Indirect Calorimetry Based on
Oxygen Luminescence Quenching
by
Craig T. Flanagan
A dissertation submitted to the faculty of The University of Utah In partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Bioengineering
The University of Utah
January 2003
Page i
Copyright Craig Thomas Flanagan 2003
All Rights Reserved
Page ii THE UNIVERSITY OF UTAH GRADUATE SCHOOL
SUPERVISORY COMMITTEE APPROVAL
of a dissertation submitted by
Craig Thomas Flanagan
This dissertation has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory.
______Chair: Dwayne R. Westenskow
______Joseph A. Orr
______Richard A. Normann
______Douglas A. Christensen
______Kenneth Johnson
Page iii THE UNIVERSITY OF UTAH GRADUATE SCHOOL
FINAL READING APPROVAL
To the Graduate Council of the University of Utah:
I have read the dissertation of Craig Thomas Flanagan in its final form and have found that (1) its format, citations and bibliographic style are consistent and acceptable; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the supervisory committee and is ready for submission to The Graduate School.
______Date Dwayne R. Westenskow Chair, Supervisory Committee
Approved for the Major Department
______Vladimir Hlady Chair/Dean
Approved for the Graduate Council
______David S. Chapman Dean of The Graduate School
Page iv ABSTRACT
This Ph.D. dissertation describes the development of an indirect calorimetry system for use in a critical care setting. Indirect calorimetry systems measure the quantity of oxygen consumed
(VO 2) by a patient, the quantity of carbon dioxide produced (VCO2), and the respiratory quotient
(RQ) or the ratio of VCO 2 to VO 2. The clinical determination of VO 2, VCO 2 and RQ values from patients undergoing mechanical ventilation therapy is useful in the determination of patient metabolic energy expenditure as well as the proportionate determination of substrate (protein, fat and carbohydrate) utilization. This information is valuable from a clinical standpoint for determination of proper nutritional management of critically ill (ventilator dependent) patient populations. Caloric mismanagement has been associated with increased morbidity and mortality as well as increased hospital stay. Further, improper management of substrate balance may produce ventilator weaning difficulties. A compact indirect calorimetry system capable of obtaining and tracking these measurements in real-time using an on airway sensor, would represent a significant advancement in the state of the art of medical care. This advancement would allow physicians to tailor nutritional support regimens to the current needs of patients as well as making possible the tracking of nutritional parameters, while at the same time not necessitating the temporary removal of patients from life support systems. The system developed herein solves algorithm challenges that such a system would present. The ultimate goal of this dissertation is to set the foundation for an improvement in the standard of critical care medicine delivery.
Page v LIST OF FIGURES Figure Page
2.1. Diagram of the metabolic simulation system. 9
2.2. Timing of gas removal. 11
2.3 . Pnuematic schematic of flow delivery system. 13
2.4. Functional Arrangement of Valve Timer Board 14
2.5. Programmable valve timer board. 15
2.6. User interface of metabolic simulator software 17
2.7. Test lung volumes 23
2.8. Valve on-time vs. delivered gas volume for CO 2. 32
2.9. Valve on-time vs. delivered gas volume for vacuum. 33
2.10. Valve on-time vs. delivered gas volume for O 2. 34
2.11. Bland-Altman plot of Valve on-time vs. delivered gas volume for vacuum. 35
2.12. Bland-Altman plot of Valve on-time vs. delivered gas volume for CO 2. 36
2.13. Bland-Altman plot of Valve on-time vs. delivered gas volume for N 2. 37
3.1. Gas partial pressures before/after the addition/removal of respiratory gases.45
3.2. RQ represented as the slope of the change in volumes of CO 2 and O 2. 48
3.3. RQ as determined from partial pressure slope vs. FIO 2. 50
3.4. Slope Algorithm and Deltatrac Energy Expenditure Results in Kcal/day 67
3.5. Slope Algorithm and Deltatrac RQ 68
3.6. Bland-Altman plot of the Slope Algorithm EE vs. the (Slope EE +
Deltatrac EE)/2 output. 69
3.7. Bland-Altman plot of the Slope Algorithm RQ vs. the (Slope RQ+
Page vi Deltatrac RQ)/2 output. 70
3.8 X-Y plot of Slope vs. Deltatrac with the addition of data from Harris-
Benedict vs. Deltatrac. 71
A.1 Details of Polarographic (Clark) cell. 78
A.2. Details of fuel cell. 80
A.3. Details of zirconium oxide fuel cell. 83
A.4. Details of Pauling cell showing torsional force on dumbbell resulting
from oxygen in sampling chamber. 85
A.5. Details of Hummel cell showing pneumatic path of sample and reference
gases through the electromagnet gap and differential pressure measurement
technique. 87
A.6. Joblinski diagram. 90
A.7. Construct of Phosphorescence Quenching Sensor. 95
A.8. Timing diagram for phosphorescence quenching sensor. 97
Page vii LIST OF TABLES
Table Page
2.1. Applicable Training/Test Lung Specifications 18
2.2. Applicable Specifications 19
2.3. Potential sources of system error 20
2.4. Typical values of input variables for a V E of 4000 ml 28
2.5. Error sensitivity coefficients. 29
2.6. Monte Carlo analysis results 30
3.1. Algorithms Compared. Mean and Std. Dev. displayed at ventilator
and lung settings. 63-64
A.1. Qualitative comparison of oxygen sensing technologies. 94
Page viii
ACKNOWLEGEMENTS
Thank you to Joe and Dwayne for helping me achieve my goal. Thanks to my mother Shirley for all of her patience and my father Lawrence who was my hero and gave me inspiration through the years.
