A Novel Iterative Method for Non-invasive Measurement of Cardiac Output

Transcription

1 A Novel Iterative Method for Non-invasive Measurement of Cardiac Output by Michael Klein A thesis submitted in conformity with the requirements for the degree of Master of Science Department of Physiology University of Toronto Copyright by Michael Klein 013

2 A Novel Iterative Method for Non-invasive Measurement of Cardiac Output Michael Klein Master of Science Department of Physiology 013 Abstract This thesis provides a first description and proof-of-concept of iterative cardiac output measurement (ICO) a respiratory, carbon-dioxide (CO ) based method of measuring cardiac output (CO). The ICO method continuously tests and refines an estimate of the CO by attempting to maintain the end-tidal CO constant. To validate the new method, ICO and bolus thermodilution CO (TDCO) were simultaneously measured in a porcine model of liver transplant. Linear regression analysis revealed the equation ICO = 0.69 TDCO with a Pearson correlation coefficient of Analysis by the method of Bland and Altman showed a bias of -0. L/min with 95% limits of agreement from -1.1 to 0.7 L/min. The trending ability of ICO was determined using the half-circle polar plot method where the mean radial bias, the standard deviation of the polar angle, and 95% confidence interval of the polar angle were -8º, ±17º, and ±33º, respectively. ii

3 Acknowledgements I am deeply indebted to my supervisor, Dr. Joseph Fisher, for his mentorship, direction, support, and patience in the execution of this project and the preparation of this manuscript. I would also like to thank the members of my supervisory committee, Dr. James Duffin, Dr. John Granton, Dr. Albert Olszowska, and Dr. John Parker for their invaluable advice. I would like to thank Dr. Markus Selzner and Dr. Matthias Knaak for allowing me to work with their animal models, and Dr. Leonid Minkovich for providing the anesthesia support during our experiments. I am grateful for their technical assistance, and more importantly, the role they played as my teachers. I am grateful to Thornhill Research Inc. for seeing the value in this project and providing the financial resources for its completion. In particular, I would like to express my appreciation for the support and guidance of Clifford Ansel, Ron Baker, Drew Miller, and Shyam Mali. I could not have completed this work without the loving support of my wife, Avital Klein, my parents, Meir and Judy Klein, and my brother, Shawn Klein. iii

4 Table of Contents List of Tables... v List of Figures... vi List of Appendices... vii Commonly used abbreviations, acronyms, and symbols... viii 1 Introduction Non-respiratory methods of measuring cardiac output Thoracic bioimpedance Transesophageal Doppler Arterial pulse contour analysis Respiratory methods of measuring cardiac output Direct Fick measurement of cardiac output Indirect Fick measurement of cardiac output A novel iterative method for non-invasive measurement of cardiac output....1 Rationale of the iterative cardiac output measurement method.... Implementation of the iterative cardiac output measurement method Imposing the alveolar ventilation Setting the alveolar ventilation Apparatus Iteratively measuring cardiac output Validation of the iterative cardiac output monitor Methods Results Discussion Advantages of the iterative cardiac output measurement method Validating the measurement Leveraging sequential gas delivery The benefits of virtual sequential gas delivery The effects of shunts The iterative cardiac output measurement method during liver transplantation Implications Limitations Conclusions and future directions Contributions References iv

5 List of Tables Table 1. Comparison of the characteristics of indirect Fick methods for measuring cardiac output... 4 Table B1. Description of the iterative cardiac output system components Table C1. Raw cardiac output measurement data v

6 List of Figures Figure 1. Operating principles of thoracic bioimpedance cardiac output measurement... 4 Figure. Measurement of cardiac output by transesophageal Doppler ultrasonography... 6 Figure 3. Derivation of aortic flow from arterial pressure... 9 Figure 4. The Fick mass balance relationship for oxygen Figure 5. The Fick mass balance relationship for carbon-dioxide Figure 6. Determination of cardiac output by extrapolation of a carbon-dioxide rebreathing curve Figure 7. Error sensitivity of cardiac output measurement by extrapolation Figure 8. Determination of cardiac output by equilibration of carbon-dioxide Figure 9. Three possible results of the iterative cardiac output maneuver... 3 Figure 10. The cyclical nature of the iterative cardiac output algorithm... 5 Figure 11. A sample of three iterations of the iterative cardiac output algorithm... 5 Figure 1. Operation of a sequential gas delivery circuit... 7 Figure 13. Using sequential gas delivery to control the... 8 Figure 14. Apparatus used to implement the iterative cardiac output method Figure 15. Time series of cardiac output measurements during liver transplantation Figure 16. Linear regression analysis of cardiac output measurements during liver transplantation.. 36 Figure 17. Bland-Altman analysis of cardiac output measurements during liver transplantation Figure 18. Polar plot analysis of cardiac output measurements during liver transplantation Figure 19. Convergence rate of the iterative cardiac output algorithm Figure 0. Validating iterative cardiac output measurements Figure 1. Various shunt flows throughout the body Figure. Respiratory cardiac output measurements with left-to-right shunts Figure B1. A detailed block diagram of the iterative cardiac output system Figure B. Volumetric blender flow chart Figure B3. Volumetric blender validation Figure B4. Virtual sequential gas delivery flow chart vi

7 List of Appendices Appendix A Derivation of the alveolar equilibration time constant Appendix B Technical details of the iterative cardiac output system Appendix C Raw data vii

8 Commonly used abbreviations, acronyms, and symbols CaCO CaO CI CO CO Arterial carbon-dioxide content Arterial oxygen content Confidence interval Cardiac output Carbon-dioxide C vco Mixed-venous carbon-dioxide content C vo Mixed-venous oxygen content DA FRC Descending aorta Functional residual capacity FI CO Inspired fractional concentration of carbon-dioxide ICO O PAC PaCO Iterative cardiac output Oxygen Pulmonary artery catheter Arterial partial pressure of carbon-dioxide PET CO End-tidal partial pressure of carbon-dioxide PI CO Inspired partial pressure of carbon-dioxide P vco Mixed-venous partial pressure of carbon-dioxide R RR S SD Pearson s correlation coefficient Respiratory rate Slope of the carbon-dioxide dissociation curve Time constant Standard deviation SGD SV TDCO V A VCO V D V E VO Sequential gas delivery Stroke volume Thermodilution cardiac output Alveolar ventilation Net ventilatory production of carbon-dioxide Anatomical dead space Minute ventilation Net ventilatory consumption of oxygen viii

9 1 1 Introduction Tissue hypo-perfusion, with its associated oxygen (O ) debt, is a primary mechanism in the development of multi-organ failure, which is a dominant cause of mortality and morbidity in perioperative and critical care medicine 1. Cardiac output (CO) is a pivotal determinant of adequate tissue perfusion and O delivery, and monitoring of CO is a mandatory part of hemodynamic goal-directed therapy. There is growing evidence that early implementation of hemodynamic goal-directed therapy improves outcomes in high-risk surgical and critically ill patients 3,4. Despite well-known limitations, measurement of CO by bolus thermodilution (TDCO) through a pulmonary artery catheter (PAC) is considered to be the clinical standard for CO monitoring 5. Unfortunately, placement of a PAC is a highly invasive procedure, and exposes the patient to life threatening complications 6. Furthermore, PAC placement is time consuming, requires skilled staff, and may be done only in dedicated intensive care or operating room environments. As a result of these drawbacks, hemodynamic monitoring by TDCO is often started after patients have already developed multi-organ failure, at which point establishment of proper hemodynamic monitoring and initiation of hemodynamic goal-directed therapy cannot significantly improve outcome 7,8. A non-invasive, accurate, robust, automated, and operator-independent monitor of CO is highly desirable in daily clinical practice 9. Unfortunately, at present, such a monitor is not yet available. Existing non-invasive techniques for monitoring CO may be broadly categorized into nonrespiratory and respiratory-based approaches. Non-respiratory methods monitor physiological parameters which vary with CO; a prediction of the CO is reported after processing these parameters through a complex series of models and equations. Respiratory methods, on the other hand, measure the flux of gases between the lungs and pulmonary capillaries from which CO can be determined based on well-established mass balance principles.

10 All methods of measuring CO are limited with respect to the patient populations and clinical situations in which they may be used. Furthermore, all methods rely on assumptions regarding the physiology of the patient. Where these assumptions are incorrect, the reported CO will be inaccurate. Nevertheless, if the error introduced into the measurement by inaccurate assumptions is constant, the absolute value of the measured CO will be incorrect, but relative changes can still be detected. A measure that does not provide an exact absolute value, but still trends with the actual CO, may find utility in some clinical situations 10. The critical limitation of all the non-respiratory methods is an assumption of constant values for parameters which are, in reality, continually changing. This assumption introduces a variable and unpredictable error into the measurement so that the relationship between the measured and actual CO cannot be defined. Respiratory-based measurements of CO are founded on simple mass balance relationships that obviate the need to assume values for highly variable and difficult to measure parameters. Despite their theoretical simplicity, each measure of CO requires the precise execution of a respiratory maneuver, and two accurate measures of gas exchange to be performed during the relatively short interval in which the mass balance equations are valid. Executing the respiratory maneuver and obtaining the required measurements during this interval is challenging, and existing methods either introduce substantial errors into the measurement or require a tedious trial-and-error approach. This thesis describes the development of a novel, respiratory-based, iterative method for measuring CO (ICO) which is easily automated and overcomes many limitations of previous approaches. Presented here is a description of the ICO method and its implementation. Also presented are results comparing ICO to TDCO in a pig model of orthotopic liver transplant (OLT). This disclosure is preceded by a review of the current state-of-the-art in non-invasive CO monitoring, and an analysis revealing the limitations of these existing methods. 1.1 Non-respiratory methods of measuring cardiac output The methods described and discussed herein will be limited to those that are commercially available and that have undergone extensive testing in a variety of clinical situations. These

11 3 methods are thoracic bioimpedance, transesophageal Doppler, and arterial pulse contour analysis Thoracic bioimpedance The thoracic bioimpedance method of measuring CO makes use of changes in the electrical impedance of the thorax to estimate the blood flow through the aorta. As the electrical resistivity of blood is far lower than the other constituents of the thorax, namely, muscle, skin, fat, lung, bone, and air, the impedance of the thorax is almost entirely defined by the impedance of the electrical path through the great vessels. Furthermore, the impedance of any fixed-length electrical conductor varies inversely to the volume of the conductor, and so the electrical impedance of the aorta varies with the volume of blood contained within its lumen. Therefore, changes in the electrical impedance of the thorax result primarily from changes in the impedance of the aorta, and by extension, the volume of blood in the aorta 11. According to Ohm s law, if the electric current flow through a conductor is constant, any changes in voltage measured across the conductor are proportional to changes in the impedance of the conductor. The bioimpedance method exploits this relationship by passing a low magnitude, high frequency alternating current through the thorax and measuring the voltage across the thorax to derive an impedance curve 1. Stroke volume (SV) is calculated from the first derivative of the impedance curve. If impedance is proportional to volume, then the derivative of impedance is proportional to flow, and the maximum rate of change of the thoracic impedance curve represents the peak aortic outflow. A value proportional to SV is thus calculated as the product of the maximum derivative of the impedance curve and the ventricular ejection time 1. The basic operating principles of thoracic bioimpedance CO measurement are shown in figure 1. Equation 1 is used to compute absolute SV.

