Article | Published:

Multiscale mathematical modeling vs. the generalized transfer function approach for aortic pressure estimation: a comparison with invasive data

Hypertension Researchvolume 42pages690698 (2019) | Download Citation



We aimed to evaluate the performance of a mathematical model and currently available non-invasive techniques (generalized transfer function (GTF) method and brachial pressure) in the estimation of aortic pressure. We also aimed to investigate error dependence on brachial pressure errors, aorta-to-brachial pressure changes and demographic/clinical conditions. Sixty-two patients referred for invasive hemodynamic evaluation were consecutively recruited. Simultaneously, the registration of the aortic pressure using a fluid-filled catheter, brachial pressure and radial tonometric waveform was recorded. Accordingly, the GTF device and mathematical model were set. Radial invasive pressure was recorded soon after aortic measurement. The average invasive aortic pressure was 141.3 ± 20.2/76 ± 12.2 mm Hg. The simultaneous brachial pressure was 144 ± 17.8/81.5 ± 11.7 mm Hg. The GTF-based and model-based aortic pressure estimates were 133.1 ± 17.3/82.4 ± 12 and 137 ± 21.6/72.2 ± 16.7 mm Hg, respectively. The Bland-Altman plots showed a marked tendency to pressure overestimation for increasing absolute values, with the exclusion of mathematical model diastolic estimations. The systolic pressure was increased from the aortic to radial locations (7.5 ± 19 mm Hg), while the diastolic pressure was decreased (3.8 ± 9.8 mm Hg). The brachial pressure underestimated the systolic and overestimated diastolic intra-arterial radial pressure. GTF errors were independently correlated with the variability in pulse pressure amplification and with the brachial error. Errors of the mathematical model were related to only demographic and clinical conditions. Neither a multiscale mathematical model nor a generalized transfer function device substantially outperformed the oscillometric brachial pressure in the estimation of aortic pressure. Mathematical modeling should be improved by including further patient-specific conditions, while the variability in pulse pressure amplification may hamper the performance of the GTF method in patients at the risk of coronary artery disease.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

These authors are joint first authors: Andrea Guala, Francesco Tosello.


  1. 1.

    Mancia G, Fagard RH, Narkiewicz K, Redon J, Zanchetti A, Böhm M, et al. 2013 ESH/ESC guidelines for the management of arterial hypertension: The Task Force for the management of arterial hypertension of the European Society of Hypertension (ESH) and of the European Society of Cardiology (ESC). Eur Heart J. 2013;34:2159–219.

  2. 2.

    Avolio AP, Van Bortel LM, Boutouyrie P, Cockcroft JR, McEniery CM, Protogerou AD, et al. Role of pulse pressure amplification in arterial hypertension: experts’ opinion and review of the data. Hypertension. 2009;54:375–83.

  3. 3.

    Roman MJ, Devereux RB, Kizer JR, Lee ET, Galloway JM, Ali T, et al. Central pressure more strongly relates to vascular disease and outcome than does brachial pressure: the Strong Heart Study. Hypertension. 2007;50:197–203.

  4. 4.

    Safar ME, Blacher J, Pannier B, Guerin AP, Marchais SJ, Guyonvarc P, et al. Central pulse pressure and mortality in end-stage renal disease. Hypertension. 2002;39:735–8.

  5. 5.

    Pini R, Cavallini MC, Palmieri V, Marchionni N, Di Bari M, Devereux RB, et al. Central but not brachial blood pressure predicts cardiovascular events in an unselected geriatric population. The ICARe Dicomano Study. J Am Coll Cardiol. 2008;51:2432–9.

  6. 6.

    Rosendorff C, Lackland DT, Allison Ma, Aronow WS, Black HR, Blumenthal RS, et al. Treatment of hypertension in patients with coronary artery disease: A scientific statement from the American Heart Association, American College of Cardiology, and American Society of Hypertension. Hypertension. 2015;65:1372–407.

  7. 7.

