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1.
J Prosthodont ; 2024 Jun 06.
Artigo em Inglês | MEDLINE | ID: mdl-38845208

RESUMO

PURPOSE: To assess the accuracy of virtual articulation in direct digital workflow (DDW) and indirect digital workflow (IDW) in arches prepared for fixed partial dentures (FPDs). MATERIALS AND METHODS: Five pairs of master models were used in this study representing different clinical scenarios of full dentate (FD), and prepared arches for fixed partial dentures as follows: FD group, short span posterior (SSP group), long span posterior (LSP group), short span anterior (SSA group), and long span anterior (LSA). Fourteen pairs of interarch reference points were added to each set of master models to measure linear interarch distance with a caliper (reference measurements). The direct digital workflow included digital scans and virtual articulation with buccal scan images using an intraoral scanner. The indirect digital workflow included conventional polyvinylsiloxane impressions and bites followed by pouring, mounting, and scanning the stone models in a laboratory scanner. The scanned stone models were virtually articulated with buccal scanning in the laboratory scanner. Digital linear interarch measurements on all virtually-articulated models were compared with reference measurements. The absolute mean differences in linear interarch distances were calculated. The Mann-Whitney test was used for statistical analysis (α = .05). RESULTS: The direct digital workflow produced significantly less linear interarch deviations in the virtually articulated models compared to the indirect digital workflow for all study groups (P < .05). However, the direct digital workflow had significantly less accuracy for virtual articulation in long span posterior, long span anterior, and short span anterior groups compared to the full dentate group.  CONCLUSIONS: Both workflows produced virtually-articulated models with acceptable accuracy. However, the direct digital workflow had significantly better accuracy in all assessed clinical scenarios.

2.
BMC Oral Health ; 24(1): 586, 2024 May 21.
Artigo em Inglês | MEDLINE | ID: mdl-38773502

RESUMO

BACKGROUND: Cement spacer is essential for compensating deformation of zirconia restoration after sintering shrinkage, allowing proper seating and better fracture resistance of the restoration. Studies assessing the effect of cement spacer on fit accuracy and fracture strength of zirconia frameworks are missing in the literature. Therefore, the aim of this study was to evaluate the effect of different cement spacer settings on fit accuracy and fracture strength of 3-unit and 4-unit zirconia frameworks. METHODS: Sixty standardized stainless-steel master dies were manufactured with 2 prepared abutments for fabricating 3-unit and 4-unit zirconia frameworks. The frameworks were assigned into 6 groups (n = 10) according to cement spacer setting (30 µm, 50 µm, and 80 µm) as follows: 3-unit frameworks; 3u-30, 3u-50, 3u-80, and 4-unit frameworks; 4u-30, 4u-50, and 4u-80. The frameworks were assessed for fit accuracy with the replica method. The specimens were cemented to their corresponding dies, and the fracture strength was measured in a universal testing machine. The Weibull parameters were calculated for the study groups and fractured specimens were inspected for failure mode. Two-Way ANOVA followed by Tukey test for pairwise comparison between study groups (α = 0.05). RESULTS: The cement spacer had a significant effect on both fit accuracy and fracture strength for 3-unit and 4-unit frameworks. The 50 µm spacer had significantly better fit accuracy followed by 80 µm, and 30 µm spacers. Both 50 µm and 80 µm spacers had similar fracture strength, and both had significantly better strength than 30 µm spacer. CONCLUSIONS: For both 3-unit and 4-unit zirconia frameworks, 50 µm cement spacer can be recommended over 30 µm and 80 µm spacers for significantly better fit accuracy and adequate fracture strength.


Assuntos
Análise do Estresse Dentário , Teste de Materiais , Zircônio , Zircônio/química , Cimentos Dentários/química , Falha de Restauração Dentária , Humanos , Cimentação/métodos
3.
J Prosthet Dent ; 132(1): 269.e1-269.e6, 2024 Jul.
Artigo em Inglês | MEDLINE | ID: mdl-38609765