12 4 Figure 1. Operating principles of thoracic bioimpedance cardiac output measurement. A low magnitude, high frequency alternating current (I) is passed through the thorax and the voltage across the thorax (E) is measured to derive an impedance curve (Z). As the impedance of the aorta varies with the volume of blood within its lumen (V), any changes in thoracic impedance reflect changes in aortic blood volume from which aortic flow and stroke volume are derived. Equation 1: L dz SV ρ VET Z 0 dt max SV stroke volume; L distance between the leads; Z 0 base thoracic impedance; VET ventricular ejection time; ρ resistivity of blood; derivative of the impedance curve. dz dt max maximum of the first The maximum of the first derivative of the impedance curve varies proportionally to SV, although computation of the absolute SV depends on the resistivity of whole blood 13. Blood resistivity, however, fluctuates significantly with hematocrit 14 17, plasma electrolytes 18 1, and blood velocity 4. As the SV computed by the thoracic bioimpedance method is directly proportional to blood resistivity, any errors in blood resistivity are mirrored in the computed SV 13. Red blood cells are the major resistive component of whole blood, and therefore, hematocrit largely determines overall blood resistivity 1. Even moderate decreases in hematocrit from 40% to 30% are associated with a 0% reduction in blood resistivity 15. The decreased use of

13 5 homologous blood products due to potential adverse effects, costs, and blood shortages, coupled with evidence that moderate dilutional anemia is well tolerated in most patients 5, has led to a greater use of asanguineous fluids to maintain normovolemia and hemodynamic stability perioperatively 6. Consequently, large fluctuations in hematocrit are common during most major procedures, and assuming a constant value for blood resistivity may lead to gross and unpredictable errors in the computed SV. In general, the error in the calculated SV becomes greater as the hemodilution becomes more severe. This effect is especially unfortunate since lower hematocrit levels necessitate more accurate hemodynamic monitoring to ensure adequate oxygen delivery 5. Similarly, perturbations in plasma electrolyte concentrations alter the resistivity of blood and the SV derived from thoracic impedance measurement. Although smaller than the effect of hematocrit, blood resistivity may vary by 5-7% with the electrolyte imbalances commonly encountered in the critically ill 1. Of critical importance is the relationship between blood resistivity and blood velocity. Erythrocytes are not spherical, but biconcave, so that the orientation and alignment of erythrocytes within the blood has a considerable impact on blood resistivity. This orientation is affected by the viscous forces of the flowing blood, and therefore, the blood velocity. In stationary blood, erythrocytes are randomly oriented by the forces of Brownian motion. As blood velocity increases, erythrocytes tend to align along the direction of motion, decreasing the overall resistivity of whole blood 7. Although this effect reaches saturation as the erythrocytes become fully aligned, physiologically relevant motion of blood in the aorta can induce a 0% decrease in blood resistivity 4. As a constant value of resistivity obtained from stationary blood is used in the bioimpedance equation, these errors in assumed resistivity will be transmitted to the computed SV. More importantly, blood velocity varies with SV, aortic geometry, heart rate, and ventricular ejection time so that the relative error induced in the computed SV by this effect is highly variable Transesophageal Doppler In anesthetized, mechanically ventilated patients, CO can be monitored by a Doppler ultrasound transducer inserted into the esophagus and positioned to insonate the descending

14 6 aorta (DA) 8. In accordance with the Doppler principle 9, the transducer measures blood velocity in the DA based on the frequency difference between the ultrasound waves transmitted towards, and reflected from, the DA. The product of the blood velocity within, and cross-sectional area of, the DA are integrated over the cardiac ejection period to provide the portion of the SV passing through the DA. Older systems calculate the cross-sectional area of the DA from patient demographics 30, while newer developments incorporate an M-mode echo transducer and Doppler transducer into a single unit for real-time, continuous measurement of the DA cross-section 31. The volume passing through the DA must be corrected for flow to the cephalic territories to arrive at a total left ventricular SV. This correction is based on the average ratio of ascending to descending aortic flow in normal healthy individuals 8,31, or computed from a one-time transthoracic ultrasound measurement of ascending aortic blood flow 30. Figure illustrates the use of a transesophageal Doppler probe to measure CO. Equation is used to compute SV. Figure. Measurement of cardiac output by transesophageal Doppler ultrasonography. A Doppler transducer is inserted into the esophagus to measure blood velocity in the descending aorta (V). The product of blood velocity and crosssectional area of the descending aorta (A) is integrated over the ventricular ejection time (VET) and corrected for blood flow to the cephalic territories (K) to arrive at stroke volume.

15 7 Equation : VET SV K Δf c A dt f cosθ 0 SV stroke volume; A cross-sectional area of the descending aorta; VET ventricular ejection time; c velocity of ultrasound waves in body tissue; Δf frequency difference between the transmitted and reflected ultrasound waves; f 0 frequency of the transmitted ultrasound signal; θ angle between the incident ultrasound wave and the descending aorta; K correction factor for blood flow to the cephalic regions. Whether a normal value is assumed, or a correction factor derived by means of a second transcutaneous Doppler probe, the partition fraction of the SV between the cephalic and caudal regions is only obtained once in each patient and assumed to remain constant 8,3. This assumption, however, is often erroneous as the distribution of the CO between the DA and the arch vessels may vary with aortic manipulations, hemorrhage, and changes in regional vascular resistance. Aortic surgery requiring cross-clamping of the aorta is associated with significant changes in hemodynamics 33 thereby demanding accurate monitoring for optimal intraoperative patient management. However, during clamping, where accurate monitoring is most critical, the distribution of blood flow between the cephalic and caudal regions is substantially altered from baseline conditions so that the CO extrapolated from a transesophageal Doppler probe becomes unreliable. For example, infrarenal cross-clamping of the DA during aortic aneurysm repair causes the DA blood flow to decrease from 70% to 55% of the total CO 34. Application of the pre-clamp distribution fraction while the cross-clamp is engaged results in a 3% underestimation of the CO by the transesophageal Doppler method. More generally, although human data is limited, animal studies demonstrate that distribution of the CO to the DA does not remain constant following hemorrhage. Immediately following acute hemorrhage resulting in a 50% reduction in the overall CO, flow in the DA is only reduced by 0%. Therefore, DA flow composes a significantly larger percentage of the CO in the early phases of hemorrhage compared to baseline conditions. Paradoxically, if the hemorrhagic hypovolemia is allowed to persist untreated, DA blood flow remains depressed

16 8 by 0% from baseline values even after reflex mechanisms have restored arterial blood pressure and CO to normal 35. Conversely, flow in the DA increases from 66% to 75% of the CO following moderate hemorrhage and subsequent transfusion 36. In this way, the CO reported by the transesophageal Doppler method is higher than the actual CO in the early phases of hemorrhage. Where a transfusion is performed to replace the lost blood, this positive error persists. On the other hand, if homeostatic mechanisms compensate sufficiently for the hemorrhage such that volume replacement is not indicated, transesophageal Doppler derived CO underestimates the actual CO. Overall, the association between the values reported by a transesophageal Doppler system and the actual CO is highly variable and unreliable during acute hemorrhage 37, thereby limiting is usefulness during many major surgical interventions and trauma. Lastly, changes in local metabolic demand or any vasoactive stimulus which does not equally affect the resistance of all vascular beds would necessarily alter this flow distribution ratio. For example, systemic perturbations as subtle as a modest increase in the carbon-dioxide (CO ) tension in the arterial blood (PaCO ) may increase CO by 10%, but, because the majority of this increased flow is to the supra-aortic vessels, it is undetectable by a transesophageal Doppler probe 38. Conversely, lower body vasodilatation provoked by lumbar epidural anesthesia causes a similar increase in CO, but is overestimated by transesophageal Doppler as the additional flow is disproportionately distributed to the caudal territories 39. Even if the assumed distribution of the CO between the upper and lower body is correct, the Doppler measurement of blood velocity varies with the position of the probe relative to the DA. More specifically, the velocity calculation is inversely proportional to the cosine of the angle between the transmitted ultrasound wave and the DA flow. It is assumed that the esophagus and the DA are parallel in the thorax, so that the angle at which the DA is insonated is equal to the angle at which the Doppler transducer is mounted on the insertion probe usually 45º or 60º depending on the system 40. The velocity calculation, however, is highly sensitive to errors in this angle. A 10º error in the angle of insonance will result in an 18% error in the calculated blood velocity in systems employing a 45º mounting angle of the Doppler transducer and a 30% error in systems where a 60º angle is used 41. Unfortunately, frequent readjustments of the longitudinal position and axial rotation of the probe are required

