The reconstruction of fractured, lost, or deformed bones is important in the fields of paleoanthropology, bioarcheology, forensics, and medicine. In the first three fields, skeletons are often incomplete because of animal scavenging, perimortem injuries, damage during recovery, or as a result of taphonomic processes over time (Krogman and İşcan,1986). In paleoanthropology, deformed or fragmented fossil remains often require complex reconstruction to prepare the fossil for morphological and morphometrical analyses (Ponce De León and Zollikofer,1999). In bioarcheology, mummies, for example, need a preliminary restoration before any further analyses or for exhibition (Fantini et al.,2005; Benazzi et al.,2010). In forensics, the recovery of the craniofacial skeleton in a fragmentary state could hamper any attempted facial reconstruction useful for positive identification (e.g., Wilkinson and Neave,2003; Benazzi et al.,2009b). Finally, bone reconstruction presents a fundamental issue within several surgical disciplines, mainly in orthodontics and maxillofacial surgery (Mehta and Deschler,2004; Young et al.,2007; Madsen et al.,2008; Baumann et al.,2010).
Though reconstructions are used for different purposes (i.e., for fossil remains, mummies, and surgery), the methods employed are essentially the same. Therefore, in a recent contribution (Benazzi et al.,2009a), a collaboration between anthropologists and surgeons was recommended, because the main difference essentially lies in the degree of accuracy each specific reconstruction requires. Highly accurate outcomes are usually more important in surgery than in paleoanthropology, bioarcheology or forensic anthropology: in fact, whereas the main goal of surgical intervention is the restoration of premorbid form and function (Mehta and Deschler,2004; Cunningham et al.,2005; Wong et al.,2010), this requirement is not so crucial for the other fields. This is particularly true for reconstruction of mandibular segment defects, where the three-dimensional (3D) external geometry of the flap or scaffold that fits the anatomical defect holds an important role both in establishing the stress distribution at the organ–implant interface (Leong et al.,2008) and in maintaining esthetic structure (Fonseca,2000; Baumann et al.,2010). Therefore, due to these important requirements, maxillofacial surgery is an appropriate field to test new approaches for bone reconstruction.
To improve the accuracy of the outcome, several noninvasive computerized methods have been developed for virtual reconstruction of the resected portion's physical characteristics (dimensions, volume, and shape). Advancements in computer-aided design/computer-aided manufacturing (CAD/CAM) and rapid prototyping (RP) technologies for scaffold construction (e.g., Hutmacher et al.,2002; Chim and Schantz,2005; Hollister et al.,2005; Lee et al.,2007; Moroni et al.,2008; Zhou et al.,2010), provide a valuable alternative to bone replacement based on autograft and allograft procedures (Mehta and Deschler,2004; Valentini et al.,2005; Moro et al.,2009). Additionally, it has been suggested that further support for “form and functional restoration” could be achieved by the generation of 3D digital models with the help of geometric morphometric methods (Benazzi et al.,2009a; Benazzi and Senck, 2011).
Despite these improvements, correction of mandibular defects after resection procedures due to tumors, developmental abnormalities or trauma, remains a surgical challenge (Mehta and Deschler,2004; Madsen et al.,2008). In fact, it is difficult to replicate the complex 3D conformation of the mandible, so that esthetic issues and functional disturbances, such as malocclusion or temporomandibular joint syndrome, could be generated because of incorrect structural alignment of the replaced portion (Lee et al.,2007).
In this contribution, different approaches for virtual scaffold surface reconstruction in a human hemimandibular body are compared. Accordingly, two resections of different extension are virtually simulated in a 3D digital model of a human hemimandible. Three reconstruction techniques are tested: 1) the mirroring of the unaffected hemimandible; 2) a morphometric approach based on the thin plate splines (TPS) interpolation function; and 3) a combination of TPS and CAD techniques. The CAD approach based on nonuniform rational B-splines (NURBS) alone is not used because of the unsatisfactory results that we would obtain in generating the curve network for wide portions of resected hemimandibular body. The purpose of this work is to visualize and quantify the differences between the outcomes and the original bone to suggest future directions for bone reconstruction.
MATERIALS AND METHODS
Computer tomography data (CT) of a 23-year-old modern human skull (Fig. 1a) were downloaded from the public space of NESPOS (Neanderthal Studies Professional Online Service) database (www.Nespos.org). As an example dataset, a male skull with a well preserved mandible was chosen (ID: CT_CSIC_OL1112). Only the right and left first molars were still present in the mandible (Fig. 1b). Partial absorption characterizes the alveolar process at the level of both the second molars. The sockets of the other teeth were slightly damaged on the buccal side.
