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MATHEMATICAL MODEL FOR OPTIMIZING ECMO SETTINGS IN CASE OF RESPIRATORY FAILURE GROUP 874, 3rd SEMESTER MASTER, BIOMEDICAL ENGINEERING, 2013 Department of Health Science and Technology Aalborg University Frederik Bajers Vej 7D2 9220 Aalborg Øst http://st.hst.aau.dk Synopsis: Title: Mathematical model for optimizing ECMO settings in case of respiratory failure Subject: Applied Biomedical Engineering and Informatics Project period: 3rd Semester Master Spring 2013 Project group: 874 Members: Anna Doležalová Supervisor: Stephen Edward Rees Copies: 3 Number of pages: 44 Completion date: May 29th 2013 Venovenous extracorporeal membrane oxygenation (VV ECMO) is a modified form of cardiopulmonary bypass in which blood is drained from the venous system of the patient, pumped through the oxygenator where the oxygenation takes place and re-infused to the venous bloodstream [Betit, 2009]. VV ECMO is used when the cardiac output is sufficient and complete or partial lung support is needed [Lindstrom et al., 2009]. The aim of this project was to create a mathematical model of blood circulation, lungs with insufficient function, tissues and VV ECMO device in order to investigate optimal ECMO settings in case of respiratory failure. The model was created in the programming language called Modelica. Set of experiments was designed in order to perform the simulations, test the model and find optimal ECMO flow and partial pressures settings. The results have shown that optimal ECMO flow, which is the major determinant of blood oxygenation, is between 60 and 70% of systemic blood flow. The optimal partial pressure settings are a carbon dioxide partial pressure (pCO 2 ) of 4.5kPa and an oxygen partial pressure (pO 2 ) of 45kPa. From work on the current project it has become apparent that mathematical modeling could be considered as a useful tool for expressing basic physiological processes and functions of medical devices. The content of this report is freely available but publication (with source reference) must only be published after agreement with the author. P REFACE AND READING INSTRUCTION P REFACE This report is written by group 874 at the 3rd semester of the master degree in Biomedical Engeering at Aalborg University. The overall theme for the project period is ’Applied Biomedical Engineering and Informatics’ and the title is ’Mathematical model for optimizing ECMO settings in case of respiratory failure’. The intended target group is primarily researchers with interest in extracorporeal membrane oxygenation and mathematical modeling. The secondary target group is supervisors, examiner and fellow students. It can be an advantage to have a basic knowledge about particularly physiology and general Biomedical Engineering techniques aswell. R EADING INSTRUCTION Some selected terms in the report are abbreviated the first time they are mentioned with the abbreviation in a parenthesis after the word. For example: extracorporeal membrane oxygenation (ECMO). The references are stated after the Harvard-method with the authors last name first comma the year for the publication. In the bibliography the references are listed in alfabetic order according the last name of the author. By signing here the author of the current project give her consent that the report is made by: Anna Doležalová TABLE OF CONTENTS Preface and reading instruction i Table of contents 7 1 . . . . . . . 9 11 12 12 14 14 15 16 . . . . . . . . . 17 17 18 19 20 20 21 23 24 25 3 Results 3.1 Experiment 1 - sO 2 in relation to ECMO flow . . . . . . . . . . . . . . . . . . . . . 3.2 Experiment 2 - pO 2 in relation to ECMO flow . . . . . . . . . . . . . . . . . . . . . 3.3 Experiment 3 - pCO 2 in relation to ECMO flow . . . . . . . . . . . . . . . . . . . . 3.4 Experiment 4 - sO 2 in relation to ECMO flow and pulmonary shunt . . . . . . . . 3.5 Experiment 5 - sO 2 in relation to ECMO flow, pulmonary shunt and Vt . . . . . . 3.6 Experiment 6 - sO 2 in relation to ECMO flow and V CO 2 and V O 2 . . . . . . . . . 3.7 Results summary of experiments 1 - 6 . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Experiment 7 - arterial blood properties in relation to pCO 2 and pO 2 in ECMO . 3.9 Experiment 8 - model behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 27 28 29 30 31 33 34 34 35 4 Discussion 4.1 Recapitulation . . . . . . . . 4.2 Results summary . . . . . . 4.3 Limitations . . . . . . . . . . 4.3.1 Acid-base chemistry 4.3.2 ECMO . . . . . . . . 4.3.3 Shunt . . . . . . . . . 4.4 Conclusion . . . . . . . . . . 37 37 37 39 39 40 40 40 2 Introduction 1.1 History . . . . . . . . . . . . . . . . 1.2 Problem statement . . . . . . . . . 1.2.1 Aim . . . . . . . . . . . . . . 1.3 ECMO models . . . . . . . . . . . . 1.4 Experimental protocol . . . . . . . 1.4.1 Experiments . . . . . . . . . 1.5 Methods - programming language Methods 2.1 General description of the model 2.1.1 Blood . . . . . . . . . . . . 2.1.2 Shunt . . . . . . . . . . . . 2.2 Segment description . . . . . . . 2.2.1 Circulation . . . . . . . . 2.2.2 Lungs . . . . . . . . . . . . 2.2.3 Tissues . . . . . . . . . . . 2.2.4 ECMO . . . . . . . . . . . 2.2.5 Entire model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 7 CHAPTER 1 I NTRODUCTION Extracorporeal membrane oxygenation (ECMO) is a modified form of cardiopulmonary bypass in which blood is drained from the venous system of the patient, pumped through the oxygenator where the oxygenation takes place and is re-infused to the patient [Betit, 2009]. There are some differences between ECMO and cardiopulmonary bypass. ECMO is often introduced by cervical cannulation, which can be provided under local anesthesia. Conversely, the transthoracic cannulation, which has to be instituted under general anesthesia, is usually used for cardiopulmonary bypass. ECMO is frequently used for long-term support measured in days (3-10), but cardiopulmonary bypass can be used just for a short period measured in hours. There is also a difference in the purpose of use. Cardiopulmonary bypass is usually used for the heart and lung support during various types of cardio surgical procedures. ECMO can provide complete or partial support of the heart and/or lung function and give the time for recovery after disease, surgery, injury or respiratory or cardiac failure [Rodriguez-Cruz, 2011, Lindstrom et al., 2009]. ECMO is a final option for the patients whose condition is refractory to other management, for instance mechanical ventilation [Lindstrom et al., 2009, Oshima et al., 2010]. The most important parts of the basic ECMO circuit are vascular cannulae to drain and return blood, circuit tubing, a pump, artificial organ - oxygenator and a heater or heater-cooler that sustain the blood temperature (figure 1.1) [Lindstrom et al., 2009]. Figure 1.1: Description of ECMO system [Rodriguez-Cruz, 2011] 9 CHAPTER 1. INTRODUCTION There are two possible methods or modalities of ECMO (figure 1.2) - venovenous (VV) and venoarterial (VA). VV is used to support mainly pulmonary function and VA supports both cardiac and pulmonary function [Betit, 2009]. Figure 1.2: Examples of cannulation for venovenous (VV) and venoarterial (VA) extracorporeal membrane oxygenation (ECMO); blue cannulae represents deoxygenated blood and red cannulae represents oxygenated blood [Lindstrom et al., 2009] In case of VV ECMO, the blood is drained from venous bloodstream and re-infused back to the venous system. This modality is used when the cardiac output is sufficient and complete or partial lung support is needed [Lindstrom et al., 2009]. The exact placement of the cannulation depends on the size of the patient. In older children and adults, the deoxygenated blood is drained from one or both femoral vessels and the oxygenated blood is returned through the right-internal jugular vein. After the return to the venous system, oxygenated blood passes through the pulmonary system and therefore the gas exchange is sufficient. The optimal ECMO flow is assured by optimization of venous drainage [Betit, 2009]. VV ECMO can also be introduced by a single double-lumen cannula, which allows drainage and return through the right internal jugular vein [Betit, 2009, Lindstrom et al., 2009]. The cannula consists of the two channels; one is used for draining the deoxygenated blood from the vena cava and the second is placed into the right atrium where the oxygenated blood is sent. When the placement is proper, the suitable gas exchange is achieved and just one vessel is affected. The insertion of doublelumen cannula is easier and the complications associated with femoral cannulation are eliminated. However, the flow limitations may occur [Betit, 2009]. In VA ECMO deoxygenated blood is drawn from venous system and oxygenated blood is reinfused into the arterial circulation, which provides gas exchange and cardiac support [Betit, 2009, Lindstrom et al., 2009]. There are two possible ways of cannulation - peripheral and central. With central cannulation, blood is drained from the right atrium and re-infused to the proximal thoracic aorta. With peripheral cannulation, blood is drawn from femoral or jugular vein and re-infused to the aorta via carotid, axillary or femoral artery. The femoral cannulation is useful, because the compressible site can help in haemorrhage control, but these vessels are usually too small in neonates, so it is most commonly used in adults. When high ECMO flow is required, it is possible to use twin drainage cannulae - jugular and femoral [Lindstrom et al., 10 of 44 CHAPTER 1. INTRODUCTION 2009]. VA ECMO, in general, is more commonly used in neonates, especially when both heart and lung function is threatened. In neonates collateral circulation develops, so cannulation and ligation of the carotid artery is tolerated and therefore cardiac and also pulmonary support is achieved [Betit, 2009]. 