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Estimation of the Time-Varying Elastance of the Left and Right Ventricles

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Estimation of the Time-Varying Elastance of the Left and Right Ventricles University of Canterbury Doctoral Thesis Estimation of the time-varying elastance of the left and right ventricles Author: Supervisor: David Stevenson Dr. Geoffrey Chase A thesis submitted in partial fulfilment for the degree of Doctor of Philosophy in Bioengineering, Department of Mechanical Engineering September 2013 Soli Deo gloria — Glory to God alone Abstract The intensive care unit treats the most critically ill patients in the hospital, and as such the clinical staff in the intensive care unit have to deal with complex, time-sensitive and life-critical situations. Commonly, patients present with multiple organ dysfunctions, require breathing and cardiovascular support, which make diagnosis and treatment even more challenging. As a result, clinical staff are faced with processing large quantities of often confusing information, and have to rely on experience and trial and error. This occurs despite the wealth of cardiovascular metrics that are available to the clinician. Computer models of the cardiovascular system can help enormously in an intensive care setting, as they can take the monitored data, and aggregate it in such a way as to present a clear and understandable picture of the cardiovascular system. With additional help that such systems can provide, diagnosis can be more accurate and arrived at faster, alone with better optimised treatment that can start sooner, all of which results in decreased mortality, length of stay and cost. This thesis presents a model of the cardiovascular system, which mimics a specific patient’s cardiovascular state, based on only metrics that are commonly measured in an intensive care setting. This intentional limitation gives rise to additional complexities and challenges in identifying the model, but do not stand in the way of achieving a model that can represent and track all the important cardiovascular dynamics of a specific patient. One important complication that comes from limiting the data set is need for an estimation for the ventricular time-varying elastance waveform. This waveform is central to the dynamics of the cardiovascular model and is far too invasive to measure in an intensive care setting. This thesis thus goes on to present a method in which the value-normalised ventricular time-varying elastance is estimated from only metrics which are commonly available in an intensive care setting. Both the left and the right ventricular time-varying elastance are estimated with good accuracy, capturing both the shape and timing through the progress of pulmonary embolism and septic shock. For pulmonary embolism, with the algorithm built from septic shock data, a time-varying elastance waveform with median error of 1.26% and 2.52% results for the left and right ventricles respectively. For septic shock, with the algorithm built from pulmonary embolism data, a time-varying elastance waveform with median error of 2.54% and 2.90% results for the left and right ventricles respectively. These results give confidence that the method will generalise to a wider set of cardiovascular dysfunctions. Furthermore, once the ventricular time-varying elastance is known, or estimated to a adequate degree of accuracy, the time-varying elastance can be used in its own right to access valuable information about the state of the cardiovascular system. Due to the centrality and energetic nature of the time-varying elastance waveform, much of the state of the cardiovascular system can be found within the waveform itself. In this manner this thesis presents three important metrics which can help a clinician distinguish between, and track the progress of, the cardiovascular dysfunctions of pulmonary embolism and septic shock, from estimations based of the monitored pressure waveforms. With these three metrics, a clinician can increase or decrease their probabilistic measure of pulmonary embolism and septic shock. Acknowledgements There are many people I would like to thank for their help and support throughout the completion of my thesis. Geoff Chase, my supervisor. Thank you for the support and guidance you have offered me, as well as your direction and academic wisdom that enabled me to finish this thesis. Thank you for the many and varied opportunities during this period of research, including the conferences I attended and the support to write several journal papers. Geoff Shaw, and Thomas Desaive, my co-supervisors. Thank you for the support and knowledge that you gave to this research. Thank you Geoff, for the medical and clinical insight and guidance, this was invaluable to the research. Thomas, thank you for hosting my time in Liege and for the guidance and support in journal publications. To