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Model-based quantification of left ventricular diastolic function in critically ill patients with atrial fibrillation from routine data: a feasibility study. (English) Zbl 1423.92034
Summary: Introduction. Left ventricular diastolic dysfunction (LVDD) and atrial fibrillation (AF) are connected by pathophysiology and prevalence. LVDD remains underdiagnosed in critically ill patients despite potentially significant therapeutic implications since direct measurement cannot be performed in routine care at the bedside, and echocardiographic assessment of LVDD in AF is impaired. We propose a novel approach that allows us to infer the diastolic stiffness, \(\beta\), a key quantitative parameter of diastolic function, from standard monitoring data by solving the nonlinear, ill-posed inverse problem of parameter estimation for a previously described mechanistic, physiological model of diastolic filling. The beat-to-beat variability in AF offers an advantageous setting for this. Methods. By employing a global optimization algorithm, \(\beta\) is inferred from a simple six parameter and an expanded seven parameter model of left ventricular filling. Optimization of all parameters was limited to the interval \(]0, 400[\) and initialized randomly on large intervals encompassing the support of the likelihood function. Routine ECG and arterial pressure recordings of 17 AF and 3 sinus rhythm (SR) patients from the PhysioNet MGH/MF Database were used as inputs. Results. Estimation was successful in 15 of 17 AF patients, while in the 3 SR patients, no reliable estimation was possible. For both models, the inferred \(\beta\) (\(0.065 \pm 0.044\) ml vs. \(0.038\pm 0.033\) ml (\(p = 0.02\)) simple vs. expanded) was compatible with the previously described (patho) physiological range. Aortic compliance, \(\alpha\), inferred from the expanded model (\(1.46\pm 1.50\) ml/mmHg) also compared well with literature values. Conclusion. The proposed approach successfully inferred \(\beta\) within the physiological range. This is the first report of an approach quantifying LVDF from routine monitoring data in critically ill AF patients. Provided future successful external validation, this approach may offer a tool for minimally invasive online monitoring of this crucial parameter.
92C30 Physiology (general)
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] Gheorghiade, M.; Zannad, F.; Sopko, G., Acute heart failure syndromes, Circulation, 112, 25, 3958-3968, (2005)
[2] Ambrosy, A. P.; Fonarow, G. C.; Butler, J., The global health and economic burden of hospitalizations for heart failure, Journal of the American College of Cardiology, 63, 12, 1123-1133, (2014)
[3] Gheorghiade, M.; Vaduganathan, M.; Fonarow, G. C.; Bonow, R. O., Rehospitalization for heart failure, Journal of the American College of Cardiology, 61, 4, 391-403, (2013)
[4] Steinberg, B. A.; Zhao, X.; Heidenreich, P. A., Trends in patients hospitalized with heart failure and preserved left ventricular ejection fraction, Circulation, 126, 1, 65-75, (2012)
[5] Ziaeian, B.; Fonarow, G. C., Epidemiology and aetiology of heart failure, Nature Reviews Cardiology, 13, 6, 368-378, (2016)
[6] Kannel, W. B., Incidence and epidemiology of heart failure, Heart Failure Reviews, 5, 2, 167-173, (2000)
[7] Psaty, B. M.; Manolio, T. A.; Kuller, L. H., Incidence of and risk factors for atrial fibrillation in older adults, Circulation, 96, 7, 2455-2461, (1997)
[8] Benjamin, E. J.; Levy, D.; Vaziri, S. M.; D’Agostino, R. B.; Belanger, A. J.; Wolf, P. A., Independent risk factors for atrial fibrillation in a population-based cohort. The Framingham Heart Study, JAMA: The Journal of the American Medical Association, 271, 11, 840-844, (1994)
[9] Farmakis, D.; Papingiotis, G.; Parissis, J., Acute heart failure: epidemiology and socioeconomic burden, Continuing Cardiology Education, 3, 3, 88-92, (2017)
[10] Fonarow, G. C.; Stough, W. G.; Abraham, W. T., Characteristics, treatments, and outcomes of patients with preserved systolic function hospitalized for heart failure, Journal of the American College of Cardiology, 50, 8, 768-777, (2007)
[11] Owan, T. E.; Hodge, D. O.; Herges, R. M.; Jacobsen, S. J.; Roger, V. L.; Redfield, M. M., Trends in prevalence and outcome of heart failure with preserved ejection fraction, New England Journal of Medicine, 355, 3, 251-259, (2006)