Page ix TABLE OF CONTENTS
ABSTRACT v
LIST OF FIGURES vi-vii
LIST OF TABLES viii
ACKNOWLEDGEMENTS ix
CHAPTER
1. INTRODUCTION TO INDIRECT CALORIMETRY 1
2. A METABOLIC SIMULATION TECHNIQUE FOR INDIRECT 7
CALORIMETRY SYSTEM VALIDATION
3. A NOVEL RESPIRATORY QUOTIENT ALGORITHM BASED 42
ON PARTIAL PRESSURE OXYGEN AND CARBON DIOXIDE
SENSORS
4. CONCLUSION 74
APPENDIX A. 75
Page x CHAPTER 1
INTRODUCTION TO INDIRECT CALORIMETRY
This dissertation focuses on a novel approach to a clinical tool known as indirect calorimetry. Indirect calorimetry is a method by which the type and rate of nutritional substrate utilization and heat production are measured in vivo from gas exchange measurements. Specifically, indirect calorimetry is useful in estimating the amounts of energy derived from protein, carbohydrate and fat substrates. Clinically, indirect calorimetry allows for an estimated assessment of the metabolic state of a patient undergoing mechanical ventilation therapy for prescription of the proper amount and makeup of parenteral nutritional support. The dissertation describes a new and novel approach to indirect calorimetry. Specifically, in this dissertation a new algorithm for determining a parameter central to indirect calorimetry measurements known as the respiratory quotient (RQ) is both derived and validated for accuracy. This validation consists of the use of a new and novel metabolic simulator constructed for this dissertation and described herein. These two improvements to the state of the art (the algorithm and the simulator) make possible the construction of an indirect calorimetry device which provides many advantages over current systems such as improved accuracy, breath-to-breath determination of indirect calorimetry parameters, a smaller form-factor device, and the ability to easily trend such parameters. Such advantages comprise an evolutionary improvement to the current art of clinical metabolic patient assessment.
Proper nutrition is important to the critically ill patient population. Improper patient nutrition has been associated with poor clinical outcome 1-6. Specifically, overfeeding can produce hyperglycemia and fatty infiltration producing liver dysfunction as well as respiratory acidosis/hypercapnia which are associated with ventilator weaning difficulties 7. Underfeeding can depress the immune system response and lead to loss of lean body mass.
Page 1 Indirect calorimetry has established itself as a useful clinical tool in patient nutritional assessment and management. Common usage of the technology includes the following patient populations:
Chronic pulmonary disease Cardiac failure Multiple organ failure Cancer Hypovolemic shock Sepsis Burn injury Major trauma or surgery Inflammatory bowel disease Obesity Thyroid disease
CLINICAL MEASUREMENTS ASSOCIATED WITH INDIRECT CALORIMETRY
Indirect calorimetry produces a number of important clinical measures of patient metabolic state.