17 9 to maintain signal quality in response to intraoperative surgical maneuvers, patient movement, and alterations in mechanical ventilation, which may, in turn, affect the angle of the Doppler beam 8,4 47. Surgical manipulations that affect the anatomical relationship between the esophagus and the DA may further alter the angle at which the Doppler beam intersects the DA blood flow Arterial pulse contour analysis Passage of the SV through the arterial circulation generates a pressure wave in the arterial vasculature. This waveform is characteristic of both the flow pattern and the mechanical properties of the arterial system most notably aortic input impedance, arterial compliance, and systemic vascular resistance. Continuous arterial pressure recording is accomplished by transduction of an indwelling intra-arterial catheter, or sensed non-invasively by the pulsatile unloading of the finger arterial walls using an inflatable finger cuff with a built-in photoelectric plethysmograph 49. To determine SV from the arterial pressure recording, a model of the mechanical properties of the arterial vasculature is used to transform the measured pressure to flow in the ascending aorta 41. In practice, the model parameters are estimated from patient demographics, or are computed by calibrating the system against an invasive reference technique 9. Although the models 50 5 and analytical techniques 53 utilized vary amongst systems, this principle of deriving aortic flow from arterial pressure forms the basis for all devices and is illustrated in figure 3. Figure 3. Derivation of aortic flow from arterial pressure. The stroke volume passes through the arterial circulation generating a pressure wave in the arterial

18 10 vasculature. A model of the arterial circulation is used to predict the aortic flow from which the measured pressure was generated. Most models simulate the systemic vascular resistance (R), arterial compliance (C), and characteristic aortic impedance (Z). Utilization of arterial pulse contour analysis to monitor CO is limited to the situations in which the model of the arterial circulation faithfully represents the current vascular status of the patient. Calibration of the model parameters with an invasive measure of CO may temporarily align the model with the mechanics of the patient s vasculature so that reliable readings are obtained as long as conditions remain stable. However, the majority of clinical situations requiring hemodynamic monitoring present with severe circulatory instability. In that case, any deviations of the mechanical properties of the arterial vasculature from the model introduce a variable and unknown degree of error into the CO measurements. Of particular concern is the effect of systemic vascular resistance on pulse contour analysis, since this variable may fluctuate considerably in any patient. Low systemic vascular resistance is associated with a substantial underestimation of the CO by arterial pulse contour analysis, while CO is overestimated where systemic vascular resistance is high This variability limits the ability of the pulse contour method to track CO changes in critically ill patients where the administration of vasopressive or vasodilatory agents is required to manage the circulation 54, Reflexive changes in vascular tone may similarly affect the reliability of this method. During acute hemorrhage, the mechanics of the arterial vasculature diverge from the model to the extent that increases in CO are reported by arterial pulse contour analysis following rapid blood loss, whereas the computed CO decreases in response to volume resuscitation 61,6. The effects of both reflexive and induced changes in the arterial vasculature on arterial pulse contour CO are well demonstrated during coronary artery surgery. In this situation, blood loss during median sternotomy causes a decrease in CO, while autoregulatory increases in vascular tone induce opposite changes in the CO computed by pulse contour analysis. Similarly, administration of phenylephrine during coronary artery surgery increases afterload, thereby reducing CO; the changes in vascular tone, however, cause the computed CO to increase 63.

19 11 1. Respiratory methods of measuring cardiac output Development of respiratory-based methods of measuring CO began in 1870 when Adolph Fick described the relationship between the ventilation, blood gas contents, and CO at steadystate 64. Fick s original development was based on the mass conservation of O across the pulmonary circulation. Described qualitatively, the total O outflow from the pulmonary circulation less the pulmonary inflow of O represents the net circulatory uptake of O from the alveolar space. This is computed quantitatively as the product of the CO and the difference between the O content of the arterialized blood leaving the pulmonary circulation (CaO ) and the O content of the mixed-venous blood entering the pulmonary circulation ( C vo ). Fick elucidated that, if the balance of O in the alveolar space is not changing, then the rate at which O enters the alveolar space via the ventilation (VO ) must be equal to the extraction of O from the alveolar space by the pulmonary capillary blood 65. Therefore, CO can be computed if VO and the arterio-venous O content difference can be determined simultaneously. The Fick principle for O is formulated mathematically in equation 3 and illustrated schematically in figure 4. Equation 3: VO CO (CvO CaO ) Figure 4. The Fick mass balance relationship for oxygen. If the balance of oxygen in the lung is steady, the net ventilatory consumption of oxygen (VO ) is equal to the uptake of oxygen from the pulmonary circulation. The net circulatory uptake of oxygen from the lung is expressed as the product of the cardiac output (CO)

20 1 and the difference between the oxygen content of the incoming mixed-venous blood ( C vo ) and the outgoing arterial blood (CaO ) Direct Fick measurement of cardiac output Clinical application of the Fick principle for the measurement of CO began midway through the 0 th century 66. Each measurement involves the analysis of the volume and composition of inspired and expired gas to determine VO. During measurement of VO, an arterial blood sample is drawn from an indwelling arterial catheter and analyzed to determine CaO ; right heart catheterization is employed to sample mixed-venous blood from the right ventricle or 67 pulmonary artery which is analyzed for CvO. Owing to the direct sampling of arterial and mixed-venous blood, this technique has become known as the direct Fick measurement of CO. Unlike non-respiratory methods, the direct Fick measure of CO does not require any assumed values for variable parameters. Computation of CO depends only on three inputs VO, CaO, and C vo all of which are directly measured at the time of each CO determination. For this reason, the direct Fick method has proven to be the most accurate measure of CO available However, despite its accuracy, the highly invasive nature of the direct Fick method precludes its general clinical use 70. Of particular concern are the numerous risks associated with the cardiac catheterization necessary to acquire mixed-venous blood samples. The right heart catheter is inserted into a central vein, advanced through the central circulation to the sinus venarum, and passed through the right cardiac chambers until the distal tip resides in the pulmonary artery. Accessing a central vein is accomplished by transcutaneous venous puncture with a large bore needle, followed by passage of a guide wire, vessel dilator, and finally a catheter introducer into the vessel lumen 71. Mechanical complications occur in up to 0% of central venous access attempts the most common being injury to contiguous arteries and pneumothorax 7. Unintentional needle puncture of an artery, if recognized immediately, is usually resolved without any serious sequelae by removal

21 13 of the needle and the application of external pressure 73. On the other hand, if arterial puncture is not diagnosed, and the procedure progresses to insertion of a dilating device or introducer, prompt surgical intervention is required to prevent acute cervical hemorrhage 74. Where access to the central venous pool is attempted via the subclavian or internal jugular veins, there exists a risk of puncturing the plural space and a consequent pneumothorax. If the patient is mechanically ventilated, the pneumothorax may evolve to tension conditions necessitating immediate tube thoracostomy to prevent cardio-respiratory collapse 75. In addition to structural trauma, central venipuncture creates a potential channel between the intravascular space and atmospheric air. If the channel is left open, even briefly, negative intrathoracic pressure generated during spontaneous inspiration can entrain air into the venous system. Collection of air in the right heart can obstruct the right ventricular outflow tract, causing systemic hypoperfusion and eventual cardiovascular collapse 76. Alternatively, the air embolus is passed to the systemic arterial circulation via a cardiac septal defect 7 or intrapulmonary shunt 76 with the possibility of equally morbid consequences 77. As the catheter is advanced through the right ventricle, mechanical irritation of the endocardium by the catheter tip frequently induces cardiac arrhythmias. These arrhythmias normally resolve after the catheter emerges from the ventricle, although sustained ventricular tachycardia and fatal ventricular fibrillation have been reported 78. As the catheter must be long and flexible to allow passage through the heart, knotting of the catheter within the right ventricle can occur, potentially damaging cardiac structures, and must be disentangled with an endovascular approach or extracted by open cardiotomy 79. Once in place, frequent contact of the catheter with the intravascular and intracardiac walls erodes the endothelium and endocardium along the catheter path. Autopsy reveals thrombotic or hemorrhagic lesions within the central veins, right heart, and pulmonary artery in more than 90% of patients who expire with right heart catheters in place 80. Catheter-related thrombi occasionally embolize to the pulmonary arteries, although pulmonary ischemic insult secondary to distal migration of the catheter is more common 81. Pulmonary artery rupture is the most feared complication of an indwelling right heart catheter as it is associated with an overall mortality rate of 70% 8.

22 14 Lastly, in addition to the abovementioned complications, the clinician must manage the local infections of the insertion site, catheter-related septicemia, and right sided infectious endocarditis that frequently develop in catheterized patients 7,83, Indirect Fick measurement of cardiac output Exposure to the hazards of right heart catheterization cannot be justified in many patient populations, and could be avoided in all patients if an equivalent, but less invasive monitoring scheme existed. Therefore, there has been a vigorous research effort to develop a method of measuring CO that utilizes, and maintains the accuracy of, the Fick principle, while averting patient exposure to the risk profile of cardiac catheterization. Non-invasive Fick methods of measuring CO, also referred to as indirect Fick methods, utilize respiratory measurements and maneuvers to estimate the blood gas contents in place of the arterial and cardiac catheterization necessary in the direct Fick approach. Non-invasive determinations of CO based on the Fick principle use CO as the indicator gas instead of O. Like O, a steady-state of CO in the lung implies equality between the net ventilatory output of CO (VCO ) and the flux of CO into the lung from the pulmonary circulation. Unlike O, the relationship between CO tension and CO content in whole blood is virtually linear 85, allowing the flux of CO into the lung to be formulated in terms of the CO, the CO tension in the incoming mixed-venous blood ( P vco ), PaCO, and the slope of the CO dissociation curve (S) which relates CO tension to CO content in whole blood 86. The mathematical representation of the Fick mass balance for CO is shown in equation 4. Equation 4: VCO CO S (PvCO PaCO ) As CO equilibrates rapidly between the alveolar space and the pulmonary circulation, it is assumed that the end-tidal partial pressure of CO ( PET CO ) and PaCO are equal. The typical formulation of the Fick equation for non-invasive determination of CO using CO is outlined in equation 5. The mass balance is illustrated in figure 5.