RESUMO

STATEMENT OF PROBLEM: The surface topography of metal substrate can affect its bond to porcelain. A neodynium-doped yttrium aluminum garnet (Nd:YAG) laser has been introduced to modify the metal surface topography and improve porcelain bond strength. However, studies on the effect of laser etching on metal to porcelain bond strength are lacking. PURPOSE: The purpose of this in vitro study was to determine the effect of Nd:YAG laser etching on the surface roughness and wettability of and the porcelain bond strength to cobalt chromium (Co-Cr) substrate fabricated by milling and direct metal laser sintering (DMLS). MATERIAL AND METHODS: Thirty-two 0.5×3×25-mm Co-Cr specimens were fabricated by milling soft Co-Cr (M group) and DMLS Co-Cr metal powder (DML group). The surface topography of representative specimens from each study group was assessed under a scanning electron microscope (SEM) and an atomic force microscope (AFM). All specimens were assessed for surface roughness using a contact profilometer, and for wettability with a contact angle goniometer. Half of the specimens of each study group (n=8) were subjected to surface laser etching by using a Nd:YAG laser. The specimens subjected to etching were assessed again for surface topography and wettability. All specimens in both study groups were veneered with porcelain. The porcelain bond strength was tested with a 3-point bend test in a universal testing machine. The results were statistically analyzed with 2-way ANOVA test followed by the post hoc Tukey test for pairwise comparisons (α=.05). RESULTS: After etching, the M group had a higher mean ±standard deviation Ra and Rz of 2.9 ±0.6 and 17.7 ±3.2 µm and significantly better wettability and bond strength of 79 ±6 and 52 ±13 MPa. In contrast, after etching, the DMLS group had a significantly lower Ra and Rz of 7.9 ±2.4 and 41.8 ±9.3 µm and significantly lower wettability and bond strength of 87 ±4 and 70 ±10 MPa. The DMLS group had a significantly higher roughness and bond strength than the M group before and after laser etching. The SEM and AFM showed different surface topography in the study groups. CONCLUSIONS: The manufacturing process of Co-Cr substrate had a significant effect on surface characteristics and porcelain bond strength. Laser etching improved the surface topography and bond strength of milled Co-Cr but not of DMLS Co-Cr.


Assuntos
Ligas de Cromo , Colagem Dentária , Porcelana Dentária , Lasers de Estado Sólido , Propriedades de Superfície , Ligas de Cromo/química , Porcelana Dentária/química , Colagem Dentária/métodos , Microscopia Eletrônica de Varredura , Corrosão Dentária/métodos , Molhabilidade , Microscopia de Força Atômica , Teste de Materiais , Análise do Estresse Dentário , Humanos , Técnicas In Vitro
4.
J Prosthet Dent ; 131(1): 93.e1-93.e6, 2024 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-37867014

RESUMO

STATEMENT OF PROBLEM: Cement spacer has a crucial influence on the adaptation of fixed restorations. Recently, digitally fabricated zirconia crowns have become more popular, but studies on the effect of occlusal cement spacer on the fit accuracy of digitally designed and milled zirconia crowns are lacking. PURPOSE: The purpose of this in vitro study was to investigate the effect of modifying digital occlusal spacer on the marginal and internal fit of digitally manufactured zirconia crowns. MATERIAL AND METHODS: A maxillary molar typodont tooth was prepared for a zirconia crown, scanned with the Medit i700 intraoral scanner (IOS), and the standard tessellation language (STL) file was used to produce 3-dimensionally (3D) printed definitive dies assigned to 3 groups (n=12). All dies were scanned with the IOS, and the obtained STL files were exported to a computer-aided design (CAD) software program for the designing and milling of 36 complete contour zirconia crowns. The zirconia crown design was identical in the 3 groups for all parameters (default parameters in the CAD software program) with a 80-µm radial spacer 1 mm from the finish lines. The occlusal cement spacer was adjusted to 80 µm, 40 µm, and 0 µm for group 80-80, group 40-80, and group 0-80 respectively. The internal and marginal fit of the crowns were measured on their corresponding definitive dies with the replica technique. The Kruskal-Wallis test followed by the Dunn test with the Bonferroni correction was used for statistical analysis of the results (α=.05). RESULTS: The modification of occlusal cement spacer significantly affected the marginal and internal fit of digitally manufactured crowns (P<.05). Group 0-80 and group 40-80 had similar marginal gap values, which were significantly lower than those of group 80-80 (P<.017). For internal fit accuracy, group 0-80 displayed significantly lower gap values than group 40-80 and group 80-80 for all measured areas. Group 40-80 had significantly lower gap values than group 80-80 at the mid-occlusal and axio-occlusal areas (P<.017). CONCLUSIONS: Modifying occlusal cement spacer significantly affected the fit of digitally fabricated zirconia crowns. Reducing or eliminating occlusal spacer resulted in significantly improved fit accuracy.