These include the respiratory quotient (RQ), minute oxygen consumption (VO 2), and resting energy expenditure (REE). VO 2 is a measure of the patient’s volumetric consumption of oxygen on a minute basis. The RQ is a measure of the ratio of per minute volumetric carbon dioxide production (VCO 2) to per minute volumetric oxygen consumption (RQ = VCO 2/VO 2). This ratio has clinical relevance in that it provides insight into patient substrate consumption. Specifically, the RQ varies according to the stoichiometry of substrate catabolism with fats producing a low RQ (~ 0.70), carbohydrates a high RQ (~ 1.0), and protein falling in between (~ 0.80). Protein is generally a minor metabolic energy source and its rate of metabolic consumption can be either measured directly using urea nitrogen concentrations or simply estimated with generally acceptable accuracy. Since protein metabolic consumption is typically small relative to fats and carbohydrates (on a per mass basis), the RQ can be used to estimate the proportionate amount of fat and carbohydrate metabolism. Further, once the VO 2 and VCO 2 values have been measured, the energy expenditure of the patient per unit time can be estimated using mathematical techniques. This energy expenditure per unit time is typically reported as the resting energy expenditure (REE): REE is the amount of calories needed to maintain the body at rest. REE is
Page 2 also sometimes referred to as resting metabolic rate (RMR) or basal metabolic rate (BMR). Armed with the number of calories the patient is burning (REE) coupled with knowledge of the estimated proportionate substrate usage, the clinician is empowered to tailor the patient’s nutritional support regimen.
SPECIFIC AIMS
The purpose of this dissertation is the development of a system which obtains indicators of patient metabolic rate while circumventing the drawbacks of systems currently in clinical use. Specifically, modern commercial indirect calorimetry systems tend to be bulky, expensive and even of poor accuracy. These systems are generally open circuit, side-stream systems meaning they rely on the removal of gas from the breathing circuit. My objective is to design an indirect calorimetry system which meets the following goals:
Mainstream - The system should analyze gas in real time at the patient airway and not remove gas from the breathing circuit. The advantage of this strategy is that the sensing technology can be more responsive to changes in gas composition while not suffering from delay and mixing effects produced by side-stream sampling.
Compact - The sensors at the patient airway should be relatively compact so as not to interfere with patient/ventilator management.
Durable - The system/sensors must be rugged due to the demanding nature of the application.
Commercially Viable - The system must compete with other indirect calorimetry technologies in cost so as to make the system competitive with existing systems.
Accurate -The system must provide an accurate assessment of patient metabolism at or above the currently accepted clinical standard of 3-5%.
Page 3
Safe - The system must not introduce significant hazards to the patient.
STRUCTURE OF THE DISSERTATION
Next two chapters in this dissertation are intended to be stand-alone papers worthy of submittal to research journals for publication. These papers outline two major avenues of innovation taken during project implementation. These are the development of an accurate human breathing simulator standard for test of the indirect calorimetry algorithms designed. The second paper consists of a mathematical treatment of the algorithm as well as bench and clinical validation results.
BACKGROUND INFORMATION
A new oxygen partial pressure ( pO2) technology, based on the measurement of phosphorescence lifetime, has been developed and will be described herein. This new oxygen sensing technology allows for real-time, on-airway assessment of oxygen partial pressure. The technology has the advantages of being small, fast, and accurate as well as boasting a disposable element. This technology was determined to be the best-fit technology for this project when compared with existing technologies. A detailed assessment of currently available techniques of pO2 measurement including electro-chemical sensors such as polarographic and galvanic cells, paramagnetic cells, zirconium oxide cells, and mass spectrometry are covered in detail in
Appendix A.
Page 4 A significant amount of signal processing groundwork relating to oxygen sensor noise attenuation issues as well as signal response and delay equalization issues for all of the sensors was performed prior to the algorithm work described in the next chapter. Noise attenuation techniques used to process the oxygen sensor signal included a linear technique (a notch filter) and a suite of non-linear techniques including Voltera (polynomial) filters, median filters and statistics-based filters. An optimized linear notch filter for noise attenuation was determined to be the best performer. Signal response and delay equalization was performed to ensure that the
O2, CO 2 and flow sensors responded equally to a given step change in the transduced parameter.
This signal response and delay equalization work consisted of two primary steps. First, the transfer functions for all sensors were determined using parametric system identification techniques based on flat spectrum psuedo-random binary input sequences. Second, sensor responses were then equalized using causal linear transforms to idealized sensor step response behavior. Delays for all sensors were equalized at the same time. The result of this process being nearly equivalent step response and delay behavior for all sensors used in this project.
References:
1. Askanazi J, Hensle TW, Starker PM, Lockhardt SH, La Sala PA, Olsson CL, Kinney JM:
Effect of immediate post-operative nutritional support on length of hospitalization. Ann Surg.
1986; 203:236
2. Warnold I, Sundholm K: Clinical significance of preoperative nutritional status in 215
noncancer patients. Ann Surg. 1984; 199:299.
3. Arora NS, Rochester DF: Respiratory muscle strength and maximal voluntary ventilation in
undernourished patients. Am Rev Resp Dis. 1982; 126: 5-8.