    Agabiti-Rosei E, Mancia G, O’Rourke MF, Roman MJ, Safar ME, Smulyan H, et al. Central blood pressure measurements and antihypertensive therapy: A consensus document. Hypertension. 2007;50:154–60.

  8. 8.

    Wang J-G, Li Y, Franklin SS, Safar ME. Prevention of stroke and myocardial infarction by amlodipine and Angiotensin receptor blockers: a quantitative overview. Hypertension. 2007;50:181–8.

  9. 9.

    McEniery CM, Cockcroft JR, Roman MJ, Franklin SS, Wilkinson IB. Central blood pressure: current evidence and clinical importance. Eur Heart J. 2014;35:1719–25.

  10. 10.

    Dhakam Z, McEniery CM, Yasmin, Cockcroft JR, Brown M, Wilkinson IB. Atenolol and eprosartan: Differential effects on central blood pressure and aortic pulse wave velocity. Am J Hypertens. 2006;19:214–9.

  11. 11.

    Williams B, Lacy PS, Thom SM, Cruickshank K, Stanton A, Collier D, et al. 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. 2006;113:1213–25.

  12. 12.

    Mahieu D, Kips J, Rietzschel ER, De Buyzere ML, Verbeke F, Gillebert TC, et al. Noninvasive assessment of central and peripheral arterial pressure (waveforms): Implications of calibration methods. J Hypertens. 2010;28:300–5.

  13. 13.

    Sharman JE, Avolio AP, Baulmann J, Benetos A, Blacher J, Blizzard CL, et al. Validation of non-invasive central blood pressure devices: Artery society task force consensus statement on protocol standardization. Eur Heart J. 2017;38:2805–12.

  14. 14.

    Vlachopoulos C, Aznaouridis K, O’Rourke MF, Safar ME, Baou K, Stefanadis C. Prediction of cardiovascular events and all-cause mortality with central haemodynamics: a systematic review and meta-analysis. Eur Heart J. 2010;31:1865–71.

  15. 15.

    Cheng H-M, Lang D, Tufanaru C, Pearson A. Measurement accuracy of non-invasively obtained central blood pressure by applanation tonometry: a systematic review and meta-analysis. Int J Cardiol. 2013;167:1867–76.

  16. 16.

    Hope SA, Meredith IT, Cameron JD. Effect of non-invasive calibration of radial waveforms on error in transfer-function-derived central aortic waveform characteristics. Clin Sci (Lond). 2004;107:205–11.

  17. 17.

    Hahn JO, Reisner AT, Jaffer FA, Asada HH. Subject-specific estimation of central aortic blood pressure using an individualized transfer function: A preliminary feasibility study. IEEE Trans Inf Technol Biomed. 2012;16:212–20.

  18. 18.

    Ghasemi Z, Lee JC, Kim CS, Cheng HM, Sung SH, Chen CH, et al. Estimation of cardiovascular risk predictors from non-invasively measured diametric pulse volume waveforms via multiple measurement information fusion. Sci Rep. 2018;8:1–11.

  19. 19.

    Guala A, Camporeale C, Ridolfi L. Compensatory Effect between Aortic Stiffening and Remodelling during Ageing. PLoS ONE. 2015;10:e0139211.

  20. 20.

    Guala A, Camporeale C, Tosello F, Canuto C. Ridolfi L. Modelling and Subject-Specific Validation of the Heart-Arterial Tree System. Ann Biomed Eng. 2014;43:227–37.

  21. 21.

    Blanco PJ, Watanabe SM. Passos MARF, Lemos P, Feijóo R a. An anatomically detailed arterial network model for one-dimensional computational hemodynamics. IEEE Trans Biomed Eng. 2014;9294(c):1–18.

  22. 22.

    Tosello F, Guala A, Leone D, Camporeale C, Bruno G, Ridolfi L, et al. Central pressure appraisal: Clinical validation of a subject-specific mathematical model. PLoS ONE. 2016;11:e0151523.

  23. 23.

    Reymond P, Bohraus Y, Perren F, Lazeyras F, Stergiopulos N. Validation of a patient-specific one-dimensional model of the systemic arterial tree. Am J Physiol Hear Circ Physiol. 2011;301:H1173–82.