Here, we present tests of three methods of virtual reconstruction of the missing part: 1) reflection and superimposition of the complete left hemimandible (model B) and replacement of the missing part with its reflection; 2) the “molding” of model B toward the preserved portion of its right counterpart using the TPS interpolation (Bookstein,1991; Gunz,2005); and 3) a combined CAD approach with the morphological and morphometrical information of the reconstruction obtained by TPS method.
Each method was tested for both of the resections to evaluate their capabilities in different situations. The virtual scaffolds were obtained by means of the same slicing planes used for the virtual resections. Table 1 provides a list of abbreviations for the 3D digital models used in the current contribution.
Table 1. Abbreviations for the 3D digital models used in the current contribution
Right hemimandibular body
Reflection of the left hemimandibular body
First resection simulated in the right hemimandibular body
Second resection simulated in the right hemimandibular body
Reconstruction of the first resection based on TPS warping
Reconstruction of the second resection based on TPS warping
Reconstruction of the first resection based on TPS warping and CAD techniques
Reconstruction of the second resection based on TPS warping and CAD techniques
The fitting between model B and, respectively, Resection-1 and Resection-2 for the first reconstruction was carried out in IMInspect module of PolyWorks. Model B was superimposed to model A using Iterative Closest Point, an algorithm that minimizes the distance between two point clouds by the least squares method (Besl and McKay,1992). Therefore, model B was virtually resected using the slicing planes mentioned above. The obtained portions were subsequently fitted in Resection-1 and Resection-2 respectively.
For the reconstruction based on the TPS interpolation a reference template, comprising five anatomical landmarks and 233 semilandmarks, was defined on model B using the Viewbox software (dHAL Software, Kifissia, Greece). In detail, six curves that followed margins of anatomical structures on the hemimandible were manually marked in the software and 75 semilandmarks were selected on them (Fig. 3a,b and Table 2). Moreover, an additional 158 semilandmarks were selected on the surface of model B. This set of semilandmarks was considered sufficient for an overall representation of the hemimandible's geometric form. The algorithm used here to describe the outlines and surface of the hemimandible requires constraining sliding semilandmarks by the 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
The next step in the Viewbox software required the creation of two corresponding sets of (semi)landmarks (landmarks and semilandmarks) on the right resected hemimandibles. The set of corresponding (semi)landmarks was generated independently for Resection-1 and Resection-2. Nevertheless, as the procedure was similar for both the models, only Resection-1 is considered in the following description.
First, the five anatomical landmarks and the six curves (Table 2) were manually digitized on Resection-1. Second, all curve semilandmarks were automatically located on the curves digitized so far. Finally, all the other surface semilandmarks were automatically warped by doing a TPS interpolation of the reference template on the currently digitized dataset, using the landmarks that have been already digitized. After this step, Resection-1 has the same set of (semi)landmarks as the reference template. These warped points were then projected onto the surface of Resection-1.
Semilandmarks that fell onto the missing area were assigned three degrees of freedom, so that they were not forced to stay on the curve or on the model's surface. By assigning three degrees of freedom, and thereby declaring the points missing, their position is estimated according to the minimum bending energy requirement of the TPS during the sliding step.
Finally, an additional process was required to reach the geometrical homology for semilandmarks between the reference template and the set of semilandmarks generated for Resection-1. Geometrical homology is obtained by relaxing semilandmarks of model A1 against the reference template. Therefore, the semilandmarks of Resection-1 were allowed to slide along tangents to the curves or tangent planes to the surface at the respective point of the location of the semilandmarks (Bookstein,1997). When bending energy of the resulting thin plate spline transformation between Resection-1 and the reference template was minimal (spline relaxation), semilandmarks were again projected onto the original curves (curve semilandmarks) and surface (surface semilandmarks; Bookstein,1997; Gunz,2005; Gunz et al.,2005). This process (sliding and projection) was reiterated until semilandmarks no longer moved; that is, the bending energy was minimized. Semilandmarks with three degrees of freedom (related to the missing parts) were involved in the sliding process, but they were not projected.
