INFLUENCE OF PARAMETERS PROCESSING ON THE
MICROSTRUCTURE OF Ti6Al4V ALLOY IN DMLS PROCESS USED
FOR CRANIOMAXILLOFACIAL RECONSTRUCTION
Maria A. Larosa1,2, André L. Jardini1,2, Cecília A. C. Zavaglia1,3, Paulo Kharmandayan1,4,
Davi Calderoni1,4, Rubens Maciel Filho1,2
1
Institute of Biofabrication (INCT-BIOFABRIS), Campinas (SP), Brazil
School of Chemical Engineering, State University of Campinas, Campinas (SP), Brazil
3
School of Mechanical Engineering, State University of Campinas, Campinas (SP), Brazil
4
School of Medical Sciences, State University of Campinas, Campinas (SP), Brazil
E-mail: malarosa@gmail.com
2
Abstract. Rapid manufacturing techniques are very useful in the medical field. This technology has been applied
in the biomodels production that allow a surgical planning and mainly in the production of personalized
implants and prostheses for craniomaxillofacial reconstruction. Fabrication of implants tailor always presented
difficulties that result in high cost. The use of rapid prototyping makes it possible to manufacture custom
prosthetic implants with sizes, shapes and mechanical properties optimized. Depending of the combination of
operational parameters is possible to control the porosity of the material. Rapid prototyping uses only digital
information, disregarding all kinds of physical models, obtaining directly the final implant and reducing the
manufacture time. The aim of this paper is to study the influence of some laser processing parameters in the
microstructure of Ti6Al4V samples produced by Direct Metal Laser Sintering (DMLS). Microstructural
characterization and microhardness tests were made to analyze the microstructures obtained in these samples.
Keywords: Rapid prototyping, Cranioplasty, DMLS, Ti6Al4V alloy
1.
INTRODUCTION
To meet the great demand for orthopedic surgical procedures for repair or replacement
of body parts, it is necessary to develop biomaterials and surgical techniques more advanced.
Implant materials for fracture fixation must be strong, ductile, and biocompatible in order to
fit the bone structure. Currently, the main materials used for this purpose are metals such as
stainless steel, cobalt chromium alloys or commercially pure titanium and its alloys.
However, titanium has been the chosen material for the craniomaxillofacial applications
[Bertol, 2010; Murr et al., 2009; Petersen et al., 2005].
Discovered in 1791 by William Gregor, British mineralogist [Leyens et al., 2003],
titanium - and more recently, its alloys - have been used for decades in fracture fixation and
reconstruction of joints because it fulfills the necessary requirements to biomedical
applications, such as corrosion resistance, biocompatibility, elasticity modulus (the closer to
human bone - 10 to 30 GPa - the better), fatigue resistance and good processability
[Parthasarathy et al., 2012; Lütjering et al., 2007; Yaszemski et al., 2004].
Severe traumas in facial structure require a large number of plates and screws, and
titanium implants are particularly suitable [Bertol, 2008]. The four commercially pure
titanium grades (ASTM F67), Ti-6Al-4V ELI (ASTM F 136) and “standard” Ti-6Al-4V
(ASTM F 1472) were the first titanium biomaterials introduced in implantable components
and devices [Brunette et al., 2001]. In these materials, some alloying elements are alpha (hcp)
phase stabilizer while others are beta (bcc) phase stabilizer. Alloying elements that stabilize
alpha titanium include aluminum, tin and zirconium, and alloying elements that act as beta
stabilizer include vanadium, molybdenum, niobium, chromium, iron and manganese. The
manipulation of these crystallographic variations, through alloying addition and
thermomechanical processing, results in a wide range of alloys and properties [Abramson et
al., 2004; Brown et al., 1996].
1.1
Rapid prototyping in medicine
Rapid prototyping (RP) is a technique of fabricating based on successive addition of
flat layers of material. This technique has been consolidated in the industrial environment as
an essential technology to speed the development of new products [Koike et al., 2011].