1.1 History Since 1953 when Gibbon used first extracorporeal oxygentation during open heart surgery, ECMO and other extracorporeal technology have continued to develop [Lindstrom et al., 2009]. Recently, ECMO is most commonly used for patient with acute respiratory distress syndrome (ARDS). Patients with the most severe forms of this disease usually have a bad prognosis and mortality can be 60%. In these situations, ECMO may minimize the trauma caused by mechanical ventilation and might be a therapeutic option for the lungs to be recovered. Nevertheless, at the beggining of ECMO use, most of the trials have shown no advantage of ECMO compared to mechanical ventilation. The complications were mostly caused by severe bleeding due to the use of anticoagulation and weak biocompatibility of the circuits [Schmidt et al., 2012]. In 1979 Zapol et al. made a randomized trial where nine medical centers collaborated in order to find out if ECMO has a benefit as therapy for patients with acute respiratory failure. It has been shown that ECMO did not increase the likelihood of long term survival [Zapol et al., 1979]. In 1994 Morris et al. have shown in a randomized study with ARDS patients that there was no significant difference in survival with use of ECMO compared to mechanical ventilation [Morris et al., 1994]. The early attempts to use ECMO for adult patients were unsuccessful, but the neonatal experience has led to better understanding and improvement in ECMO technology [Betit, 2009]. In 1996 Green et al. made a study for investigating the impact of ECMO in pediatric patients with acute respiratory failure. They have found that ECMO had a positive effect on survival; the mortality in patients treated with ECMO has been reduced [Green et al., 1996]. UK collaborative ECMO trial group has shown the effectiveness of ECMO in neonatal patients. They demonstrated that ECMO should be considered as an option for neonates with severe but potentially reversible respiratory failure [Group, 1996]. As early as 1985, it was shown that ECMO improves survival in neonatal patients with severe respiratory failure compared to conventional ventilation [Bartlett et al., 1985]. However, the patient outcomes in children with respiratory failure associated with hematopoietic stem-cell transplantation have not been found encouraging. The survival in these patients was reported to be poor [Gow et al., 2006]. In the last ten years, outcomes in adult patients have improved. Linden et al. have shown a high survival in patients with severe ARDS when treated with ECMO and pressure-supported ventilation [Linden et al., 2000]. In 2004 Hemmila et al. also proved the effectiveness of ECMO in adult patients with ARDS. They have found ECMO as a good option for treatment in cases when patients are not responsive to conventional approach [Hemmila et al., 2004]. Recently, the encouraging results continue to appear mostly due to higher biocompatibility and performance as well as increased durability [Schmidt et al., 2012]. In 2009 after their randomized trial, Mugford et al. have recommended ECMO as a good option for adult patients with severe but potentially reversible respiratory failure [Mugford et al., 2009]. Good outcomes were also reported in patients who received ECMO as a therapy during A(H1N1) influenza pandemic in 2009. Several studies have reported lower mortality in patients who received ECMO than in patients who have not been treated with ECMO [Patroniti et al., 2011, Noah et al., 2011, Australia and Investigators, 2009]. These new encouraging results started an increased interest in ECMO as a treatment for ARDS. In the past, the unsuccessful tries could be caused by a lack of adequately educated and qualified medical, nursing and perfusion staff. The availability of 11 of 44 CHAPTER 1. INTRODUCTION assistant devices such as echocardiography was also limited and the concerns about safety and efficacy were presented [Lindstrom et al., 2009]. A lot of these concerns and deficiencies have been improved in last ten years. The knowledge about ECMO has been developed as well as the experience of the staff. The technology has been improved; devices are miniaturized and therefore more available. All these changes and improved patient’s outcomes in last few years signals a strong potential of ECMO application. 1.2 Problem statement The purpose of using VV ECMO is to take the place of lung function providing time for the lungs to recover from disease, injury or surgery [Rodriguez-Cruz, 2011, Lindstrom et al., 2009]. The most important functions of the lungs are oxygenation and carbon dioxide removal. The gas exchange takes place in alveoli where the oxygen passes to the blood and the carbon dioxide passes to the air by diffusion. The air is afterwards breathe out. Adequate gas exchange maintains balance of important parameters providing acid-base homeostasis of the blood. The normal ranges for parameters relevant to acid-base homeostasis, as measured in arterial and venous blood are listed in the tables 1.1 and 1.2 [Silbernagl and Despopoulos, 2009]. If the lungs do not work sufficiently, ECMO has the responsibility to manage the gas exchange and therefore maintain the acid-base homeostasis. The main problems in introducing and leading ECMO are both anatomical and physiological and include issues such as bleeding usually caused by anticoagulation, insufficient perfusion of some parts of the patient’s body and the introduction of drainage. Furthermore, there are some technical aspects which are necessary to adjust in order to achieve successful use of ECMO. These are mainly ECMO flow (blood flow), gas flow and oxygen level, which are dependent on the level of patient’s lung and heart function. The values have to be modified according to the function present in the patient’s body [Schmidt et al., 2012]. A model of VV ECMO, blood circulation, lungs with insufficient function and tissues may help with adjusting the values of ECMO settings in order to achieve proper oxygenation and carbon dioxide removal. Since a computer model is not a threat for the patient, it might be helpful for educational purposes to implement a model with explanatory or predictive functions. It might be especially useful in the training of new medical staff and for teaching students of medicine and biomedical engineering. Trainees might learn the basic functions and features of the device and understand the way it works. More experience and better understanding of the technology can possibly improve the outcomes of using this device and result in the saving of lives. 1.2.1 Aim The aim of this project is to design computer model of blood circulation, lungs, tissues and VV ECMO in order to find out which ECMO settings are optimal for achieving sufficient oxygenation and carbon dioxide removal in different states of lung function presented. 12 of 44 CHAPTER 1. INTRODUCTION Variable Normal value Unit Description ph p ph e pO 2 mmHg kPa mmHg kPa mmol/l Potential of hydrogen in plasma Potential of hydrogen in erythrocytes Partial pressure of oxygen HCO 3− 7.35 - 7.45 7.19 74.3 - 108 10 - 13 35 - 45 4.67 - 6 22 - 26 CO 2,p 1.23 mmol/l N B B (H ) 17.2 mmol/l BB H N B B (H A) 41.7 6.3 mmol/l mmol/l t N B B (t A) 23.5 mmol/l pK HCO 3 6.1 - pK N B B 6.96 - DPG 5 mmol/l Hb 135 - 180 7.4 - 10.9 0.00023 g/l mmol/l mmol/l.Pa 0.00001 21 95 - 99 7.1 - 9.9 200 25.7 mmol/l.Pa % % mmol/l ml/l mmol/l pCO 2 αCO 2 αO 2 F iO 2 sO 2 tO 2 tCO 2 Partial pressure of carbon dioxide Concentration of bicarbonate buffer base in plasma Concentration of physically dissolved carbon dioxide in plasma Concentration of non-bicarbonate buffer base in plasma Concentration of buffer base in plasma Concentration of non-bicarbonate buffer acid in plasma Concentration of non-bicarbonate buffer in plasma Dissociation constant for bicarbonate in plasma Dissociation constant for non-bicarbonate buffers in plasma Concentration of 2,3-diphosphoglycerate in blood Amount of hemoglobin in the blood Solubility coefficient of carbon dioxide in plasma Solubility coefficient of oxygen in plasma Fraction of oxygen in the air Percent of blood cells filled with oxygen Total concentration of oxygen in blood Total concentration of carbon dioxide in plasma Table 1.1: Normal range of blood variables in arterial blood [Rees and Andreassen, 2005, Martin, 1999, council UK, 2012, Siggaard-Andersen et al., 1987] 13 of 44 CHAPTER 1. INTRODUCTION Variable Normal value Unit Description ph p ph e HCO 3,p − 7.371 7.169 26.2 mmol/l CO 2,p 1.403 mmol/l N B B (H ) 16.9 mmol/l B Bp B Be BB H N B B (H A) 43.1 70.7 55.3 6.6 mmol/l mmol/l mmol/l mmol/l t N B B (t A) 23.5 mmol/l pK HCO 3 6.1 - pK N B B 6.96 - DPG 5 mmol/l Hb 135 - 180 7.4 - 10.9 27.6 g/l mmol/l mmol/l Potential of hydrogen in plasma Potential of hydrogen in erythrocytes Concentration of bicarbonate buffer base in plasma Concentration of physically dissolved carbon dioxide in plasma Concentration of non-bicarbonate buffer base in plasma Concentration of buffer base in plasma Concentration of buffer base in erythrocytes Concentration of buffer base in blood Concentration of non-bicarbonate buffer acid in plasma Concentration of non-bicarbonate buffer in plasma Dissociation constant for bicarbonate in plasma Dissociation constant for non-bicarbonate buffers in plasma Concentration of 2,3-diphosphoglycerate in blood Amount of hemoglobin in the blood tCO 2,p Total concentration of carbon dioxide in plasma Table 1.2: Normal range of blood variables in venous blood [Rees and Andreassen, 2005] 1.3 ECMO models 1.4 Experimental protocol The project consists of several goals which are necessary to achieve. First, it is required to build a model which has particular functions. It should represent human blood circulation through the lungs, tissues and additionally VV ECMO device. The model of the lungs should contain mechanical ventilation which supports the insufficient pulmonary function together with ECMO. The lung insufficiency should be represent by a pulmonary shunt. Two important processes of gas exchange should be described in the lungs and ECMO - carbon dioxide removal and transfer of oxygen into the bloodstream. The model of the tissues should describe opposite processes than lungs and ECMO - oxygen uptake and carbon dioxide production. In order to demonstrate changes of oxygen saturation, oxygen and carbon dioxide concentrations and partial pressures during the passage throughout the circulation, the model should describe the basic acid-base chemistry of the blood. Since the aim is to find the optimal settings of ECMO in order to keep the acid-base balance, it is necessary to design a set of experiments which will provide the answer. The experiments should simulate the dependency of blood properties on ECMO settings and the level of pulmonary shunt. My focus is on ECMO flow and partial pressures of oxygen and carbon dioxide 14 of 44 CHAPTER 1. INTRODUCTION in the ECMO compartment and how these variables should be set to give normal properties of arterial blood. When the experiments are designed, the last step of the project is to perform the simulations and test the model to find the optimal settings under different conditions. 