23 15 Equation 5: VCO CO S (PvCO PETCO ) Figure 5. The Fick mass balance relationship for carbon-dioxide. If the balance of carbon-dioxide in the lung is steady, the net ventilatory output of carbon-dioxide (VCO ) is equal to the flux of carbon-dioxide into the lung from the pulmonary circulation. The relationship between carbon-dioxide tension and carbon-dioxide content in whole blood is highly linear, allowing the flux of carbon-dioxide into the lung to be formulated in terms of the cardiac output (CO), the carbon-dioxide tension in the incoming mixed-venous blood ( P vco ), the carbon-dioxide tension in the outgoing arterialized blood (PaCO ), and the slope of the carbon-dioxide dissociation curve (S). As carbon-dioxide equilibrates rapidly between the alveolar space and the pulmonary circulation, the end-tidal partial pressure of carbondioxide ( PET CO ) may be substituted for PaCO As VCO, PETCO, and S 86 are readily calculated or accurately measured non-invasively, a non-invasive determination of P vco yields a non-invasive determination of CO. Many methods have been developed to non-invasively determine P vco, and hence, CO. These methods attempt to derive P vco by observing the change in PET CO resulting from a change in ventilation Yet, despite being non-invasive, various physiological constraints limit their accuracy to an extent which precludes their use in clinical practice 9 94.

24 Measurement of cardiac output from the exponential rise in carbon-dioxide during rebreathing The first practical, CO -based, indirect Fick method of measuring CO was proposed by Defares 89. In this method, VCO and PET CO are measured during a stable baseline state. Non-invasive determination of P vco is accomplished immediately following baseline measurements by using the lung as an aerotonometer. The subject rebreathes a gas mixture which is initially devoid of CO, and since rebreathing prevents any CO elimination from the lungs, PETCO equilibrates to P vco. The Fick equation requires simultaneous determinations of VCO, PET CO, and P vco. Rebreathing, however, causes an increase in PaCO concomitant with the increase in PET CO, and this increase will traverse the circulation and perturb P vco from the baseline state. Therefore, the determination of P vco must be accomplished within a recirculation time from the start of rebreathing. However, the time required for PET CO to equilibrate with P vco is approximately -3 times longer than the recirculation time. For example, the time constant for equilibration is approximately 11 seconds for an average adult male at rest (Appendix A). As three to four time constants are generally required for equilibration, 33 to 44 seconds must elapse before PET CO accurately reflects P vco. On the other hand, a gas introduced into the pulmonary circulation by inhalation reappears in the pulmonary artery within 1-0 seconds 95,96. Defares proposed that, prior to recirculation, PET CO exponentially equilibrates with P vco, and therefore, P vco could be determined from the asymptote of an exponential function fitted to the first few breaths of the rebreathing maneuver. Figure 6 shows the expected PET CO trace during CO determination. As the period between the start of rebreathing and recirculation is short, only a small number of PET CO values are available for the exponential fit. Consequently, determination of P vco from an exponential fit is exquisitely sensitive to errors in the measurement of PET CO. To

25 17 demonstrate this aspect, normal values of 40 mmhg for PaCO, 46 mmhg for P vco, and the completion of 5 breaths before recirculation are assumed. In this case, a -0.5 mmhg error in the measurement of PET CO during the second breath of rebreathing results in overestimation of P vco by 4.4 mmhg and underestimation of the CO by 4% (figure 7). Figure 6. Determination of cardiac output by extrapolation of a carbon-dioxide rebreathing curve. As the subject rebreathes, the end-tidal partial pressure of carbon-dioxide ( PET CO ) exponentially equilibrates with the mixed-venous partial pressure of carbon-dioxide ( P vco ). As recirculation occurs before equilibration, P vco during the baseline state is determined from the asymptote of an exponential function fitted to the first breaths of the rebreathing maneuver (long dashes). Figure 7. Error sensitivity of cardiac output measurement by extrapolation. If there are no errors in the determination of the end-tidal partial pressures of carbondioxide ( PET CO circles), the asymptote of an exponential curve fit (long dashes)

26 18 accurately represents the mixed-venous carbon-dioxide tension ( P vco ) prior to rebreathing. A very small error in any of the PET CO measurements (diamonds) causes gross errors between the asymptote of the curve fit (solid line) and P vco. Similarly, errors in the determination of PaCO can significantly distort the measurements of CO. While it is assumed that PET CO is a non-invasive surrogate for PaCO during the baseline state, differences between PET CO and PaCO may be introduced by ventilation/perfusion inequalities. These gradients arise from the dilution of equilibrated gas from well-perfused lung regions with inspired gas from under-perfused regions of aleveoli, and result in an underestimation of PaCO in the presence of high ventilation/perfusion regions. The effect of these errors on CO determination depends on the veno-arterial difference in CO tension. Assuming a normal difference of 6 mmhg, CO will be underestimated by 14% for every 1 mmhg difference between PET CO and PaCO. The effect of these errors is magnified in high CO states where the veno-arterial difference in CO tension is reduced Measurement of cardiac output from the equilibration of carbon-dioxide during rebreathing A refinement of the extrapolation method for determination of P vco, known as the equilibration technique, was proposed by Collier 90. This method is very similar to the extrapolation method except that rebreathing is commenced from a gas mixture primed with a CO bolus. The initial bolus of CO is intended to, upon the first inspiration, mix with the functional residual capacity (FRC) of the lung and result in a PET CO as close as possible to P vco. With the initial PET CO during rebreathing closer to P vco, the equilibration time is reduced; if equilibration can be achieved before recirculation, P vco can be determined directly from PET CO without the need for extrapolation. Full equilibration is characterized by the elimination of gas exchange between the lungs and circulation, and can be identified as plateau in the PET CO trace during rebreathing. The equilibration technique is illustrated in figure 8.

27 19 Unlike the extrapolation method, the equilibration method does not require error-prone curve fitting to identify P vco, although it is similarly sensitive to end-tidal to arterial CO gradients. The difficulty in implementing this method is the selection of an appropriate bolus of CO with which to prime the rebreathing mixture. As P vco is unknown, the bolus required to increase PET CO precisely to P vco cannot be calculated. Furthermore, the required bolus varies with the rebreathed volume, the FRC, the tidal volume, and the CO. With these restrictions, a plateau in the rebreathing curve can only be obtained by tedious trial-and-error of various bolus sizes. As a further complication, where the bolus is too large, washout of CO from the lungs can be exactly offset by increases in PvCO from recirculation, leading to false plateaus at artificially elevated values of PET CO. Lastly, the plateau is difficult to detect algorithmically, making the equilibration method particularly difficult to automate. Figure 8. Determination of cardiac output by equilibration of carbon-dioxide. The subject rebreathes a gas mixture primed with a bolus of carbon-dioxide. The initial carbon-dioxide bolus is chosen so that, upon the first inspiration, the end-tidal partial pressure of carbon-dioxide ( PET CO ) is as close as possible to the mixedvenous partial pressure of carbon-dioxide ( P vco ). A plateau in the PET CO trace during rebreathing indicates full equilibration of CO P vco. PET with

28 Measurement of cardiac output by the Differential Fick method Current state-of-the-art respiratory-based CO monitors are based on partial CO rebreathing 86. In this method, VCO and PET CO are measured during a stable baseline state of ventilation, and again during a subsequent test state in which the alveolar ventilation (V A) is reduced from baseline conditions. A step-wise decrease in V A reduces VCO so that PET CO and PaCO exponentially increase towards a new steady-state value at which VCO will once again equal the flux of CO into the lung from the pulmonary circulation. Like other indirect Fick techniques, this method depends on equilibration occurring before the changes in PaCO traverse the circulation and perturb P vco. In this case, a Fick mass balance equation may be formulated for each of the two states. A first equation describes the equality between VCO B in the baseline state ( VCO ) and the flux of CO into the lung from the pulmonary circulation formulated in terms of the CO, the baseline CO PET ( B PETCO ), and P vco (equation 6A). A similar equation expresses the same relationship between VCO at the end of the test state ( T VCO ), the CO, baseline state (equation 6B). T PET CO at the end of the test state ( PETCO ), and the same P vco as the B B Equation 6A: VCO CO S (PvCO PETCO ) Equation 6B: T T VCO CO S (PvCO PETCO ) These two Fick equations are solved simultaneously for CO to reveal the Differential Fick equation (equation 7). Equation 7: CO S (P VCO ET B T CO VCO P ET T CO B ) The Differential Fick method of CO measurement is advantageous as it depends only on the differences between two measurements, and not on any single absolute value. This lessens the demands on the accuracy and calibration of the measurement equipment. Similarly, any

29 1 constant gradient between PET CO and PaCO does not enter the equation as it effects both states equally. On the other hand, V A in the baseline and test states must be fixed, so execution is only possible in well sedated, mechanically ventilated subjects 97. Reduction of V A is normally accomplished by manipulating the ventilator settings, or more recently, by interposing a serial dead space in the breathing circuit 98. In practice a 3 mmhg increase in PET CO is typical 98, as ventilation is only partially reduced to avoid rendering the alveoli hypoxic. With these methods, an error of 1 mmhg in either of the PET CO measurements can result in a 5-50% error in the measured CO. Most critically, as with the extrapolation method, equilibration of PET CO following the reduction in ventilation does not occur before recirculation. As such, short rebreathing periods do not allow for complete equilibration of PET CO, while measurements made with longer rebreathing durations violate the assumption of a constant P vco.

30 A novel iterative method for non-invasive measurement of cardiac output The novel ICO method is a respiratory-based, iterative method for non-invasive CO determination which obviates the need for both error-prone extrapolation and tedious trialand-error, while providing significantly reduced sensitivity to errors in measured parameters..1 Rationale of the iterative cardiac output measurement method Following a baseline steady-state of ventilation, inhalation of CO -rich gas for a single breath will result in an acute increase in PET CO on the exhalation of that breath. The increased T0 PET CO of this first test breath ( P ETCO ) can be precisely maintained for subsequent breaths if the correct inspired partial pressure of CO ( P ICO ) is added to those breaths. Computation of P ICO required to maintain PET CO at the level of P ETCO ( P T0 T ICO ) during the test is accomplished by expansion and rearrangement of the differential Fick equation. More specifically, V A and the difference between B VCO in the differential Fick equation may be expanded as the product of B PETCO and PICO in the baseline state ( P ICO B ) (equation 8A). Similarly, T VCO may be expanded as the product of V A and the difference between ETCO T P and PICO in the test state ( P T ICO ) (equation 8B). Partial pressures are converted to fractional concentrations by division over the barometric pressure corrected for the presence of water vapour in the gas (P B). Equation 8A: Equation 8B: VCO VCO B B B VA (PETCO PICO ) PB T T T VA (PETCO PICO ) PB As the actual CO is unknown, an estimate of the CO (CO E ) is substituted in its place. The T modified Differential Fick equation (equation 9) can be solved for P ICO (equation 10).