Using RP in medicine is a quite complex task which implies a multidisciplinary
approach and very good knowledge of engineering as well as medicine; it also demands many
human resources and tight collaboration between doctors and engineers [Popat, 1998]. As it is
well known, the term "rapid prototyping" refers to a number of different but related
technologies that can be used for building very complex physical models and prototype parts
directly from 3D CAD model. There are more than 20 rapid prototyping systems on the
market and the main RP technologies used are stereolithography (SLA), selective laser
sintering (SLS), direct metal laser sintering (DMLS), selective laser melting (SLM), fused
deposition modeling (FDM), 3D inkjet printing (3DP) and electron beam melting (EBM)
[Khan and Dalgarno, 2009]. These systems are classified according to the initial state of raw
material, which can be liquid, solid or powder form. RP technologies can use wide range of
materials (from paper, plastic to metal and nowadays biomaterials) which gives possibility for
their application in different fields. Preliminary research results show significant potential in
application of RP technologies in many different fields including medicine [Milovanović and
Trajanović, 2007].
In the late 80's, the rapid prototyping was integrated into the computer tomography
(CT) and magnetic resonance (MR) techniques, making it possible to obtain solid biomodels
that reproduce the anatomic structures [Antas et al., 2008; Truscott et al., 2007]. These
biomodels can be used for teaching purposes, diagnosis and treatment of patients, surgical
planning and communication between professional and patient. Thus, the biomodels facilitate
surgery, improve results, reduce infection and rejection risks, complications and duration of
surgery [Hench, 1991; Gopakumar, 2004; Wu et al., 2009; Bertol et al., 2010; Oliveira et al.,
2007]. The use of integrated techniques offers a significant potential cost savings for health
systems, as well as the possibility of offering a dignified life for a huge number of people.
Rapid prototyping can be used by professionals working in orthopedics, neurosurgery,
surgery and traumatology orthognathic and maxillofacial, craniomaxillofacial surgery and
plastic, implant dentistry, oncology, among others.
An application of rapid prototyping in the medical field to be considered is the bone
reconstructive surgery, for example, craniofacial reconstruction [Gopakumar, 2004; Hieu et
al., 2003]. Among the congenital defects, craniofacial anomalies are a group of highly diverse
and complex that, together, affects a significant proportion of people in the world [Niinomi,
2002]. Besides the cases of congenital deformities, there is an occurrence of acquired
craniofacial defects due to other diseases - tumors, for example. In the last four decades, a
growing volume of cases of facial trauma has also been observed, the being closely connected
with the increase of traffic accidents and urban violence [Abramson et al., 2004]. It can also
be used in dental implants, because the models provide information on size, direction and
location of implants, as well as anatomical information, for example, the path of the
mandibular canals. In cases of bone abnormalities, it is important note that the gain in the
patient's functional and psychological terms and the increased quality of life after surgery
justifies the costs of the application of new technologies [Foggiato, 2006].
Fabrication of prostheses and implants tailor always presented difficulties that result in
high cost. This is mainly to anatomical differences of patients. The solution employed until
now has been to produce prostheses with a number of sizes and use what best fits the patient.
With the use of rapid prototyping makes it possible to manufacture custom prosthetic
implants prior to surgery. The implants can be designed specifically for a particular patient,
with sizes, shapes and mechanical properties optimized. For this, it uses only digital
information, disregarding all kinds of physical models, obtaining directly the final implant
and reducing the manufacture time.
1.2
Medical model manufacturing
According to Milovanović and Trajanović [2007], the procedure for making 3D
medical models using RP technologies implies few steps:
• 3D digital image;
• Data transfer, processing and segmentation;
• Evaluation of design;
• RP medical model production and validation.
3D digital image
3D digital image can be obtained by using computer tomography - CT scanner or MRI
data. These imaging technologies are used for modeling internal structures of human’s body.
Medical models made from this data must be very accurate and because of this they require a
spiral scanning technique which allows to do full volume scanning. This makes possible to
generate a high number of slices (recommended thickness 1-2 mm) and what is very
important, the pixel dimension in each slice could be reduced depending on each case. Most
CT and MRI units have the ability of exporting data in common medical file format - DICOM
– digital imaging and communication in medicine [Maciel Filho, Bineli and Jardini, 2009;
Milovanović and Trajanović, 2007].
Data transfer, processing and segmentation
After saving CT or MRI image data, they should be transferred to RP laboratory. The
next step is processing these data, which is a very complex and important step, that the quality
of the final medical model depends on [Schneider, Decker and Kalender, 1999; Berce, Chezan
and Balc, 2005].
