Blood Flow Modeling to Improve Cardiovascular Diagnostics: Application of A GTF to Predict Central Aortic Pressure using a 1-D Model

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    This study aims to demonstrate that a comprehensive one-dimensional model of the arterial network can be used in conjunction with the generalized transfer function (GTF) technique to estimate central aortic pressure using pressure waveforms obtained from peripheral sites. The peripheral and central pressure waveforms for a healthy subject are used to estimate transfer functions, which are then used to reconstruct central aortic pressure waveforms for a second model that simulates arterial stiffening. The similarities between the simulated aortic waveform and the waveforms estimated using the transfer function are and   from the brachial, carotid and iliac arteries, respectively. The root-mean-square errors (RMSE) for the reconstructed waveforms from the brachial, carotid and iliac arteries are and  mmHg, respectively. The results from this study illustrate that the proposed method provides a feasible alternative to higher dimensional models as well as experimental studies and can greatly enhance the accuracy of central aortic pressure estimation.   

     

     


  • Keywords


    Arterial network; Central aortic pressure; Computational fluid dynamics; One-dimensional modelling; Transfer function

  • References


      [1] G. P. Gravlee, A. B. Wong, T. G. Adkins, L. Douglas Case, and A. L. Pauca, “A comparison of radial, brachial, and aortic pressures after cardiopulmonary bypass,” J. Cardiothorac. Anesth., vol. 3, no. 1, pp. 20–26, Feb. 1989.

      [2] M. Karamanoglu, M. F. O’Rourke, a P. Avolio, and R. P. Kelly, “An analysis of the relationship between central aortic and peripheral upper limb pressure waves in man.,” Eur. Heart J., vol. 14, no. 2, pp. 160–167, 1993.

      [3] R. P. Kelly, H. H. Gibbs, M. F. O’Rourke, J. E. Daley, K. Mang, J. J. Morgen, and A. P. Avolio, “Nitroglycerin has more favourable effects on left ventricular afterload than apparent from measurement of pressure in a peripheral artery,” Eur. Heart J., vol. 11, no. 2, pp. 138–144, 1990.

      [4] N. Stergiopulos, D. F. Young, and T. R. Rogge, “Computer simulation of arterial flow with applications to arterial and aortic stenoses,” J. Biomech., vol. 25, no. 12, pp. 1477–1488, 1992.

      [5] M. Karamanoglu, D. E Gallagher, A. Avolio, and M. F O’Rourke, “Pressure wave propagation in a multibranched model of the human upper limb,” Am. J. Physiol., vol. 269, pp. H1363-9, 1995.

      [6] G. M. Drzewiecki, J. Melbin, and A. Noordergraaf, “Arterial tonometry: Review and analysis,” J. Biomech., vol. 16, no. 2, pp. 141–152, 1983.

      [7] R. P. Kelly, M. Karamanoglu, H. Gibbs, A. P. Avolio, and M. F. O’Rourke, “Noninvasive carotid pressure wave registration as an indicator of ascending aortic pressure,” J. Vasc. Med. Biol., vol. 1, pp. 241–247, 1989.

      [8] R. P. Kelly, C. Hayward, J. Ganis, J. Daley, A. P. Avolio, and M. F. O"Rourke, “Noninvasive registration of the arterial pressure pulse waveform; using high-fidelity applanation tonometry,” J. Vasc. Med. Biol., vol. 1, pp. 142–149, 1989.

      [9] W. J. Verberk, H. Cheng, L.-C. Huang, C.-M. Lin, Y.-P. Teng, and C.-H. Chen, “Practical Suitability of a Stand-Alone Oscillometric Central Blood Pressure Monitor: A Review of the Microlife WatchBP Office Central,” Pulse, vol. 3, no. 3–4, pp. 205–216, 2016.

      [10] J. E. Lewis, P. Williams, and J. H. Davies, “Non-invasive assessment of peripheral arterial disease: Automated ankle brachial index measurement and pulse volume analysis compared to duplex scan,” SAGE Open Med., vol. 4, no. 5, p. 205031211665908, 2016.

      [11] Y. Watanabe, H. Masaki, Y. Yunoki, A. Tabuchi, I. Morita, S. Mohri, and K. Tanemoto, “Ankle-Brachial Index, Toe-Brachial Index, and Pulse Volume Recording in Healthy Young Adults,” Ann. Vasc. Dis., vol. 8, no. 3, pp. 227–235, 2015.

