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Journals / ODÜ Tıp Dergisi / 2025 / Cilt: 12 Sayı: 3

The Clinical Significance of Volume Calculation Using The Cavalieri Method: A Review

CAVALIERI YÖNTEMİ KULLANILARAK HACİM HESAPLAMASININ KLİNİK ÖNEMİ: DERLEME

Orhan Bas(SAMSUN ÜNİVERSİTESİ, TIP FAKÜLTESİ, TEMEL TIP BİLİMLERİ BÖLÜMÜ, ANATOMİ ANABİLİM DALI)0000-0002-7449-2699
Burak Oguzhan Karapinar(ORDU ÜNİVERSİTESİ, TIP FAKÜLTESİ, TEMEL TIP BİLİMLERİ BÖLÜMÜ, ANATOMİ ANABİLİM DALI)0000-0001-9005-5504
Adem Tokpinar(ORDU ÜNİVERSİTESİ, TIP FAKÜLTESİ, TEMEL TIP BİLİMLERİ BÖLÜMÜ, ANATOMİ ANABİLİM DALI)0000-0001-7661-9588
Muhammet Degermenci(ORDU ÜNİVERSİTESİ, TIP FAKÜLTESİ, TEMEL TIP BİLİMLERİ BÖLÜMÜ, ANATOMİ ANABİLİM DALI)0000-0002-4751-6202
Halil Yilmaz(ORDU ÜNİVERSİTESİ, TIP FAKÜLTESİ, TEMEL TIP BİLİMLERİ BÖLÜMÜ, ANATOMİ ANABİLİM DALI)0000-0002-8234-4901
Hakan Timur(ORDU ÜNİVERSİTESİ, TIP FAKÜLTESİ, CERRAHİ TIP BİLİMLERİ BÖLÜMÜ, KADIN HASTALIKLARI VE DOĞUM ANABİLİM DALI)0000-0002-4312-4199
Pages
144–157
Publication Date
2025-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, its integration with digital imaging modalities (CT, MRI) and computer-aided analysis software minimizes observer errors and enhances reproducibility.

📌 3 Key Takeaways

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Objective & Hypothesis:Volumetric measurements are a fundamental parameter in the quantitative assessment of the morphological characteristics of organs, tissues, and pathological structures.
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Key Findings & Data:In this context, the Cavalieri method, developed by Bonaventura Cavalieri in the 17th century, stands out as a reliable stereological technique for volume estimation.
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Conclusion & Impact:Furthermore, its integration with digital imaging modalities (CT, MRI) and computer-aided analysis software minimizes observer errors and enhances reproducibility.
🔬Design:Review & Systematic Survey
📍Scope:2025 Verileri
⚙️Variables:Cavalieri yöntemi · Stereolojik hacim ölçümü · Klinik volümetri

Abstract

Volumetric measurements are a fundamental parameter in the quantitative assessment of the morphological characteristics of organs, tissues, and pathological structures. However, the irregular geometry of biological structures limits the accuracy of classical geometric volume calculation methods, creating a need for approaches that are independent of geometric assumptions, unbiased, and reproducible. In this context, the Cavalieri method, developed by Bonaventura Cavalieri in the 17th century, stands out as a reliable stereological technique for volume estimation. It is based on multiplying the sum of two-dimensional areas obtained from equidistant sections by the section thickness and, when combined with the systematic random sampling (SRS) principle, provides an accurate representation of three-dimensional structures. This review was conducted by screening the literature in PubMed, Scopus, and Web of Science databases between 1985 and 2025 using the keywords “Cavalieri method,” “stereology,” “volume estimation,” “clinical volumetry,” and “morphometry.” Original research articles, clinical studies, and methodological papers directly involving stereological volume estimation were included, while conference abstracts, and studies without stereological methodology were excluded. The review evaluates both the methodological foundations of the Cavalieri principle and its clinical applications in fields such as neuroanatomy, hepatology, oncology, orthopedics, and the respiratory system. Accurate measurement of brain, liver, tumor, muscle, and bone volumes has significant clinical importance in early diagnosis, treatment monitoring, and surgical planning. A major advantage of the method is its independence from geometric assumptions, allowing unbiased volume estimation even in irregularly shaped structures. Furthermore, its integration with digital imaging modalities (CT, MRI) and computer-aided analysis software minimizes observer errors and enhances reproducibility.

