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Relation between blood pressure and pulse wave velocity for human arteries

Yinji Ma, Jungil Choi, Aurélie Hourlier-Fargette, Yeguang Xue, Ha Uk Chung, Jong Yoon Lee, Xiufeng Wang, Zhaoqian Xie, Daeshik Kang, Heling Wang, Seungyong Han, Seung-Kyun Kang, Yisak Kang, Xinge Yu, Marvin J. Slepian, Milan S. Raj, Jeffrey B. Model, Xue Feng, Roozbeh Ghaffari, John A. Rogers, and Yonggang Huang
PNAS October 30, 2018 115 (44) 11144-11149; published ahead of print October 15, 2018 https://doi.org/10.1073/pnas.1814392115
Yinji Ma
aDepartment of Engineering Mechanics, Tsinghua University, 100084 Beijing, China;bCenter for Flexible Electronics Technology, Tsinghua University, 100084 Beijing, China;
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Jungil Choi
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;eSimpson Querrey Institute for Bio-Nanotechnology, Northwestern University, Evanston, IL 60208;
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Aurélie Hourlier-Fargette
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;eSimpson Querrey Institute for Bio-Nanotechnology, Northwestern University, Evanston, IL 60208;
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Yeguang Xue
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;fDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;gDepartment of Mechanical Engineering, Northwestern University, Evanston, IL 60208;
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  • ORCID record for Yeguang Xue
Ha Uk Chung
dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;eSimpson Querrey Institute for Bio-Nanotechnology, Northwestern University, Evanston, IL 60208;
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Jong Yoon Lee
dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;eSimpson Querrey Institute for Bio-Nanotechnology, Northwestern University, Evanston, IL 60208;
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Xiufeng Wang
hSchool of Materials Science and Engineering, Xiangtan University, 411105 Hunan, China;
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Zhaoqian Xie
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;fDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;gDepartment of Mechanical Engineering, Northwestern University, Evanston, IL 60208;
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Daeshik Kang
iDepartment of Mechanical Engineering, Ajou University, 16499 Suwon-si, Republic of Korea;
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Heling Wang
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;fDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;gDepartment of Mechanical Engineering, Northwestern University, Evanston, IL 60208;
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Seungyong Han
iDepartment of Mechanical Engineering, Ajou University, 16499 Suwon-si, Republic of Korea;
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Seung-Kyun Kang
jDepartment of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology, 34141 Daejeon, Republic of Korea;
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Yisak Kang
kDepartment of Electrical and Computer Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801;
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Xinge Yu
lDepartment of Biomedical Engineering, City University of Hong Kong, 999077 Hong Kong, China;
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Marvin J. Slepian
mDepartment of Medicine and Biomedical Engineering, Sarver Heart Center, University of Arizona, Tucson, AZ 85724;
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Milan S. Raj
dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;
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Jeffrey B. Model
dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;
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Xue Feng
aDepartment of Engineering Mechanics, Tsinghua University, 100084 Beijing, China;bCenter for Flexible Electronics Technology, Tsinghua University, 100084 Beijing, China;
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Roozbeh Ghaffari
dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;eSimpson Querrey Institute for Bio-Nanotechnology, Northwestern University, Evanston, IL 60208;nDepartment of Chemistry and Biomedical Engineering, Northwestern University, Evanston, IL 60208;
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John A. Rogers
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;eSimpson Querrey Institute for Bio-Nanotechnology, Northwestern University, Evanston, IL 60208;gDepartment of Mechanical Engineering, Northwestern University, Evanston, IL 60208;nDepartment of Chemistry and Biomedical Engineering, Northwestern University, Evanston, IL 60208;oDepartment of Dermatology, Northwestern University, Evanston, IL 60208;pFeinberg School of Medicine Center for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;qDepartment of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208;rDepartment of Neurological Surgery, Northwestern University, Evanston, IL 60208;sDepartment of Chemistry, Northwestern University, Evanston, IL 60208;tDepartment of Materials Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801;uFrederick Seitz Materials Research Laboratory, University of Illinois at Urbana–Champaign, Urbana, IL 61801
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  • For correspondence: jrogers@northwestern.eduy-huang@northwestern.edu
Yonggang Huang
cDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;dCenter for Bio-Integrated Electronics, Northwestern University, Evanston, IL 60208;fDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;gDepartment of Mechanical Engineering, Northwestern University, Evanston, IL 60208;
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  • For correspondence: jrogers@northwestern.eduy-huang@northwestern.edu
  1. Contributed by John A. Rogers, September 10, 2018 (sent for review August 21, 2018; reviewed by Markus J. Buehler and Pradeep Sharma)