  24. 24.

    Guala A, Leone D, Milan A, Ridolfi L. In silico analysis of the anti-hypertensive drugs impact on myocardial oxygen balance. Biomech Model Mechanobiol. 2017;16:1035–47.

  25. 25.

    Bollache E, Kachenoura N, Redheuil A, Frouin F, Mousseaux E, Recho P, et al. Descending aorta subject-specific one-dimensional model validated against in vivo data. J Biomech. 2014;47:424–31.

  26. 26.

    Mynard JP, Smolich JJ. One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann Biomed Eng. 2015;43:1443–60.

  27. 27.

    Epstein S, Willemet M, Chowienczyk PJ, Alastruey J. Reducing the number of parameters in 1D arterial blood flow modelling: Less is more for patient-specific simulations. Am J Physiol Hear Circ Physiol. 2015;309:H222–34.

  28. 28.

    Laurent S, Cockcroft J, Van Bortel L, Boutouyrie P, Giannattasio C, Hayoz D, et al. Expert consensus document on arterial stiffness: Methodological issues and clinical applications. Eur Heart J. 2006;27:2588–605.

  29. 29.

    Blanco PJ, Feijóo Ra. A dimensionally-heterogeneous closed-loop model for the cardiovascular system and its applications. Med Eng Phys. 2013;35:652–67.

  30. 30.

    Picone DS, Schultz MG, Otahal P, Aakhus S, Al-Jumaily AM, Black JA, et al. Accuracy of cuff-measured blood pressure: Systematic reviews and meta-analyses. J Am Coll Cardiol. 2017;70:572–86.

  31. 31.

    White WB, Berson AS, Robbins C, Jamieson MJ, Prisant LM, Roccella E. et al. National standard for measurement of resting and ambulatory blood pressures with automated sphygmomanometers. Hypertension. 1993;21:504–9.

  32. 32.

    McEniery CM, Yasmin, McDonnell B, Munnery M, Wallace SML, Rowe CV, et al. Central pressure: variability and impact of cardiovascular risk factors: the Anglo-Cardiff Collaborative Trial II. Hypertension. 2008;51:1476–82.

  33. 33.

    Fazeli N, Kim CS, Rashedi M, Chappell A, Wang S, MacArthur R, et al. Subject-specific estimation of central aortic blood pressure via system identification: preliminary in-human experimental study. Med Biol Eng Comput. 2014;52:895–904.

Download references


This work has been funded by the Italian Ministry of Health, through Progetto di Ricerca Sanitaria Finalizzata e Giovani Ricercatori 2013–CUP GR-2013-02356887 to the PI Dr. Alberto Milan. A. Guala has received funding from the European Union Seventh Framework Program FP7/People under grant agreement no. 267128.

Author information


  1. Vall d’Hebron Institut de Recerca, Barcelona, Spain

    • Andrea Guala
  2. Internal and Hypertension Division, Department of Medical Sciences, University of Turin, Turin, Italy

    • Francesco Tosello
    • , Dario Leone
    • , Luca Sabia
    • , Martina Bollati
    • , Franco Veglio
    •  & Alberto Milan
  3. Hemodynamic Laboratory, Department of Medical Sciences, University of Turin, Turin, Italy

    • Fabrizio D’Ascenzo
    •  & Claudio Moretti
  4. DIATI, Politecnico di Torino, Turin, Italy

    • Luca Ridolfi


  1. Search for Andrea Guala in:

  2. Search for Francesco Tosello in:

  3. Search for Dario Leone in:

  4. Search for Luca Sabia in:

  5. Search for Fabrizio D’Ascenzo in:

  6. Search for Claudio Moretti in:

  7. Search for Martina Bollati in:

  8. Search for Franco Veglio in:

  9. Search for Luca Ridolfi in:

  10. Search for Alberto Milan in:

Conflict of interest

The authors declare that they have no conflict of interest.

Corresponding author

Correspondence to Andrea Guala.

About this article

Publication history





Issue Date