[12] Ponikowski, P.; Voors, A. A.; Anker, S. D., 2016 ESC guidelines for the diagnosis and treatment of acute and chronic heart failure, European Heart Journal, 37, 27, 2129-2200, (2016)
[13] Kirchhof, P.; Benussi, S.; Kotecha, D., 2016 ESC guidelines for the management of atrial fibrillation developed in collaboration with EACTS, European Heart Journal, 37, 38, 2893-2962, (2016)
[14] Pai, R. G.; Varadarajan, P., Prognostic significance of atrial fibrillation is a function of left ventricular ejection fraction, Clinical Cardiology, 30, 7, 349-354, (2007)
[15] Kotecha, D.; Lam, C. S. P.; Van Veldhuisen, D. J.; Van Gelder, I. C.; Voors, A. A.; Rienstra, M., Heart failure with preserved ejection fraction and atrial fibrillation, Journal of the American College of Cardiology, 68, 20, 2217-2228, (2016)
[16] Sartipy, U.; Dahlström, U.; Fu, M.; Lund, L. H., Atrial fibrillation in heart failure with preserved, mid-range, and reduced ejection fraction, JACC: Heart Failure, 5, 8, 565-574, (2017)
[17] Vermond, R. A.; Geelhoed, B.; Verweij, N., Incidence of atrial fibrillation and relationship with cardiovascular events, heart failure, and mortality, Journal of the American College of Cardiology, 66, 9, 1000-1007, (2015)
[18] Vignon, P., Ventricular diastolic abnormalities in the critically ill, Current Opinion in Critical Care, 19, 3, 242-249, (2013)
[19] Artucio, H.; Pereira, M., Cardiac arrhythmias in critically ill patients, Critical Care Medicine, 18, 12, 1383-1388, (1990)
[20] Eisen, L. A.; Davlouros, P.; Karakitsos, D., Left ventricular diastolic dysfunction in the intensive care unit: trends and perspectives, Critical Care Research and Practice, 2012, (2012)
[21] Nagueh, S. F.; Appleton, C. P.; Gillebert, T. C., Recommendations for the evaluation of left ventricular diastolic function by echocardiography, European Journal of Echocardiography, 10, 2, 165-193, (2008)
[22] Bai, X.; Wang, Q., Time constants of cardiac function and their calculations∼!2010-05-30∼!2010-06-24∼!2010-08-09∼!, Open Cardiovascular Medicine Journal, 4, 1, 168-172, (2010)
[23] Glower, D. D.; Spratt, J. A.; Snow, N. D., Linearity of the Frank–Starling relationship in the intact heart: the concept of preload recruitable stroke work, Circulation, 71, 5, 994-1009, (1985)
[24] Gosselink, A. T.; Blanksma, P. K.; Crijns, H. J. G. M., Left ventricular beat-to-beat performance in atrial fibrillation: contribution of Frank–Starling mechanism after short rather than long RR intervals, Journal of the American College of Cardiology, 26, 6, 1516-1521, (1995)
[25] Brookes, C. I. O.; White, P. A.; Staples, M., Myocardial contractility is not constant during spontaneous atrial fibrillation in patients, Circulation, 98, 17, 1762-1768, (1998)
[26] Clermont, G.; Zenker, S., The inverse problem in mathematical biology, Mathematical Biosciences, 260, 11-15, (2015) · Zbl 1315.92033
[27] Zenker, S., Parallel particle filters for online identification of mechanistic mathematical models of physiology from monitoring data: performance and real-time scalability in simulation scenarios, Journal of Clinical Monitoring and Computing, 24, 4, 319-333, (2010)
[28] Zenker, S.; Rubin, J.; Clermont, G., From inverse problems in mathematical physiology to quantitative differential diagnoses, PLoS Computational Biology, 3, 11, (2007)
[29] Goldberger, A. L.; Amaral, L. A. N.; Glass, L., PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals, Circulation, 101, 23, e215-e220, (2000)
[30] Welch, J. P.; Ford, P. J.; Teplick, R. S.; Rubsamen, R. M., The Massachusetts general hospital-marquette foundation hemodynamic and electrocardiographic database – comprehensive collection of critical care waveforms, Journal of Clinical Monitoring, 7, 1, 96-97, (1991)
[31] Arzeno, N. M.; Deng, Z.-D; Poon, C.-S., Analysis of first-derivative based QRS detection algorithms, IEEE Transactions on Biomedical Engineering, 55, 2, 478-484, (2008)
[32] Zong, W.; Heldt, T.; Moody, G. B.; Mark, R. G., An open-source algorithm to detect onset of arterial blood pressure pulses, Proceedings of the Computers in Cardiology Conference, 2003, Thessaloniki
[33] Griewank, A.; Juedes, D.; Utke, J., Algorithm 755; ADOL-C: a package for the automatic differentiation of algorithms written in C/C++, ACM Transactions on Mathematical Software, 22, 2, 131-167, (1996) · Zbl 0884.65015
[34] Sanderson, C.; Curtin, R., Armadillo: a template-based C++ library for linear algebra, Journal of Open Source Software, 1, 2, 26, (2016)
