Parameter estimation in a minimal model of cardio-pulmonary interactions.

Cardio-pulmonary interactions; Cardiovascular system model; Intensive care unit; Mechanical ventilation; Parameter estimation; Respiratory system model

Abstract :

[en] Mechanical ventilation is a widely used breathing support for patients in intensive care. Its effects on the respiratory and cardiovascular systems are complex and difficult to predict. This work first presents a minimal mathematical model representing the mechanics of both systems and their interaction, in terms of flows, pressures and volumes. The aim of this model is to get insight on the two systems' status when mechanical ventilation settings, such as positive end-expiratory pressure, are changing. The parameters of the model represent cardiac elastances and vessel compliances and resistances. As a second step, these parameters are estimated from 16 experimental datasets. The data come from three pig experiments reproducing intensive care conditions, where a large range of positive end-expiratory pressures was imposed by the mechanical ventilator. The data used for parameter estimation is limited to information available in the intensive care unit, such as stroke volume, central venous pressure and systemic arterial pressure. The model is able to satisfactorily reproduce this experimental data, with mean relative errors ranging from 1 to 26 %. The model also reproduces the dynamics of the cardio-vascular and respiratory systems, and their interaction. By looking at the estimated parameter values, one can quantitatively track how the two coupled systems mechanically react to changes in external conditions imposed by the ventilator. This work thus allows real-time, model-based management of ventilator settings.

Disciplines :

Anesthesia & intensive care

Author, co-author :

de Bournonville, Sebastien

Pironet, Antoine

Pretty, Chris

Chase, J. Geoffrey

Desaive, Thomas ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Thermodynamique des phénomènes irréversibles

Language :

English

Title :

Parameter estimation in a minimal model of cardio-pulmonary interactions.

Publication date :

2019

Journal title :

Mathematical Biosciences

ISSN :

0025-5564

Publisher :

Elsevier, Netherlands

Peer reviewed :

Peer Reviewed verified by ORBi

Commentary :

Available on ORBi :