The last step involved the 3D surface warping of model B onto the (semi)landmarks of Resection-1. This was accomplished by TPS warping the 238 (semi)landmarks coordinates of model B (reference) onto Resection-1 in Amira 4.1 software. The surface of model B was warped accordingly following the transformation of its set of (semi) landmarks exactly onto the corresponding points on Resection-1. As a result of the TPS warping, a third model (TPS-Resection-1), which is morphologically and morphometrically similar to Resection-1, was obtained. Finally, TPS-Resection-1 was virtually resected by the two slicing planes used in the first resection test.
The same procedures were followed to identify the set of (semi)landmarks for Resection-2, as well as to relax the latter against the reference template and to create the final model in Amira 4.1 (TPS-Resection-2). The only difference lies in the amount of (semi)landmarks with three degrees of freedom for Resection-2 compared to Resection-1. This is due to the larger extension of the resected mandibular body. Using the two planes identified for the second resection test, a portion of TPS-Resection-2 was virtually isolated and placed into Resection-2.
In the third method, CAD techniques were combined with TPS method. In detail, the reconstructed portions obtained by TPS warping were used to assist curve network design, which is useful for NURBS surface generation (Piegl Les and Tiller,1966; Piegl Les,1991). The whole process was carried out in IMEdit module of PolyWorks. First, the two sides of the resected part of each hemimandible (Resection-1 and Resection-2) were marked by curves, setting the external limits of the curve network. Second, further curves between the external limits were subsequently created. The control points of these last curves were marked directly on the surface of the models obtained by TPS interpolation (TPS-Resection-1 and TPS-Resection-1, respectively), so that mathematical representations of the models' geometrical shape were recreated (Fig. 4a). Therefore, the curve network preserves the original morphological information of the resected hemimandible on the sides, which are joined to the morphological information of the models obtained by TPS interpolation.
By augmenting the number of curves that compose the curve network, it is possible to refine the quality of the outcome. In the following example, 13 curves were used: three transverse curves (two in correspondence to the resection's margins and one approximately in the middle between them) and 10 longitudinal curves digitized onto TPS-Resection-2 (four external, four internal, one in the lower, and one in the upper margin of the models; Fig. 4a).
The curve network allows for the creation of NURBS surfaces (Fig. 4b). From this, a mesh—3D surface defined by a set of triangular faces—can be extracted (TPS/CAD-Resection-1 and TPS/CAD-Resection-2, respectively; Fig. 4c).
As statistical analysis cannot be applied because of small sample size, surface deviation analyses in IMInspect module of PolyWorks 10.1 were carried out to visualize and quantify the differences between the reconstructions and the original surface of the resected parts visible in Fig. 2.
With the original models considered as the reference surface, IMInspect computes the shortest point-to-surface distance of the data points from the reconstructions to the reference surface and displays the result by means of an error color scale. Color values range from the minimum to maximum deviation between the reference specimen (the original surface) and the reconstructed forms: negative values (from light blue to purple) show areas smaller than the original surface, whereas positive values (from green to red) represent areas larger than the original surface.
The morphological and morphometric features of the resected portion directly from model B (mirror image of the left hemimandible) did not integrate well into the virtual resections (Fig. 5). In the first resection, model B follows the trend of Resection-1, but its size is larger (Fig. 5a,b). In the lower border of the hemimandible the difference reaches almost 2 mm, and it enlarges up to 3 mm in the upper/posterior margin (Fig. 5c).
Additionally, further problems arise when the size of the resection increases. Asymmetry between the left and right sides becomes more evident, so that the anterior border of model B does not fit with the margin of Resection-2 (Fig. 5d,e). In detail, the major errors are emphasized in the external/anterior border, in which the deviation is almost 3 mm (Fig. 5f).
Better results were obtained using TPS interpolation (Fig. 6). The shape and the size of the reconstructed missing parts fit properly in the resected portions. As displayed in the inspection analysis, the reconstructed models show deviations between −0.5 and 0.5 mm (Fig. 6c,f). Both TPS-Resection-1 and TPS-Resection-2 follow the contour of the original mandible.
It is worthwhile to note the continuity of the lower border of the original hemimandibular body, for TPS-Resection-1 (Fig. 6a) and TPS-Resection-2(Fig. 6d), respectively. As displayed in Fig. 6b, the size of TPS-Resection-1 is reduced when compared to the portion obtained by the resection of model B (compare Figs. 5b, 6b). However, slight deviations from the border of the original hemimandible are still detectable, mainly in the anterior margin of TPS-Resection-2 (Fig. 6e). Furthermore, another limit can be observed using TPS interpolation. In fact, the new model obtained by warping procedures maintains some of the reference shape's morphological characteristics. As shown in Fig. 6d,e, the alveolar sockets of TPS-Resection-2 are not accurate, and, for instance, they could disturb the preparation of dental implants.