For this step engineers need software package (InVesalius) in which they can make
segmentation of this anatomy image, achieve high resolution 3D rendering in different colors,
make 3D virtual model and finally make possible to convert CT or MRI scanned image data
from DICOM to .STL (structure triangularization language) file format. These software
packages allow making segmentation by threshold technique, considering the tissue density.
In this way, at the end of image segmentation, there are only pixels with a value equal or
higher than the threshold value [Martins et al., 2008].
The virtual model of internal structures of human’s body, which is needed for final
production of 3D physical model, requests very good segmentation with a good resolution and
small dimensions of pixels. This demands good knowledge in this field which should help
engineers to exclude all structures which are not the subject of interest in the scanned image
and choose the right region of interest ROI (separate bone from tissue, include just part of a
bone, exclude anomalous structures, noise or other problems which can be faced). Depending
on complexity of the problem this step usually demands collaboration of engineers with
radiologists and surgeons who will help to achieve good segmentation, resolution and a
finally accurate 3D virtual model. Figure 1 shows the CT-images of a jaw using the
InVesalius software and 3D CAD.
Figure 1. InVesalius Free-Software Packages for Image Segmentation.
Evaluation of design
The CT-images together with the surface model of the defect are no longer exclusively
used for diagnostic purposes. The images give a clear picture of the geometric aspect of the
problem and the surgeon can get an idea on what problems he or she will meet during surgery.
With this information it is possible to make a detailed planning of the surgery [Ma, Lin and
Chua, 2001].
Usually, implants are made of relative flexible material so they can me shaped and
reshaped if necessary during the operation. Since the planning can now be done with a
controlled accuracy, it is possible to design a custom fit implant based on the surface model of
the defect and the planning of the surgeon. Since there was a considerable amount of time
between the scanning and the actual surgery, a serious clearance was taken into in account in
the design to compensate for the possibility that more bone needed to be removed.
The design of the implant itself requires the possibility to work easily with scanned
data. Since models of the skull are extremely complex and literally organic in shape, it is very
difficult to do the modeling with conventional CAD-systems. The models coming from
InVesalius are surface models that are build up out of facets (triangles). They are transferred
through an STL-file1. Conventional CAD-systems usually can import these files but in order
to do operations on these data, it is necessary to convert the facet model into CAD-surfaces
through the usually lengthy and difficult process of reverse engineering. For making surgical
tools, incorporating other objects (fixation devices, implants), bone replacements, producing
patterns for making fixtures or templates or other complex problems in different fields of
medicine, this virtual model in IGES or STL format is processed using some CAD package.
This is necessary for evaluation of design, quality of the made model, checking possible
errors or other important steps which depends on the concrete case.
Designing implants is usually a matter of combining organic, scanned shapes together
with engineering components (like fixtures). In this case study this is clearly visible. On the
jaw implant, the holes are made to enable fixing the implant into the existing bone with
conventional titanium screws. After this step 3D virtual model is ready for production.
RP medical model production and validation
Using the rapid prototyping technologies, the objects are manufactured by adding the
material in successive layers. This step implies choosing the right RP technology according to
the purpose of model itself as well as demanding accuracy, surface finish, visual appearance
of internal structures, number of desired colors in the model, strength, material, and
mechanical properties. Finally 3D virtual model in STL format should be inputted into the RP
commercial software for production of 3D physical model. The quality of physical model is
influenced, in the first place, by quality of input STL file but also by orientation of the model
in RP machine and by choosing the right parameters for building the model in the same
machine. The design of the jaw implant is shown in Fig. 2.
Figure 2. The jaw implant in ABS jaw model and titanium.
After production of 3D physical model, it is performed a digital inspection to validate
the dimensional precision of process. For this, the surface of built part is scanned using a
three-dimensional laser scanning system. Through this analysis, it is possible to compare the
original CAD three-dimensional model with the physical model [Bertol et al, 2010]. If there
are no errors the physical model is ready for application.
In the craniomaxillofacial repair have been reported several cases of successful
application of 3D modeling technologies and in achieving rapid prototyping of customized
implants.