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Significance

Continuous, cuffless, and noninvasive blood pressure monitoring by measuring the pulse wave velocity is generally considered to be a promising technique for noninvasive measurements. Previously reported relations between blood pressure and pulse wave velocity relation involve unrealistic assumptions that do not hold for human arteries, and also rely on empirical expressions without any theoretical basis. Here, an analytical model without such assumptions or empirical expressions is established to yield a relation between blood pressure and pulse wave velocity that has general utility for future work in continuous, cuffless, and noninvasive blood pressure monitoring.

Abstract

Continuous monitoring of blood pressure, an essential measure of health status, typically requires complex, costly, and invasive techniques that can expose patients to risks of complications. Continuous, cuffless, and noninvasive blood pressure monitoring methods that correlate measured pulse wave velocity (PWV) to the blood pressure via the Moens−Korteweg (MK) and Hughes Equations, offer promising alternatives. The MK Equation, however, involves two assumptions that do not hold for human arteries, and the Hughes Equation is empirical, without any theoretical basis. The results presented here establish a relation between the blood pressure P and PWV that does not rely on the Hughes Equation nor on the assumptions used in the MK Equation. This relation degenerates to the MK Equation under extremely low blood pressures, and it accurately captures the results of in vitro experiments using artificial blood vessels at comparatively high pressures. For human arteries, which are well characterized by the Fung hyperelastic model, a simple formula between P and PWV is established within the range of human blood pressures. This formula is validated by literature data as well as by experiments on human subjects, with applicability in the determination of blood pressure from PWV in continuous, cuffless, and noninvasive blood pressure monitoring systems.

  • blood pressure
  • pulse wave velocity
  • hemodynamics
  • arterial stiffness
  • artery hyperelastic model

Footnotes

  • ↵1Y.M. and J.C. contributed equally to this work.

  • ↵2To whom correspondence may be addressed. Email: jrogers{at}northwestern.edu or y-huang{at}northwestern.edu.
  • Author contributions: Y.M., Z.X., and J.A.R. designed research; Y.M., J.C., A.H.-F., and Z.X. performed research; Y.M. contributed new reagents/analytic tools; Y.M., J.C., A.H.-F., Y.X., H.U.C., J.Y.L., Z.X., D.K., H.W., S.H., S.-K.K., Y.K., X.Y., M.J.S., M.S.R., J.B.M., X.F., R.G., and Y.H. analyzed data; and Y.M., J.C., X.W., R.G., J.A.R., and Y.H. wrote the paper.

  • Reviewers: M.J.B., Massachusetts Institute of Technology; and P.S., University of Houston.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1814392115/-/DCSupplemental.

Published under the PNAS license.

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Relation between blood pressure and pulse wave velocity for human arteries
Yinji Ma, Jungil Choi, Aurélie Hourlier-Fargette, Yeguang Xue, Ha Uk Chung, Jong Yoon Lee, Xiufeng Wang, Zhaoqian Xie, Daeshik Kang, Heling Wang, Seungyong Han, Seung-Kyun Kang, Yisak Kang, Xinge Yu, Marvin J. Slepian, Milan S. Raj, Jeffrey B. Model, Xue Feng, Roozbeh Ghaffari, John A. Rogers, Yonggang Huang
Proceedings of the National Academy of Sciences Oct 2018, 115 (44) 11144-11149; DOI: 10.1073/pnas.1814392115

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Relation between blood pressure and pulse wave velocity for human arteries
Yinji Ma, Jungil Choi, Aurélie Hourlier-Fargette, Yeguang Xue, Ha Uk Chung, Jong Yoon Lee, Xiufeng Wang, Zhaoqian Xie, Daeshik Kang, Heling Wang, Seungyong Han, Seung-Kyun Kang, Yisak Kang, Xinge Yu, Marvin J. Slepian, Milan S. Raj, Jeffrey B. Model, Xue Feng, Roozbeh Ghaffari, John A. Rogers, Yonggang Huang
Proceedings of the National Academy of Sciences Oct 2018, 115 (44) 11144-11149; DOI: 10.1073/pnas.1814392115
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