1.4.1 Experiments The following experiments have one common feature, the purpose of performing them is to find out what is the optimal ECMO flow and partial pressures settings in ECMO. In total eight experiments will be performed. Experiments 1 to 6 will be focused on optimization of ECMO flow. Experiment number 7 will be oriented on finding ideal settings of partial pressures in the ECMO compartment. Experiment number 8 will be concentrated on investigating if the model has satisfactory physiological behavior. Schmidt et al. have investigated the relationship between ECMO flow/cardiac output and oxygen saturation (sO 2 ) in different parts of circulation. They have also reported the changes in oxygen partial pressure (pO 2 ) and carbon dioxide partial pressure (pCO 2 ) in relation to ECMO flow/cardiac output. In order to compare results from the former study and my project, first three experiments represent the relationship between sO 2 , pO 2 , pCO 2 and ECMO flow. Experiment 1 will be performed in order to find out what ECMO flow is needed to achieve good value of sO 2 in the peripheral and pulmonary artery. Experiment 2 will be related to the first experiment and the question is what ECMO flow is necessary in order to achieve a good value of pO 2 in the peripheral and pulmonary artery. Experiment 3 is analogous to experiment 2, but in this case, I am interested in finding optimal ECMO flow in order to have a good value of pCO 2 in the peripheral and pulmonary artery. Experiment 4 will be performed in order to find out if or how the ECMO flow should be changed compared to results from experiment 1 in cases of different pulmonary shunt, specifically 20, 30, 40 and 50%. In other words, the task will be to search for the ideal value of ECMO flow for achieving well saturated arterial blood under different conditions of lung function. Experiment 5 will be carried out with a view to find what the optimal ECMO flow is for different settings of mechanical ventilation under various states of pulmonary shunt. During this experiment, pulmonary shunt will be 20, 30, 40 and 50%. For each of these pathological states, I would like to investigate if there is different optimal settings of ECMO flow when tidal volume (Vt ) settings in mechanical ventilation vary. During experiment 6 the production of carbon dioxide, and therefore the oxygen uptake in the tissues, will be changed. I would like to find out what ECMO flow is optimal in order to keep the oxygen supply and carbon dioxide concentration in arterial blood at a sufficient level. The goal is to find out the ideal ECMO flow for different states of patient’s metabolism. Experiment 7 will be performed in order to find the optimal settings of pO 2 and pCO 2 in ECMO subcompartment. I assume that partial pressures are analogous to the fraction of gases in the real ECMO device. For instance, if the oxygen fraction in real ECMO is 50%, I assume that it is equal to pO 2 of 50kPa in my mathematical model. pO 2 and pCO 2 in the ECMO subcompartment will be set on different values and the ideal settings for achieving good arterial blood properties will be investigated. The blood properties which will be observed are pCO 2 , pO 2 , sO 2 , total concentration of carbon dioxide (tCO 2 ) and total concentration of oxygen (tO 2 ). Under normal conditions, pO 2 and pCO 2 in the ECMO subcompartment are set to be 50 and 3kPa, respectively. Experiment 8 will be carried out in order to observe behavior of the model. The settings of the model will be chosen due to the results from experiments 1 to 7. Specific blood properties will be investigated during the passage throughout the body and compared with the physiological values. The blood properties which will be observed are pCO 2 , pO 2 , sO 2 , tCO 2 and tO 2 . 15 of 44 CHAPTER 1. INTRODUCTION 1.5 Methods - programming language The model will be created in the programming language called Modelica. The effort to design an object oriented modeling language was initiated by Hilding Elmqvist in 1978 and started in 1996 within an action of the ESPRIT project "Simulation in Europe Basic Research Working Group" [Otter and Elmqvist, 2001]. The language has been created by the developers of objectoriented modeling languages such as Allan, Dymola, NMF, ObjectMath, Omola, SIDOPS+, Smile as well as practitioners in different domains. The first version used in real application, version 1.3. was finished in December 1999. One year later in December 2000, an update version 1.4., was made [Otter and Elmqvist, 2001]. Modelica is an object-oriented, equation-based programming language. This language specializes in high complex computational applications which require high performance. There are four important features of this programming language which make it powerful and easy to use. Firstly, Modelica is primarily based on equations instead of assignment statements and it allows acausal modeling. Equations do not specify certain data flow direction so it provides better reuse of classes. Modelica class is able to adapt to more than one data flow context [Fritzon, 2004]. Secondly, Modelica is a multidomain programming language, meaning that it is possible to describe and connect model parts from a varying domains such as electrical, mechanical, thermodynamic, hydraulic, biological, and control applications. Thirdly, Modelica has a general class concept that unifies classes, generics and general subtyping into a single language construct. This feature makes it easier to reuse components and aids in development of the models. Finally, Modelica has a strong software for designing and connecting components, meaning that this language is suitable for an architectural description of complex physical and software systems [Fritzon, 2004]. 16 of 44 CHAPTER 2 M ETHODS In this chapter, the way of building the model will be described. Firstly, the explanation about the general overview of the model will be given. Secondly, a description about each part of the model will be provided. 2.1 General description of the model The entire model consists of several major parts as shown in the figure 2.1. The first major part is the model of human circulation which includes six segments - pulmonary veins, pulmonary arteries, system veins, system arteries, left and right heart. The second main part is the model of the lungs which is composed of four segments - alveolar space, arterial blood, resistor and shunt. In the alveolar space, mechanical ventilation helps to fulfill the processes of oxygenation and carbon dioxide removal. In the arterial blood compartment, venous and capillary blood are mixed. The compartments shunt and resistor represent the pulmonary shunt. The third major part of the system is the compartment tissues where two important processes take place - oxygen uptake and carbon dioxide production. The last main segment of the model is the ECMO compartment where the same processes as in the lungs take place - oxygenation and carbon dioxide removal. ECMO contains four segments - ECMO, blood mixing, resistor and shunt. These four parts have analogous functions as the subcompartments in the lungs. As the the figure 2.1 shows, each compartment or subcompartment has its own code which describes the particular processes happening inside. The entire model demonstrates a human whose lungs are not working properly and have to be supported with slight mechanical ventilation and VV ECMO. 17 CHAPTER 2. METHODS Figure 2.1: Hierarchy of the model with labeled parts, each of the compartments has its own parts and each part has its own code, the particular parts are manually connected as you can see on the picture Before focusing on the particular parts of the model it is necessary to describe two essential components. First, the way the blood is represented in the system is explained. Second, the way the shunt is expressed in the model is described. 