31 3 Equation 9: CO E V A (P ET CO B S P B PICO ) B P ET V CO A T (P P ET ET CO CO T B T PICO ) Equation 10: T PICO CO E S P B (P ET CO T P ET B CO) V V A A B (PICO P ET CO T P ET CO B ) T Herein, the only uncertain parameter in the computation of P ICO is CO E ; all other parameters are easily measured. Consequently, if CO E is correct, P ETCO will remain steady until recirculation occurs; if the estimate is incorrect, P ETCO will exponentially drift towards equilibrium with the delivered P ICO and the actual CO. Provided that the test maneuver is T terminated prior to recirculation, the baseline state and the end of the test state represent two states with the same PvCO but different VCO. As such, these two states provide inputs to the Differential Fick equation to yield a measure of the CO. This is illustrated schematically in figure 9. Figure 9. Three possible results of the iterative cardiac output (CO) maneuver. A bolus of inspiratory carbon-dioxide acutely increases the end-tidal partial pressure of carbon-dioxide ( PET CO ) from a baseline level ( PETCO B ). Following the bolus, an estimate of the CO (CO E ) is used to compute the inspired partial pressure of carbon-dioxide ( P ICO ) required to maintain PET CO stable at the elevated level

32 4 0 ( T T P ETCO ) for a short test period. If inspiration of the computed P ICO ( PICO ) results in a stable PET CO (circles) during the test period, CO E is equal to the actual CO; a drift upwards (triangles) or downwards (inverted triangles) in PET CO indicates over-estimation or under-estimation of the CO, respectively. As the test maneuver is terminated prior to recirculation, PET CO of the last breath of the test ( PETCO T ), together with the baseline measurements, may be used in the Differential Fick equation to refine CO E. However, the Differential Fick equation assumes two steady-states, while equilibration during the test state may not be complete if it is terminated prior to recirculation. Consequently, the accuracy of the newly computed value of CO depends on the extent to which PET CO during the test maneuver reaches equilibrium. Nevertheless, the value computed by this maneuver will necessarily lie between the original CO E used to compute PICO T and the actual CO. In repeatedly executing this procedure, each time using the refined value of the CO from the previous iteration as the estimate of CO, the algorithm converges to the actual CO. Figure 10 demonstrates the cyclical nature of the algorithm as CO E is continually refined and converges while the actual CO fluctuates. Figure 11 is a time-linear representation of three iterations of the algorithm as a CO E of 3 L/min is refined and converges to an actual CO of 5 L/min.

33 5 Figure 10. The cyclical nature of the iterative cardiac output (CO) algorithm. The test maneuver is executed continuously at regular intervals to eliminate any error in the estimated CO (CO E ). As CO E converges to the actual CO, the delivered partial pressure of inspired carbon-dioxide ( P ICO ) varies such that the drift in the partial pressure of end-tidal carbon-dioxide ( PET CO ) during the test is eliminated. Figure 11. A sample of three iterations of the iterative cardiac output algorithm. An estimate of the cardiac output (CO E ) of 3 L/min converges upon the actual cardiac output of 5 L/min. As CO E converges to the actual cardiac output, the delivered partial pressure of inspired carbon-dioxide ( P ICO ) varies such that the

34 6 drift in the partial pressure of end-tidal carbon-dioxide ( PET CO ) during the test is eliminated. The largest refinement in CO E occurs in the first iteration.. Implementation of the iterative cardiac output measurement method The ICO method demands accurate determination of V A and PET CO, and the precise control of P ICO...1 Imposing the alveolar ventilation The V A is imposed on the subject under test by the method of sequential gas delivery (SGD) described in detail elsewhere 99. With reference to figure 1, a typical SGD circuit is constructed from two reservoirs connected to the airway through an inspiratory, expiratory, and crossover check valve. The inspiratory and expiratory valves have a negligible opening pressure, while the cross-over valve is designed to open only under negative pressure. A gas blender delivers a mixture of precisely controllable composition to a first inspiratory reservoir at a set flow rate; the second reservoir collects expired gas. In the first part of any breath, gas is inspired from the inspiratory reservoir containing the controlled gas. It is arranged that the flow of controlled gas into the reservoir is less than the minute ventilation (V E) by an amount slightly greater than the anatomical dead space (V D). Therefore, in any breath, the inspiratory reservoir will be completely depleted, upon which the cross-over valve opens and the remainder of the inspiratory gas is provided from previously expired gas in the expiratory reservoir. The expiratory valve directs the expired gas into the expiratory reservoir for inspiration on the next breath.

35 7 Figure 1. Operation of a sequential gas delivery circuit. A gas blender fills an inspiratory reservoir with a controllable mixture at a set flow rate. The first part of inspiration is drawn from the controlled gas mixture in the inspiratory reservoir. Upon emptying the inspiratory reservoir, the remainder of inspiration is drawn from the expiratory reservoir containing previously expired gas. When utilizing SGD, rebreathed gas fills V D ensuring that all of the controlled gas mixture enters the alveoli and contributes to gas exchange. Although some rebreathed gas may also enter the alveoli, previously expired gas has already equilibrated with the pulmonary blood. Therefore, any volume of previously expired gas which is re-inspired into the alveoli does not contribute to gas exchange. For example, doubling the V E will increase the inspiration of previously exhaled gas only, but will not change the gas available for gas exchange. In this way, the effective V A is determined only by the flow of the controlled gas mixture, and, as demonstrated in figure 13, is independent of the V E. The efficacy of the SGD method for

36 8 controlling V A has been proven in previous studies demonstrating a constant PET CO despite marked changes in V E 100,101. Figure 13. Using sequential gas delivery to control the alveolar ventilation (V A). Inspiration of previously expired gas after the controlled gas mixture ensures that all of the controlled gas mixture enters the alveoli. Increases in minute ventilation (V E) only increase the inspired volume of previously expired gas. As previously expired gas does not participate in gas exchange, the effective V A is determined by the flow of controlled gas mixture, and is independent of the total V E... Setting the alveolar ventilation In utilizing the SGD technique, the V A is limited to the flow of controlled gas mixture, independent of the V E. The flow of the controlled gas mixture must be set low enough to ensure that all of the controlled gas mixture enters the alveoli; it should be high enough as to not significantly impair CO elimination. To accomplish this, in each iteration, the algorithm measures the average V E and respiratory rate (RR). The minute volume of gas which enters 10 V D is computed from RR and a nomogram computed value of V D. The total gas that enters the alveoli is computed by subtracting the minute volume of gas which enters the V D from V E, and the flow of controlled gas mixture is set to 90% of this value (equation 11). Equation 11: V 0.9 (V -RR V ) A E D

37 9..3 Apparatus The ICO method utilizes hardware which simulates the function of an SGD breathing circuit instead of using actual reservoirs. A flow sensor (AWM70P1, Honeywell International) interposed between the inspiratory inlet of the ventilator wye-piece and the inspiratory limb of the ventilator circuit is used to measure inspiratory flows delivered by the ventilator. A flow controller consisting of a CO flow sensor (4116, TSI) and proportional flow control valve (EVP, Clippard) delivers a synchronized flow of CO into the inspiratory limb to provide a desired inspiratory concentration of CO. A microprocessor is connected to the flow controller and programmed to precisely simulate the concentrations and flow pattern of gases provided by an SGD breathing circuit for a given composition and flow rate of controlled gas mixture. A rapid CO analyzer (IRMA, Masimo) is attached to the expiratory outlet of the wye-piece to monitor end-tidal gas values. More specifically, the system tracks the volume that would be in an inspiratory reservoir of controlled gas mixture filled at a given rate and depleted by the subject s inspiration. This virtual reservoir is continually incremented by the desired flow rate of controlled gas mixture, and decremented according the inspiratory flow measured by the flow sensors. During inspiration, while the virtual reservoir is not empty, the CO flow controller blends CO into the inspiratory stream to achieve the inspired concentration of CO in the controlled gas mixture. When the virtual reservoir is empty, the CO flow controller blends CO to achieve a final inspired concentration equal to the P ETCO of the previous breath. A laptop computer running a software implementation of the ICO algorithm computes and commands the required flows and compositions of controlled gas mixture from the SGD system. Figure 14 illustrates the apparatus. Detailed descriptions and schematics of each component can be found in Appendix B.

38 30 Figure 14. Apparatus used to implement the iterative cardiac output method. A flow sensor is interposed into the inspiratory limb of the ventilator circuit. A carbon-dioxide (CO ) flow controller delivers a synchronized flow of CO into the inspiratory limb to simulate the concentrations and flow patterns of a sequential gas delivery circuit for a given composition and flow rate of controlled gas mixture. A rapid CO analyzer is attached to the expiratory outlet of the wye-piece to monitor end-tidal gas values. A laptop computer running a custom software implementation of the algorithm is connected to the sequential gas delivery system...4 Iteratively measuring cardiac output During an 80 second baseline period, the controlled gas mixture is free of CO ( PICO B 0 ). The PET CO of the last four breaths of the baseline state are averaged to compute P ETCO. The test state commences with delivery of a single breath bolus of CO -rich gas, which, upon inspiration, increases the P ETCO from P ETCO to B P ETCO T 0 B. Equation 10 is then used with the current CO E to compute the PICO T in the controlled gas mixture which would keep P ETCO stable at P ETCO T 0. Delivery of the controlled gas mixture containing the computed PICO T is then maintained for 10 seconds. The last breath of the test phase provides

39 31 PETCO T, which, together with the baseline parameters, may be used in the Differential Fick equation to refine CO E according to equation 9. The initial CO E is obtained from a nomogram based on patient demographics 103. Similarly, the concentration of CO in the bolus breath is computed to target a 10 mmhg increase in P ETCO using an estimate of the subject s FRC obtained from a nomogram 104.

