficient to carry out reconstruction of the missing part on the left hemimandible. The geometric morphometric warping of the shapes in accordance with homologous landmarks has provided considerably better results than the mere reflection of the right part. Moreover, the bilateral asymmetry of the human face is nonuniform preventing the usage of uniform scaling as the only means of reconstruction after reflection.

A similar procedure can be used to reconstruct other missing parts of a hemimandible. In case no symmetric part is available for reconstruction, GMM can still provide an opportunity to recreate lost areas by means of using either another individual who is similar to the “patient” by age and major morphological characteristics or a consensus shape between a number of individuals in a population. An even more precise method for reconstruction of missing data involves the calculation of multivariate shape regression within a population of individuals (Gunz et al.,2004). The major constraint of the 3D geometric morphometric approach to reconstruction is in the size of the region to be reconstructed in comparison to the data present. Although still possible, the resulting reconstruction may be quite dissimilar to the original. In palaeoanthropology, for example, it is not considered reasonable to reconstruct posterior neurocranium if only the face is present (Gunz,2005). The same cautious guidance should be adopted in other areas of application of the GM methods.


The multidisciplinary integration of different fields and techniques combining anthropological–anatomical expertise, technical modeling skills, and GMMs for the reconstruction of the left condylar process of the Pico della Mirandola's mandible is a straightforward example that demonstrates how virtual anthropology could be successful if used in surgical fields.

The usage of GM methods and methods of virtual reconstruction on the one hand and ever wider availability of biomaterials for prototyping on the other have a high potential in facilitating improvement of the physical models to be created in replacement of missing skeletal parts.

For this reason, a closer collaboration is recommended between virtual anthropology and the medical field.


The authors thank Michael Coquerelle and Demetrios Halazonetis for their help and precious advices. They also thank the staff of the Radiology Department of Ravenna Hospital (Ravenna, Italy) for the support provided on technical aspects about CT scanning. They are grateful to Bruno Kuen and z-werkzeugbau-gmbh in Dornbirn, Austria for the production of the stereolithographic 3D-models. They thank Stephanie Kozakowski for editing this manuscript. Two anonymous reviewers gave important remarks and helped to increase the quality of a former version of the manuscript significantly.