2.1.1 Blood For the purpose of modeling the acid-base balance of blood, there are two, nearly separate, parts of the blood description - carbon dioxide and oxygen part. Carbon dioxide content is described by two chemical equations (2.1, 2.2) which take place in plasma and six mathematical equations (2.3, 2.4, 2.5, 2.6, 2.7, 2.8) which explain these processes in plasma. There are some assumptions which have been made in order to make very complex system manageable. Concentrations of buffer base (B B ) and non-bicarbonate buffer (t A or t N B B ) in plasma are set to be parameters with values 42.3 and 23.5 mmol/l, respectively. Values of dissociation constant for bicarbonate in plasma (pK HCO 3 ), dissociation constant for non-bicarbonate buffers in plasma (pK A − or pK N B B ) and solubility coefficient of carbon dioxide (αCO 2 ) are listed in the introduction of the report in the table 1.1. H + + HCO 3− ←→ CO 2 + H2O (2.1) H + + A − ←→ H A − (2.2) 18 of 44 CHAPTER 2. METHODS p H = pK HCO 3 + l og 10 p H = pK A − + l og 10 HCO 3− CO 2 A− H A− (2.3) (2.4) B B = HCO 3− + A − (2.5) tCO 2 = HCO 3− +CO 2 (2.6) t A = A− + H A− (2.7) CO 2 = αCO 2 · pCO 2 (2.8) In the case of oxygen, a dissociation curve, which represents the relationship between oxygen saturation and oxygen partial pressure, has been made. Several assumptions have been made in order to make the computations less complex. For instance, concentration of hemoglobin (H b) was set to be fixed as a parameter with the value 9.3mmol/l and the fraction of methemoglobin (F Met H b) and fraction of carboxyhemoglobin (F COH b) were set to be 0. F Met H b is the ratio between the concentration of methemoglobin (Met H b) and total concentration of H b. F COH b is the ratio between the concentration of carboxyhemoglobin (COH b) and total concentration of H b. The value of solubility coefficient of oxygen (αO 2 ) can be found in the table 1.1 in the introduction. The most important relations which describe oxygen status of the blood are equations about free dissolved oxygen (2.9) and total concentration of oxygen (2.10). O 2 = αO 2 · pO 2 (2.9) tO 2 = O 2 + sO 2 · (H b − (F Met H b · H b) − (F COH b · H b)) (2.10) The acid-base chemistry of the blood described in the model is simplified. The focus is centered on oxygenation and carbon dioxide removal. Since the strong base is left out from the description, B B and t A are assumed to be constants. Carbon dioxide content is described just in the plasma, the content in erythrocytes is ignored. Oxygen content is defined in the blood in general. 2.1.2 Shunt In order to represent lung failure in the system, it was necessary to model the insufficiency of gas exchange. This was provided by creating pulmonary shunt in the compartment lungs. Pulmonary shunt is the pathological state of the lungs when deoxygenated blood is mixed with oxygenated blood and thereby the overall efficiency of gas exchange in the lungs is reduced [Lovering and Goodman, 2012]. The shunt was modeled as two parallel resistances, the first resistance was incorporated to the alveolar space compartment and the second was simply made as a resistor (figure 2.2). The compartment shunt is a control panel which sets the values of resistances in the alveolar space and the resistor according to pulmonary shunt. The function of the compartment shunt is described by two equations (2.11, 2.12). 19 of 44 CHAPTER 2. METHODS Figure 2.2: Segments of the lung compartment where the representation of the shunt is seen 1 R t ot al = 1 R al veol ar + 1 R r esi st or shunt · R r esi st or = (1 − shunt ) · R al veol ar (2.11) (2.12) The same system was used when the ECMO compartment was created. The shunt was used as a tool for setting how much blood would go through the ECMO, so in other words for setting ECMO flow. 2.2 Segment description In this section each part of the model will be described separately. 2.2.1 Circulation For the purpose of the model of circulation, a simple model from my home university in Prague was used [Tribula et al., 2013]. This model was adjusted and upgraded for my own use. The circulation consists of six parts. All four blood-vessel compartments (pulmonary veins, pulmonary arteries, system veins, system arteries) have the same basis, but they have different initial values and different values of the parameters; all of the them are shown in the table 2.1. In these compartments, change of the total volume (Vt ot al ) is described as sum of inflow (Q i n ) and outflow (Q out ) (equation 2.13). It is necessary to note that the blood-vessels have unstressed volume (VU ), the volume when the transmural pressure is equal to zero. The stressed volume (VS ) means the remainder of the volume when the transmural pressure is above zero. VU is a parameter defined in each of the four blood-vessel compartments, Vt ot al is a variable which is initialized and then calculated as previously mentioned and VS is a variable which is computed by substracting VU from Vt ot al (equation 2.14). The next variable which is defined in the blood-vessel compartments is pressure (p) which is calculated by dividing VS and compliance (C ) (equation 2.15). There is one assumption what has been made in the context of the blood-vessel compartments, that the concentration of the blood properties which are transported through the entire system are not changed by passing through the veins and arteries. There are just different initial values of the mass (M ) of the substances. In each of the bloodvessel compartments, the change of the mass is calculated as a multiple of Q i n and inflowing 20 of 44 CHAPTER 2. METHODS concentration (c i n ) plus multiple of Q out and outflowing concentration (c out ) (equation 2.16). The last important equation to be mentioned is the calculation of concentration (c) which is described as a division of M by VS (equation 2.17). d (Vt ot al ) = Q i n +Q out dt (2.13) VS = Vt ot al − VU (2.14) p= VS C (2.15) d (M ) = Q i n · c i n +Q out · c out dt c= (2.16) M VS (2.17) Variable Unit Pulmonary veins System arteries System veins Pulmonary arteries Compliance Initial volume Unstressed volume Initial mass CO 2 Initial mass O 2 l/Pa l l mmol mmol 0.000225 0.7 0.4 5 2 0.000012 0.67 0.5 3.8 1.5 0.0015 3.9 2.7 25 6 0.0000225 0.37 0.3 1.8 1 Table 2.1: Parameters and their values which have been used for modeling blood-vessels [Tribula et al., 2013] The left and right heart are similar and very simple segments of the circulation. They use the pressure (p i n ) produced by veins to build the flow (Q) in the whole system. The equations in the left and right heart have one common parameter - starling slope (SS). SS is approximated by the linear relationship between p i n and cardiac output (Q) (equation 2.18) [Tribula et al., 2013]. The values of SS for both left and right heart are listed in table 2.2. Q = p i n · SS Side of the heart Starling Slope Value [l/Pa.s] Right Left 0.00012751 0.00007501 (2.18) Table 2.2: Values of the starling slope in both sides of the heart [Tribula et al., 2013] 2.2.2 Lungs Gas exchange in the lungs in the present model is insufficient and therefore their function has to be supported by mechanical ventilation with low Vt . The lung compartment consists of four segments - alveolar space, resistor, shunt and arterial blood (figure 2.2). In the alveolar space the oxygenation and carbon dioxide removal take place. In this part of the lungs, all of the equations describing the carbon dioxide (2.3, 2.4, 2.5, 2.6, 2.7, 21 of 44 CHAPTER 2. METHODS 2.8) and oxygen (2.9, 2.10) content are used. The alveolar space also contains the mechanical ventilation output which is the source for calculating the partial pressures of oxygen and carbon dioxide. Mechanical ventilation is described by nine equations. There are few parameters which are necessary to know in order to be able to compute those nine equations and they are listed in table 2.3. Parameter Unit Value Description F iO 2 F iCO 2 Vt f Vl ung s % % l breaths/s l 21 0 0.1 0.2 2 Fraction of inspired oxygen Fraction of inspired carbon dioxide Tidal volume Frequency of breathing Volume of the lungs Table 2.3: Values of the mechanical ventilation parameters Few assumptions have been made when the partial pressures have been calculated. The fraction of alveolar oxygen (F AO 2 ) and carbon dioxide (F ACO 2 ) are considered to be equal with partial pressures, so if pCO 2 or pO 2 is 5kPa, the fraction is 5%. Minute volume (Vm ) is assumed to have different units by approximating l/s into mmol/s by multiplying by 40, so that 1l/s is equal to 40mmol/s. The same approximation is used when the mass of oxygen and carbon dioxide are calculated. The first two equations of the mechanical ventilation set describe the equality between fraction and partial pressures (2.19, 2.20). They are adjusted in order to have the value of the partial pressures in Pa. The next equation describes the calculation of Vm . The fourth and fifth calculation are used to define the mass of carbon dioxide (MCO 2 ) and oxygen (MO 2 ) in the alveolar space (2.22, 2.23). The next equations are describing the addition of oxygen (mV O 2 ) and removal of carbon dioxide (mV CO 2 ) in the lungs, so the difference between the concentrations inflowing (tO 2,i n and tCO 2,i n ) multiplied with Q i n and outflowing concentrations (tO 2,out and tCO 2,out ) multiplied with Q out (2.24, 2.25). The last couple of equations are the final change of mass dependent on inspired fraction, alveolar fraction, minute volume and also addition or removal of the substance (2.26, 2.27). pCO 2 = 100000 · F ACO 2 (2.19) pO 2 = 100000 · F AO 2 (2.20) Vm = Vt · f · 40 (2.21) MCO 2 = F ACO 2 · Vl ung s · 40 (2.22) MO 2 = F AO 2 · Vl ung s · 40 (2.23) mV CO 2 = Q i n · tCO 2,i n −Q out · tCO 2,out (2.24) mV O 2 = Q i n · tO 2,i n −Q out · tO 2,out (2.25) 22 of 44 CHAPTER 2. METHODS d (MCO 2 ) dt = Vm · F iCO 2 − Vm · F ACO 2 + mV CO 2 (2.26) d (MO 2 ) = Vm · F iO 2 − Vm · F AO 2 + mV O 2 (2.27) dt The resistor is one of the necessary parts for building pulmonary shunt. The function of this segment is expressed by two equations. The first equation (2.28) is definition of the pressure drop (pD), which is the difference between inflow pressure (p i n ) and outflow pressure (p out ). The second equation is an analogy to the Ohm’s law where voltage is represented as pD, resistance is simply blood resistance (bl ood R) with units Pa.s/l and finally the current is defined as the blood flow (Q). pD = p i n − p out (2.28) pD = bl ood R · Q (2.29) Resistances in the alveolar space and in the resistor are controlled by the compartment shunt. The system of the shunt was described in detail in the section 2.1.2. The total pulmonary resistance is known (9333 [(Pa.s)/l] [Tribula et al., 2013]) and the shunt computes the resistances for the alveolar space and the resistor according to pulmonary shunt. Based on parallel resistors rule, if the pulmonary shunt is 50% both resistances are 18666 (Pa.s)/l. The last segment of the lung compartment is the arterial blood. This compartment could be considered as a transition point where the blood from alveolar space and ECMO compartment (venous blood) are mixed and the balance of the blood is recalculated. The process of mixing is described by equations 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 2.10. The output from arterial blood compartment is oxygenated blood with new properties which is distributed throughout the body. 2.2.3 Tissues Two very important processes take place in the tissues - oxygen uptake and carbon dioxide production. Oxygen and carbon dioxide content in the tissues is expressed by equations 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 2.10. Moreover, four equations define oxygen uptake, carbon dioxide production and total outflowing concentrations of oxygen and carbon dioxide. The amount of carbon dioxide which is added to the blood from tissues (ad dCO 2 ) is calculated by dividing the production of carbon dioxide (V CO 2 ) with the cardiac output (Q) (equation 2.30). Therefore, the resulting outflowing concentration of carbon dioxide (tCO 2 ) is inflowing concentration (tCO 2,i n f l ow ) plus ad dCO 2 (equation 2.31). ad dCO 2 = V CO 2 Q tCO 2 = tCO 2,i n f l ow + ad dCO 2 (2.30) (2.31) In contrast with carbon dioxide, oxygen is in the tissues removed from the blood. Two equations describe this process. First, the amount of oxygen which is removed from the blood (r emO 2 ) is defined as division of oxygen uptake (V O 2 ) by cardiac output (Q) (equation 2.32). Second, the final outflowing concentration of oxygen (tO 2 ) is calculated as the subtraction of r emO 2 from the inflowing concentration (tO 2,i n f l ow ) (equation 2.33). 