Assuntos
Adaptação Marginal Dentária , Planejamento de Prótese Dentária , Planejamento de Prótese Dentária/métodos , Coroas , Zircônio , Desenho Assistido por Computador
5.
Syst Rev ; 12(1): 95, 2023 06 08.
Artigo em Inglês | MEDLINE | ID: mdl-37291652

RESUMO

BACKGROUND: Shade determination is a critical step for the fabrication of a satisfactory restoration. Visual shade selection with conventional shade guides is subjective and influenced by variables related to light, observer, and object. Shade selection devices have been introduced to provide subjective and quantitative shade values. This systematic review and meta-analysis aimed to compare the color difference for shade selection with visual and instrumental methods. METHODS: An initial search was conducted on databases (MEDLINE via PubMed, Scopus, and Web of Science) in addition to a manual search through references of identified articles. Studies comparing the accuracy of visual and instrumental shade selection based on ΔΕ were included in data synthesis. Mean differences (MDs) and 95% confidence intervals (CIs) were calculated to estimate the effect size for global and subgroup meta-analysis using the inverse variance weighted method and random-effects model (P ˂ 0.05). Results were presented as forest plots. RESULTS: The authors identified 1776 articles from the initial search. Seven in vivo studies were included in the qualitative analysis of which six studies were included in the meta-analysis. For the global meta-analysis, the pooled mean (95% CI) was - 1.10 (- 1.92, - 0.27). Test for overall effect showed that instrumental methods were significantly more accurate than visual methods with significantly less ΔΕ (P = 0.009). Test for subgroup difference showed that the type of instrumental shade selection method used had a significant effect on accuracy (P ˂ 0.001). Instrumental methods including spectrophotometer, digital camera, and smartphone showed significantly better accuracy compared with visual shade selection (P ˂ 0.05). The greatest mean difference was found between the smartphone and visual method with a mean (95% CI) of - 2.98 (- 3.37, - 2.59) with P ˂ 0.001 followed by digital camera and spectrophotometer. There was no significant difference in accuracy between IOS and visual shade selection (P = 1.00). CONCLUSIONS: Instrumental shade selection with a spectrophotometer, digital camera, and smartphone showed significantly better shade matching compared with a conventional shade guide, whereas IOS did not improve the shade matching significantly compared with shade guides. REVIEW REGISTRATION: PROSPERO CRD42022356545.


Assuntos
Percepção de Cores , Pigmentação em Prótese , Humanos , Cor , Espectrofotometria , Projetos de Pesquisa
6.
J Prosthet Dent ; 130(1): 28-34, 2023 Jul.
Artigo em Inglês | MEDLINE | ID: mdl-34696907

RESUMO

STATEMENT OF PROBLEM: Available studies comparing fit accuracy of zirconia fixed partial dentures (FPDs) fabricated from conventional impressions and digital scans provide contradictory results. In addition, studies have been heterogeneous and of a limited number to provide conclusive evidence. PURPOSE: The purpose of this systematic review and meta-analysis was to compare the marginal and intaglio fit of tooth-supported zirconia FPDs fabricated from conventional impressions and digital scans and to investigate the effect of different variables on the fit results. MATERIAL AND METHODS: An electronic search was performed on the National Library of Medicine (NLM), Cochrane Central Register of Controlled Trials, and Scopus databases. In addition, a manual search was carried out. Studies comparing the fit of tooth-supported zirconia FPDs fabricated from conventional impressions and digital scans and reporting sufficient data for qualitative and quantitative analysis were included. Standard mean differences (SMDs) and 95% confidence intervals (CI) were calculated for meta-analysis. Subgroup analysis was performed to study the effect of variables including restoration form (monolithic or framework), units number, intraoral scanner (IOS) type, conventional impression material, spacer thickness, and abutments region. RESULTS: The initial search resulted in a total of 608 articles. Nine articles were included in the analysis (1 clinical and 8 in vitro) evaluating 118 restorations. Digital scan displayed significantly better marginal fit (P<.001; SMD: -0.68; 95% CI: -0.92, -0.09) and intaglio fit (P=.020; SMD: -0.51; 95% CI: -0.94, -0.42). Test for subgroup difference showed a significant influence of only impression material type (P=.008) and units number (P=.030) on marginal fit. Digital scan showed significantly better marginal accuracy for 3-unit FPDs than 4-unit FPDs (P<.001; SMD: -1.02; 95% CI: -1.41, -0.63). In addition, digital scanning had significantly better marginal fit with polyvinyl siloxane than polyether (P<.001; SMD: -0.98; 95% CI: -1.32, -0.64). A cement spacer ≤50 µm improved both marginal and intaglio fit in the digital group. The TRIOS scanner resulted in the best performance in the digital group for marginal fit. CONCLUSIONS: Digital scanning provides significantly better marginal and intaglio fit than conventional impression making for fabricating zirconia FPDs up to 4 units, either in monolithic form or frameworks and at any region of the arch. However, further clinical studies are recommended to obtain more substantial results.