40 3 3 Validation of the iterative cardiac output monitor 3.1 Methods The institutional animal care committee approved the study and all procedures were conducted according to the guidelines of the Canadian Council on Animal Care. Experiments were carried out in Yorkshire pigs ranging in weight from 7-34 kg (mean 30 kg). Premedication was performed with intramuscular administration of Atropine (0.04 mg/kg), Ketamine (10 mg/kg), and Acepromazine (0.05 mg/kg). Upon arrival in the surgical suite, monitoring of electrocardiogram, non-invasive arterial blood pressure, heart rate, and pulse oximetry was immediately commenced with an integrated monitor (AS/3, Datex-Ohmeda). Anesthesia was induced with Isoflurane (4-5%) using a standard cone large animal veterinary mask and maintained after establishment of the airway with Isoflurane (1.5-.5%). Dissection to the trachea, internal carotid artery, and internal jugular veins was performed by cut-down through a median incision in the neck. An airway was established by tracheostomy, and mechanical ventilation was commenced through a circuit outfitted with the ICO hardware. Tidal volumes of 5 ml/kg were delivered at a rate of 15 breaths/min. Ventilation and anesthetic agents were delivered by an anesthetic machine/ventilator (Narcomed C Anesthesia Delivery System, North American Drager). The carotid artery was cannulated with a 0 gauge, 4.5 inch catheter (REF FA-04018, Arrow International). A 6 Fr percutaneous introducer (Introflex CI500F6, Edwards Life Sciences) was inserted into the internal jugular vein using Seldinger s technique 105. A pediatric thermodilution PAC (135F5, Edwards Life Sciences) was inserted through the introducer and advanced into the pulmonary artery. Arterial blood pressure, central venous pressure, and pulmonary artery pressures were monitored and displayed continuously using a triple pressure transducer kit (Px3x37, Edwards Life Sciences). Continuous observation of the typical pulmonary artery and central venous pressure waveforms confirmed the correct location of the PAC throughout the entire experiment.

41 33 Once inserted, the PAC was connected to a CO computer (Vigelance, Edwards Life Sciences), which also displayed blood temperature from the thermistor integrated into the PAC. A heated blanket (Baer Hagger, 3M company) was used to keep blood temperature in the range of C. Thermodilution was performed by bolus injection of 5 ml of iced (0-3 C) normal saline into the right atrium port of the PAC. Fluid infusions were stopped before measurement, and measurements were not performed during the application of electrocautery or during rapid fluctuations in blood temperature. Measurements were not synchronized to the ventilatory cycle. Each TDCO value was determined from four sequential injections, by discarding the first measurement and averaging the last three. Only TDCO measurements with a coefficient of variation less than 0% between individual injections were included in the final analysis. Measurement of CO by ICO was started immediately following initiation of mechanical ventilation. Measurements were obtained every 90 seconds (80 second baseline, 10 second test). As infusion of sodium bicarbonate causes a large release of CO which interferes with ICO determination, measurements of ICO obtained within 5 minutes of sodium bicarbonate administration were excluded. The average of the ICO determination immediately before and after each TDCO determination was used in the comparison with TDCO. The surgical technique of OLT is described in detail elsewhere 106. During the anhepatic phase of surgery, complete cross-clamp of the inferior vena cava, portal vein, and hepatic artery was applied. A custom made passive shunt was used for venting the portal vein and inferior vena cava flows into the superior vena cava. The shunt consisted of an inflow cannula placed into the splenic vein and an outflow cannula inserted into the internal jugular vein contra lateral to the insertion side of the PAC. A 50 cm long PVC tube connected the inflow and outflow cannulas. Blood was impelled through the veno-venous bypass by the positive pressure gradient occurring below the venous cross-clamps. Administration of fluids, vaso-constrictors, and positive inotropic agents was left to the discretion of the anesthesiologist in charge of the case.

42 34 3. Results A total of 165 paired measurements of TDCO and ICO were gathered in seven animals over the dissection, anhepatic, and reperfusion phases of surgery. Figure 15 shows the time series of cardiac output measurements during liver transplantation for all 7 animals; the complete data set can be found in Appendix C. As expected, OLT was accompanied by dramatic changes in CO and other hemodynamic parameters, especially during the anhepatic and reperfusion stages of the procedure. The range of TDCO and ICO were L/min (mean.8 L/min) and L/min (mean.6 L/min), respectively. Linear regression analysis revealed the equation ICO = 0.69 TDCO with a Pearson correlation coefficient (R) of 0.89 (figure 16). Analysis by the method of Bland and Altman 107 showed a bias of -0. L/min with 95% limits of agreement from -1.1 to 0.7 L/min (figure 17). The percent error 10 between the two measurements was 3%. The trending ability of ICO was determined using the half-circle polar plot method 108 after applying an exclusion radius of 15% of the mean CO (0.4 L/min). Herein, the mean radial bias was found to be -8º. The standard deviation (SD) and 95% confidence interval (CI) of the polar angle was ±18º and ±33º, respectively (figure 18). The convergence rate of ICO following an acute change in CO was computed from ICO measurements immediately following cross-clamping of the inferior vena cava. In five of the seven surgeries, the inferior vena cava was rapidly clamped causing an acute decrease in mean ± SD CO from 4.1 ± 0.8 L/min to 1.7 ± 0. L/min. An exponential function was fitted by the method of least squares to the ICO measurements following application of the crossclamp, from which the time constant of convergence could be calculated. This analysis revealed a mean ± SD time constant of 1. ± 0. iterations. As expected, there was no relationship between the time constant of convergence and the change in CO (R = 0.1). In two other cases, the cross-clamp was applied step-wise, causing a gradual and sporadic

43 35 decrease in CO which could not be analyzed for convergence in this way. Figure 19 is a sample of the convergence analysis from one animal. Figure 15. Time series of cardiac output measurements during liver transplantation for all 7 animals. The upper graph shows cardiac output measured by the iterative method (ICO) and bolus thermodilution (TDCO).

44 36 Figure 16. Linear regression analysis of cardiac output measurements during liver transplantation. ICO iterative cardiac output; TDCO bolus thermodilution cardiac output. Figure 17. Bland-Altman analysis of cardiac output measurements during liver transplantation. ICO iterative cardiac output; TDCO bolus thermodilution cardiac output.

45 37 Figure 18. Polar plot analysis of cardiac output measurements during liver transplantation. An exclusion zone of 15% of the mean cardiac output (0.4 L/min) was applied. Figure 19. Convergence rate of the iterative cardiac output (ICO) algorithm. An exponential function (grey line) was fitted to ICO measurements following crossclamping of the inferior vena cava (iteration 0). The time constant (red) is determined from the exponential fit.

46 38 4 Discussion This thesis provides a first description and proof-of-concept of ICO a novel, iterative, noninvasive, respiratory method of measuring CO which furthers the art of CO measurement using CO. To validate the new method, ICO and TDCO were simultaneously measured over a wide range of CO. The results suggest that this new method is feasible in mechanically ventilated subjects; provides automated measures of CO every 90 seconds; and is highly correlated, and trends with TDCO. 4.1 Advantages of the iterative cardiac output measurement method The ICO method described herein takes advantage of the benefits of all the previous respiratory methods, while overcoming many of the previously insurmountable limitations. As the Differential Fick equation is used to refine the estimate of CO in each iteration, this method is less sensitive to the absolute accuracy and calibration of the measurement equipment while also being less susceptible to errors arising from constant end-tidal to arterial CO gradients. The ICO method requires a very short duration increase in PET CO as it is only testing an estimate of the CO in maintaining a constant PET CO unlike previous methods, the test duration is not pinched between equilibration of gases in the lung on the one hand, and recirculation on the other. Furthermore, the short duration of the iterative test also allows for a larger increase in PET CO with less concern for patient discomfort. As a 10 mmhg increase in PET CO was used in this study, an error of 1 mmhg in either of the baseline or test state PET CO measurements would result in only 9-11% error in the measured CO. Lastly, like the equilibration method, ICO is only dependent on direct measurements of PET CO without the need for curve fitting or extrapolation. As a trade-off, ICO requires multiple maneuvers before converging on the actual CO. The rate of convergence depends on the extent to which CO equilibrates in the lung during the test maneuver. Theoretically, a test duration of 10 seconds should allow for about one time constant of equilibration while almost certainly avoiding recirculation. In this configuration,

47 39 the algorithm converges the estimate of CO by approximately 63% per iteration resulting in a 95% approach to the true CO by the third test. The analysis of ICO immediately following cross-clamping of the inferior vena cava in the experimental OLT pigs confirms a time constant of 1. iterations. While this may be suitable for many clinical situations, ICO is not well suited for detecting transient changes in CO. 4. Validating the measurement Unlike any other respiratory-based measure of CO, ICO provides the ability to assess the validity of the output of the algorithm. The PET CO obtained during the test indicates, semiquantitatively, the relationship between the ICO measurement and the actual CO. On one hand, if the algorithm has converged, PETCO will be relatively unchanged during the test phase. On the other hand, a CO E above or below the actual CO can be easily identified by an upward or downward drift in the PET CO tracing, respectively. Furthermore, the magnitude of the observed drift indicates the severity of the discrepancy. Therefore, the method provides a clear indication of when the measurements are valid. Figure 0 shows PET CO values as ICO converges following an acute decrease in CO from 4.6 to 1.8 L/min after cross-clamping of the inferior vena cava in an experimental OLT pig. Figure 0. Validating iterative cardiac output measurements. The magnitude and direction of the drift in the end-tidal partial pressure of carbon-dioxide ( PET CO ) during the test indicates when the algorithm has converged. Following an acute decrease in cardiac output, it is clear that the actual cardiac output is lower than

48 40 the estimated cardiac output (CO E ), and that the algorithm has not converged until the third iteration. 4.3 Leveraging sequential gas delivery The implementation of ICO is in turn dependent on the implementation of the SGD technique. Utilization of SGD allows the imposition of V A, independent of V E, by regulating the flow of a controlled gas mixture. This characteristic will enable the method in spontaneously breathing subjects whose V E is uncontrollable and unpredictable 109. Additionally, precise knowledge of V A allows the calculation of VCO as the product of V A and the difference between the PET CO and PI CO thereby obviating the need for time-aligned flow and CO sensors in the expiratory limb. Furthermore, while the Differential Fick equation is not affected by constant end-tidal to arterial gradients, the difference between PET CO and PaCO in the baseline and test phases is not necessarily the same. These gradients arise from the dilution of equilibrated gas from well-perfused lung regions with inspired gas from under-perfused regions. As the difference between CO PI and PET CO changes between the baseline and test phase, so does the dilution of equilibrated alveolar gas with inspired gas and the end-tidal to arterial gradient. Breathing through an SGD circuit, however, has the added benefit of equalizing PET CO and PaCO, thereby removing this source of error The benefits of virtual sequential gas delivery The virtual implementation of SGD using a microprocessor-controlled inline gas blender, developed specifically for this method, is far superior to previous implementations using physical bags and valves. With older circuits constructed from physical reservoirs, the expiratory bag does not only contain gas from the previous expiration, but acts as a buffer which contains gas from multiple previous breaths. As a result of this buffering, in any breath, the re-inspiration of expired gas is not strictly neutral with respect to gas exchange. Its deviation from an ideal neutral gas depends on previous PET CO values, the volume of the reservoir, and V E. In the case of ICO specifically, the gas in the expiratory reservoir during