23 of 44 CHAPTER 2. METHODS r emO 2 = V O2 Q tO 2 = tO 2,i n f l ow − r emO 2 (2.32) (2.33) V CO 2 and V O 2 are assumed to be equal - 10mmol/min; it means that the respiratory quotient (RQ) is equal to 1. RQ is the ratio between V CO 2 and V O 2 (equation 2.34) and it varies between 0.7 and 1. If RQ is equal to 1, patient’s body is burning carbohydrates (figure 2.3). RQ = V CO 2 /V O 2 [Si l ber nag l and Despopoul os, 2009] (2.34) Figure 2.3: Relationship between respiratory quotient and caloric equvivalent [Silbernagl and Despopoulos, 2009] The blood coming out of the tissues is deoxygenated (venous) blood with new values of concentrations, pH, partial pressures and oxygen saturation. Concentration and partial pressure of carbon dioxide are higher, oxygen concentration, saturation and partial pressure are lower and pH is lower than in arterial blood. Venous blood needs to be oxygenated and deprived of carbon dioxide in ECMO and later on in the lungs. 2.2.4 ECMO The last part of the model is the ECMO compartment (figure 2.4). It has similar functions and structure as the model of the lungs. This segment is composed of four subcompartments ECMO, resistor, shunt and blood mixing. In the ECMO subcompartment, the oxygenation and carbon dioxide removal take place. Except for one difference, it is structured as the alveolar space in the lungs. Partial pressures in the alveolar space are calculated from mechanical ventilation, however in the ECMO subcompartment they are set to be parameters. pCO 2 and pO 2 are set to be 3kPa and 50kPa, respectively. The process which takes place in the ECMO subcompartment is an equilibrium of the blood balance towards new partial pressures of oxygen and carbon dioxide. For the adaptation on the new partial pressures, all the mathematical equations describing acid-base balance in the system are used (equations 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10). The shunt and resistor are used in similar way as in the lungs. The resistor is in parallel with the ECMO subcompartment and both have their own resistance. The shunt is a control panel which sets the resistances in the resistor and ECMO subcompartment according to needed ECMO flow. For instance, desired ECMO flow is 50% and the total resistance is 500Pa, therefore resistance in both the resistor and ECMO subcompartment is 1000Pa. Last segment of the ECMO compartment is blood mixing, which is analogous to the arterial blood in the lungs. Two important processes take place in this subcompartment. First, 24 of 44 CHAPTER 2. METHODS deoxygenated blood from the tissues and oxygenated blood from the ECMO subcompartment are mixed. Second, the balance of the blood is recalculated by equations 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 2.10. The output from the ECMO compartment is blood partly oxygenated and deprived of carbon dioxide which continues to the lungs where oxygenation and carbon dioxide removal are fulfilled. The level of oxygenation and carbon dioxide removal depends on ECMO flow. Figure 2.4: ECMO compartment and its parts 2.2.5 Entire model All segments of the model have been described in the former sections and it is appropriate to describe how the system works together. The flow in the model is mediated by left and right heart by the pressure which is provided by the blood-vessels. When the flow is secured, the blood can circulate through the entire system and the processes of oxygenation, deoxygenation and carbon dioxide production and removal may begin: oxygen uptake and carbon dioxide removal take place in the tissues, in other words, particular amount of the oxygen is taken by the tissues and carbon dioxide is added to the blood. Afterwards, usually some part of venous blood goes through ECMO where the opposite processes take place. Oxygen is added and carbon dioxide is removed from the blood. Then the blood from ECMO and the rest from the tissues which did not go through ECMO are mixed. The processes of oxygenation and carbon dioxide removal are completed in the lungs. Even though pulmonary shunt is presented, venous blood is partially oxygenated and deprived of carbon dioxide by ECMO, so the properties of arterial blood should be sufficient in order to provide enough oxygen and normal amount of carbon dioxide to the tissues and the entire body. 25 of 44 CHAPTER 3 R ESULTS In this chapter, the results from all eight experiments will be presented. 3.1 Experiment 1 - sO 2 in relation to ECMO flow In experiment 1, optimal value of ECMO flow for achieving good sO 2 was investigated. Mechanical ventilation Vt and pulmonary shunt are set to be 100ml and 35%, respectively. As we can see on figure 3.1 sO 2 is highly dependent on the ECMO flow. When 20% of the blood is going through the ECMO device, it means that ECMO flow is 1.2 l/min (cardiac output is 5.8 l/min), sO 2 is low in both the peripheral and pulmonary artery. sO 2 in the pulmonary artery is in this case just 74% and in the peripheral artery 85%. As the ECMO flow is increased, sO 2 also increases. As soon as ECMO flow is more than 70%, the blood is well oxygenated (sO 2 of >97%) in both the pulmonary and peripheral artery. Schmidt et al. have performed similar trial with patients. It was shown that as soon as the ECMO flow/cardiac output is above 60%, sO 2 is always above 90% (figure 3.3). sO 2 has the same behavior in the right atrium, pulmonary artery and also the peripheral artery during increasing of the ECMO flow/cardiac output. sO 2 increases with enhancement of ECMO flow (figure 3.2) [Schmidt et al., 2012]. The results from a study of Schmidt et al. are corresponding with results from my mathematical model, but sO 2 of >90% in the model occurs earlier than during ECMO flow of 60%. sO 2 >90% occurs in the pulmonary artery when ECMO flow is 50% and in the peripheral artery when ECMO flow is just 30%. Nevertheless, sO 2 of >97% occurs in the pulmonary as well as peripheral artery if ECMO flow is 70%. 100 pulmonary artery peripheral artery 95 sO2 [%] 90 85 80 75 70 100 90 80 70 60 50 40 30 20 ECMO flow [%] Figure 3.1: Experiment 1 - Relationship between oxygen saturation (sO 2 ) in the peripheral and pulmonary artery and ECMO flow; tidal volume (Vt ) is 100ml, pulmonary shunt is 35% 27 CHAPTER 3. RESULTS Figure 3.2: Impact of ECMO flow reduction on oxygen saturation (sO 2 ) in the right atrium, pulmonary artery and peripheral artery [Schmidt et al., 2012] Figure 3.3: Relationship between ECMO flow/cardiac output and oxygen saturation (sO 2 ) in the peripheral artery [Schmidt et al., 2012] 3.2 Experiment 2 - pO 2 in relation to ECMO flow Experiment 2 is related to the first experiment, since both sO 2 and pO 2 describe oxygenation of the blood. This experiment was performed in order to determine the optimal value of ECMO flow for achieving a sufficient value of pO 2 in the peripheral and pulmonary artery. Vt and the pulmonary shunt are set to be 100ml and 35%, respectively. Schmidt et al. have shown that with an increase of ECMO flow/cardiac output pO 2 rises in all of the three parts of the circulation (figure 3.5). Results from the model follow the same pattern (figure 3.4). pO 2 is higher with an enhancement of ECMO flow. The normal value of pO 2 is 13kPa or 100mmHg. pO 2 in the model reaches normal value when ECMO flow is 63% in the peripheral artery and 73% in the pulmonary artery compared to 80% or max flow in the study of Schmidt et al.. 28 of 44 CHAPTER 3. RESULTS 20 18 pO2 [kPa] 16 14 12 pulmonary artery peripheral artery 10 8 6 80 75 70 65 60 55 50 45 40 35 30 ECMO flow [%] Figure 3.4: Experiment 2 - Relationship between oxygen partial pressure (pO 2 ) in the peripheral and pulmonary artery and ECMO flow; tidal volume (Vt ) is 100ml, pulmonary shunt is 35% Figure 3.5: Impact of ECMO flow reduction on oxygen partial pressure (pO 2 ) in the right atrium, pulmonary artery and peripheral artery [Schmidt et al., 2012] 3.3 Experiment 3 - pCO 2 in relation to ECMO flow In experiment 3, ideal ECMO flow for achieving a good value of pCO 2 in the pulmonary and peripheral artery was investigated. Vt and pulmonary shunt are set to be 100ml and 35%, respectively. As Schmidt et al. have shown, pCO 2 is increased with increasing of ECMO flow/cardiac output in the right atrium and also the pulmonary and peripheral artery (figure 3.7). My model shows the same behavior in the peripheral and pulmonary artery (figure 3.6). When ECMO flow is only 30%, pCO 2 in the pulmonary artery is 5.8kPa and in the peripheral artery 5.4kPa. With the enhancement of ECMO flow, pCO 2 decreases towards 3kPa which is the set value of pCO 2 in ECMO. The normal value of pCO 2 is 5kPa or 37mmHg. Since the default value of pCO 2 in the ECMO subcompartment is set to be 3kPa, pCO 2 reaches normal value already during low ECMO flow of 40%. The results from the study by Schmidt et al. confirm my findings. In their trial, pCO 2 reaches a normal value when ECMO flow/cardiac output is 40%. As both figure 3.6 and 3.7 display, ECMO flow from 40 to 100% provides good values of pCO 2 . 