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Geometric Morphometric Methods for Bone ReconstructionThe Mandibular Condylar Process of Pico della Mirandola.

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THE ANATOMICAL RECORD 292:1088–1097 (2009)
Geometric Morphometric Methods for
Bone Reconstruction: The Mandibular
Condylar Process of Pico
della Mirandola
Department of Palaeoanthropology and Messel Research,
Senckenberg Research Institute, Frankfurt am Main, Germany
Department of History and Methods for the Conservation of Cultural Heritage,
University of Bologna, Ravenna, Italy
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 fitC 2009 Wiley-Liss, Inc.
ting accuracy. Anat Rec, 292:1088–1097, 2009. V
Key words: virtual anthropology; condylar process; geometric
morphometrics; stereolithography
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).
Grant sponsor: EU Marie Curie Training Network; Grant
number: MRTN-CT-2005-019564 EVAN.
*Correspondence to: Dr. Stefano Benazzi, Senckenberganlage
25, D-60325 Frankfurt am Main, Germany.
Fax: 0049-(0)-6975421558. E-mail:
Received 15 December 2008; Accepted 25 April 2009
DOI 10.1002/ar.20933
Published online in Wiley InterScience (www.interscience.wiley.
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 (Is can 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. Selfevidently, 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 simu-
lated 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).
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
C Mercury Computer Systems, Chelmsford, MA). The
models were achieved semiautomatically by thresholdbased 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).
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 PolyWorksV 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).
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
Fig. 1. (a) Left lateral view of the skull of Pico della Mirandola; (b) 3D digital model of the mandible of
Pico della Mirandola.
Fig. 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 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).
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.
TABLE 1. List of hemimandible digital models
Model A
Mirror copy of the right hemimandible
Model B
Left hemimandible after condilar
process resection
Hemimandible obtained ‘‘molding’’
model A toward model B
Model C
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;
Fig. 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.
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).
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;
TABLE 2. List of landmarks and curves identified on the
3D digital models of the hemimandibles
Landmark name
Curve name
Smlm counta
Infradentale (I)
Coronoid process (Cp)
Lingula (L)
Mental tubercle (Mt)
Symphysis (Sy)
Lower mandible (Lm)
Internal alveolar arc (Ia)
External alveolar arc (Ea)
Ramus anterior ridge (Ra)
Mandibular notch (Mn)
Total semilandmarks on curves
Semilandmarks identified on the curves.
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 4.1V
software. To do so, the complete sets of landmarks and
semilandmarks coordinates for model A and model B after sliding were imported into Amira 4.1V 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 4.1V 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 PolyWorksV 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 PolyWorksV 10.1. IMInspect comR
putes 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).
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 þ1.5 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
Fig. 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.
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).
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 10.1V.
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.
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).
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
Fig. 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.
Fig. 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.
Fig. 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.
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 custommade implants using SLA-generated models from materials that are biocompatible and exhibit osteoconduction
and induction characteristics (Wong et al., 2002; PerezArjona 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.
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process, morphometric, pico, condylar, mandibular, method, mirandola, dell, bones, geometrija, reconstruction
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