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Modelling and Control of the Human Cardiovascular System

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Modelling and Control of the Human Cardiovascular System Research Collection Master Thesis Modelling and control of the human cardiovascular system Author(s): Gisler, Stefan Publication Date: 2011 Permanent Link: https://doi.org/10.3929/ethz-a-007207574 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library Master Thesis Modelling and control of the human cardiovascular system Stefan Gisler Advisers Martin Wieser and Dr. Heike Vallery and Prof. Dr. Robert Riener Sensory Motor Systems Lab (SMS) Swiss Federal Institute of Technology Zurich (ETH) Submission: April 2011 Contents 1 Introduction 1 2 Human cardiovascular system 5 2.1 Hemodynamic system . 5 2.2 Blood pressure regulation . 7 2.3 Orthostatic reaction and muscle pump . 9 2.4 Cardiovascular pathology . 10 2.5 Literature review . 11 2.5.1 Cardiovascular responses to passive tilting . 11 2.5.2 Cardiovascular modelling . 13 3 Cardiovascular model 15 3.1 Hemodynamic system . 16 3.2 Blood pressure regulation . 18 3.3 Influence of gravity . 21 3.4 Influence of stepping . 22 3.5 Model simulations . 24 3.5.1 Fast tilt-up and tilt-down . 24 3.5.2 Stepping . 25 3.5.3 Quasi-static . 26 3.6 Model validation . 33 4 Control design 37 4.1 Model predictive control (MPC) design . 37 4.2 Simulation . 46 5 Methods 49 5.1 Healthy subjects . 49 5.1.1 Implementation . 49 5.1.2 Blood pressure recording . 49 5.1.3 Experimental design . 50 i 5.2 Patients . 53 5.2.1 Implementation . 53 5.2.2 Blood pressure recording . 53 5.2.3 Experimental design . 54 6 Results 55 6.1 Healthy subjects . 55 6.1.1 Heart rate control . 55 6.1.2 Blood pressure control . 55 6.1.3 Combined heart rate and blood pressure control . 56 6.2 Patients . 57 6.3 Controller performance . 60 7 Discussion 61 8 Conclusion and Outlook 65 A Model summary 73 A.1 List of variables . 75 A.2 List of parameters . 76 A.3 Model equations in non-linear state-space form . 78 A.4 Steady-state equations in non-linear state-space form . 80 A.5 Parameter identification . 82 A.6 Model constraints . 85 B Summarised results 87 References 95 ii Abstract Bed-rest leads to cardiovascular deconditioning and may induce a decline in stroke volume, cardiac output and oxygen uptake. Further, it increases the risk of orthostatic intolerance. In an early phase of rehabilitation, it is there- fore important to prevent the development of cardiovascular deconditioning which can be done by verticalisation and mobilisation. In the future, the enhanced ERIGO tilt-table will be able to control physiological signals and hence, stabilise the patient's cardiovascular system. This thesis focuses on the control of heart rate and blood pressure by means of verticalisation (tilting) and mobilisation (stepping). In a first step, a car- diovascular non-linear model with two inputs (tilting and stepping) and three outputs (heart rate, systolic and diastolic blood pressure) is developed based on physiological principles and existing work. The model is then used for designing a model predictive controller which was found well suited for the given control problem. Five healthy subjects have been tested with three different configurations: isolated heart rate control, isolated blood pressure control and combined control. One patient has been tested with blood pressure control which yiel- ded promising results. Keywords{ Orthostatic intolerance, cardiovascular modelling, model pre- dictive control iii Acknowledgements First, I want to thank Prof. Dr. Riener for being accepted to do this thesis at the Sensory-Motor Systems Lab. Then I want to thank my advisers Martin Wieser and Dr. Heike Vallery for their valuable support during the work. Special thanks go to Martin Wieser for his great efforts while testing and debugging the system. This thesis would not have been possible without the probands and patients. A big thanks goes to all the probands, the \Z¨urcher H¨ohenklinik"in Wald, and all the patients that participated in this study. At this point, I also want to thank Rafael R¨ustand Lilith B¨utlerfor their support during the patient measurements in Wald. Last but not least, I want to thank all the students in the student room for the nice and inspiring atmosphere. iv Chapter 1 Introduction One major problem with neurological patients suffering from stroke, trau- matic brain injury or paraplegia is the long bed rest after the accident. It leads to deconditioning of the patients' cardiovascular system and evokes secondary complications such as orthostatic intolerance. Further complica- tions can include venous thrombosis, muscle atrophy, joint contractures and osteoporosis [1], [2]. Therefore, early mobilisation of the patient is crucial as it can reduce the risk of cardiovascular deconditiong and improves the state of health. This thesis focuses on the cardiovascular aspects of bed-ridden