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. 2018 May;52(2):105-110.
doi: 10.26650/eor.2018.478. Epub 2018 May 1.

Comparative assessment of 3D reconstruction technique and Cavalieri's principle in predicting the mandibular bone defect volumes

Mehmet Ali Altay  1 , Faisal A Quereshy  2 , Sumit K Nijhawan  2 , Jose F Teppa  2 , Michael P Horan  3 , Nelli Yıldırımyan  1 , Dale A Baur  2
Affiliations

Comparative assessment of 3D reconstruction technique and Cavalieri's principle in predicting the mandibular bone defect volumes

Mehmet Ali Altay et al. Eur Oral Res. 2018 May.

Abstract
in English, Turkish

Purpose: The objective of this study was to compare the accuracy of the Cavalieri's principle and 3D reconstruction in predicting the volume of a bony defect.

Materials and methods: Defects of the same approximate size were created on nine artificial mandibles. The actual volume of the defect on each mandible was measured by water displacement, and served as the control. Each mandible was then scanned using a CBCT and volume measurements were made for each defect using two techniques: Cavalieri's principle and 3D reconstruction. For each defect, the volume obtained by each of the two techniques was compared to the control volume using the analysis of variances (ANOVA) with p<0.05.

Results: ANOVA between the control, 3D reconstruction and Cavalieri's principle groups showed no statistically significant differences (p=.058). When the control group was further analyzed by Dunnett's post-hoc test, the results from Cavalieri's principle were found to be statistically different than the control group (p=.035), whereas the results of 3D reconstruction technique did not reach the level of significance (p=.523).

Conclusion: Cavalieri's principle significantly underestimates the actual control volume, and is less accurate than the 3D reconstruction technique. The 3D reconstruction method is a reliable technique in measuring volume of bony defects.

Amaç: Bu çalışmanın amacı kemik defektlerinin hacimsel tahmininde Cavalieri prensibi ve 3 boyutlu rekonstrüksiyon tekniğinin doğruluklarının karşılaştırılmasıdır.

Gereç ve yöntem: Dokuz adet yapay mandibula üzerinde yaklaşık olarak aynı boyutlarda defektler oluşturulmuştur. Her mandibulaki defektin gerçek hacmi suyun yer değiştirmesi ile ölçülmüş ve kontrol grubu olarak belirlenmiştir. Ardından, her mandibula konik ışınlı bilgisayarlı tomografi (cone-beam computed tomography – CBCT) ile taranmış ve defektlerin hacimsel ölçümleri iki teknik kullanılarak yapılmıştır: Cavalieri prensibi ve 3 boyutlu rekonstrüksiyon. Defektlerin her iki teknikle elde edilen hacimsel ölçümleri, kontrol hacimleri ile karşılaştırılmış ve istatistiksel anlamlılık düzeyi p<0.05 olacak şekilde varyans analizi ile (ANOVA) değerlendirilmiştir.

Bulgular: Kontrol, 3 boyutlu rekonstrüksiyon ve Cavalieri’nin prensibi gruplarının ANOVA ile değerlendirilmesi sonucunda gruplar arasında istatistiksel olarak anlamlı bir farklılık bulunamamıştır (p=.058). Kontrol grubu Dunnett’in post-hoc testi ile ileri analize tabi tutulduğunda, Cavalieri’nin prensibi ile yapılan ölçümlerin kontrole kıyasla anlamlı farklılık gösterdiği (p=.035); ancak 3 boyutlu rekonstrüksiyon tekniğinin anlamlılık seviyesine ulaşmadığı görülmüştür (p=.523).

Sonuç: Cavalieri prensibi, kontrol hacminin olması gerekenden daha az ölçülmesine neden olmaktadır. Bu prensibinin doğruluğu, 3 boyutlu rekonstrüksiyon tekniğine göre daha düşüktür. Üç boyutlu rekonstrüksiyon metodu, kemik defektlerinin hacimsel ölçümünde daha güvenilir bir tekniktir.

Keywords: Cavalieri’s principle; Cone-beam CT; defect; image reconstruction; three-dimensional imaging.

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Conflict of interest statement

Conflict of Interest: The authors have no conflicts of interest to declare.

Figures

Figure 1
Figure 1
Cavalieri’s principle. (∑ cross-sectional area of each slice) X S, where S is the thickness of each slice on the CBCT, given that S remains constant. (from: Mandarim-de-Lacerda CA. Stereological tools in biomedical research. An Acad Bras Cienc. 2003 Dec;75(4):469–86. Epub 2003 Nov 4).
Figure 2. a, b
Figure 2. a, b
On an artificial mandible, a defect has been created on the buccal alveolar aspect with a bur. The defects were made to be clinically proportional in all mandibles (a). Putty is molded into the defect to reconstitute the volume (b).
Figure 3
Figure 3
A CBCT image of the defect created in one of the artificial mandibles.
Figure 4
Figure 4
Using the 3D reconstruction method, the defect being isolated. Once the defect has been completely isolated, the image is inverted, leaving only the volume of the defect. The program measures the volume of the isolated defect.
Figure 5
Figure 5
Application of Cavalieri’s principle. The cut for each slice is set at 2 mm. At each cross section a geometric measurement tool is used to measure the area in each defect. The sum of the areas is then multiplied by 2, the total thickness of each slice, to give the volume of the defect.
See this image and copyright information in PMC

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