      [12] R. E. D. Climie, M. G. Schultz, S. B. Nikolic, K. D. K. Ahuja, J. W. Fell, and J. E. Sharman, “Validity and reliability of central blood pressure estimated by upper arm oscillometric cuff pressure,” Am. J. Hypertens., vol. 25, no. 4, pp. 414–420, 2012.

      [13] W. Nichols, M. O’Rourke, and C. Vlachopoulos, “Mcdonaldʼs Blood Flow in Arteries,” Shock, vol. 9, no. 6, p. 456, 1998.

      [14] B. Williams, P. S. Lacy, S. M. Thom, K. Cruickshank, A. Stanton, D. Collier, A. D. Hughes, H. Thurston, and M. O’Rourke, “Differential impact of blood pressure-lowering drugs on central aortic pressure and clinical outcomes: Principal results of the Conduit Artery Function Evaluation (CAFE) study,” Circulation, vol. 113, no. 9, pp. 1213–1225, 2006.

      [15] M. E. Safar, J. Blacher, B. Pannier, A. P. Guerin, S. J. Marchais, P.-M. Guyonvarctextquoterighth, and G. M. London, “Central Pulse Pressure and Mortality in End-Stage Renal Disease,” Hypertension, vol. 39, no. 3, pp. 735–738, 2002.

      [16] T. K. Waddell, A. M. Dart, T. L. Medley, J. D. Cameron, and B. A. Kingwell, “Carotid Pressure Is a Better Predictor of Coronary Artery Disease Severity Than Brachial Pressure,” Hypertension, vol. 38, no. 4, pp. 927–931, 2001.

      [17] M. J. Roman, R. B. Devereux, J. R. Kizer, E. T. Lee, J. M. Galloway, T. Ali, J. G. Umans, and B. V. Howard, “Central pressure more strongly relates to vascular disease and outcome than does brachial pressure: The strong heart study,” Hypertension, vol. 50, no. 1, pp. 197–203, 2007.

      [18] C.-H. Chen, E. Nevo, B. Fetics, P. H. Pak, F. C. P. Yin, W. L. Maughan, and D. A. Kass, “Estimation of Central Aortic Pressure Waveform by Mathematical Transformation of Radial Tonometry Pressure,” Circulation, vol. 95, no. 7, pp. 1827–1836, 1997.

      [19] B. Fetics, E. Nevo, C. H. Chen, and D. A. Kass, “Parametric model derivation of transfer function for noninvasive estimation of aortic pressure by radial tonometry,” IEEE Trans. Biomed. Eng., vol. 46, no. 6, pp. 698–706, 1999.

      [20] A. L. Pauca, M. F. O’Rourke, and N. D. Kon, “Prospective evaluation of a method for estimating ascending aortic pressure from the radial artery pressure waveform.,” Hypertension, vol. 38, no. 4, pp. 932–937, 2001.

      [21] S. Soderstrom, G. Nyberg, M. F. O’Rourke, J. Sellgren, and J. Pontén, “Can a clinically useful aortic pressure wave be derived from a radial pressure wave?,” Br. J. Anaesth., vol. 88, no. 4, pp. 481–488, 2002.

      [22] D. Gallagher, A. Adji, and M. O’Rourke, “Validation of the transfer function technique for generating central from peripheral upper limb pressure waveform,” Am. J. Hypertens., vol. 17, no. 11, pp. 1059–1067, 2004.

      [23] J. E. Sharman, R. Lim, A. M. Qasem, J. S. Coombes, M. I. Burgess, J. Franco, P. Garrahy, I. B. Wilkinson, and T. H. Marwick, “Validation of a generalized transfer function to noninvasively derive central blood pressure during exercise,” Hypertension, vol. 47, no. 6, pp. 1203–1208, 2006.

      [24] T. Weber, S. Wassertheurer, M. Rammer, E. Maurer, B. Hametner, C. C. Mayer, J. Kropf, and B. Eber, “Validation of a brachial cuff-based method for estimating central systolic blood pressure,” Hypertension, vol. 58, no. 5, pp. 825–832, 2011.

      [25] M. F. O’Rourke, “Method for Ascertaining the Pressure Pulse and Related Parameters in the Ascending Aorta from the Contour of the Pressure Pulse in the Peripheral Arteries,” US 5,265,011, 1993.