Bertol et al. [2010] reported the use of computer tomography images to obtain a 3D
virtual model for the virtual procedure of resection of affected part of the jaw by a tumor and
subsequent design of the implant to replace the region affected by the technique of mirroring
a plane of symmetry, where the healthy portion of the jaw is mirrored and used for
reconstruction of the region removed. To begin the study, a Computer Tomography (CT) of
one patient’s skull was taken. With CT data images, it was possible to visualize the osseous
structure of the skull, as well as the regions affected by a tumor. To obtain the 3D
visualization, some software such as Materialise Mimics™ is able to join the CT data slices to
produce an accurate 3D representation model. To obtain a virtual model with an appropriate
accuracy, some specifications were required, such as maximum of 1.0 mm of slice thickness,
1.0 mm of reconstruction distance and a 512 x 512 matrix.
The first step for the implant design was to remove the area affected by the tumor.
After resection, the file was manipulated in Rhinoceros software. A mirroring operation using
a symmetry plane was enough to generate the 3D implant model on the left side, using a bone
structure from a non-injured site as a reference. Therefore, it was possible to design the
suitable shape for the implant. The virtual models are shown in Fig. 3a. The implant was
manufactured of titanium (Ti-6Al-4V) using the technique of direct metal laser sintering, as
shown in Fig. 3b. After the production, this implant was scanned by 3D laser scanning system
for comparison with the dimensional virtual model, with differences no more than 0.05mm,
which demonstrates the precision of the method (Figure 3c).
Drstvensek et al. [2008] also reported successful cases that demonstrate the great
potential of rapid prototyping in the medical field. In one case reported was dealt a severe
facial asymmetry. The methodology used was similar to that used by Bertol et al. [2010]. 3D
models were obtained from Computer Tomography images and the implant has been
developed in the virtual environment by mirroring the unaffected region, as shown in Fig. 4a.
Figure 4b shows the implant produced in Ti-6Al-4V alloy.
Another case reported by Drstvensek et al. [2008] used the same techniques in the
construction of an implant for skull and subsequent 3D scanning for dimensional control. In
comparison with the virtual model, the implant (Figure 5a) presented variations of 0.8 to 1.0
mm in some regions (Figure 5b). According to the author, due to the fact the region in
question is not located at a critical point, the implant was successfully approved and
implemented. In both cases were used the DMLS prototyping tecnhique and Ti-6Al-4V alloy.
Figure 3. Obtaining of 3D model (a), implant manufactured by DMLS (b) and virtual
inspection [Bertol et al., 2010].
Figure 4. Virtual model of the region to be reconstructed (a) and implant manufactured by
DMLS (b) [Drstvensek et al., 2008].
Figure 5. Prosthesis manufacture by DMLS (a) and virtual geometric inspection result (b)
[Drstvensek et al., 2008].
1.3
Direct metal laser sintering (DMLS)
In 2004, the EOS GmbH developed the EOSINT M 270 system, which uses a solidstate fibre laser enabling fast processing with high detail resolution. The ytterbium fibre laser
used in the EOSINT M 270 has a beam quality M2 of almost 1.0, which enables it to be
focused to less than 100 μm beam diameter over the entire 250 mm x 250 mm build area. The
200 W power corresponds to an average power intensity of up to 25 kW/mm 2. This laser also
has a shorter wavelength than CO2 lasers, giving higher absorption in metals and therefore
resulting in higher effective power and enabling higher build speeds [Nyrhilä et al., 2007;
Shellabear and Nyrhilä, 2004a; Freitag, Wohlers and Philippi, 2003].
The choice of material is of course critical to the performance of DMLS for any
particular intended application, as it is for most manufacturing methods (casting, forging,
deep drawing, machining etc.). And as with other manufacturing methods, the process
parameters must be adapted to the material in order to produce optimal results. The choice of
material is of course critical to the performance of DMLS for any particular intended
application, as it is for most manufacturing methods (casting, forging, deep drawing,
machining etc.). And as with other manufacturing methods, the process parameters must be
adapted to the material in order to produce optimal results. At first, some materials were
developed specifically for the DMLS process, with the focus on achieving a good
processability and acceptable properties for the main users' applications [Santos et al., 2006;
Shellabear and Nyrhilä, 2004a].
Today, a wide variety of alloys are available for use in DMLS, as the light alloys of
titanium, which are commonly used in applications with demanding requirements, but parts
are typically expensive to manufacture conventionally, because titanium is generally difficult
to cast and machine. This makes titanium alloys an ideal target for DMLS. Of special interest
in medicine, the Ti-6Al-4V and TiCP (commercially pure titanium) are characterized by
excellent mechanical properties and corrosion resistance combined with low specific weight
and biocompatibility [Shellabear and Nyrhilä, 2004b].