49 41 the test phase would necessarily contain expired gas from the immediately preceding baseline state. As the bolus at the start of the test phase acutely increases PET CO, the rebreathing of gas expired during the baseline state would necessarily exchange gas with the pulmonary circulation. This, in turn, will cause deviations of the actual V A from the ideal V A that is to be imposed, and result in errors in the computation of CO. Furthermore, ICO requires rapid and precise breath-by-breath changes in the PICO of the controlled gas mixture. Although the inspiratory reservoir is emptied in every breath, when using physical reservoirs, a small amount of residual gas always remains in the reservoir and tubing of the circuit. The inspiratory reservoir therefore contains the gas delivered from the blender for the current breath, but also reflects the recent history of controlled gas mixtures. This effect is especially pronounced following the bolus breath, as the gas in the bolus contains a very high PI CO, some of which would linger in the inspiratory reservoir during the test state. Again, this difference in the actual PICO compared to the PICO ICO will manifest as errors in the CO measurement. required to implement The simulation of reservoirs to implement SGD is far more precise than mechanical realizations of the technique. Unlike with physical reservoirs, the gas delivered in every breath can be precisely controlled and is not influenced by any previous breaths. The controlled gas mixture inspired in each breath is exactly that required by the algorithm, and, once the virtual volume of controlled gas is depleted, the CO flow controller blends CO to a final inspired concentration exactly equal to the PETCO from the previous breath. The virtualization of the SGD method could only be realized following the development of a very rapid CO flow controller which could respond, in real-time, to changes in the inspiratory flow. Rather than being a technical burden, this implementation of SGD greatly improves the practicality of the ICO method. Although SGD circuits constructed from physical reservoirs and valves can be adapted for mechanically ventilated patients, the resulting circuit is very large, complex to troubleshoot, and cannot be used with inhalational anesthetics 111. These circuits contain a large valve block and reservoirs near the airway interface, which increases the risk of accidental extubation with patient movement, and interferes with ready access to the patient for mouth care and pulmonary toilet.

50 4 With virtual SGD, on the other hand, the flow sensor and inlet for the CO injector interposed between the patient and the breathing circuit are minimally intrusive while their attachments to the computer and gas source can be remote. Furthermore the highly optimized response time of the CO flow controller allows rapid breath-by-breath, and within-breath changes in PI CO which optimizes the accuracy of the ICO method. A comparison of the characteristics of indirect Fick techniques is provided in table 1. Table 1. Comparison of the characteristics of indirect Fick methods for measuring cardiac output. Extrapolation Equilibration Differential Iterative Affected by recirculation No Yes Yes No Sensitivity to measurement Very high High Very high Low errors Automatable Yes No Yes Yes Suitable for spontaneous Yes Yes No Yes breathers Suitable for mechanical Yes Yes Yes Yes ventilation Validates measure No No No Yes 4.4 The effects of shunts Respiratory-based measures of CO, including ICO, are based on the mass balance of pulmonary gases and gas exchange dynamics at the interface between the alveolar space and pulmonary circulation. These methods, therefore, can only measure blood flow which

51 43 perfuses, and exchanges gas with, the alveoli. In healthy subjects, virtually all of the CO perfuses the alveoli and participates in gas exchange. However, in various states of disease, there may be shunts present so that a portion of the CO does not perfuse the alveoli, or a portion of the blood flow which perfuses the alveoli may not exchange any gas. The various shunt flows are depicted in figure 1. Figure 1. Various shunt flows throughout the body. A portion of the cardiac output may bypass the tissues through peripheral shunts (CO PS) caused by peripheral arteriovenous malformations. Additionally, cardiac defects can result in intracardiac shunts (CO ICS) in either direction between the left and right cardiac chambers. Lastly, pulmonary blood flow may bypass the pulmonary capillaries through intrapulmonary arteriovenous malformations (CO IPS), or pass through pulmonary capillaries which perfuse unventilated regions of alveoli (black region), so that gas exchange (grey arrows) cannot occur. Within the pulmonary circulation, blood may bypass the pulmonary capillaries by way of pulmonary arteriovenous malformations. These malformations are normally congenital lesions, and can range from complex vascular structures to small-caliber vessels 11. In addition, blood passing through the pulmonary capillaries may perfuse unventilated regions of alveoli, such as atelectatic regions 113 or regions of high edema 114, in which case the lack of ventilation prevents alveolar gas exchange from occurring. In either case, this blood flow

52 44 cannot be detected by respiratory-based CO measurements. Similarly, blood shunted directly from the right heart to the left heart, as may occur through a patent foramen ovale during pathological increases in right atrial pressure, will bypass the pulmonary capillaries and cannot be detected by respiratory-based CO measures. The contribution of left-to-right shunts to the CO measured by respiratory methods is variable, and depends on the duration of the respiratory maneuver and the recirculation time through the shunt. If the recirculation time from the pulmonary capillaries through the shunt is longer than the duration of the respiratory maneuver, then, during the test, the shunt returns blood to pulmonary capillaries that was arterialized before the start of the test. In this case, the shunted blood exchanges gas with the alveoli during the test and is therefore measured as part of the CO. If, however, the recirculation time through the shunt is shorter than the respiratory maneuver, the shunt returns blood to the pulmonary circulation which was arterialized during the test and does not further exchange gas with the alveoli. These shunts do not contribute to the CO measurement. In general, when using any respiratory approach, blood flow which exits and returns to the pulmonary circulation within the duration of the respiratory maneuver neither brings CO to the lung nor takes any away, and therefore, will not be measured. For example, as shown in figure, left-to-right intracardiac shunts, such as occur through a ventricular septal defect, immediately return equilibrated blood from the pulmonary vein back into the pulmonary artery. As this blood has already equilibrated with the gas in the lungs, it does not contribute to the CO measured by respiratory techniques. The recirculation time through more peripheral shunts, such as peripheral arteriovenous malformations or pathophysiological peripheral shunts as may occur in sepsis or liver failure, is longer than intracardiac shunts and may therefore contribute to the CO computed by the respiratory test.

53 45 Figure. Respiratory cardiac output measurements with left-to-right shunts. The respiratory maneuver increases the end-tidal partial pressure of carbon-dioxide in the lung (dark grey). Peripheral shunts return blood to the lungs that was arterialized before the start of the maneuver (light grey). This blood exchanges gas with the alveoli during the test and is measured as part of the cardiac output. Intracardiac shunts return blood which was arterialized during the test and has the same partial pressure of carbon-dioxide as the alveoli. This blood does not exchange gas and is not detected by respiratory measures of cardiac output. The presence of shunts may cause discrepancies between respiratory-based measures of CO and total ventricular output, but does not preclude their clinical use where shunts are suspected. In all cases, shunted blood does not contribute to oxygenation of the tissues. Right-to-left shunts intrapulmonary or intracardiac return deoxygenated blood to the tissues where no further oxygen can be extracted. Conversely, the blood which flows through left-to-right shunts is oxygenated, although this blood returns to the venous circulation without perfusing the tissues. Clearly, where significant shunts exist, adequate ventricular output does not ensure adequate O delivery to the tissues. For example, a patient with a large ventricular septal defect may have normal or high TDCO measurements, although much of this flow does not reach the tissues. Therefore, discrepancies between respiratory-based measures of CO and measures of ventricular output can provide useful diagnostic information which is otherwise difficult to obtain.

54 The iterative cardiac output measurement method during liver transplantation The OLT model was chosen to validate ICO during the extreme shifts in CO and other hemodynamic parameters that accompany this procedure. As an added benefit, in partnering with the transplant research group, animal sacrifice was minimized. Various criteria have been established to compare two CO monitors. When using TDCO as a reference technique, a percentage error of no greater than 30% has been demarcated as the limit permitting the use of a new monitor interchangeably with the reference TDCO 115. This 30% limit is based upon an assumed 0% precision error of TDCO measurements. In these experiments, although there was close agreement between ICO and TDCO, the percentage error just barely exceeded the 30% limit required to conclude that ICO and TDCO may be used interchangeably. However, in vitro characterization of thermodilution measurements has demonstrated that the precision error may exceed the assumed 0%, and is most likely even wider in vivo 116. Based on these finding, the 30% limit must be interpreted cautiously. Similarly, radial limits of agreement (95% CI) of ±3 or less (after central zone data exclusion), and an SD of ±17 or less is considered demonstrative of modest-to-good trending ability 108. The polar plot analysis showed an angular bias of -8, SD of ±18, and 95% CI of ±33 with the vast majority of points lying within a 3 envelope. Therefore, ICO provides moderate-good trend information compared to TDCO during OLT. 4.6 Implications This work describes the first novel indirect Fick technique of CO measurement in over 30 years. Like previous respiratory methods, ICO is based solely on simple mass balance equations, and does not require any calibration or adjustment factors to account for parameters which are not easily measured. On the other hand, the ICO method is the first non-invasive respiratory-based measure of CO that is not confounded by recirculation, while obviating any need for extrapolation or tedious trial-and-error. Similarly, in contrast with

55 47 previous attempts, it is fully automated, continuous, self-validating, and applicable to controlled and spontaneous ventilation. As a result, ICO can bring reliable and accurate non-invasive determination of CO to the outpatient setting, emergency room, operating room, and intensive care unit. This will allow for earlier and more reliable diagnoses, and therefore, better hemodynamic management of all patients. At the same time, ICO may be applied in research protocols where a reliable noninvasive measure of CO was previously not available. In this way, ICO may be used as tool to aid further investigation into basic cardiovascular physiology. The technology developed to implement ICO has implications beyond the ICO method itself. The real-time volumetric gas blender can be used to deliver precisely controlled inspiratory fractions of any compressible gas to mechanically ventilated or spontaneous breathing patients, and can be retrofitted onto any existing breathing apparatus. Lastly, the virtualization of SGD presents a significant advance to the method, which will benefit all existing systems into which SGD is incorporated. For example, virtual SGD will allow for more precise and robust targeting of end-tidal gases 99 during cerebrovascular imaging studies Limitations Cross clamping of the inferior vena cava and portal vein during OLT leads to extreme shifts in CO. The circulation is further compromised by significant blood loss and hemodynamic turmoil secondary to liver graft reperfusion syndrome 118. The experimental model of OLT was chosen to validate ICO during the extreme changes of CO which consistently accompany this procedure. However, in addition to other well-known limitations of TDCO, the chosen experimental model might also be linked to thermal instability at the site of the PAC thermistor, and hence influence the precision error of the reference technique. For example, incomplete mixing of unheated blood from the extra-corporeal veno-venous bypass with the venous return has been shown to affect the accuracy of TDCO 119. In general, the temperature fluctuations during OLT have been found to greatly reduce the precision of all thermal based CO measurements 10.

