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

doi:10.1016/j.ultrasmedbio.2022.07.013

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

Biomedical Engineering Department

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 language	English
Pages (from-to)	2476-2485
Number of pages	10
Journal	Ultrasound in Medicine and Biology
Volume	48
Issue number	12
DOIs	https://doi.org/10.1016/j.ultrasmedbio.2022.07.013
Publication status	Published - Dec 2022

Keywords

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

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@article{5a3972a7fa384a70b5bad3e039df5d15,

title = "Beyond Simpson's Rule: Accounting for Orientation and Ellipticity Assumptions",

abstract = "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.",

keywords = "Apical chamber views, Left ventricle volumes, Modified Simpson's biplane rule, Two-dimensional echocardiography",

author = "Kim, {Woo Jin Cho} and Arian Beqiri and Lewandowski, {Adam J.} and Esther Puyol-Ant{\'o}n and Markham, {Deborah C.} and King, {Andrew P.} and Paul Leeson and Pablo Lamata",

note = "Funding Information: The authors acknowledge funding from Ultromics Limited, the EPSRC Centre for Doctoral Training in Medical Imaging (No. EP/L015226/1) and the Wellcome/EPSRC Centre for Medical Engineering (No. WT203148/Z/16/Z). Pablo Lamata holds a Wellcome Trust Senior Research Fellowship (No. 209450/Z/17/Z). Funding Information: The authors acknowledge funding from Ultromics Limited, the EPSRC Centre for Doctoral Training in Medical Imaging (No. EP/L015226/1) and the Wellcome/EPSRC Centre for Medical Engineering (No. WT203148/Z/16/Z). Pablo Lamata holds a Wellcome Trust Senior Research Fellowship (No. 209450/Z/17/Z). W.J.C.K. is a PhD student funded at a 50% level by Ultromics Ltd. P. Leeson is the Academic Founder and Non-Executive Director of Ultromics. A.B. and D.M. are Ultromics employees. P. Lamata is a member of the Ultromics Advisory Board. Ultromics is not seeking to protect the intellectual property of the BOD formulation, hoping that all vendors quickly adopt it. The source code and anatomical models are available to other researchers. Source code: https://github.com/woojinchokimm/simpsonsvolume. Anatomical models: DOI: 10.6084/m9.figshare.14933463. Publisher Copyright: {\textcopyright} 2022 The Authors",

year = "2022",

month = dec,

doi = "10.1016/j.ultrasmedbio.2022.07.013",

language = "English",

volume = "48",

pages = "2476--2485",

journal = "Ultrasound in medicine & biology",

issn = "0301-5629",

publisher = "Elsevier",

number = "12",

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T2 - Accounting for Orientation and Ellipticity Assumptions

AU - Kim, Woo Jin Cho

AU - Beqiri, Arian

AU - Lewandowski, Adam J.

AU - Puyol-Antón, Esther

AU - Markham, Deborah C.

AU - King, Andrew P.

AU - Leeson, Paul

AU - Lamata, Pablo

N1 - Funding Information: The authors acknowledge funding from Ultromics Limited, the EPSRC Centre for Doctoral Training in Medical Imaging (No. EP/L015226/1) and the Wellcome/EPSRC Centre for Medical Engineering (No. WT203148/Z/16/Z). Pablo Lamata holds a Wellcome Trust Senior Research Fellowship (No. 209450/Z/17/Z). Funding Information: The authors acknowledge funding from Ultromics Limited, the EPSRC Centre for Doctoral Training in Medical Imaging (No. EP/L015226/1) and the Wellcome/EPSRC Centre for Medical Engineering (No. WT203148/Z/16/Z). Pablo Lamata holds a Wellcome Trust Senior Research Fellowship (No. 209450/Z/17/Z). W.J.C.K. is a PhD student funded at a 50% level by Ultromics Ltd. P. Leeson is the Academic Founder and Non-Executive Director of Ultromics. A.B. and D.M. are Ultromics employees. P. Lamata is a member of the Ultromics Advisory Board. Ultromics is not seeking to protect the intellectual property of the BOD formulation, hoping that all vendors quickly adopt it. The source code and anatomical models are available to other researchers. Source code: https://github.com/woojinchokimm/simpsonsvolume. Anatomical models: DOI: 10.6084/m9.figshare.14933463. Publisher Copyright: © 2022 The Authors

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

KW - Apical chamber views

KW - Left ventricle volumes

KW - Modified Simpson's biplane rule

KW - Two-dimensional echocardiography

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VL - 48

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JO - Ultrasound in medicine & biology

JF - Ultrasound in medicine & biology

IS - 12

ER -

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

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Keywords

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