A stereological study of MRI and the Cavalieri principle combined for diagnosis and monitoring of brain tumor volume

doi:10.1016/j.jocn.2010.03.044

Journal of Clinical Neuroscience

Volume 17, Issue 12, December 2010, Pages 1499-1502

https://doi.org/10.1016/j.jocn.2010.03.044 Get rights and content

Abstract

In this study, we aimed to describe the application of the Cavalieri principle for the assessment of tumor volume using MRI without an over-projection/estimation effect. For this purpose, the volume of a patient’s brain and the brain tumor volume, or the volume of the former tumor region, were estimated preoperatively and postoperatively using a combination of the Cavalieri principle and MRI. The previously described formula was modified for MRI measurements to eliminate the over-estimation effects of imaging. The total brain and tumor volumes estimated using the MRI of a representative patient with glioblastoma multiforme were: preoperative, 1562.46 cm³ and 81.59 cm³, respectively; and postoperative, 1571.72 cm³ and 86.92 cm³, respectively. The mean time to count points for an estimation of brain and tumor volume (or the volume of the former tumor region) were 14 minutes and 3 minutes, respectively. The coefficients of the errors of the estimates for brain and tumor volume (former tumor volume, postoperative) measurements were: preoperative 0.01 and 0.02; and postoperative 0.01 and 0.03, respectively. Our results show that the combination of MRI and the Cavalieri principle can provide an unbiased, direct and assumption-free estimate of the regions of interest. Therefore, the presented method could be applied efficiently without any need for special software, additional equipment or personnel other than that required for routine MRI in daily use.

Introduction

Multiple techniques and measurements using radiological images are frequently carried out to obtain tumor volume values to assess tumor size.[1], [2], [3], [4] In addition to quantitative values obtained from measurements, volumetric ratios are also used for this purpose. The common aspect of these two approaches is that they assume that the 2-dimensional images directly reflect the real 3-dimensional properties of the tumor under investigation. However, the geometric features of 3-dimensional structures cannot be accurately judged from 2-dimensional images. Methods that rely solely on the properties of CT scans or MRI introduce serious bias in the resulting quantitative estimates.[5], [6], [7]

The definition of the tumor volume is a critical step in radiotherapy and surgical planning. Treatment design and its subsequent delivery are based on this step, and an error may lead to inaccurate delivery, which could reduce tumor control.⁸ Most physicians decide on the details of the treatment design after examination of 2-dimensional CT scans or MRI,[4], [9], [10] which is affected by their training and personal experience.

The aim of the present study is to describe the application of the Cavalieri principle, a stereological method that provides unbiased volume estimates, to assess tumor size using MRI without an over-projection/under-projection effect (over-/under-estimation).[6], [7], [11], [12] We present an MRI from an illustrative patient for this purpose. We utilized a previously described formula modified for MRI measurements to the eliminate over-estimation effects of imaging.¹³ The technique presented here can be applied easily in routine MRI since no additional equipment or experienced personnel are needed.

Section snippets

Measurement of brain tumor volume by the Cavalieri principle

In the Cavalieri principle, the structure of interest is cut in parallel plane sections from end to end, beginning at a randomly chosen starting point, with a series of parallel plane sections at a constant distance apart (Fig. 1A) that meet standard MRI techniques.[13], [14], [15], [16] The surface areas of the cut sections are estimated and multiplied by the mean section thickness to provide a volume of the examined object.[17], [18] The cut surface area of each section or slab is estimated

Results

The point counting procedure applied to preoperative images yielded 1357 points for the brain volume (a/p = 1.207 cm²; corrected for linear reduction) and 209 points for the tumor (a/p = 0.434 cm²; corrected for linear reduction). These data were used for volume estimations; hence, the total volume of the brain and the tumor were estimated at 1562.46 cm³ and 81.59 cm³, respectively.

Point counting on the postoperative images resulted in 1443 points (a/p = 1.141 cm²) for the brain and 232 points (a/p = 0.411 cm

Discussion

In most biological studies, researchers can only estimate the real quantity of what they are trying to find out, and a variety of methods are often in use. If the sampling or measuring methods are biased, assumption-based or wrong, the flaws might not be recognized until an unbiased, assumption-free gold standard study reveals the importance of an unbiased method to obtain quantitative results.[7], [23], [28] Stereology is used to evaluate unbiased properties of structures existing in three

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Clinical StudyA stereological study of MRI and the Cavalieri principle combined for diagnosis and monitoring of brain tumor volume

Abstract

Introduction

Section snippets

Measurement of brain tumor volume by the Cavalieri principle

Results

Discussion

Comput Biol Med

Arch Med Res

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

J Neurosci Methods

Psychiatry Res

Radiother Oncol

Clin Neurol Neurosurg

J Neurosci Methods

J Neurosci Methods

Eur J Radiol

Am J Obstet Gynecol

Eur J Radiol

Eur J Radiol

Clin Neurol Neurosurg

Comput Med Imaging Graph

J Clin Neurosci

The benefit of stereology for quantitative radiology

Br J Radiol

Spinal leptomeningeal metastasis from cerebral glioblastoma multiforme presenting with radicular pain: case report and literature review

Surg Neurol

Unbiased estimation of human body composition by the Cavalieri method using magnetic resonance imaging

J Microsc

Magnetic resonance imaging (MRI) and model free estimates of brain volumes determined using the Cavalieri principle

J Anat

Comparison of compartment volumes estimated from MR images and physical sections of formalin fixed cerebral hemispheres

Acta Stereol

Clinical Study
A stereological study of MRI and the Cavalieri principle combined for diagnosis and monitoring of brain tumor volume