since 29 May 2019

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Bibliography

Esteban, A., Anzueto, A., Alia, I., Gordo, F., Apezteguia, C., Palizas, F., Cide, D., Goldwaser, R., Soto, L., Bugedo, G., Rodrigo, C., Pimentel, J., Raimondi, G., Tobin, M.J., How is mechanical ventilation employed in the intensive care unit? An international utilization review. Am. J. Respir. Crit. Care Med. 161:5 (2000), 1450–1458.
Soni, N., Williams, P., Positive pressure ventilation: what is the real cost?. Br. J. Anaesth. 101:4 (2008), 446–457.
Starfinger, C., Chase, J.G., Hann, C.E., Shaw, G.M., Lambert, P., Smith, B.W., Sloth, E., Larsson, A., Andreassen, S., Rees, S., Model-based identification of PEEP titrations during different volemic levels. Comput. Methods Programs Biomed. 91:2 (2008), 135–144.
Pironet, A., Desaive, T., Chase, J., Morimont, P., Dauby, P., Model-based computation of total stressed blood volume from a preload reduction manoeuvre. Math. Biosci. 265 (2015), p.28–39.
Revie, J.A., Stevenson, D., Chase, J.G., Pretty, C.J., Lambermont, B.C., Ghuysen, A., Kolh, P., Shaw, G.M., Desaive, T., Evaluation of a model-based hemodynamic monitoring method in a porcine study of septic shock. Comput. Math. Methods Med., 2013, 2013, 505417.
Lansdorp, B., van Putten, M., de Keijzer, A., Pickkers, P., van Oostrom, J., A mathematical model for the prediction of fluid responsiveness. Cardiovasc. Eng. Technol. 4:1 (2013), 53–62.
Fan, H.-H., Khoo, M., Pneuma - a comprehensive cardiorespiratory model. Engineering in Medicine and Biology, 2002. 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society EMBS/BMES Conference, 2002. Proceedings of the Second Joint, 2002.
Chase, J.G., Preiser, J.C., Dickson, J.L., Pironet, A., Chiew, Y.S., Pretty, C.G., Shaw, G.M., Benyo, B., Moeller, K., Safaei, S., Tawhai, M., Hunter, P., Desaive, T., Next-generation, personalised, model-based critical care medicine: a state-of-the art review of in silico virtual patient models, methods, and cohorts, and how to validation them. Biomed. Eng. Online, 17(1), 2018, 24.
Samar, Z., Heldt, T., Verghese, G., Mark, R., Model-based cardiovascular parameter estimation in the intensive care unit. Comput. Cardiol., 2005, 635–638.
Heldt, T., Shim, E.B., Kamm, R.D., Mark, R.G., Kamm, R.D., Computational modeling of cardiovascular response to orthostatic stress. J. Appl. Physiol. 92:3 (2002), 1239–1254.
Ursino, M., A mathematical model of the carotid baroregulation in pulsating conditions. IEEE Trans. Biomed. Eng. 46:4 (1999), 382–392.
Messerges, J., Modeling systolic pressure variation due to positive pressure ventilation. Conf. Proc. IEEE Eng. Med. Biol. Soc. 1 (2006), 1806–1809.
Pironet, A., Docherty, P., Dauby, P., Chase, J., Desaive, T., Practical identifiability analysis of a minimal cardiovascular system model. Comput. Methods Programs Biomed., 2017.
Pironet, A., Dauby, P., Morimont, P., Janssen, N., Chase, J., Davidson, S., Desaive, T., Model-based decision support algorithm to guide fluid resuscitation. IFAC-PapersOnLine 49:5 (2016), 224–229.
Pironet, A., Model-Based Prediction of the Response to Vascular Filling Therapy, 2016, Universit de Lige Ph.D. thesis.
Smith, B.W., Chase, J.G., Nokes, R.I., Shaw, G.M., Wake, G., Minimal haemodynamic system model including ventricular interaction and valve dynamics. Med. Eng. Phys. 26:2 (2004), 131–139.
Revie, J.A.M., Model-Based Cardiovascular Monitoring in Critical Care for Improved Diagnosis of Cardiac Dysfunction, 2012, University of Canterburry, Christchurch, New Zealand Ph.D. thesis.
Starfinger, C., Patient-Specific Modelling of the Cardiovascular System for Diagnosis and Therapy Assistance in Critical Care, 2008, University of Canterburry, Christchurch, New Zealand Ph.D. thesis.