29 of 44 CHAPTER 3. RESULTS 6 pulmonary artery peripheral artery 5.5 pCO2 [kPa] 5 4.5 4 3.5 3 2.5 100 90 80 70 60 50 40 30 ECMO flow [%] Figure 3.6: Experiment 3 - Relationship between carbon dioxide partial pressure (pCO 2 ) in the peripheral and pulmonary artery and ECMO flow; tidal volume (Vt ) is 100ml, pulmonary shunt is 35% Figure 3.7: Impact of ECMO flow reduction on carbon dioxide partial pressure (pCO 2 ) in the right atrium, pulmonary artery and peripheral artery [Schmidt et al., 2012] 3.4 Experiment 4 - sO 2 in relation to ECMO flow and pulmonary shunt This experiment was performed in order to determine optimal ECMO flow for achieving well saturated arterial blood under different values of pulmonary shunt. Vt is set to be 100ml. Figure 3.8 displays the relationship between pulmonary shunt and sO 2 in arterial blood during changes of ECMO flow. As the figure 3.8 shows, sO 2 decreases with an increase of pulmonary shunt. When pulmonary shunt is 20%, an ECMO flow of 50% provides good arterial sO 2 of >97%. With an increase of pulmonary shunt, increase of ECMO flow is needed. When the shunt is 50%, an ECMO flow of 60 - 70% is necessary for achieving well saturated arterial blood. 30 of 44 CHAPTER 3. RESULTS 100 98 96 sO2 [%] 94 92 90 88 pulmonary shunt = 20% pulmonary shunt = 30% pulmonary shunt = 40% pulmonary shunt = 50% 86 84 82 100 90 80 70 60 50 40 30 20 ECMO flow [%] Figure 3.8: Experiment 4 - Relationship between oxygen saturation (sO 2 ) in arterial blood and level of pulmonary shunt during changes in ECMO flow; tidal volume (Vt ) is 100ml 3.5 Experiment 5 - sO 2 in relation to ECMO flow, pulmonary shunt and Vt Experiment 5 was carried out in order to investigate what ECMO flow is sufficient for achieving well saturated arterial blood (sO 2 >97%) when the pulmonary shunt is changed and how it is affected by different values of Vt . Figures 3.9, 3.10, 3.11 and 3.12 show the relation between sO 2 in arterial blood and ECMO flow during changes in Vt and in cases of different stages of pulmonary shunt. In all states of lung insufficiency the process has similar behavior. When ECMO flow is low, sO 2 is poor and it obviously depends on Vt . For instance, if pulmonary shunt is 20%, ECMO flow is 20% and Vt is 100ml, sO 2 is just 87%. As Vt is increased towards 500ml, sO 2 is already 97% (figure 3.9). During an increase of ECMO flow, the dependency of sO 2 on Vt is vanishing. For example, if pulmonary shunt is still 20%, ECMO flow is 70%, the difference between sO 2 under variation of Vt is insignificant (figure 3.9). All stages of pulmonary shunt show similar characteristics, but there is a slight disparity between the values of sO 2 during changes of pulmonary shunt. If ECMO flow is 20 or 30% sO 2 is shifted towards lower values with an increase of pulmonary shunt in all cases of Vt , but the difference almost disappears as soon as the ECMO flow is between 60 and 70%. It means that as soon as the ECMO flow is 60 - 70%, Vt can easily be low and ECMO provides good oxygenation and carbon dioxide removal even when pulmonary shunt is 50%. 31 of 44 CHAPTER 3. RESULTS 100 98 sO2 [%] 96 94 92 Vt = 100ml Vt = 200ml Vt = 300ml Vt = 400ml Vt = 500ml 90 88 86 100 90 80 70 60 50 40 30 20 ECMO flow [%] Figure 3.9: Experiment 5 - Relationship between oxygen saturation (sO 2 ) in arterial blood and ECMO flow during changes in tidal volume (Vt ); pulmonary shunt is 20% 100 98 sO2 [%] 96 94 92 90 Vt = 100ml Vt = 200ml Vt = 300ml Vt = 400ml Vt = 500ml 88 86 85 100 90 80 70 60 50 40 30 20 ECMO flow [%] Figure 3.10: Experiment 5 - Relationship between oxygen saturation (sO 2 ) in arterial blood and ECMO flow during changes in tidal volume (Vt ); pulmonary shunt is 30% 100 98 sO2 [%] 96 94 92 90 Vt = 100ml Vt = 200ml Vt = 300ml Vt = 400ml Vt = 500ml 88 86 84 100 90 80 70 60 50 40 30 20 ECMO flow [%] Figure 3.11: Experiment 5 - Relationship between oxygen saturation (sO 2 ) in arterial blood and ECMO flow during changes in tidal volume (Vt ); pulmonary shunt is 40% 32 of 44 CHAPTER 3. RESULTS 100 98 96 sO2 [%] 94 92 90 88 Vt = 100ml Vt = 200ml Vt = 300ml Vt = 400ml Vt = 500ml 86 84 82 100 90 80 70 60 50 40 30 20 ECMO flow [%] Figure 3.12: Experiment 5 - Relationship between oxygen saturation (sO 2 ) in arterial blood and ECMO flow during changes in tidal volume (Vt ); pulmonary shunt is 50% 3.6 Experiment 6 - sO 2 in relation to ECMO flow and V CO 2 and V O 2 This experiment was performed in order to find out the optimal value of ECMO flow under different activity of patient’s metabolism. In other words, the experiment was an investigation on which value of ECMO flow is good enough to achieve sufficient sO 2 in arterial blood (>97%) when oxygen uptake (V O 2 ) and carbon dioxide production (V CO 2 ) in the tissues are changed. Pulmonary shunt and Vt are set to be 35% and 100ml, respectively. Under normal conditions of the model, V O 2 and V CO 2 are set to be equal 10mmol/min. Figure 3.13 displays the dependency of sO 2 on ECMO flow and on changes of V O 2 and V CO 2 . It is clear that sO 2 rises as the ECMO flow increases. The plot also displays that as soon as V O 2 and V CO 2 are higher, an increase of ECMO flow is necessary in order to keep the blood saturated enough. If V O 2 and V CO 2 are 10mmol/min, an ECMO flow of 60% is sufficient for well saturated arterial blood. As soon as V O 2 and V CO 2 increase, higher ECMO flow is needed. When ECMO flow is 80%, sO 2 in arterial blood is sufficient for all values of V O 2 and V CO 2 . 100 95 90 sO2 [%] 85 80 75 70 65 VCO2 = VO2 = 10 mmol/min VCO2 = VO2 = 15 mmol/min VCO2 = VO2 = 22 mmol/min 60 55 80 75 70 65 60 55 50 45 40 35 30 ECMO flow [%] Figure 3.13: Experiment 6 - Relationship between oxygen saturation (sO 2 ) in arterial blood and ECMO flow during changes of oxygen uptake (VO2) and carbon dioxide production (VCO2) (considering equality between V O 2 and V CO 2 ); tidal volume (Vt ) is 100ml, pulmonary shunt is 35% 33 of 44 CHAPTER 3. RESULTS 3.7 Results summary of experiments 1 - 6 The goal of experiments 1 to 6 was to optimize ECMO flow. Most of the experiments have shown that sufficient ECMO flow is between 60 and 70% (3.5 - 4.1l/min) in order to achieve good arterial blood properties. Nevertheless, from experiment 3 it is clear that the optimal value of ECMO flow for reaching satisfactory pCO 2 is 40%. However, an ECMO flow of 40% would not be sufficient in order to achieve well saturated arterial blood and a normal value of pO 2 . Experiment 6 has shown that an ECMO flow of 80% is necessary to reach good sO 2 in arterial blood if V O 2 and V CO 2 are 22mmol/l. Since default values of V O 2 and V CO 2 are set to be 10mmol/min, an ECMO flow of 60% is sufficient. The rest of the experiments have shown that an ECMO flow of 70% or between 60 and 70% provides good arterial blood properties under different conditions. In summary, optimal value of ECMO flow is between 60 and 70%. 3.8 Experiment 7 - arterial blood properties in relation to pCO 2 and pO 2 in ECMO Experiment 7 was carried out in order to find out which settings of partial pressures in the ECMO subcompartment are optimal for achieving good arterial blood properties. Pulmonary shunt, ECMO flow and Vt were set to be 35%, 70% and 100ml, respectively. A former study has suggested the normal value of oxygen fraction in ECMO around 50% [Schmidt et al., 2012]. The typical value of pCO 2 in arterial blood is 5kPa [Martin, 1999]. Therefore, similar values were chosen to be potential optimal settings. The results are summarized in table 3.1. In comparison with table 1.1, the results show that all of the values in the chosen range provide good properties of arterial blood. There are no significant differences between combinations of partial pressures and reached values of blood properties. Although the differences are not significant, the ideal combination seems to be pCO 2 of 4.5kPa and pO 2 of 45kPa. Partial pressures [kPa] tCO 2 [mmol/l] tO 2 [mmol/l] sO 2 [%] pCO 2 [kPa] pO 2 [kPa] pCO 2 = 3 pO 2 = 40 pCO 2 = 3 pO 2 = 45 pCO 2 = 3 pO 2 = 50 24.08 9.29 98.40 3.30 13.46 24.08 9.30 98.54 3.30 13.99 24.08 9.32 98.67 3.30 14.56 pCO 2 = 3.5 pO 2 = 45 pCO 2 = 4 pO 2 = 45 pCO 2 = 4.5 pO 2 = 45 pCO 2 = 5 pO 2 = 45 24.62 9.30 98.46 3.77 14.28 25.13 9.30 98.39 4.24 14.54 25.61 9.29 98.32 4.70 14.77 26.06 9.29 98.26 5.16 14.98 Table 3.1: Experiment 7 - Dependency of arterial blood properties on partial pressures settings in the ECMO subcompartment; pulmonary shunt is 35%, ECMO flow is 70%, Vt is 100ml 34 of 44 CHAPTER 3. RESULTS 3.9 Experiment 8 - model behavior Since the optimal settings seem to be ECMO flow of 60 to 70% and pCO 2 of 4.5kPa and pO 2 of 45kPa, an observing experiment was performed. The purpose of this experiment was to observe how the blood properties change during the passage throughout the circulation. Pulmonary shunt was set to be 35% to simulate severe damage of the lungs. Vt was set to be 100ml to show low support from mechanical ventilation. The results are summarized in table 3.2. Compared to tables 1.1 and 1.2 it was shown that the modeled blood has similar properties as the physiological values. Part of the circulation tCO 2 [mmol/l] tO 2 [mmol/l] sO 2 [%] pCO 2 [kPa] pO 2 [kPa] Tissues ECMO After ECMO Alveolar space Arterial blood 27.30 25.40 25.97 25.41 25.61 7.59 9.74 9.09 9.40 9.29 80.96 99.84 96.55 99.06 98.32 6.52 4.50 5.07 4.51 4.70 6.45 45.00 11.43 18.56 14.77 Table 3.2: Experiment 8 - Summary of blood properties in different parts of circulation under chosen optimal settings; pulmonary shunt is 35%, Vt is 100ml, ECMO flow is 70%, pCO 2,ecmo is 4.5kPa and pO 2,ecmo is 45kPa 35 of 44 CHAPTER 4 D ISCUSSION In this chapter, the purpose, aim and solution strategy of the project will be recapitulated. Later on, the results from the experiments will be summarized and compared with the literature. Afterwards, the critical view on some aspects of my model will be presented. Finally, the conclusion will be drawn. 