Among the advantages of DMLS is the ability to process titanium and other metal
powders directly on the machine, without the use of ligands and without the need for
aftercare. The manufacturing stage of a model and a mold for casting is not necessary, which
reduces cost and manufacturing time of implant. Moreover, geometries inadequate to casting
process and hollow models can be produced [Traini et al., 2008].
DMLS is a complex thermo-physical process that depends on a lot of material, laser,
scan and environmental parameters. The determination of parameters is very important to
reach high precision. The optimal parameter setting can be found by a combination of
empirical research and numerical simulations. For each kind of material, a parameter study
must be performed to optimize the process regarding material density. The porosity, which
has a harmful effect on the mechanical properties, can be avoided by an optimal scan strategy
and appropriate energy density [Facchini et al., 2010; Kruth et al., 2005; Ramesh, Srinivas
and Srinivas, 2007].
According to Vandenbroucke and Kruth [2007], the energy density is a parameter that
represents the energy supplied by the laser beam to a volumetric unit of powder material and
can be determined by four process parameters, as shown in Eq. (1):
E density 
Plaser
v scan  s hatch  t layer
(1)
where, Edensity = energy density [J/mm3], Plaser = laser power [W], vscan = scan speed [mm/s],
shatch = hatch spacing [mm] and tlayer = layer thickness [mm].
In the present work was investigated the influence of some laser processing parameters
in the porosity and microstructure of Ti6Al4V samples produced by Direct Metal Laser
Sintering (DMLS). Porosity of samples with different processing parameters was analyzed by
optical microscopy. Microstructural characterization and microhardness tests were made to
analyze the microstructures obtained in these samples.
2.
MATERIALS AND METHODS
2.1
Specimens manufacturing
Specimens studied in this work were manufactured by Direct Metal Laser Sintering
(DMLS) using the EOSINT M 270 machine (Figure 6a). In DMLS technique, the powder is
spread and processed by the action of a CO2 laser in an inert environment and thermally
controlled inside the chamber. A scanning mirror system controls the laser beam describing
the geometry of the layer on the surface of the material spread. With the incidence of the
laser, the particles of material are heated and reach its melting point, joining each other and
also to the previous layer. When the material solidifies, a new layer of powder is added and
the laser scans again the desired areas, in other words, after a layer to be sintered, a new layer
is deposited, and so on to finish the construction of the piece [Truscott, 2007; Volpato, 2007].
The material used to production of the specimens was a Ti6Al4V alloy commercial
powder. Figure 6b shows that this powder presents a spherical morphology with average
particle size of 57 µm. During processing, argon gas was used to control the oxygen levels
inside the chamber, acting also as a protective gas.
To investigate the influence of energy density in the microstructure of Ti6Al4V alloy,
several specimens, with 12 mm in diameter and 12 mm thick, were manufactured with
different combinations of processing parameters, varying the laser power and scan speed and
keeping constant the layer thickness and hatch spacing. Laser power varied between 150 and
190 W and the scan speed between 1000 and 1500 mm/s. The values of layer thickness and
hatch spacing used were of 30 µm and 100 µm, respectively.
(a)
(b)
Figure 6. DMLS machine (cortesy of EOS company) (a) and micrograph of Ti6Al4V alloy
powder used (b).
2.2
Specimens characterization
Specimens manufactured by DMLS were sectioned using a Buehler diamond blade
and prepared by conventional metallographic techniques. Final polishing was made using a
mixture of colloidal silica (0.04 µm) and hydrogen peroxide. Porosity of polished samples
was analyzed by optical microscopy using Olympus microscope model BX 60M and the
software Image Pro Plus 5.1 of Media Cybernetics.
Then, polished samples were etched with Kroll’s reagent (5%HNO3 – 10%HF).
Microstructural characterization was made by scanning electron microscopy, using Zeiss
microscope model EVO MA15 and the software Smart SEM.
Vickers microhardness tests were performed according to ASTM E384-10 standard,
using Shimadzu digital microdurometer, model HMV-2T. The applied load was 500 gf for 10
s. It were performed 20 readings and calculated an average value from them.
3.