my lovely wife, Emma, thank you for supporting me throughout the trials of re- search, studying abroad in Belgium, and your help with navigating the final write up. You have been a blessing to me in so many unnamed ways. Thank you to my immediate and extended family, for your support, encouragement, understanding and always taking an interest in my work. Also a special thank you for the help with the final proof reading. Finally, to Jesus Christ, my saviour, “through whom all things were made” – John 1:3, and “in Him all things hold together” – Colossians 1:17. It is truly an honour to study God’s creation with the highest level of academic rigour that is required for a doctoral thesis. Also to all my brothers and sisters in Christ, thank you for your support, both in my faith and studies. Contents List of Figures xiv List of Tables xx Nomenclature xxiii 1 Introduction1 1.1 Cardiovascular disease.............................2 1.1.1 Septic shock...............................3 1.1.2 Pulmonary Embolism.........................3 1.1.3 Diagnosis and Treatment.......................4 1.2 Current practice.................................4 1.3 Time-varying elastance.............................6 1.4 Goals for this research.............................6 1.5 Preface......................................7 2 Cardiovascular Physiology and Background9 2.1 Anatomy of the heart..............................9 2.1.1 Heart chambers.............................9 2.1.2 Cardiac muscle............................. 11 2.1.3 Ventricular interaction......................... 12 2.1.4 Pericardium............................... 13 2.2 Circulation.................................... 14 2.2.1 Arterial system............................. 14 2.2.2 Capillary system............................ 15 2.2.3 Venous system............................. 15 2.2.4 Blood distribution........................... 16 2.2.5 Blood pressure and flow........................ 16 2.3 Mechanical properties of the heart...................... 18 2.3.1 Cardiac cycle.............................. 20 2.3.2 Preload.................................. 20 2.3.3 Afterload................................ 21 2.3.4 Contractility............................... 22 2.3.5 Frank-Starling Mechanism...................... 24 2.3.6 Cardiac work.............................. 25 2.4 Electrical function of the heart........................ 26 2.4.1 Electrocardiogram........................... 27 ix CONTENTS 2.5 Cardiac Dysfunction.............................. 27 2.5.1 Pulmonary Embolism......................... 28 2.5.1.1 Physiology and clinical presentation of PE........ 28 2.5.1.2 Diagnosis........................... 29 2.5.1.3 Treatment........................... 31 2.5.2 Septic Shock............................... 31 2.5.2.1 Physiology and clinical presentation........... 31 2.5.2.2 Diagnosis........................... 33 2.5.2.3 Treatment........................... 34 3 Cardiovascular System Model 35 3.1 Introduction................................... 35 3.1.1 The model................................ 36 3.1.1.1 The six chambers...................... 36 3.1.1.2 Inter-chamber properties.................. 37 3.1.1.3 The atria........................... 38 3.2 Electrical analogy and equations....................... 38 3.3 Model background............................... 40 3.3.1 Windkessel model........................... 40 3.4 Schematic model derivation.......................... 40 3.5 Equation derivation............................... 43 3.5.1 The valves................................ 44 3.5.2 Peripheral flow............................. 45 3.5.3 Pressure and volume.......................... 45 3.5.4 Ventricle pressure and volume.................... 46 3.5.5 Ventricular interaction......................... 48 3.6 The full model equations............................ 51 3.7 Simulation.................................... 56 3.7.1 Parameters................................ 58 3.7.2 Simulation example.......................... 59 3.8 Discussion.................................... 59 3.8.1 Simplifications............................. 60 3.8.2 Assumptions.............................. 60 3.8.3 Limitations............................... 62 3.9 Summary..................................... 63 4 CVS Model Identification 65 4.1 Introduction................................... 65 4.2 Pre-requisites.................................. 67 4.2.1 Identification Assumptions...................... 67 4.2.1.1 Steady state.......................... 67 4.2.1.2 Inertia is negligible..................... 67 4.2.1.3 Valve timing......................... 67 4.2.1.4 Change in contractilities are proportional........ 68 4.2.1.5 GEDV ∝ LVEDV + RVEDV................ 68 4.2.1.6 Valve resistances....................... 68 4.2.1.7 Unidentified parameters.................. 69 x CONTENTS 4.2.2 Measured data in the ICU......................
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