Assessment of imaging studies used with radiosurgery: a volumetric algorithm and an estimation of its error

Technical note

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✓ The Gamma Knife has played an increasingly important role in the neurosurgical treatment of patients. Intracranial lesions are not removed by radiosurgery. Rather, the goal of treatment is to induce tumor control. During planning, the creation of dose–volume histograms requires an accurate volumetric analysis of intracranial lesions selected for radiosurgery. In addition, an accurate follow-up imaging analysis of tumor volume is essential for assessing the results of radiosurgery. Nevertheless, sources of volumetric error and their expected magnitudes must be properly understood so that the operator may correctly interpret apparent changes in tumor volume. In this paper, the authors examine the often-neglected contributions of imaging geometry (principally image slice thickness and separation) to overall volumetric error.

One of the fundamental sources of volumetric error is that resulting from the geometry of the acquisition protocol. The authors consider the image sampling geometry of tomographic modalities and its contribution to volumetric error through a simulation framework in which a synthetic digital tumor is taken as the primary model. Because the exact volume of the digital phantom can be computed, the volume estimates derived from tomographic “slicing” can be directly compared precisely and independently from other error sources. In addition to providing empirical bounds on volumetric error, this approach provides a tool for guiding the specification of imaging protocols when a specific volumetric accuracy, or volume change sensitivity, for particular structures is sought a priori.

Using computational geometry techniques, the volumetric error associated with image acquisition geometry was shown to be dependent on the number of slices through the region of interest (ROI) and the lesion volume. With a minimum of five slices through the ROI, the volume of a compact lesion could be calculated accurately with less than 10% error, which was the predetermined goal for the purposes of computing accurate dose–volume histograms and determining follow-up changes in tumor volume.

Accurate dose–volume histograms can be generated and follow-up volumetric assessments performed, assuming accurate lesion delineation, when the object is visualized on at least five axial slices. Volumetric analysis based on fewer than five slices yields unacceptably larger errors (that is, > 10%). These volumetric findings are particularly relevant for radiosurgical treatment planning and follow-up analysis. Through the application of this volumetric methodology and a greater understanding of the error associated with it, neurosurgeons can better perform radiosurgery and assess its outcome.

Abbreviations used in this paper: CT = computerized tomography; MR = magnetic resonance; ROI = region of interest; SD = standard deviation; 3D = three-dimensional.

Article Information

Address reprint requests to: Jason Sheehan, M.D., Ph.D., Box 800–212, University of Virginia Health System, Charlottesville, Virginia 22908. email:

© AANS, except where prohibited by US copyright law.



  • View in gallery

    Illustration depicting a sliced lesion. Intercepting the lesion model with a plane representing the imaging slice plane simulates tomographic imaging. Each triangle of the surface is intercepted by the plane resulting in one or no (zero) line segment. These segments are linked end to end to form closed contours, from which the enclosed area can be exactly computed. Several contours resulting from this simulated slicing are superimposed on the surface model.

  • View in gallery

    Graph demonstrating the volumetric error for a typical compact lesion (shown in Fig. 1). A polygonal approximation of an actual compact lesion was resliced, with varying slice separations. When using the trapezoidal method with end caps, at least five slices must be visualized to guarantee a volumetric error less than 10%.

  • View in gallery

    Examples of volume estimation strategies: rectangular rule (left), trapezoidal rule (center), and trapezoidal rule with end caps (right). The end caps contribute d(a1/3) and d(a5/3) in area, respectively. The shaded area represents the estimated volume.


  • 1

    Arvo J: Graphics Gems II San Diego, CAAcademic Press1991

  • 2

    Bevington PR: Data Reduction and Error Analysis for the Physical Sciences New YorkMcGraw-Hill1969

  • 3

    Brassow FSpielmann RPHerberhold C: Computertomographische Volumetrie des pneumatischen Systems des Ohres. Ein Vergleich zwischen Normalkollektiv und Patienten mit Ohrerkrankungen. ROFO Fortschr Geb Rontgenstr Nuklearmed 140:1581611984

  • 4

    Cernica Gde Boer SFDiaz AFenstermaker RAPodgorsak MB: Dosimetric accuracy of a staged radiosurgery treatment. Phys Med Biol 50:199120022005

  • 5

    Georgi PStrauss LSturm VOsterag HSinn HRommel T: Pra- und intraoperative volumenbestimmung bei Craniopharyngiomcysten. Nuklearmedizin 19:1871901980

  • 6

    Goodman JEO’Rourke J: Handbook of Discrete and Computational Geometry Boca Raton, FLCRC Press1997

  • 7

    Igarashi MO-Uchi TIsago HWright WK: Utricular and saccular volumetry in human temporal bones. Acta Otolaryngol 95:75801983

  • 8

    Kondziolka DNathoo NFlickinger JCNiranjan AMaitz AHLunsford LD: Long-term results after radiosurgery for benign intracranial tumors. Neurosurgery 53:8158222003

  • 9

    Kuo JSChen JCYu CZelman VGiannotta SLPetrovich Z: Gamma knife radiosurgery for benign cavernous sinus tumors: quantitative analysis of treatment outcomes. Neurosurgery 54:138513942004

  • 10

    Lim MGibbs ICAdler JR JrMartin DPChang SD: The efficacy of linear accelerator stereotactic radiosurgery in treating glomus jugulare tumors. Technol Cancer Res Treat 2:2612652003

  • 11

    Linskey MELunsford LDFlickinger JC: Neuroimaging of acoustic nerve sheath tumors after stereotaxic radiosurgery. AJNR Am J Neuroradiol 12:116511751991

  • 12

    Linskey MELunsford LDFlickinger JC: Tumor control after stereotactic radiosurgery in neurofibromatosis patients with bilateral acoustic tumors. Neurosurgery 31:8298391992

  • 13

    Losa MValle MMortini PFranzin Ada Passano CFCenzato M: Gamma knife surgery for treatment of residual nonfunctioning pituitary adenomas after surgical debulking. J Neurosurg 100:4384442004

  • 14

    Mizrahi ASullivan M: Calculus and Analytic Geometry Belmont, CAWadsworth1982

  • 15

    Noren GGreitz DHirsch ALax I: Gamma knife surgery in acoustic tumors. Acta Neurochir Suppl (Wien) 58:1041071993

  • 16

    Orthner HSeler W: Planimetrische Volumetrie an menschlichen Gehirnen. Fortschr Neurol Psychiatr Grenzgeb 43:1912091975

  • 17

    Pollock BECarpenter PC: Stereotactic radiosurgery as an alternative to fractionated radiotherapy for patients with recurrent or residual nonfunctioning pituitary adenomas. Neurosurgery 53:108610942003

  • 18

    Sheehan JPSun MHKondziolka DFlickinger JLunsford LD: Radiosurgery for non–small cell lung carcinoma metastatic to the brain: long-term outcomes and prognostic factors influencing patient survival time and local tumor control. J Neurosurg 97:127612812002

  • 19

    Shirley PTuchman AA: Polygonal approximation to direct scalar volume rendering. Proceedings San Diego Workshop on Volume Visualization Computer Graphics 24:63701990

  • 20

    Steiner LBergvall UZwetnow N: Quantitative estimation of intracerebral and intraventricular hematoma by computer tomography. Acta Radiol Suppl 346:1431541975

  • 21

    Stepanek VZavada M: Prakticke vyuziti rentgenove plicni voluminometrie, planimetrie a koeficientu roztazlivosti hrudniku. Cesk Radiol 23:2242301969


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