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Comparison of stenosis models for usage in the estimation of pressure gradient across aortic coarctation

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Abstract

Non-invasive estimation of the pressure gradient in cardiovascular stenosis has much clinical importance in assisting the diagnosis and treatment of stenotic diseases. In this research, a systematic comparison is conducted to investigate the accuracy of a group of stenosis models against the MRI- and catheter-measured patient data under the aortic coarctation condition. Eight analytical stenosis models, including six from the literature and two proposed in this study, are investigated to examine their prediction accuracy against the clinical data. The two improved models proposed in this study consider comprehensively the Poiseuille loss, the Bernoulli loss in its exact form, and the entrance effect, of the blood flow. Comparison of the results shows that one of the proposed models demonstrates a cycle-averaged mean prediction error of −0.15 ± 3.03 mmHg, a peak-to-peak prediction error of −1.8 ± 6.89 mmHg, which is the best among the models studied.

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Abbreviations

A :

Sectional area of the vessel

HR:

Heart rate

k :

Coefficient

L :

Length of the vessel segment; Inertial effect of blood flow

Q :

Flow rate

P :

Pressure

r :

Radius

R :

Resistance (frictional loss) of blood flow

T :

Heart period

v :

Flow velocity

ρ :

Density of the blood

μ :

Dynamic viscosity of the blood

asc:

Ascending aorta (aortic root position)

d :

Distal side of the vessel stenosis

dsc:

Descending aorta (diaphragm position)

s :

Stenosis

u :

Proximal side of the vessel stenosis

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Funding

This research was funded by the European Community’s Seventh Framework Programme (FP7/2007–2013) under the grant agreement number 224495 (euHeart project).

Author information

Authors and Affiliations

  1. Institute of Integrative Medicine, Shaanxi University of Chinese Medicine, Xianyang, Shaanxi, People’s Republic of China

    Yubing Shi

  2. Mathematics and Modelling in Medicine Group, Department of Infection Immunity and Cardiovascular Disease, Faculty of Medicine, Dentistry and Health, University of Sheffield, Sheffield, S10 2RX, UK

    Yubing Shi, Patricia V. Lawford & D. Rodney Hose

  3. Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK

    Israel Valverde, Heynric B. Grotenhuis & Philipp Beerbaum

  4. Department of Paediatric and Adult Congenital Heart Disease, Guy’s and St Thomas’ NHS Foundation Trust, London, UK

    Israel Valverde, Heynric B. Grotenhuis & Philipp Beerbaum

  5. Cardiovascular Pathology Unit, Institute of Biomedicine of Seville, Hospital Virgen de Rocio/CSIC/University of Seville, Seville, Spain

    Israel Valverde

  6. Insigneo Institute for in silico Medicine, Sheffield, UK

    Patricia V. Lawford & D. Rodney Hose

  7. Clinic for Paediatric Cardiology and Paediatric Intensive Care Medicine, University Children’s Hospital, Hannover Medical University, Hannover, Germany

    Philipp Beerbaum

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  1. Yubing Shi
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Contributions

YS and DRH contributed to conception and design; IV, HBG, and PB provided the clinical data; YS, IV, PVL, and DRH analysed and interpreted the data; YS drafted the manuscript; and YS, PVL, and DRH critically revised the manuscript. All authors read and gave final approval of the final manuscript.

Corresponding author

Correspondence to D. Rodney Hose.

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Ethical approval

All procedures performed in the study involving human participants were in accordance with the ethical standards of the Ethical Committee of King’s College London on human experimentation and with the Helsinki Declaration of 1975, as revised in 2000. This article does not contain any study with animals performed by any of the authors.

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Informed consent was obtained from all individual participants included in the study.

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The authors declare no competing interests.

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Shi, Y., Valverde, I., Lawford, P.V. et al. Comparison of stenosis models for usage in the estimation of pressure gradient across aortic coarctation. J Biol Phys 47, 171–190 (2021). https://doi.org/10.1007/s10867-021-09572-x

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  • DOI: https://doi.org/10.1007/s10867-021-09572-x

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