Assuntos
Desenho Assistido por Computador , Adaptação Marginal Dentária , Técnica de Moldagem Odontológica , Zircônio , Prótese Parcial Fixa , Materiais para Moldagem Odontológica , Planejamento de Prótese Dentária/métodos
7.
BMC Oral Health ; 22(1): 559, 2022 12 01.
Artigo em Inglês | MEDLINE | ID: mdl-36456986

RESUMO

BACKGROUND: Clinical studies comparing the accuracy of digital and conventional records for static interocclusal registration are lacking. Therefore, the purpose of this clinical study was to assess the precision of digital interocclusal registration compared to conventional registration for full arch and quadrant arch conditions. METHODS: Nine individuals with complete natural dentition were enrolled in this study. Each participant received digital scans, conventional impressions, and static interocclusal records according to the following groups: group DF, full arch digital scans and bilateral buccal scans with Medit i700 intraoral scanner (IOS); group DQ, quadrant arch digital scans and unilateral buccal scans with Medit i700 IOS; group CF, full arch polyvinyl siloxane (PVS) impressions and PVS interocclusal records; group CQ, quadrant arch PVS impressions and PVS interocclusal records. For group CF and group CQ, the impressions were poured, mounted with the silicone bites, scanned with a laboratory scanner, and articulated virtually with buccal scans with the laboratory scanner. In each group, each participant received three interocclusal records to repeat the virtual articulation three times and the articulated models were saved as STL files. The STL files were imported into a 3D-processing software to calculate the discrepancies between repeated measures using best-fit-alignment method. The significance between the study groups was calculated with two-tailed paired t-test at P < 0.05. RESULTS: For full arch, group DF showed significantly better precision with a mean value of 31 ± 19 µm compared to 204 ± 81 µm for group CF (P = 0.0003). Similarly, for quadrant arch, group DQ showed significantly better precision with a mean value of 18 ± 6 µm compared to 255 ± 136 µm for group CQ (P = 0.0009). No significant difference in precision was found between quadrant arch and full arch when the digital or the conventional method was used. CONCLUSIONS: The digital approach had significantly better precision for static interocclusal registration compared to the conventional method in both full and quadrant arch situations. Trial Registry This clinical trial was registered on 06/07/2022 in the Pan African Clinical Trial Registry database, the number for the registry is PACTR202207648490275.


Assuntos
Projetos de Pesquisa , Siloxanas , Humanos , Cintilografia , Sistema de Registros
8.
J Prosthet Dent ; 2022 Nov 01.
Artigo em Inglês | MEDLINE | ID: mdl-36333175