      [26] W. J. Stok, “Changes in finger-aorta pressure transfer function during and after exercise,” J. Appl. Physiol., vol. 101, no. 4, pp. 1207–1214, 2006.

      [27] G. C. Cloud, C. Rajkumar, J. Kooner, J. Cooke, and C. J. Bulpitt, “Estimation of central aortic pressure by SphygmoCor requires intra-arterial peripheral pressures.,” Clin. Sci. (Lond)., vol. 105, no. 2, pp. 219–225, 2003.

      [28] P. Segers, D. Mahieu, J. Kips, E. Rietzschel, M. De Buyzere, D. De Bacquer, S. Bekaert, G. De Backer, T. Gillebert, P. Verdonck, and L. Van Bortel, “Amplification of the pressure pulse in the upper limb in healthy, middle-aged men and women,” Hypertension, vol. 54, no. 2, pp. 414–420, 2009.

      [29] W. B. White, A. S. Berson, C. Robbins, M. J. Jamieson, L. M. Prisant, E. Roccella, and S. G. Sheps, “National standard for measurement of resting and ambulatory blood pressures with automated sphygmomanometers,” Hypertension, vol. 21, no. 4, pp. 504–509, 1993.

      [30] G. Swamy, Q. Ling, T. Li, and R. Mukkamala, “Blind identification of the aortic pressure waveform from multiple peripheral artery pressure waveforms.,” Am. J. Physiol. Heart Circ. Physiol., vol. 292, no. 5, pp. H2257-64, 2007.

      [31] J. O. Hahn, A. T. Reisner, F. A. Jaffer, and H. H. Asada, “Subject-specific estimation of central aortic blood pressure using an individualized transfer function: A preliminary feasibility study,” IEEE Trans. Inf. Technol. Biomed., vol. 16, no. 2, pp. 212–220, 2012.

      [32] G. Swamy, D. Xu, N. B. Olivier, and R. Mukkamala, “An adaptive transfer function for deriving the aortic pressure waveform from a peripheral artery pressure waveform,” Am. J. Physiol. Circ. Physiol., vol. 297, no. 5, pp. H1956–H1963, 2009.

      [33] N. Fazeli, M. Rashedi, A. Chappell, S. Wang, R. Macarthur, M. S. Mcmurtry, B. Finegan, and J. Hahn, “Subject - Specific Estimation of Aortic Blood Pressure via System Identification : Preliminary In - Human Experimental Study *,” 2013.

      [34] Y. Shi, P. Lawford, and R. Hose, “Review of zero-D and 1-D models of blood flow in the cardiovascular system.,” Biomed. Eng. Online, vol. 10, no. 1, p. 33, 2011.

      [35] N. Stergiopulos, B. E. Westerhof, and N. Westerhof, “Physical basis of pressure transfer from periphery to aorta: a model-based study,” Am. J. Physiol. Circ. Physiol., vol. 274, no. 4, pp. H1386–H1392, 1998.

      [36] P. Segers, S. Carlier, a Pasquet, S. I. Rabben, L. R. Hellevik, E. Remme, T. De Backer, J. De Sutter, J. D. Thomas, and P. Verdonck, “Individualizing the aorto-radial pressure transfer function: feasibility of a model-based approach.,” Am. J. Physiol. Heart Circ. Physiol., vol. 279, no. 2, pp. H542-9, 2000.

      [37] C.-J. Thore, J. Stålhand, and M. Karlsson, “Toward a noninvasive subject-specific estimation of abdominal aortic pressure.,” Am. J. Physiol. Heart Circ. Physiol., vol. 295, no. 3, pp. H1156–H1164, 2008.

      [38] M. S. Olufsen, “Structured tree outflow condition for blood flow in larger systemic arteries.,” Am J Physiol, vol. 276, no. 1 Pt 2, pp. H257--H268, 1999.

      [39] M. S. Olufsen, C. S. Peskin, W. Y. Kim, E. M. Pedersen, A. Nadim, and J. Larsen, “Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions,” Ann. Biomed. Eng., vol. 28, no. 11, pp. 1281–1299, 2000.

      [40] K. S. Matthys, J. Alastruey, J. Peiró, A. W. Khir, P. Segers, P. R. Verdonck, K. H. Parker, and S. J. Sherwin, “Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements.,” J. Biomech., vol. 40, no. 15, pp. 3476–3486, 2007.

