Geometry and Subdural Hematoma Volume

HomeStrokeVol. 30, No. 1Geometry and Subdural Hematoma Volume Free AccessOtherPDF/EPUBAboutView PDFView EPUBSections ToolsAdd to favoritesDownload citationsTrack citationsPermissions ShareShare onFacebookTwitterLinked InMendeleyReddit Jump toFree AccessOtherPDF/EPUBGeometry and Subdural Hematoma Volume Scott E. Kasner Scott E. KasnerScott E. Kasner Comprehensive Stroke Center, Department of Neurology, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania Originally published1 Jan 1999https://doi.org/10.1161/01.STR.30.1.188Stroke. 1999;30:188To the Editor: Gebel and colleagues1 reported a seemingly simple and accurate method for estimating the volume of a subdural hematoma. However, as 17th century philosopher and mathematician Thomas Hobbes wrote about a similarly bewildering calculation, "To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad."2The ABC/2 method for an intraparenchymal hematoma is based on the formula for the volume of a ellipsoid which is given by 4/3 π r1r2r3 (where the r represents each radius). With an approximation of 3 for π, and substitution of each of the radii with each diameter (d) divided by 2, the formula becomes d1d2d3/2, or ABC/2.At first, it seems quite unlikely that this formula should be useful in the estimation of the volume of a crescent-shaped subdural hematoma. Nevertheless, the method has proven accuracy, and its derivation must be explained. Consider the 3-dimensional crescent as the difference between 1 large outer ellipsoid and 1 small inner ellipsoid, which is then cut in half (ie, the crescent is akin to a solid semicircle). The volume of the crescent is then given by (4/3 π r1r2r3 −4/3 π r4r5r6)/2. Using the measurements as defined by Gebel et al1 (Figure ), the length (L) represents 1 diameter, the thickness (T) represents another, and these are the same for both the inner and outer ellipsoids. The width (w) of the 2 ellipsoids differs, so the formula can then be approximated as (LTw2−LTw1)/2. Since the difference between the widths is represented by W, the entire formula simplifies to LTW/2, or ABC/2.Thus, "Though this be madness, yet there is method in 't."3 Was this the method of Gebel et al?Download figureDownload PowerPoint Figure 1. Volume of a subdural hematoma (gray area) can be approximated by halving the difference in volume between a large outer ellipsoid (solid line) and a small inner ellipsoid (dashed line). Two of the 3 diameters of both ellipsoids are identical: the length (L), and the thickness (T) which is perpendicular to the plane shown. The third radius is designated as the width (w), and the difference between the widths of the 2 ellipsoids is marked by W. References 1 Gebel JM, Sila CA, Sloan MA, Granger CB, Weisenberger JP, Green CL, Topol EJ, Mahaffey KW. Comparison of the ABC/2 estimation technique to computer-assisted volumetric analysis of intraparenchymal and subdural hematomas complicating the GUSTO-1 trial. Stroke.1998; 29:1799–1801.CrossrefMedlineGoogle Scholar2 Hobbes T. In: Rose N, ed. Mathematical Maxims and Minims. Raleigh, NC: Rome Press Inc; 1988.Google Scholar3 Shakespeare W. Hamlet. New York, NY: Bantam Books; 1988.Google ScholarstrokeahaStrokeStrokeStroke0039-24991524-4628Lippincott Williams & WilkinsResponseGebel James M., MD and Sila Cathy A., MD011999We wish to thank Dr Kasner for his most eloquent and convincing mathematical explanation of our serendipitous madness. Previous Back to top Next FiguresReferencesRelatedDetailsCited By Sam J, Kandasamy R, Wong A, Ghani A, Ang S, Idris Z and Abdullah J (2021) Vacuum Drains versus Passive Drains versus No Drains in Decompressive Craniectomies–A Randomized Controlled Trial on Subgaleal Drain Complication Rates (VADER Trial), World Neurosurgery, 10.1016/j.wneu.2021.09.074, 156, (e381-e391), Online publication date: 1-Dec-2021. Kuhn E, Erwood M, Oster R, Davis M, Zeiger H, Pittman B and Fisher W (2018) Outcomes of Subdural Hematoma in the Elderly with a History of Minor or No Previous Trauma, World Neurosurgery, 10.1016/j.wneu.2018.07.168, 119, (e374-e382), Online publication date: 1-Nov-2018. Jack A, O'Kelly C, McDougall C and Max Findlay J (2015) Predicting Recurrence after Chronic Subdural Haematoma Drainage, Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques, 10.1017/cjn.2014.122, 42:1, (34-39), Online publication date: 1-Jan-2015. Kim B, Park K, Park D, Lim D, Kwon T, Chung Y and Kang S (2014) Risk factors of delayed surgical evacuation for initially nonoperative acute subdural hematomas following mild head injury, Acta Neurochirurgica, 10.1007/s00701-014-2151-4, 156:8, (1605-1613), Online publication date: 1-Aug-2014. Kim J, Hyun D, Yoon S, Park H, Kim E, Park H and Park C (2010) Prediction of Postoperative Drainage Volume and Brain Expansion of Chronic Subdural Hematoma: Supplementary Study-Clinical Study, Journal of Korean Neurotraumatology Society, 10.13004/jknts.2010.6.1.33, 6:1, (33), . Djonlagic I and Malhotra A (2014) Risk of stroke from sleep apnea in men and women, Expert Review of Neurotherapeutics, 10.1586/ern.10.102, 10:8, (1267-1271), Online publication date: 1-Aug-2010. Freeman W, Barrett K, Bestic J, Meschia J, Broderick D and Brott T (2008) Computer-Assisted Volumetric Analysis Compared With ABC/2 Method for Assessing Warfarin-Related Intracranial Hemorrhage Volumes, Neurocritical Care, 10.1007/s12028-008-9089-4, 9:3, (307-312), Online publication date: 1-Dec-2008. Oh C, Hyun D, Yoon S, Park H, Kim E, Park H and Park C (2008) The Relationship between Postoperative Drainage Volume and Brain Shifting Index in Chronic Subdural Hematoma, Journal of Korean Neurotraumatology Society, 10.13004/jknts.2008.4.2.70, 4:2, (70), . Sucu H, Gokmen M and Gelal F (2005) The Value of XYZ/2 Technique Compared With Computer-Assisted Volumetric Analysis to Estimate the Volume of Chronic Subdural Hematoma, Stroke, 36:5, (998-1000), Online publication date: 1-May-2005. Arikan F, Sahuquillo J, Ibáñez J, Vilalta J, Poca M, Rubio E, Riveiro M, Mena M and Gamacho A (2005) Variabilidad en las indicaciones quirúrgicas de las lesiones intradurales postraumáticas, Neurocirugía, 10.1016/S1130-1473(05)70415-2, 16:2, (108-116), . January 1999Vol 30, Issue 1 Advertisement Article InformationMetrics Copyright © 1999 by American Heart Associationhttps://doi.org/10.1161/01.STR.30.1.188 Originally publishedJanuary 1, 1999 PDF download Advertisement