Fresiello, L., Ferrari, G., Di Molfetta, A., Zieliński, K., Tzallas, A., Jacobs, S., Darowski, M., Kozarski, M., Meyns, B., Katertsidis, N.S., Karvounis, E.C., Tsipouras, M.G., Trivella, M.G., A cardiovascular simulator tailored for training and clinical uses. J. Biomed. Inform. 57 (2015), 100–112.
Abdolrazaghi, M., Navidbakhsh, M., Hassani, K., Mathematical modelling and electrical analog equivalent of the human cardiovascular system. Cardiovasc. Eng. 10:2 (2010), 45–51, 10.1007/s10558-010-9093-0.
Burkhoff, D., Tyberg, J.V., Why does pulmonary venous pressure rise after onset of lv dysfunction: a theoretical analysis. Am. J. Physiol. Heart Circulat. Physiol. 265:5 (1993), H1819–H1828.
Chung, D.C., Ventricular Interaction in a Closed-Loop Model of the Canine Circulation, 1996, Rice University, Houston, Texas Master's thesis.
Danielsen, M., Ottesen, J.T., Describing the pumping heart as a pressure source. J. Theor. Biol. 212:1 (2001), 71–81, 10.1006/jtbi.2001.2348.
Ellwein, L.M., Tran, H.T., Zapata, C., Novak, V., Olufsen, M.S., Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure. Cardiovasc. Eng. 8:2 (2008), 94–108.
Pope, S.R., Ellwein, L.M., Zapata, C.L., Novak, V., Kelley, C.T., Olufsen, M.S., Estimation and identification of parameters in a lumped cerebrovascular model. Math. Biosci. Eng. 6 (2009), 93–115.
Pironet, A., Desaive, T., Dauby, P.C., Chase, J.G., Docherty, P.D., Parameter identification methods in a model of the cardiovascular system. Preprints of the 9th IFAC Symposium on Biological and Medical Systems, 2015, 366–371.
Starfinger, C., Hann, C., Chase, J., Desaive, T., Ghuysen, A., Shaw, G., Model-based cardiac diagnosis of pulmonary embolism. Comput. Methods Programs Biomed., 2007.
Ottesen, J.T., Novak, V., Olufsen, M.S., Development of patient specific cardiovascular models predicting dynamics in response to orthostatic stress challenges. Mathematical Modeling and Validation in Physiology, 2013, Springer, 177–213.
Revie, J.A., Stevenson, D.J., Chase, J.G., Hann, C.E., Lambermont, B.C., Ghuysen, A., Kolh, P., Shaw, G.M., Heldmann, S., Desaive, T., Validation of subject-specific cardiovascular system models from porcine measurements. Comput. Methods Programs Biomed., 2011.
Starfinger, C., Chase, J.G., Hann, C.E., Shaw, G.M., Lambert, P., Smith, B.W., Sloth, E., Larsson, A., Andreassen, S., Rees, S., Prediction of hemodynamic changes towards PEEP titrations at different volemic levels using a minimal cardiovascular model. Comput. Methods Programs Biomed. 91:2 (2008), 128–134.
Parlikar, T., Verghese, G., A simple cycle-averaged model for cardiovascular dynamics. Conf. Proc. IEEE Eng. Med. Biol. Soc. 5 (2005), 5490–5494.
D. Rüschen, M. Rimke, J. Gesenhues, S. Leonhardt, M. Walter, Continuous cardiac output estimation under left ventricular assistance, IFAC-PapersOnLine 48(20) (2015) 569 – 574. 9th IFAC Symposium on Biological and Medical Systems BMS 2015. https://doi.org/10.1016/j.ifacol.2015.10.202
Olufsen, M.S., Ottesen, J.T., Tran, H.T., Ellwein, L.M., Lipsitz, L.A., Novak, V., Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation. J. Appl. Physiol. 99:4 (2005), 1523–1537.
Fresiello, L., Ferrari, G., Di Molfetta, A., Zieliński, K., Tzallas, A., Jacobs, S., Darowski, M., Kozarski, M., Meyns, B., Katertsidis, N.S., Karvounis, E.C., Tsipouras, M.G., Trivella, M.G., A cardiovascular simulator tailored for training and clinical uses. J. Biomed. Inform. 57 (2015), 100–112, 10.1016/j.jbi.2015.07.004.
Mogensen, M.L., A Physiological Mathematical Model of the Respiratory System, 2011, Aalborg University Ph.D. thesis.
Schranz, C., Knobel, C., Kretschmer, J., Zhao, Z., Moller, K., Hierarchical parameter identification in models of respiratory mechanics. IEEE Trans. Biomed. Eng. 58:11 (2011), 3234–3241.