The above-mentioned problems were solved by combining TPS method with CAD techniques (Fig. 7). The curve networks were constructed following the surfaces of TPS-Resection-1 and TPS-Resection-2, respectively, therefore restoring the continuity of the hemimandible's shape (Fig. 7a,d). Also in this case, a greater extent of the model surface shows deviations from the original model between −0.5 and 0.5 mm (Fig. 7c,f).
At the same time, the anterior and posterior borders of the reconstructed portions follow exactly the borders identified on the resected hemimandible by the slicing planes. Furthermore, alveolar sockets were removed from the reconstructed models, supporting thus future dental implant surgery (Fig. 7a,b,d,e).
Correction of mandibular defects after resection procedures due to tumors, developmental abnormalities, or trauma remains a surgical challenge (Mehta and Deschler,2004; Madsen et al.,2008; Baumann et al.,2010; Wong et al.,2010). Traditional procedures for the reconstruction of mandibular defects are mainly based on vascularized free flaps (Valentini et al.,2005; Moro et al.,2009; Baumann et al.,2010). However, this approach has several shortcomings: 1) the geometry of the flap, usually a free fibular flap, is difficult to construct and cannot be accurately shaped resemble mandibular form, thus increasing the probability of malocclusion and esthetic problems (Lee et al.,2007); 2) in most cases, two surgical procedures are necessary, namely bone harvesting and implantation (Schuckert et al.,2008); and 3) the accuracy of the reconstruction is difficult to achieve through manual placement of the flap (Roser et al.,2010).
To provide a more precise reconstruction of mandibular defects, computer-based methods have recently been suggested either for virtual surgical planning (Thankappan et al.,2008; Cohen et al.,2009; Roser et al.,2010; Sharaf et al.,2010) or for fabricating customized mandibular scaffolds (Zhou et al.,2010). In both cases, the 3D external geometry of the reconstructed part was mainly achieved by mirroring the unaffected side of the mandible to cover the defect area (Cunningham et al.,2005; Gibson et al.,2006; Lee et al.,2007; Thankappan et al.,2008; Cohen et al.,2009; Zhou et al.,2010). Finally, by means of RP technologies adept to deal with biocompatible, biomimetic, and biodegradable materials, custom-made scaffolds generated in a virtual environment could be used either to accurately reproduce the resection created in a surgical environment (direct method) or to fabricate a positive mold that is subsequently casted with biomaterials (indirect method; Schuckert et al.,2008; Yoshikawa et al.,2009; Xu et al.,2010). Accordingly, methods that reduce the discrepancy between the external shape morphology of the original unaffected bone and the reconstruction should be promoted.
For this reason, starting from CT-data of a human mandible (clinical CT scans can also be used), three methods to produce the 3D external geometry of the scaffold to replace hemimandibular body defects were tested.
The first method concerns the mirroring of the unaffected hemimandible to reconstruct defects on the opposite side. It is well known that human face is asymmetric (Melnik,1992; Song et al.,2007), so that using one side to reconstruct the other one without suitable adjustment provides unsatisfactory results (Benazzi et al.,2009a). Here, we confirm previous results, because some regions of the mirror copy of the unaffected hemimandible show deviations up to 3 mm compared to the original bone (Figs. 5, 8).
In general, both the TPS interpolation and the combination between TPS interpolation and CAD techniques provide the more suitable outcomes, with deviations generally included between −0.5 and 0.5 mm. The TPS interpolation is increasingly used in paleoanthropology for the reconstruction of human fossil remains (Weber,2001; Weber et al.,2001; Gunz,2005; Gunz et al.,2009). Here, the TPS interpolation based on geometric homologous (semi)landmarks has provided considerably better results than the mere reflection and superimposition of the left (opposite) hemimandible. For both of the virtual resections (Resection-1 and Resection-2), TPS method has provided two models (TPS-Resection-1 and TPS-Resection-2), in which the shape and size follow the morphology of the right hemimandible.