RESULTS AND DISCUSSION
3.1
Porosity
The different combinations of processing parameters used in DMLS process resulted
in fabrication of samples with different values of energy density. Figure 7 shows, for each
sample, the value of energy density (Edensity) involved in its manufacturing and one
micrograph with its porosity.
Figure 7a shows that for lowest energy density used in DMLS process there was the
formation of large pores. This means that the energy of 38 J/mm3 was not sufficient to melt
completely the Ti6Al4V powder during the process, which can be attributed to the high laser
scan speed used in this case (1500 mm/s). Higher the laser speed, lower is the energy
absorbed by the powder at the time of sintering, resulting in a material with high porosity.
Figure 7. Influence of operating parameters on the Ti6Al4V alloy. Energy density supplied
during manufacturing and porosity obtained for each sample.
3.2
Microstructural characterization
Figure 8 shows the microstructure obtained for the samples with different processing
parameters. All samples present a fine microstructure, constituted by hexagonal α’ martensite
with acicular morphology.
Some authors report that the transformation of the bcc β phase to the hexagonal α
phase in titanium alloys can occurs martensitically or by a diffusion controlled nucleation and
growth process depending on cooling rate and alloy composition. On fast cooling through the
β transition temperature, the β phase can transform martensitically to α’. On slower cooling, β
can transform by nucleation and growth to Widmanstätten α phase [Lütjering and Williams,
2007; Joshi, 2006].
The presence of orthogonally oriented martensite plates are shown by micrographs
with higher magnification in Fig. 8. According to Ramosoeu et al. [2010], the formation of
martensite plates in material means that the cooling rate during laser sintering was high
enough to induce the martensitic transformation. Since the process involves melting of thin
layers, with approximately 30 μm, the fast cooling enables this transformation.
Figure 9 shows the results of the microhardness tests. Comparing the porosity, shown
in Fig. 7, with the average hardness obtained to the samples produced with different energy
densities, it is possible to note no significant variation in the microhardness, except for the
sample with energy density of 38 J/mm3. In this case, microhardness decreased (325 HV) with
decreasing energy density due to increasing porosity (Figure 7a). The sample with energy
density of 45 J/mm3 presents the highest average microhardness (370 HV) and, as shown in
Fig. 7d, its microstructure is the less porous.
Figure 8. Microstructure of samples produced by DMLS.
Vickers microhardness (HV)
380
370
360
350
340
330
320
310
300
35
40
45
50
55
60
3
Energy density (J/mm )
Figure 9. Vickers microhardness of samples with different energy densities.
3.3
Prosthesis fabrication by DMLS
In this work, it was constructed an implant for temporomandibular (Figure 10) using
the DMLS technique and subsequent 3D scanning for dimensional control. The parameters
used to manufacturing were energy density of 45 J/mm3, layer thickness of 30 µm and hatch
spacing of 100 µm. These parameters were defined as optimal based on the porosity and
microhardness of the material. In comparison with the virtual model, the implant (Figure 10d)
showed variations of 0.1 to 0.5 mm in some regions (Figure 10e). These values were lower
than those presented by Drstvensek et al. [2008].
Figure 10. Building of temporomandibular device. 3D reconstruction from DICOM data (a),
virtual model (b), orientation of 3D model in machine (c), physical model (d) and virtual
inspection for dimensional control (e).
CONCLUSIONS
Rapid prototyping techniques have been used for the production of custom prosthetic
implants. The implants can be designed according to physical characteristics of each patient.
Microstructural and mechanical properties of implants built by DMLS can be controlled
through by an optimal scan strategy and by combination of some processing parameters as
laser power, scan speed, hatch spacing and layer thickness.
The different processing parameters used in this work showed that it is possible to
control the porosity of material through the energy density supplied during DMLS process.
Lower energy density resulted in a most porous material and with lowest microhardness
value. Despite the different parameters, all samples presented a martensitic microstructure
with acicular morphology, which means that the cooling rate during laser sintering was high
enough to induce the martensitic transformation.
A temporomandibular implant was constructed using the energy density of 45 J/mm3
and it presented variations of 0.1 to 0.5 mm in some regions. These values show the precision
of the DMLS method.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the financial support provide by CNPq (National
Council for Scientific and Technological Development) and FAPESP (Scientific Research
Foundation for the State of São Paulo).
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