RESUMO

STATEMENT OF PROBLEM: Static virtual articulation with intraoral scanners (IOSs) can eliminate the human errors related to conventional articulation methods and enhance accuracy. A systematic review and meta-analysis based on multiple accuracy outcomes can combine the available literature and provide an evidence-based conclusion. PURPOSE: The purpose of this systematic review and meta-analysis was to investigate whether static virtual articulation with IOSs has acceptable accuracy for completely dentate and partially edentulous patients. MATERIAL AND METHODS: An electronic search was conducted on the PubMed, Web of Science, and Scopus databases. In addition, a manual search through reference lists of selected articles was performed. Clinical and in vitro studies evaluating the accuracy of static virtual articulation with IOSs based on diagnostic accuracy, trueness, precision, and occlusion of fabricated fixed restorations were included. The pooled results included sensitivity, specificity, positive likelihood ratio (+LR), negative likelihood ratio (-LR), diagnostic odds ratios (DORs), mean values, and 95% confidence intervals (CIs). Results were presented as forest plots. The summary receiver operator characteristic (SROC) was displayed to summarize the diagnostic test performance. RESULTS: The initial search resulted in a total of 5061 articles, of which 29 articles were included in the analysis. The virtual interocclusal records (VIRs) with IOSs showed acceptable pooled results for diagnostic accuracy (sensitivity: 0.76; specificity: 0.80; DOR: 14.77, area under the SROC (AUC): 0.87; cut off point Q∗: 80; +LR: 3.66; -LR: 0.31). The pooled data for trueness and precision were within the acceptable limits. The pooled mean (95% CI) for trueness based on linear deviations was 243.53 (144.90, 342.17). The pooled mean (95% CI) for precision based on 3D deviation of articulated models was 54.97 (43.49, 66.46). In addition, the included studies reported accurate occlusion for fixed restorations fabricated by using VIRs with IOSs. Moreover, most of the studies on trueness based on virtual occlusal contact area reported acceptable accuracy. CONCLUSIONS: VIRs with IOSs had acceptable accuracy for static virtual articulation.

9.
Clin Oral Investig ; 25(9): 5363-5373, 2021 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-33619632

RESUMO

OBJECTIVES: This study aimed to compare the accuracy of conventional and digital impressions based on the fit of produced three-unit fixed partial dentures (FPDs) in vivo and the trueness and precision of both impression techniques. MATERIALS AND METHODS: Twelve patients received a conventional polyether impression (group C, control, n=12) and a digital impression with CS3500 (group D, test, n=12) for each participant. Monolithic multilayer zirconia FPDs were fabricated, and the internal and marginal fit were assessed using the replica technique. Trueness and precision of both impression methods were assessed in vitro. A master model was used to create a reference scan. The master model received conventional impressions (group C, control, n=5) and digital impressions (group D, test, n=5). The virtual models of both groups were superimposed over the reference scan (5 superimpositions) using a three-dimensional (3D) processing software, and the 3D deviations were measured and averaged to obtain trueness value. For precision, the virtual models of each group were superimposed over each other (10 superimpositions) and the average deviation value was calculated. The data were analyzed using one-tailed Mann-Whitney U test at P ≤ 0.05. RESULTS: Group D resulted in a significantly better marginal and internal fit (30.91±15.15 and 30.86±13.57 µm for group D and 40.02±19.50 and 41.86±18.94 µm for group C). The mean values of trueness and precision for conventional and digital techniques were comparable (trueness: 62.8±5.45 and 62.72±12.01 µm and precision: 56.47±27 and 60.9±14.5 µm, respectively). CONCLUSIONS: No significant difference was found between conventional and digital impressions in 3D datasets accuracy. In addition, both techniques resulted in FPDs with an acceptable clinical fit. However, the FPDs fabricated using the digital technique displayed better internal and marginal fit. CLINICAL RELEVANCE: The applied impression technique as well as the computer-aided processing of the produced virtual models can significantly affect the fit of the final restoration. Direct digital impression is recommended over conventional impression for fabricating accurate monolithic zirconia 3-unit FPDs. TRIAL REGISTRATION: This clinical trial was retrospectively registered on August 11, 2020, in the Pan African Clinical Trial Registry database, and the number for the registry is PACTR202008685699453.