Özet

Hacimsel ölçümler, organların, dokuların ve patolojik yapıların morfolojik özelliklerinin nicel değerlendirmesinde temel bir parametredir. Bununla birlikte, biyolojik yapıların düzensiz geometrisi, klasik geometrik hacim hesaplama yöntemlerinin doğruluğunu sınırlamakta ve geometrik varsayımlardan bağımsız, tarafsız ve tekrarlanabilir yaklaşımlara olan ihtiyacı ortaya çıkarmaktadır. Bu bağlamda, 17. yüzyılda Bonaventura Cavalieri tarafından geliştirilen Cavalieri yöntemi, hacim tahmini için güvenilir bir stereolojik teknik olarak öne çıkmaktadır. Eşit aralıklı kesitlerden elde edilen iki boyutlu alanların toplamının kesit kalınlığı ile çarpılmasına dayanır ve sistematik rastgele örnekleme (SRS) prensibiyle birleştirildiğinde, üç boyutlu yapıların doğru bir temsilini sağlar. Bu inceleme, 1985 ile 2025 yılları arasında PubMed, Scopus ve Web of Science veritabanlarında "Cavalieri yöntemi", "stereoloji", "hacim tahmini", "klinik volümetri" ve "morfometri" anahtar kelimeleri kullanılarak literatür taraması yapılarak gerçekleştirilmiştir. Stereolojik hacim tahminini doğrudan içeren orijinal araştırma makaleleri, klinik çalışmalar ve metodolojik makaleler dahil edildi; konferans özetleri ve stereolojik metodoloji içermeyen çalışmalar ise hariç tutuldu. Bu inceleme, Cavalieri yönteminin metodolojik temellerini ve nöroanatomi, hepatoloji, onkoloji, ortopedi ve solunum sistemi gibi alanlardaki klinik uygulamalarını değerlendirmektedir. Beyin, karaciğer, tümör, kas ve kemik hacimlerinin doğru ölçümü, erken teşhis, tedavi takibi ve cerrahi planlamada önemli klinik öneme sahiptir. Yöntemin en büyük avantajı, geometrik varsayımlardan bağımsız olması ve düzensiz şekilli yapılarda bile tarafsız hacim tahminine olanak sağlamasıdır. Ayrıca, dijital görüntüleme yöntemleriyle (BT, MR) ve bilgisayar destekli analiz yazılımlarıyla entegrasyonu, gözlemci hatalarını en aza indirir ve tekrarlanabilirliği artırır.

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Cite This Article

Bas, O., Karapinar, B. O., Tokpinar, A., Degermenci, M., Yilmaz, H., Timur, H. (2025). The Clinical Significance of Volume Calculation Using The Cavalieri Method: A Review. ODÜ Tıp Dergisi, Cilt: 12 Sayı: 3, 144–157. https://doi.org/10.56941/odutip.1833900

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References (44)