Nevertheless, even if the result is better than the simple mirroring of the left side, some problems still remain using the TPS approach. First, the borders of the reconstructed models could not perfectly fit with the contour of the resected portion (Figs. 6, 8). This depends on the position of the (semi)landmarks in relation to the slicing planes. During surface warping from model B to Resection-1/2, whereas (semi)landmarks of the reference (model B) were transformed exactly into the corresponding (semi)landmarks of the resected hemimandibles (Resection-1 and Resection-2), the surface not covered by (semi)landmarks is obtained by interpolation. When the slicing planes pass through this surface, depending on the distance among the (semi)landmarks and the morphological complexity of the surface, the resulting contour of the reconstructed virtual scaffold could fit more or less precisely with the limits of the resection. For example, as shown in Figs. 6e, 8, some discrepancies can be observed in the anterior margin of TPS-Resection-2, where the hemimandible bends toward the symphysis, as well as at the level of the alveolar process in the posterior part of both the models (Figs. 6a,b,d, 8).
Second, the surface of the reconstructed model maintains features of the reference model, particularly the presence of the alveolar sockets. The position of these sockets obtained by the TPS method could not match the position of the original sockets, thus disturbing the insertion of dental implants at a second stage (Sieg et al.,2002).
In connection with the previous issue, a third limit arises. The TPS function bends the spline in proximity to the (semi)landmarks positioned in the preserved mandibular portion, providing the best prediction of the missing landmarks. When the estimation occurs too far from the preserved part, that is, too far from existing landmarks, the TPS grid tends to be almost square (Gunz,2005). In this case, the location of the estimated (semi)landmarks will resemble those of the reference shape (i.e., the alveolar sockets). If the entire ramus has to be reconstructed, the condyle (namely, the farthest part from the mandibular body) will tend to resemble more the reference shape than, for example, the first third of the anterior part of ascending ramus. Consequently, the reconstructed condyle could not fit properly into the glenoid fossa. In this case, further expedients have to be developed in combination with the TPS approach. However, this general problem is a lesser concern in hemimandibular body reconstruction, because the preserved parts delimit well enough the missing portion, giving the possibility to identify the necessary (semi)landmarks for an accurate reconstruction. Moreover, the same procedure based on TPS interpolation could be used to reconstruct other portions of the hemimandible, for example the mid-ramus or the condylar process (Benazzi et al.,2009a).
An interesting approach for reconstruction of the missing part involves the combination of TPS interpolation and CAD techniques. In the latter, defects observed in the margins between the models reconstructed by TPS interpolation (TPS-Resection-1 and TPS-Resection-2) and the original hemimandible, as well as problems related to the presence of the alveolar sockets, were completely solved (Figs. 7, 8). A similar procedure can be used to reconstruct other lacking parts of the right hemimandible (such as the gonion angle).
There are, however, some limits that will be faced in future investigations, as a result of this study. Our results test a special case of virtual reconstruction, where only the mandibular corpus of one side needs to be reconstructed based on an unaffected side. For cases where defects affect both sides of the mandible or affect the midline, other approaches may be required. For example, a mandible from another individual may be used as a reference shape if it is similar to the patient in age, major morphological characteristics, or in the average shape between a number of individuals in a population.
Moreover, it can also be assumed that a less asymmetric mandible could reduce the morphological differences we observed between Method 1 and Methods 2 and 3. When dealing with symmetric mandibles, it may be possible to combine both the mirror and CAD technique instead of using a TPS/CAD approach. Nonetheless, because we believe that symmetric mandibles represent a rare condition, we suggest to use a TPS/CAD approach for mandibular reconstruction.
As emphasized in previous works (Benazzi et al.,2009a; Benazzi and Senck, 2011), here, we have demonstrated how virtual anthropology could provide support for the design process of virtual customized scaffolds. With the development of biomaterials suitable for prototyping, as well as the progress in new 3D printing methods for scaffold material (Schuckert et al.,2008; Yoshikawa et al.,2009; Xu et al.,2010), custom-made scaffolds can be created by combining TPS method and CAD/CAM techniques. Subsequently, the 3D digital model could be prototyped and used directly for mandiblular reconstruction. Through this approach, restoration of mandibular form and function would improve in comparison with autograft and allograft procedures, removing at the same time problems related to invasive surgical procedure and donor site morbidity.
We thank Michael Coquerelle for his help and precious advices to use Viewbox software (dHAL Software, Kifissia, Greece). We are grateful to NESPOS (www.Nespos.org) for providing the CT-Dicom data of the skull CSIC_OL1112.