Assuntos
Técnica de Moldagem Odontológica , Laboratórios , Desenho Assistido por Computador , Materiais para Moldagem Odontológica , Adaptação Marginal Dentária , Prótese Parcial Fixa , Humanos , Zircônio
11.
J Food Biochem ; : e13428, 2020 Aug 14.
Artigo em Inglês | MEDLINE | ID: mdl-32794233

RESUMO

Thermal inactivation of peroxidase (POD) and polyphenol oxidase (PPO) in both pomegranate arils crude enzyme extract and fresh juice was investigated. The optimum conditions for reactions were studied using a mixture of guaiacol and H2 O2 as substrate for POD and pyrogallol for PPO. The experimental work indicated that optimum pH for both enzymes was 7.0; meanwhile optimum temperature was 30°C for POD and 25°C for PPO. Michaelis-Menten constant (Km) values for POD were 8.33 and 8.00 mM for guaiacol and H2 O2, respectively. The Km value was 5.88 mM pyrogallol for PPO. Thermal inactivation results revealed that the inactivation kinetics followed a monophasic first-order model. Activation energies (Ea) were 74.68 and 112.97 kJ/mol for POD and PPO, respectively. Therefore, POD was more heat-stable than PPO. This result is very useful to optimize pomegranate processing (canning or freezing), which represents the most important food industries in many tropical and subtropical regions. PRACTICAL APPLICATIONS: Pomegranate has been attracted more interest due to its antioxidant and nutritional values. For industrial applications, there is a growing interest to obtain pomegranate products such as juice, jams, food supplements, etc. It is well established that the residual activities of endogenous enzymes in either raw materials or processed products may cause loss of quality during storage. Inhibition of enzymatic browning is an important factor to maintain pomegranate quality. This work offers a better insight of characterization of browning enzymes and their thermosatbility, which will be useful to control the possible browning of pomegranate arils during processing and storage. In addition, the results of this study is very important in pomegranate processing where it showed a higher temperature with shortened time can be applied.

12.
J Food Sci Technol ; 55(2): 523-531, 2018 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-29391616

RESUMO

The present study investigated the effects of adding the powder of cactus Opuntia dillenii (O. dillenii) seeds on the functional properties, fiber, antioxidants and acceptability of rice-based extrudates. The control blend consisting basically of rice flour was replaced with O. dillenii seed powder at 2, 4, 6, 8, 10, 15 and 20% then extruded at the optimum processing conditions. The extruded products were evaluated for their chemical composition, functional properties, color attributes, antioxidant activity and sensory characteristics. The results revealed that adding O. dillenii seeds powder enhanced the fiber, phenolics, flavonoid contents and antioxidant activity of extrudates. Expansion, bulk density and breaking strength were significantly decreased, while water absorption index, water solubility index and oil absorption index were significantly increased compared to the control. Furthermore, the mean scores of sensory evaluation indicated clear improvements in all tested sensory attributes, which significantly increased by increasing the level of O. dillenii seed powder up to 15%. The results confirmed that O. dillenii seed powder could be incorporated in rice to develop snack products of acceptable functional, nutritional and sensory properties.

13.
Meat Sci ; 93(2): 292-302, 2013 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-23040181

RESUMO

This study aimed to evaluate the potential of near infrared spectroscopy (NIRS) as a fast and non-destructive tool for detecting and quantifying different adulterants in fresh and frozen-thawed minced beef. Partial least squares regression (PLSR) models were built under cross validation and tested with different independent data sets, yielding determination coefficients (R(P)(2)) of 0.96, 0.94 and 0.95 with standard error of prediction (SEP) of 5.39, 5.12 and 2.08% (w/w) for minced beef adulterated by pork, fat trimming and offal, respectively. The performance of the developed models declined when the samples were in a frozen-thawed condition, yielding R(P)(2) of 0.93, 0.82 and 0.95 with simultaneous augments in the SEP of 7.11, 9.10 and 2.38% (w/w), respectively. Linear discriminant analysis (LDA), partial least squares-discriminant analysis (PLS-DA) and non-linear regression models (logistic, probit and exponential regression) were developed at the most relevant wavelengths to discriminate between the pure (unadulterated) and adulterated minced beef. The classification accuracy resulting from both types of models was quite high, especially the LDA, PLS-DA and exponential regression models which yielded 100% accuracy. The current study demonstrated that the VIS-NIR spectroscopy can be utilized securely to detect and quantify the amount of adulterants added to the minced beef with acceptable precision and accuracy.


Assuntos
Contaminação de Alimentos/análise , Manipulação de Alimentos/métodos , Congelamento , Carne/análise , Espectroscopia de Luz Próxima ao Infravermelho/métodos , Animais , Bovinos , Análise Discriminante , Análise dos Mínimos Quadrados , Análise Multivariada , Dinâmica não Linear
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