4.1 Recapitulation The aim of this project was to build a mathematical model of human circulation, lungs, tissues and VV ECMO device and investigate the optimal ECMO settings in order to obtain good oxygenation and carbon dioxide removal. The purpose of the present project was to create a mathematical model which can be useful for understanding and explaining the functions and processes of the physiological system and medical device. The model was created in programming language called Modelica. Four major parts of the model were built separately - blood circulation, lungs with insufficient function, tissues and VV ECMO device. Set of experiments was designed in order to test the model and find the optimal ECMO settings. 4.2 Results summary Two important findings have emerged from this project. First, for a patient with insufficient lung function and slight support by mechanical ventilation (Vt = 100ml) the optimal ECMO flow is between 60% and 70% (3.5 - 4.1l/min). Under these conditions, arterial blood is well saturated and deprived from carbon dioxide. Second, partial pressures ECMO settings in chosen range do not have a strong influence on arterial blood properties compared to ECMO flow. However, pCO 2 of 4.5kPa and pO 2 of 45kPa are chosen to be the optimal settings of partial pressures in the ECMO subcompartment. Former study has investigated that using femoro-jugular ECMO settings and ECMO flow of >60% of systemic blood flow is associated with arterial sO 2 of >90% [Schmidt et al., 2012]. Results from the present project confirm this finding. However, sO 2 in the peripheral artery of 90% is achieved already when ECMO flow is 30% of cardiac output. sO 2 in the pulmonary artery was found to be lower than in the peripheral artery under the same conditions of ECMO flow [Schmidt et al., 2012]. The same finding has emerged from the present experiment. Specifically, sO 2 in the pulmonary artery of >90% is achieved when ECMO flow is set to be 50%. Nevertheless, sO 2 of >97% in both the pulmonary and peripheral artery is achieved when ECMO flow is 70%. 37 CHAPTER 4. DISCUSSION The previous study has observed that an ECMO flow of >60% of systemic blood flow is associated with arterial pO 2 of >60mmHg (8kPa). It was shown that pO 2 is lower in the pulmonary than in the peripheral artery under the same conditions of ECMO flow [Schmidt et al., 2012]. Similar findings have emerged from the present project. However, pO 2 of >60mmHg (8kPa) occurs in the pulmonary artery and in the peripheral artery when ECMO flow is 50% and 30%, respectively. Optimal pO 2 of 100mmHg (13kPa) is achieved in pulmonary and peripheral artery when ECMO flow is 73% and 63%, respectively. Schmidt et al. have shown that during an ECMO flow reduction to 40%, pCO 2 is unaffected. This finding is consistent with results from the present project. It has emerged that an ECMO flow of 40% provides normal values of pCO 2 (37mmHg or 5kPa). The default value of pCO 2 in ECMO compartment is set to be 3kPa. Therefore, when ECMO flow increases pCO 2 decreases towards the default value. Nevertheless, ECMO flow does not have a strong influence on arterial pCO 2 . Pulmonary shunt is a medical condition when oxygenated blood is mixed with deoxygenated blood and therefore efficiency of gas exchange is affected [Lovering and Goodman, 2012]. The higher the shunt is, the worse the patient’s health conditions expected to be. The result from experiment 4 has confirmed such a theory. It was shown that with an increase of pulmonary shunt, higher ECMO flow is needed in order to achieve well saturated arterial blood. If pulmonary shunt is 20%, an ECMO flow of 50% is sufficient for arterial blood sO 2 of >97%. Nevertheless, an ECMO flow of 60 - 70% is associated with arterial sO 2 of >97% for all states of pulmonary shunt. The previous study has suggested that optimal mechanical ventilation Vt is 110ml [Schmidt et al., 2012]. Experiment 5 has investigated an influence of mechanical ventilation Vt on optimal ECMO flow in different stages of pulmonary shunt. The results have shown that under low ECMO flow (20%) and pulmonary shunt of 20%, Vt of 500ml is necessary in order to achieve arterial sO 2 of >97%. However, with an increase of pulmonary shunt, Vt of 500ml is not sufficient for reaching well saturated arterial blood. As soon as pulmonary shunt is 30%, arterial sO 2 is under 95% although Vt is 500ml. In order to keep sO 2 on sufficient level, ECMO flow has to be increased with an enhancement of pulmonary shunt. Experiment 5 has shown that as soon as ECMO flow is 70%, sO 2 of >97% is achieved for all states of pulmonary shunt and Vt of 100ml is sufficient support of mechanical ventilation. Therefore, experiment 5 has suggested the same level of mechanical ventilation support as the study by Schmidt et al.. During strenuous exercise the human body requires up to 500 times more oxygen than when at rest. At the same time, the body has to get rid of carbon dioxide and other metabolic products whose production suddenly significantly increases [Silbernagl and Despopoulos, 2009]. The present study has investigated that ECMO flow has to be increased if the activity of the patient’s metabolism increases. Although patients receiving ECMO are usually bedridden, metabolism activity may be at some point slightly higher. For example, if the patient is firstly sedated and afterwards able to communicate with relatives and doctors. When the patient is at rest, V CO 2 is 10mmol/min [Silbernagl and Despopoulos, 2009]. I assume that V CO 2 is equal to V O 2 under standard conditions. Under normal conditions, an ECMO flow of 60% is needed in order to achieve arterial sO 2 of >97%. As soon as V CO 2 and V O 2 are increased towards 15mmol/min, an ECMO flow of 70% is necessary to keep arterial sO 2 on >97%. Nevertheless, an ECMO flow of 80% is sufficient in order to reach arterial sO 2 of >97% for all the levels of the patient’s metabolism. A previous study has suggested that the optimal value of oxygen fraction in ECMO is 50% [Schmidt et al., 2012]. The most commonly used optimal value of pCO 2 in arterial blood is 5kPa [Martin, 1999]. I assume that partial pressures in the ECMO subcompartment are analogous to a fraction of the gases. Experiment 7 has investigated the optimal settings of partial 38 of 44 CHAPTER 4. DISCUSSION pressures in the ECMO subcompartment. It was shown that the chosen range of the partial pressures provides good arterial blood properties compared to the values suggested by Rees and Andreassen and Martin. The interval of potential optimal values was from 3 to 5kPa for pCO 2 and from 40 to 50kPa for pO 2 . The results have suggested no significant difference between combinations of partial pressures. Although no significant difference was shown, pCO 2 of 4.5kPa and pO 2 of 45kPa could be considered as the optimal settings. The chosen optimal settings are consistent with the values suggested by the literature. Experiment 8 has observed behavior of the model under optimal settings which have emerged from previous experiments. The conditions of this experiment are as follows: ECMO flow of 70%, pulmonary shunt of 35%, Vt of 100ml, pCO 2,ecmo of 4.5kPa and pO 2,ecmo of 45kPa. The results have shown values of arterial blood properties which are consistent with values suggested by Rees and Andreassen and Martin. The model behaves in relation with expected outcomes. Carbon dioxide is added and oxygen is removed to/from the blood in the tissues. The blood is deprived of carbon dioxide in the ECMO and lungs, oxygen is added to the blood in the ECMO and lungs. The resulting arterial blood properties are a mix of venous blood and the blood going from alveolar space according to shunt level. A previous study has suggested that ECMO flow is the main determinant of blood oxygenation. It was shown that an ECMO flow of >60% of systemic blood flow obtain adequate arterial oxygenation. An ECMO flow of 4 to 7 l/min is usually required to achieve sO 2 of >88-90% depending on patient size, cardiac output, oxygen consumption and lung shunt. Safe ventilation supports the pulmonary function while on ECMO [Schmidt et al., 2012]. The present experiments do not consider all of the conditions. The goal during most of the experiments is to achieve sO 2 of >97% and cardiac output in the model is 5.8l/min. Under these circumstances, ideal ECMO flow is between 60 and 70%. All of the present experiments have shown that ECMO flow is the major determinant of blood oxygenation. 4.3 Limitations Mathematical or computer model is never able to fully substitute or express the real system, but it may be very useful in describing and explaining basic processes and functions of any system. My intention in this project was to try to reproduce the behavior of human blood circulation when the lungs are not working properly and it is necessary to support their function with slight mechanical ventilation and an ECMO device. After designing the model which expresses the behavior of human body, the goal was to find optimal ECMO settings which are sufficient in providing oxygen and carbon dioxide in particular amounts within the patient’s body. The model works satisfactorily, but there are few limitations which are necessary to mention. 4.3.1 Acid-base chemistry The first limitation is an imperfect buffering system in the model. Since a strong base is not considered as a blood component in the model, concentrations of tA (tNBB) and BB are assumed to be constants. Next inaccuracy is the description of oxygen and carbon dioxide content in the blood. Each of these two substances are described almost separately and in different ways. Carbon dioxide content is described only in plasma, its part in erythrocytes is ignored. Therefore, tCO 2 in the model means total concentration in plasma. Oxygen content is defined in the entire blood volume, since H b concentration was set to be 9.3mmol/l, which is oxygen carrying capacity of hemoglobin per liter of blood. As you can see, the ways of describing oxygen and carbon dioxide are not completely consistent. In summary, acid-base chemistry in the model is simplified. 