  1. Sonmez OF, Odaci E, Bas O, Colakoglu S, Sahin B, Bilgic S, et al. A stereological study of MRI and the Cavalieri principle combined for diagnosis and monitoring of brain tumor volume. J Clin Neurosci. 2010;17(12):1499–1502.
  2. Sahin B, Emirzeoglu M, Uzun A, Incesu L, Bek Y, Bilgic S, et al. Unbiased estimation of the liver volume by the Cavalieri principle using magnetic resonance images. Eur J Radiol. 2003;47(2):164–170.
  3. Sorensen AG, Patel S, Harmath C, Bridges S, Synnott J, Sievers A, et al. Comparison of diameter and perimeter methods for tumor volume calculation. J Clin Oncol. 2001;19(2):551–557.
  4. Iliadis G, Selviaridis P, Kalogera-Fountzila A, Fragkoulidi A, Baltas D, Tselis N, et al. The importance of tumor volume in the prognosis of patients with glioblastoma: comparison of computerized volumetry and geometric models. Strahlenther Onkol. 2009;185(11):743–750.
  5. Canan S, Şahin B, Odacı E, Ünal B, Aslan H, Bilgiç S, et al. Estimation of the reference volume, volume density and volume ratios by a stereological method: Cavalieri’s principle. Turkiye Klin J Med Sci. 2002;22(1):7–14.
  6. Say F, Gölpınar M, Kılınç CY, Sahin B. The estimation of bone cyst volume using the Cavalieri principle on computed tomography images. J Orthop Surg. 2018;26(2):2309499018772373.
  7. Karaca O, Buyukmert A, Tepe N, Ozcan E, Kus I. Volume estimation of brain ventricles using Cavalieri’s principle and atlas-based methods in Alzheimer disease: consistency between methods. J Clin Neurosci. 2020;78:333–338.
  8. Duran C, Aydinli B, Tokat Y, Yuzer Y, Kantarci M, Akgun M, et al. Stereological evaluation of liver volume in living donor liver transplantation using MDCT via the Cavalieri method. Liver Transpl. 2007;13(5):693–698.
  9. Akgun M, Kantarci M, Cayir K, Bayraktutan U, Doganay S, Araz O, et al. Stereological evaluation of tumor regression rates in lung cancer using CT via the Cavalieri method. Eurasian J Med. 2008;40(3):109.
  10. Howard CV, Reed MG. Unbiased stereology: three-dimensional measurement in microscopy. 2nd ed. New York: Garland Science; 2005.
  11. Gundersen HJG, Jensen EB. The efficiency of systematic sampling in stereology and its prediction. J Microsc. 1987;147(3):229–263.
  12. Tschanz S, Schneider JP, Knudsen L. Design-based stereology: planning, volumetry and sampling are crucial steps for a successful study. Ann Anat. 2014;196(1):3–11.
  13. Mayhew TM. A review of recent advances in stereology for quantifying neural structure. J Neurocytol. 1992;21(5):313–328.
  14. Schmitz C, Hof PR. Design-based stereology in neuroscience. Neuroscience. 2005;130(4):813–831.
  15. Boyce RW, Dorph-Petersen KA, Lyck L, Gundersen HJG. Design-based stereology: introduction to basic concepts and practical approaches for estimation of cell number. Toxicol Pathol. 2010;38(7):1011–1025.
  16. Gundersen HJG, Bendtsen TF, Korbo L, Marcussen N, Møller A, Nielsen K, et al. Some new, simple and efficient stereological methods and their use in pathological research and diagnosis. APMIS. 1988;96(1–6):379–394.
  17. Altunkaynak BZ, Altunkaynak E, Unal D, Unal B. A novel application for the Cavalieri principle: a stereological and methodological study. Eurasian J Med. 2009;41(2):99.
  18. Roberts N, Puddephat MJ, McNulty V. The benefit of stereology for quantitative radiology. Br J Radiol. 2000;73(871):679–697.
  19. Sahin B, Ergur H. Assessment of the optimum section thickness for the estimation of liver volume using magnetic resonance images: a stereological gold standard study. Eur J Radiol. 2006;57(1):96–101.
  20. Bas O, Kayaci S, Celiker FB, Ucuncu Y, Ozveren MF, Yilmaz A, et al. A comparison of lateral ventricle volume estimation on magnetic resonance and cadaveric section images using the planimetry method. J Clin Neurosci. 2019;64:264–268.
  21. Odaci E, Sahin B, Sonmez OF, Kaplan S, Bas O, Bilgic S, et al. Rapid estimation of the vertebral body volume: a combination of the Cavalieri principle and computed tomography images. Eur J Radiol. 2003;48(3):316–326.
  22. Odaci E, Bahadir A, Yildirim Ş, Sahin B, Canan S, Bas O, et al. Volume estimation using the Cavalieri principle on computerized tomography and magnetic resonance images and its clinical application: review. Turkiye Klin J Med Sci. 2005;25(3):421–428.
  23. Tasyapan SA, Kayipmaz S, Ozcan I. Evaluating cross-sectional accuracy of volumetric calculations for intraosseous defects in cone-beam computed tomography: effects of slice intervals and section orientation using planimetry and point counting. IJ Radiol. 2025;22(1): e157224.