      [41] N. Stergiopulos, “Computer simulation of arterial blood flow,” 1990.

      [42] S. J. Sherwin, V. Franke, J. Peiró, and K. Parker, “One-dimensional modelling of a vascular network in space-time variables,” J. Eng. Math., vol. 47, no. 3–4, pp. 217–250, 2003.

      [43] J. Lee and N. P. Smith, “Development and application of a one-dimensional blood flow model for microvascular networks.,” Proc. Inst. Mech. Eng. H., vol. 222, no. 4, pp. 487–511, 2008.

      [44] P. Reymond, F. Merenda, F. Perren, D. Rüfenacht, and N. Stergiopulos, “Validation of a one-dimensional model of the systemic arterial tree.,” Am. J. Physiol. Heart Circ. Physiol., vol. 297, no. 1, pp. H208–H222, 2009.

      [45] X. Wang, “1D modeling of blood ow in networks : numerical computing and applications.”, Ph.D. dissertation, Universitie Pierre et Marie Curie - Paris VI, 2014.

      [46] A. Noordergraaf, Circulatory System Dynamics. 1978.

      [47] F. N. van de Vosse, “Mathematical modelling of the cardiovascular system,” J. Eng. Math., vol. 47, no. 3, pp. 175–183, 2003.

      [48] M. S. Olufsen, “Structured tree outflow condition for blood flow in larger systemic arteries.,” Am J Physiol, vol. 276, no. 1 Pt 2, pp. H257--H268, 1999.

      [49] C. D. Murray, “The physiological principle of minimum work applied to the angle of branching of arteries,” J. Gen. Physiol., vol. 9, no. 6, pp. 835–841, 1926.

      [50] M. S. Pollanen, “Dimensional optimization at different levels of the arterial hierarchy,” J. Theor. Biol., vol. 159, no. 2, pp. 267–270, 1992.

      [51] H. B. M. Uylings, “Optimization of diameters and bifurcation angles in lung and vascular tree structures,” Bull. Math. Biol., vol. 39, no. 5, pp. 509–520, 1977.

      [52] G. L. Papageorgiou, B. N. Jones, V. J. Redding, and N. Hudson, “The area ratio of normal arterial junctions and its implications in pulse wave reflections,” Cardiovasc. Res., vol. 24, no. 6, pp. 478–484, 1990.

      [53] H. B. Atabek, “Wave Propagation through a Viscous Fluid Contained in a Tethered, Initially Stressed, Orthotropic Elastic Tube,” Biophys. J., vol. 8, no. 5, pp. 626–649, 1968.

      [54] T. Pedley, The Fluid Mechanics of Large Blood Vessels. Cambridge,G.B.: Cambridge University Press, 1980.

      [55] M. F. O’Rourke, Arterial function in health and disease. Newyork , USA: Churchill Livingstone, 1982.

      [56] M. F. O’Rourke and T. Yaginuma, “Wave reflections and the arterial pulse.,” Arch. Intern. Med., vol. 144, no. 2, pp. 366–371, 1984.

      [57] I. Ferreira, R. J. van de Laar, M. H. Prins, J. W. Twisk, and C. D. Stehouwer, “Carotid Stiffness in Young Adults: A Life-Course Analysis of its Early Determinants,” Hypertension, vol. 59, no. 1, pp. 54–61, 2012.

      [58] M. AlGhatrif, J. B. Strait, C. H. Morrell, M. Canepa, J. Wright, P. Elango, A. Scuteri, S. S. Najjar, L. Ferrucci, and E. G. Lakatta, “Longitudinal Trajectories of Arterial Stiffness and the Role of Blood PressureNovelty and Significance,” Hypertension, vol. 62, no. 5, pp. 934–941, 2013.

      [59] M. F. O’Rourke, “Vascular impedance in studies of arterial and cardiac function.,” Physiol. Rev., vol. 62, no. 2, pp. 570–623, 1982.

      [60] S. C. Millasseau, S. J. Patel, S. R. Redwood, J. M. Ritter, and P. J. Chowienczyk, “Pressure wave reflection assessed from the peripheral pulse: Is a transfer function necessary?,” Hypertension, vol. 41, no. 5, pp. 1016–1020, 2003.


 

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Article ID: 22156
 
DOI: 10.14419/ijet.v7i4.26.22156




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