patients, i.e. how the cardiovascular system can be prevented from deconditioning and be- coming unstable. Prolonged bed rest leads to a decrease in circulating blood volume, a decrease in stroke volume and pulse pressure, and an increased heart rate. A direct result of these indications is the inability of the patient's cardiovascular system to regulate blood pressure when standing up (ortho- static intolerance). In the upright position, the patient suddenly starts to feel dizzy or even faints due to excessive blood pooling in the lower extre- mities and reduced blood perfusion of the upper body. However, orthostatic intolerance is not only caused by prolonged bedrest but can also be a conse- quence of an impaired vegetative nervous system. In paraplegia patients, the sympathetic effector nerves to the heart and the smooth musculature are disrupted or even broken. This leads to a malfunction of the baroreflex which is responsible for regulating arterial blood pressure (see chapters 2.2, 2.4). As a consequence, the sudden decrease in arterial blood pressure cannot be regulated and the patient faints. A tilt-table therapy is aimed at reconditioning the patient's cardiovascular system by verticalising to an angle of about 80 degrees. Additional leg mo- 1 vements which can include stepping or cycling movements increase venous return due to the effects of the muscle pump and improve orthostatic tole- rance. The ERIGO device which has been used at the institute since the beginning of the AwaCon project combines these therapies and allows for an optimal treatment of patients with neurological disorders (Figure 1.1). More information about the ERIGO device can be found on the homepage of HO- COMA AG 1. On the ERIGO, physiological signals such as blood pressure, Figure 1.1: Left: Schematic representation of the ERIGO device with the three inputs. Right: ERIGO during therapy session. heart rate, respiration frequency, skin conductance, oxygen saturation, EEG and EMG can be recorded. However, for this thesis only blood pressure and heart rate need to be recorded, where EMG recordings may be helpful to analyse muscle activity during mobilisation. The goal of the project is to control and stabilise the cardiovascular system of patients with neurological disorders by verticalisation, mobilisation and cyclic loading of the lower limbs (Figure 1.1). This will help to improve the cardiovascular status of these patients and will have the potential to reduce medication, enhance physiotherapy and shorten the duration of early reha- bilitation [3]. Furthermore, the risk of deconditioning of the cardiovascular system, and complications resulting from this, can be decreased. Additional project information is available on the homepage of the SMS Lab 2. In earlier projects at the SMS, isolated control of heart rate and diastolic 1http://www.hocoma.com/en/products/erigo/ 2http://www.sms.mavt.ethz.ch/research/projects/awacon 2 blood pressure with the inclination angle α as the only control input has been done [4], [5]. In a next step, combined control of heart rate and dias- tolic blood pressure has been succesfully tested with healthy subjects [6]. This latest version also contained another technical innovation: the idea was to not only use α as a control input, but also the stepping frequency fstep which enables the controller to operate over an enlarged bandwith. For this project, the described line of innovation is continued: the goal of this thesis is to control heart rate, systolic and diastolic blood pressure with the two control inputs α and fstep. It is a fact, that the control strategy from the isolated control problem, which consisted of an ordinary PI controller can not be adopted for the new more complex control problem. The challenge is that with an increasing number of inputs and outputs, there are more couplings inside the system and PI control is not suitable anymore. For a multi-input multi-output (MIMO) system, other control strategies have to be applied. The first step consists of developing a cardiovascular model which is the topic of chapter 3 which directly follows after the subsequent chapter about human cardiovascular physiology (chapter 2). Chapter 4 continues with the control design, followed by the results, the discussion and the conclusion (chapters 6, 7 and 8). 3 4 Chapter 2 Human cardiovascular system This chapter will give a short introduction to physiology and pathophysio- logy of the human cardiovascular system and summarises some results from literature. 2.1 Hemodynamic system Head Right lung Left lung Right Left heart heart Splanchnic & renal circulation Legs Figure 2.1: Schematic representation of the human circulatory system. Adap- ted from: http://www.ionwave.ca The major task of the hemodynamic system is to supply every single cell 5 of the organsim with oxygen and nutrients and carry away carbon dioxide (CO2) as well as metabolic waste products.
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