  24. Emirzeoglu M, Sahin B, Selcuk MB, Kaplan S. The effects of section thickness on the estimation of liver volume by the Cavalieri principle using computed tomography images. Eur J Radiol. 2005;56(3):391–397.
  25. Tatar A, Ozmen HK, Yoruk O. Evaluation of volume of nasopharyngeal cancers by the Cavalieri principle. Asian Pac J Cancer Prev. 2018;19(9):2403.
  26. Okur A, Kantarci M, Akgun M, Alper F, Cayir K, Koc M, et al. Unbiased estimation of tumor regression rates during chemoradiotherapy for esophageal carcinoma using CT and stereology. Dis Esophagus. 2005;18(2):114–119.
  27. Nordez A, Jolivet E, Südhoff I, Bonneau D, de Guise JA, Skalli W. Comparison of methods to assess quadriceps muscle volume using magnetic resonance imaging. J Magn Reson Imaging. 2009;30(5):1116–1123.
  28. Bilgic S, Sahin B, Sonmez OF, Odaci E, Colakoglu S, Kaplan S, et al. A new approach for the estimation of intervertebral disc volume using the Cavalieri principle and computed tomography images. Clin Neurol Neurosurg. 2005;107(4):282–288.
  29. Acer N, Demir M, Uçar T, Pekmez H, Göktaş A. Estimation of the eyeball and orbital volume using the Cavalieri principle on computed tomography images. Balkan Med J. 2011;2011(2):184–188.
  30. Acer N, Bayar B, Basaloglu H, Öner E, Bayar K, Sankur S. Unbiased estimation of the calcaneus volume using the Cavalieri principle on computed tomography images. Ann Anat. 2008;190(5):452–460.
  31. Sezgin ÖS, Kayıpmaz S, Sahin B. The effect of slice thickness on the assessment of bone defect volumes by the Cavalieri principle using cone beam computed tomography. J Digit Imaging. 2013;26(1):115–118.
  32. Ünalmış D, Acer N, Yılmaz S, Tokpınar A, Doğan S, Demir H. The calculation of the femoral condyle cartilage volume and surface area in patients with osteoarthritis. J Clin Pract Res. 2020;42(2):178.
  33. Balcioglu HA, Uyanikgil Y, Yuruker S, Tuna HS, Karacayli U. Volumetric assessment of lateral pterygoid muscle in unilateral chewing: a stereologic study. J Craniofac Surg. 2009;20(5):1364–1366.
  34. Michel RP, Cruz-Orive LM. Application of the Cavalieri principle and vertical sections method to lung: estimation of volume and pleural surface area. J Microsc. 1988;150(2):117–136.
  35. Emirzeoglu M, Sahin B, Bilgic S, Celebi M, Uzun A. Volumetric evaluation of the paranasal sinuses in normal subjects using computer tomography images: a stereological study. Auris Nasus Larynx. 2007;34(2):191–195.
  36. Öztürk FY, Nahir M, Beyhan M. The impact of nasal septum deviation on paranasal sinus volumes. Hitit Med J. 2023;6(2):208–215.
  37. Değermenci M, Ertekin T, Ülger H, Acer N, Coşkun A. The age-related development of maxillary sinus in children. J Craniofac Surg. 2016;27(1):e38–e44.
  38. Keleş Aİ, Yıldırım M, Gedikli Ö, Çolakoğlu S, Kaya H, Baş O, et al. The effects of a continuous 1-ha day 900-MHz electromagnetic field applied throughout early and mid-adolescence on hippocampus morphology and learning behavior in late adolescent male rats. J Chem Neuroanat. 2018;94:46–53.
  39. Aslan A, İkinci A, Baş O, Sönmez OF, Kaya H, Odacı E. Long-term exposure to a continuous 900 MHz electromagnetic field disrupts cerebellar morphology in young adult male rats. Biotechnic Histochem. 2017;92(5):324–330.
  40. Odaci E, Kaplan S, Sahin B, Bas O, Gevrek F, Aygün D, et al. Effects of low-dose oxcarbazepine administration on developing cerebellum in newborn rat: a stereological study. Neurosci Res Commun. 2004;34(1):28–36.
  41. Fernández García MT, Núñez Martínez P, García de la Fuente V, Sánchez Pitiot M, Muñiz Salgueiro MDC, Perillán Méndez C, et al. Practical application of stereological kidney methods in experimental animal models. Nefrología (Engl Ed). 2017;37(1):29–33.
  42. Tüfek NH, Yahyazadeh A, Altunkaynak BZ. Protective effect of indole-3-carbinol on testis of a high fat diet induced obesity. Biotechnic Histochem. 2023;98(1):1–12.
  43. Firoozi A, Alizadeh A, Zarifkar A, Esmaeilpour T, Namavar MR, Alavi O, Dehghani F. Comparison of the efficacy of human umbilical cord mesenchymal stem cells conditioned medium and platelet-rich plasma on the hippocampus of STZ–induced rat model of Alzheimer’s disease: a behavioral and stereological study. IBRO Neurosci Rep. 2023;15:209–217.
  44. Roodbari AS, Solhjoo S, Palmerini MG, Mansouri M, Ezzatabadipour M. The effect of human menstrual blood-derived stem cells on ovarian folliculogenesis, angiogenesis and collagen volume in female rats affected by the polycystic ovary syndrome. J Ovarian Res. 2023;16(1):170.