Beyond Simpson's Rule: Accounting for Orientation and Ellipticity Assumptions

Woo Jin Cho Kim, Arian Beqiri, Adam J. Lewandowski, Esther Puyol-Antón, Deborah C. Markham, Andrew P. King, Paul Leeson, Pablo Lamata*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Simpson's biplane rule (SBR) is considered the gold standard method for left ventricle (LV) volume quantification from echocardiography but relies on a summation-of-disks approach that makes assumptions about LV orientation and cross-sectional shape. We aim to identify key limiting factors in SBR and to develop a new robust standard for volume quantification. Three methods for computing LV volume were studied: (i) SBR, (ii) addition of a truncated basal cone (TBC) to SBR and (iii) a novel method of basal-oriented disks (BODs). Three retrospective cohorts representative of the young, adult healthy and heart failure populations were used to study the impact of anatomical variations in volume computations. Results reveal how basal slanting can cause over- and underestimation of volume, with errors by SBR and TBC >10 mL for slanting angles >6°. Only the BOD method correctly accounted for basal slanting, reducing relative volume errors by SBR from –2.23 ± 2.21% to –0.70 ± 1.91% in the adult population and similar qualitative performance in the other two cohorts. In conclusion, the summation of basal oriented disks, a novel interpretation of SBR, is a more accurate and precise method for estimating LV volume.

Original languageEnglish
Pages (from-to)2476-2485
Number of pages10
JournalUltrasound in Medicine and Biology
Issue number12
Publication statusPublished - Dec 2022


  • Apical chamber views
  • Left ventricle volumes
  • Modified Simpson's biplane rule
  • Two-dimensional echocardiography


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