Chiew, Y.S., Pretty, C.G., Docherty, P.D., Lambermont, B., Shaw, G.M., Desaive, T., Chase, J.G., Time-varying respiratory system elastance: aphysiological model for patients who are spontaneously breathing. PLoS ONE, 2015.
Chiew, Y.S., Chase, J.G., Shaw, G.M., Sundaresan, A., Desaive, T., Model-based peep otpimisation in mechanical ventilation. Biomed. Eng. Online, 10, 2011, 111.
Burrowes, K., Burrowes, A., Swan, N., Warren, M., Tawhai, M., Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system. Philos. Trans. R. Soc. A 366:1879 (2008), pp.3247–3263.
Schranz, C., Docherty, P.D., Chiew, Y.S., Chase, J.G., Moller, K., Structural identifiability and practical applicability of an alveolar recruitment model for ARDS patients. IEEE Trans. Biomed. Eng. 59:12 (2012), 3396–3404.
Chiew, Y.S., Pretty, C.G., Shaw, G.M., Chiew, Y.W., Lambermont, B., Desaive, T., Chase, J.G., Feasibility of titrating peep to minimum elastance for mechanically ventilated patients. Pilot Feasibil. Stud., 2015.
Chase, J.G., Le Compte, A.J., Preiser, J.C., Shaw, G.M., Penning, S., Desaive, T., Physiological modeling, tight glycemic control, and the ICU clinician: what are models and how can they affect practice?. Ann. Intensive Care, 1(1), 2011, 11.
Docherty, P.D., Chase, J.G., Lotz, T.F., Desaive, T., A graphical method for practical and informative identifiability analyses of physiological models: a case study of insulin kinetics and sensitivity. Biomed. Eng. Online, 10, 2011, 39.
Davidson, S.M., Kannangara, D.O., Pretty, C.G., Kamoi, S., Pironet, A., Desaive, T., Chase, J.G., Modelling of the nonlinear end-systolic pressure-volume relation and volume-at-zero-pressure in porcine experiments. Conf. Proc. IEEE Eng. Med. Biol. Soc., 2015.
Sundaresan, A., Chase, J.G., Shaw, G.M., Chiew, Y.S., Desaive, T., Model-based optimal peep in mechanically ventilated ards patients in the intensive care unit. Biomed. Eng. Online, 2011.
Sundaresan, A., Chase, J.G., Positive end expiratory pressure in patients with acute respiratory distress syndrome the past, present and future. Biomed. Signal Process. Control, 7(93–103), 2012.
Choi, J., Xia, G., Tawhai, M.H., Hoffman, E.A., Lin, C.-L., Numerical study of high-frequency oscillatory air flow and convective mixing in a CT-based human airway model. Ann. Biomed. Eng. 38:12 (2010), 3550–3571.
van Drunen, E.J., Chiew, Y.S., G., C.J., Shaw, G.M., Lambermont, B., Janssen, N., Damanhuri, N.S., Desaive, T., Expiratory model-based method to monitor ARDS disease state. Biomed. Eng. Online, 2013, 12:57.
Luecke, T., Pelosi, P., Clinical review: positive end-expiratory pressure and cardiac output. Crit. Care 9:6 (2005), 607–621.
Kass, D.A., Maughan, W.L., Guo, Z.M., Kono, A., Sunagawa, K., Sagawa, K., Comparative influence of load versus inotropic states on indexes of ventricular contractility: experimental and theoretical analysis based on pressure-volume relationships. Circulation 76:6 (1987), 1422–1436.
Nelder, J.A., Mead, R., A simplex method for function minimization. Comput. J. 7:4 (1965), 308–313.
Kass, D.A., Beyar, R., Lankford, E., Heard, M., Maughan, W.L., Sagawa, K., Influence of contractile state on curvilinearity of in situ end-systolic pressure-volume relations. Circulation 79:1 (1989), 167–178.
Klabunde, R., Dalley, A., Cardiovascular Physiology Concepts. 2004, Lippincott Williams & Wilkins.
Michard, F., Changes in arterial pressure during mechanical ventilation. Anesthesiology 103:2 (2005), 419–428.
B. Laufer, P. Docherty, A. Knörzer, Y. Chiew, R. Langdon, K. Möller, J. Chase, Performance of variations of the dynamic elastance model in lung mechanics, Control Engineering Practice (2016) –. In press. http://dx.doi.org/10.1016/j.conengprac.2016.03.004
Westerhof, N., Stergiopulos, N., Noble, M.I.M., Snapshots of Hemodynamics. 2010, Springer.