[35] Schling, B., The Boost C++ Libraries, (2011), Durham, North Carolina: XML Press, Durham, North Carolina
[36] Bauke, H.; Mertens, S., Random numbers for large-scale distributed Monte Carlo simulations, Physical Review E, 75, 6, (2007)
[37] Python Software Foundation, Python Language Reference, (2003), Boston, MA, USA: Network Theory Limited, Boston, MA, USA
[38] van der Walt, S.; Colbert, S. C.; Varoquaux, G., The NumPy array: a structure for efficient numerical computation, Computing in Science & Engineering, 13, 2, 22-30, (Mar. 2011)
[39] Hunter, J. D., Matplotlib: a 2D graphics environment, Computing in Science & Engineering, 9, 3, 90-95, (2007)
[40] McKinney, W., Data structures for statistical computing in python, Proceedings of the 9th Python in Science Conference
[41] Jones, E.; Oliphant, T.; Peterson, P., SciPy: Open Source Scientific Tools for Python, (2001)
[42] Meguro, T.; Akaishi, M.; Suzuki, Y.; Matsubara, T.; Yokozuka, H.; Ogawa, S., Application of mechanical restitution, Japanese Circulation Journal, 62, 11, 829-836, (1998)
[43] Edmands, R. E.; Greenspan, K.; Fisch, C., The role of inotropic variation in ventricular function during atrial fibrillation, Journal of Clinical Investigation, 49, 4, 738-746, (1970)
[44] Earl, D. J.; Deem, M. W., Parallel tempering: theory, applications, and new perspectives, Physical Chemistry Chemical Physics, 7, 23, 3910-3916, (2005)
[45] Gill, J.; King, G., What to do when your hessian is not invertible, Sociological Methods & Research, 33, 1, 54-87, (2004)
[46] Mann, H. B.; Whitney, D. R., On a test of whether one of two random variables is stochastically larger than the other, Annals of Mathematical Statistics, 18, 1, 50-60, (1947) · Zbl 0041.26103
[47] Kass, D. A.; Midei, M.; Brinker, J.; Maughan, W. L., Influence of coronary occlusion during PTCA on end-systolic and end-diastolic pressure-volume relations in humans, Circulation, 81, 2, 447-460, (Feb. 1990)
[48] Schmitt, B.; Steendijk, P.; Lunze, K., Integrated assessment of diastolic and systolic ventricular function using diagnostic cardiac magnetic resonance catheterization, JACC: Cardiovascular Imaging, 2, 11, 1271-1281, (2009)
[49] Cohn, J. N.; Finkelstein, S.; McVeigh, G., Noninvasive pulse wave analysis for the early detection of vascular disease, Hypertension, 26, 3, 503-508, (1995)
[50] Duprez, D.; De Buyzere, M. L.; Rietzschel, E. R., Inverse relationship between aldosterone and large artery compliance in chronically treated heart failure patients, European Heart Journal, 19, 9, 1371-1376, (1998)
[51] Liu, Z. R.; Ting, C. T.; Zhu, S. X.; Yin, F. C., Aortic compliance in human hypertension, Hypertension, 14, 2, 129-136, (1989)
[52] McVeigh, G. E.; Bratteli, C. W.; Morgan, D. J., Age-related abnormalities in arterial compliance identified by pressure pulse contour analysis: aging and arterial compliance, Hypertension, 33, 6, 1392-1398, (1999)
[53] Dünser, M. W.; Hasibeder, W. R., Sympathetic overstimulation during critical illness: adverse effects of adrenergic stress, Journal of Intensive Care Medicine, 24, 5, 293-316, (2009)
[54] Malik, V.; Subramanian, A.; Hote, M.; Kiran, U., Effect of levosimendan on diastolic function in patients undergoing coronary artery bypass grafting, Journal of Cardiovascular Pharmacology, 66, 2, 141-147, (2015)
[55] Axelsson, B.; Arbeus, M.; Magnuson, A.; Hultman, J., Milrinone improves diastolic function in coronary artery bypass surgery as assessed by acoustic quantification and peak filling rate: a prospective randomized study, Journal of Cardiothoracic and Vascular Anesthesia, 24, 2, 244-249, (2010)
[56] Albrecht, C. A.; Giesler, G. M.; Kar, B.; Hariharan, R.; Delgado, R. M., Intravenous milrinone infusion improves congestive heart failure caused by diastolic dysfunction: a brief case series, Texas Heart Institute Journal, 32, 2, 220-223, (2005)
[57] Almeida, C. A. de M.; Nedel, W. L.; Morais, V. D.; Boniatti, M. M.; de Almeida-Filho, O. C., Diastolic dysfunction as a predictor of weaning failure: a systematic review and meta-analysis, Journal of Critical Care, 34, 135-141, (2016)
[58] Doucet, A.; de Freitas, N.; Gordon, N.; Doucet, A.; de Freitas, N.; Gordon, N., An introduction to sequential Monte Carlo methods, Sequential Monte Carlo Methods and Particle Filters Resources, 3-14, (2001), New York, NY, USA: Springer, New York, NY, USA · Zbl 1056.93576
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