39 of 44 CHAPTER 4. DISCUSSION However, it shows the most important behaviors, processes and dependencies of concentrations, partial pressures and saturation in the lungs, tissues and ECMO. 4.3.2 ECMO The next limitation is the simplified structure of the ECMO compartment. In real ECMO device, air supply is an independent unit with its own flow. The air unit sets the fraction of oxygen and carbon dioxide. In the model, oxygen and carbon dioxide are incorporated to the ECMO subcompartment without any additional flow settings. I assume that fractions of the gases are analogous to partial pressures. Therefore the settings of oxygen and carbon dioxide fraction are changed by changing partial pressures. 4.3.3 Shunt The last limitation which I want to mention is the mixing of venous blood in pulmonary shunt and the shunt in the ECMO compartment. At some point, the oxygenation in the lungs does not make physiological sense. This occurs specifically if the entire blood volume is going through ECMO. The blood is well oxygenated with the appropriate concentration of carbon dioxide after passing through ECMO. Since the model represents VV modality and blood from ECMO is returned to the venous bloodstream, venous blood becomes well oxygenated and deprived of carbon dioxide. After passing through ECMO, venous blood comes to the lungs and it is supposed to be more oxygenated and deprived of carbon dioxide. However, it is not possible, because it already is very well saturated with oxygen and carbon dioxide concentration is appropriate. The next problem arises with pulmonary shunt when the entire blood volume is going through ECMO. Pulmonary shunt is a pathological state when oxygenated blood is mixed with deoxygenated blood. The higher pulmonary shunt is, the more of the venous blood is mixed with the arterial blood and the worse the patient’s condition is expected to be. However, since venous blood in the model is under mentioned conditions well saturated and deprived of carbon dioxide, it is actually better to have higher shunt which does not make any physiological sense. Nevertheless, it is not that common even in real ECMO device, that the entire blood volume is going through, since drainage is most often located in femoral vein or inferior or superior vena cava. The problem about comparison of the model with the real body is also the fact that each human is different and it is not possible to generalize the behavior. However, it would be interesting to use the model as a preparation for a particular patient by fixing the parameters and settings according to specific details of his or her body and design the optimal use of ECMO. My intention is to expand and elaborate the model in my future master thesis and it may lead to possible improvements. 4.4 Conclusion The aim of the project was to investigate optimal extracorporeal membrane oxygenation (ECMO) settings by creating a mathematical model and performing testing experiments. The present project can conclude that mathematical modeling could be considered as a useful tool for expressing basic physiological processes and functions of medical devices. The model demonstrates basic behavior of human circulation, processes in tissues, lungs and venovenous ECMO (VV ECMO) with satisfactory results. Results from the experiments have shown that ECMO flow is the main determinant of blood oxygenation. Optimal ECMO flow in order to achieve good arterial oxygen saturation (sO 2 ) is between 60% and 70% (3.5 - 4.1l/min). Optimal 40 of 44 CHAPTER 4. DISCUSSION partial pressures settings in ECMO are a carbon dioxide partial pressure (pCO 2 ) of 4.5kPa and an oxygen partial pressure (pO 2 ) of 45kPa. 41 of 44 B IBLIOGRAPHY The Australia and New Zealand Extracorporeal Membrane Oxygenation (ANZ ECMO) Influenza Investigators. Extracorporeal membrane oxygenation for 2009 influenza a(h1n1) acute respiratory distress syndrome. JAMA, 302:1888–1895, 2009. R.H. Bartlett, D.W. Roloff, R.G. Cornell A.F. Andrews, P.W. Dillon, and J.B. Zwischenberger. Extracorporeal circulation in neonatal respiratory failure: a prospective randomized study. Pediatrics, 76:479–487, 1985. P. Betit. Extracorporeal membrane oxygenation: Quo vadis? Respiratory Care, 54:948–957, 2009. Resuscitation council UK. Arterial blood gas analysis workshop, January 2012. URL http: //www.resus.org.uk/pages/alsabgGd.pdf. P. Fritzon. Principles of object-oriented modeling and simulation with Modelica 2.1. John Wiley and Sons, INC, 2004. K.W. Gow, M.L. Wulkan, K.F. Heiss, A.E. Haight, M.L. Heard, and P. Rycus J.D. Fortenberry. Extracorporeal membrane oxygenation for support of children after hematopoietic stem cell transplantation: the extracorporeal life support organization experience. J Pediatr Surg, 41: 662–667, 2006. T.P. Green, O.D. Timmons, J.C. Fackler, F.W. Moler, A.E. Thompson, and M.F. Sweeney. The impact of extracorporeal membrane oxygenation on survival in pediatric patiens with acute respiratory failure. pediatric critical care study group. Crit Care Med, 24:323–329, 1996. UK Collaborative ECMO Trial Group. Uk collaborative randomised trial of neonatal extracorporeal membrane oxygenation. The Lancet, 348:75–82, 1996. M.R. Hemmila, S.A. Rowe, T.N. Boules, J. Miskulin, J.W. McGillicuddy, D.J. Schuerer, J.W. Haft, F. Swaniker, S. Arbabi, R.B. Hirschl, and Robert H. Bartlett. Extracorporeal life support for severe acute respiratory distress syndrome in adults. Annals of Surgery, 240:595–607, 2004. V. Linden, K. Palmer, J. Reinhard, R. Westman, H. Ehren, T. Granholm, and B. Frenckner. High survival in adult patients with acute respiratory distress syndrome treated by extracorporeal membrane oxygenation, minimal sedation, and pressure supported ventilation. Intensive Care Med, 26:1630–1637, 2000. S.J. Lindstrom, V.A. Pellegrino, and W.W. Butt. Extracorporeal membrane oxygenation. MJA, 191:178–182, 2009. A.T. Lovering and R.D. Goodman. Detection of intracardiac and intrapulmonary shunts at rest and during exercise using saline contrast echocardiography. Intech, pages 160– 175, 2012. URL http://cdn.intechopen.com/pdfs/35866/InTech-Detection_of_ intracardiac_and_intrapulmonary_shunts_at_rest_and_during_exercise_using_ saline_contrast_echocardiography.pdf. L. Martin. All You Really Need to Know to Interpret Arterial Blood Gases. Lippincott Williams and Wilkins, second edition, 1999. 43 BIBLIOGRAPHY A.H. Morris, C.J. Wallace, R.L. Menlove, T.P. Clemmer, J.F. Orme Jr, L.K. Weaver, N.C. Dean, F. Thomas, T.D. East, N.L. Pace nad M.R. Suchyta, E. Beck, M. Bombino, D.F. Sittig S. Bohm, B. Hoffmann, H. Becks, S. Butler, J. Pearl, and B. Rasmusson. Randomized clinical trial of pressure-controlled inverse ratio ventilation and extracorporeal co2 removal for adult respiratory distress syndrome. Am J Respir Crit Care Med, 149:295–305, 1994. G.J. Peek M. Mugford, R. Tiruvoipati, A. Wilson, E. Allen, M.M. Thalanany, C.L. Hibbert, A. Truesdale, F. Clemens, N. Cooper, R.K. Firmin, and D. Elbourne; CESAR trial collaboration. Efficacy and economic assessment of conventional ventilatory support versus extracorporeal membrane oxygenation for severe adult respiratory failure (cesar): a multicentre randomised controlled trial. Lancet, 374:1351–1363, 2009. M.A. Noah, G.J. Peek, S.J. Finney, M.J. Griffiths, D.A. Harrison, R. Grieve nad M.Z. Sadique, J.S. Sekhon, D.F. McAuley, R.K. Firmin, Ch. Harvey, J.J. Cordingley, S. Price, A. Vuylsteke, D.P. Jenkins, D.W. Noble, R. Bloomfield, T.S. Walsh, G.D. Perkins, D. Menon, B.L. Taylor, and K.M. Rowan. Referral to an extracorporeal membrane oxygenation center and mortality among patients with severe 2009 influenza a(h1n1). JAMA, 306:1659–1668, 2011. K. Oshima, F. Kunimoto, H. Hinohara, M. Ohkawa, N. Mita, and Y. Tajima. Extracorporeal membrane oxygenation for respiratory failure: Comparison of venovenous versus venoarterial bypass. Surg Today, 40:216–222, 2010. M. Otter and H. Elmqvist. Modelica language, libraries, tools, workshop and eu-project realsim. pages 1–8, 2001. URL https://modelica.org/documents/ModelicaOverview14.pdf. N. Patroniti, A. Zangrillo, F. Pappalardo, A. Peris, G. Cianchi, A. Braschi, G.A. Iotti, A. Arcadipane, G. Panarello, M.V. Ranieri, P. Terragni nad M. Antonelli, L. Gattinoni, F. Oleari, and A. Pesenti. The italian ecmo network experience during the 2009 influenza a(h1n1) pandemic: preparation for severe respiratory emergency outbreaks. Intensive Care Med, 37:1447–1457, 2011. S. E. Rees and S. Andreassen. Mathematical models of oxygen and carbon dioxide storage and transport:the acid-base chemistry of blood. Critical reviews in biomedical engineering, 33: 209–264, 2005. E. Rodriguez-Cruz. Extracorporeal membrane oxygenation. Medscape Reference, 2011. M. Schmidt, G. Tachon, Ch. Devilliers anf G. Muller, G. Hekimian, N. Brechot, S. Merceron, Ch.E. Luyt, J.-L. Trouillet, J. Chastre, P. Leprince, and A. Combes. Blood oxygenation and decarboxylation determinants during venovenous ecmo for respiratory failure in adults. Intensive Care Med, 2012. O. Siggaard-Andersen, R.A. Durst, and A.H.J. Maas. Acid-base and oxygen status of the blood, 1987. S. Silbernagl and A. Despopoulos. Color Atlas of Physiology. Thieme, sixth edition, 2009. M. Tribula, F. Jezek, P. Privitzer J. Kofranek, and J. Kolman. Webovy vyukovy simulator krevniho obehu. Sbornik prispevku MEDSOFT 2013, pages 197–204, 2013. URL http: //creativeconnections.cz/medsoft/2013/Medsoft_2013_Tribula.pdf. W.M. Zapol, M.T. Snider, J.D. Hill, R.J. Fallat, R.H. Bartlett, L.H. Edmunds, A.H. Morris, E.C. Peirce, A.N. Thomas nad H.J. Proctor, P.A. Drinker, P.C. Pratt, and A. Bagniewski nad R.G. Miller. Extracorporeal membrane oxygenation in severe acute respiratory failure; a randomized prospective study. JAMA, 242:2193–2196, 1979. 44 of 44