56 48 In addition, the reference technique provides an instantaneous measure of CO, while ICO requires a finite interval before re-converging following a change in CO. Therefore, additional errors are introduced for measures made soon after an acute change in CO. When using TDCO, it is not possible to determine the precise time of a change in CO only that the change occurred between the last two measurements. Therefore, the data could not be filtered or analyzed exclusively for steady-state measurements. Future studies could include a continuous reference technique, such as continuous thermodilution 11 or aortic flowmetry 1, so that states of stable CO can be better identified. This study was carried out in mechanically ventilated animals. Although the method is suitable for spontaneous breathers in theory, it has yet to be proven in practice. The animal model used in this study did not include high CO states. Therefore, conclusions cannot be drawn regarding the validity of ICO at elevated CO.

57 49 5 Conclusions and future directions A non-invasive, accurate, robust, automated, and operator-independent monitor of CO is not currently available in clinical practice. This thesis describes the development of an entirely novel respiratory-based measure of CO which overcomes previously insurmountable limitations of older approaches. The development of the ICO method could only be achieved following an exhaustive review and analysis of the operating principles of previous methods, and a comprehensive understanding of all the relevant physiology. It was through this study that the fundamental limitation of all respiratory-based measures of CO the conflict between equilibration and recirculation was identified; and only after this realization that the technique of iteration could be introduced into the art of CO monitoring. Following conception of the method, advanced hardware was developed for practical implementation of the method in a wide variety of patients and environments. This hardware was required for the implementation of ICO, but also presents significant advances to the fields of respiratory gas control, delivery, and monitoring in general. To validate ICO, ICO and TDCO were simultaneously executed in an animal model of OLT. The results indicate that ICO is highly correlated and nearly interchangeable with TDCO during OLT, and that ICO presents adequate trending information compared to TDCO. Although it is the standard in clinical practice, TDCO has many drawbacks as a reference technique especially during OLT. To further investigate the potential of ICO, additional comparison studies with more precise and continuous reference techniques are required. The work completed was not able to validate ICO during high CO states, and high CO protocols should be included in future studies. The device used in this study was a prototype, and future work should also be directed towards optimization of the ICO hardware. Human studies to validate ICO should be initiated once animal studies demonstrate sufficient agreement with standard reference techniques, and the hardware has been finalized.

58 50 Contributions Michael Klein Conception and development of ICO method o Algorithm development o Implementation in software Conception and development of gas blending apparatus o Algorithm development o Microprocessor programing o Hardware configuration o Sensor selection o Verification and validation Conception and development of virtual SGD o Algorithm development o Microprocessor programing o Verification and validation Data gathering and analysis Manuscript preparation Joe Fisher Conception and development of SGD method Drew Miller Design of printed circuit boards Leonid Minkovich Anesthesia support Marcus Selzner and Matthias Knaak Experimental liver transplantation

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71 63 Appendix A Derivation of the alveolar equilibration time constant The dynamics of CO in the lung can be described by a single, first-order differential equation. Equation A1: dpetco VA (PICO PETCO ) PB CO S (PvCO P dt FRC ET CO ) The solution to equation A1 is an exponential function with a time constant ( ) given by equation A. Equation A: P FRC CO S B V A For an adult male at rest, we assume a functional residual capacity of 4 L, V A of 4 L/min, and CO of 5 L/min. Using the normal barometric pressure at sea level (760 mmhg), and the average slope of the CO dissociation curve (0.48 vol.%/mmhg) 1, the for CO equilibration in the lung is 11.3 seconds. 1 Paterson, D. H., & Cunningham, D. A. (1976). Comparison of methods to calculate cardiac output using the CO rebreathing method. European journal of applied physiology and occupational physiology, 35(3), 3 30.

72 64 Appendix B Technical details of the iterative cardiac output system B.1 Detailed block diagram Figure B1. A detailed block diagram of the iterative cardiac output system. Refer to table B1 for a description of each component. Table B1. Description of the iterative cardiac output system components. Component (Make, model) Key Specifications Purpose 1 Carbon-dioxide tank (Praxair, CD-ME) Size: M-E Max pressure: 830 psig CGA: 940 Supply carbondioxide to the flow controller. Nominal contents: 6 lb Tank pressure regulator (Western Medica, M1-940-PG) Inlet pressure: 3000 psig Outlet pressure: psig Reduce the carbondioxide tank pressure to 50 psig. 3 Quick-connect coupling (McMaster-Carr, 5478K419) Max pressure: 50 psig Connect the carbondioxide tank to the flow controller.

73 65 4 Inline liquid/gas filter (Cole Parmer, EW ) 5 Fine pressure regulator (Clippard, MAR-1-3) 6 Proportional solenoid valve (Clippard, EV-P V) 7 Carbon-dioxide flow sensor (TSI, 4116) 8 Check valve (Swagelok, SS-C-1/3) 9 Tubing (McMaster-Carr, 538K738) 10 Wye-connector (Qosina, 51089) 11 Ventilator flow sensor (Honeywell, AWM70P1) 1 Carbon-dioxide analyzer (Masimo, IRMA) Max pressure: 15 psig Efficiency: 99.99% Inlet pressure: 100 psig Outlet pressure: 0-30 psig Max pressure: 5 psig Max flow: 19 SLPM Response: 8 ms full cycle Range: 0-0 SLPM Response: 4 ms T63 Accuracy: ±% OR Max pressure: 000 psig Cracking pressure: 0.33 psig Material: Braid-reinforced PVC ID: ¼ in. Max pressure: 350 psig Material: Polypropylene Connections: //-15 mm Range: 0-00 SLPM Response: 6 ms T90 Repeatability: ±0.5% OR Range: 0-15% Accuracy: ±0.% abs ± % OR Response: 90 ms T90 Protect the pneumatic equipment. Reduce the pressure to 0 psig. Control the flow of carbon-dioxide. Measure the flow of carbon-dioxide. Prevent backflow of carbon-dioxide into the flow controller. Deliver carbondioxide to the ventilator circuit. Connect the ventilator circuit to the airway. Measure the inspiratory flow delivered by the ventilator. Measure end-tidal carbon-dioxide.

74 66 13 Microprocessor (Microchip, PIC3MX675F51L) 13A Pulse width modulation peripheral 13B Universal asynchronous receive/transmit peripheral 13C Analog to digital conversion peripheral 13D Universal asynchronous receive/transmit peripheral 13E Volumetric gas blending algorithm 13F Sequential gas delivery algorithm Frequency: 80MHz Architecture: 3-bit RAM: 64 KB UARTs: 6 ports ADC: 16 channels PWM: 5 channels Frequency: 0 khz Baud: Line control: 8-N-1 Resolution: 10 bits Baud: 9600 Line control: 8-N-1 Language: C Loop frequency: 1 khz Language: C Loop frequency: 1 khz Control the virtual sequential gas delivery system. Refer to section B. for further details. Vary the voltage applied across the proportional solenoid valve. Read the carbondioxide flow sensor. Read the ventilator flow sensor. Read the carbondioxide analyzer. Control the proportional valve to achieve a target inspired concentration of carbon-dioxide by volume. Refer to section B.3 for further details. Determine which virtual reservoir is being inspired from. Refer to section B.4 for further details.

75 67 13G Universal asynchronous receive/transmit peripheral Baud: Line control: 8-N-1 14 Laptop Processor: Intel T9300 (Lenovo, ThinkPad T61 RAM: GB 6465 CTO) Operating system: Linux Mint 13 14A Serial port Baud: Line control: 8-N-1 14B Iterative cardiac output Language: C++ software Framework: Qt Communicate with the laptop. Execute the iterative cardiac output software. Communicate with the microprocessor. Command appropriate gas flows and compositions from sequential gas delivery system to execute iterative cardiac output algorithm. Log data.

76 68 B. B..1 Electrical schematics Analog inputs

77 69 B.. Processor

78 70 B..3 Valve drivers

79 71 B..4 High resolution analog components

80 7 B..5 Pressure sensors

81 73 B..6 Serial communication

82 74 B..7 Laptop communication

83 75 B.3 Volumetric blender B.3.1 Flow chart Figure B. Volumetric blender flow chart. The algorithm runs in a continuous loop. During each inspiration, the system tracks the total inspired volume and the inspired volume of carbon-dioxide (CO ). The error is computed as the volume of CO that must be inspired to achieve a target concentration of CO ( F I CO ) by volume. The error is used in a PID controller to signal the CO flow control valve to release a volume of CO which will achieve the target.

84 76 B.3. Implementation in C code

85 77

86 78

87 79 B.3.3 Blender validation Figure B3. Volumetric blender validation. The volumetric blender was interposed into a ventilator circuit connecting a ventilator (MA-1, Bennet) to an artificial lung (QuickLung, IngMar Medical). The blender was set to deliver % inspired CO. Respiratory rate and inspiratory flow were varied over the physiological range while the inspired concentration of CO was monitored by a CO analyzer (OCAP, Oxigraf).