Page 5 4. Kahan DB: Nutrition and host defense mechanisms. Surg Clin North Am. 1981; 61:557-70.
5. Heymsfield SB, Bethel RA, Ansley JD, Gibbs DM, Felner JM, Nutter DO: Cardiac
abnormalities in cachectic patients before and during nutritional repletion. Am Heart J. 1978;
95:584-594.
6. Askanazi J, Carpentier YA, Elwyn DH, Nordenstrom J, Jeevanandam M, Rosenbaum SH,
Gump FE, Kinney JM: Influence of total parenteral nutrition of fuel utilization in injury and
sepsis. Ann Surg. 1980; 191:40-6.
7. Covelli HD, Black JW, Olsen MS, Beekman JF: Respiratory failure predicted by high
carbohydrate loads. Ann Intern Med. 1981; 95:579-81.
Page 6 CHAPTER 2
A METABOLIC SIMULATION TECHNIQUE FOR INDIRECT CALORIMETRY SYSTEM
VALIDATION
ABSTRACT
A novel metabolic system for the validation of indirect calorimetry systems was developed. The system allows for the variable setting of oxygen consumption (VO 2) values, carbon dioxide production (VCO 2) values, lung compliance and airway restrictance values. The metabolic system consists of a human lung simulator in combination with a precise gas delivery system which operationally spans a wide variety of respiratory physiologies and metabolic rates typical of an adult patient population. Gas exchange is performed by removing known quantities of inspiratory gas from the lung simulator and replacing it with nitrogen thus, diluting the oxygen content seen during exhalation. Carbon dioxide is added by precise titration of the gas into the artificial lung during this same inspiratory period. Validation of the metabolic system was performed using a mercury-sealed spirometer to assess the accuracy and precision of gas flow to/from the simulator as affected by the gas delivery system. A Monte Carlo based sensitivity analysis was performed using this spirometer data. The Monte Carlo analysis indicated a worse case VO 2 error of 0.981% (SD = 1 of setting), a worse case VCO 2 error of 0.774% (SD = 1 of setting) and a worse case respiratory quotient (RQ = VCO2/VO 2) of +/- 1.77% (SD = 1 of setting).
Key Words: Indirect Calorimetry, Metabolic Simulator, VO 2, VCO 2, Respiratory Quotient.
Page 7 Introduction:
The monitoring of respiratory gas exchange (indirect calorimetry) in the medical field is used in the assessment of patient energy expenditure and substrate (fat, protein, and carbohydrate) utilization for determination of proper nutritional management of ventilator dependent patient populations. Such indirect calorimetry systems require, for the purposes of accuracy validation during device development, a human breathing simulator 1-15 . To date, a number of such simulators have been constructed, unfortunately most lack the capacity to reproduce the range of lung physiologies typically encountered clinically. Further, other systems use alcohol burn strategies which are cumbersome 16-18 . Unfortunately, a validation system which provides for simulation of both a range of lung physiologies as well as gas exchange in the sub-2% range has not been described in the literature. This paper describes such a validation system and provides a mathematical sensitivity analysis of the system’s accuracy.
Materials and Methods:
The metabolic simulator uses a Michigan Instruments Inc. (Grand Rapids, Michigan) TTL test lung with lung compliance simulation from 0.01 to 0.15 L/cmH 2O range as well as (parabolic) airway restrictances from 5–200 L/min/cmH 2O. A bank of three mass flow controllers and valves are used to both add and remove gas from the test lung during the inspiratory phase of ventilator breath delivery. Figure 2.1 illustrates the system at a component level. Inspiratory gas
(containing oxygen) is removed and replaced by nitrogen to simulate oxygen consumption.
Page 8
IBM Compatible Computer
Metabolic Simulator COSMO Respiratory Monitor
Training/Test Lung
Mechanical Ventilator
Figure 2.1 Diagram of the metabolic simulation system.
Page 9
Carbon dioxide production is simulated by a concomitant flow of CO 2 into the lung during breath inspiration (Figures 2.2 and 2.3). The simulator is driven by a personal computer running a custom software program which receives sensor feedback from a NICO Respiratory Profile
Monitor (Novametrix Inc, Wallingford CT). Finally, breath delivery into the test lung is provided by a mechanical ventilator (Siemens-Elema 900-C, Sweden).
Simulation of respiratory gas exchange is provided by means of valve and mass flow controller modulated introduction and removal of respiratory gases from the test lung during the inspiratory phase of breath delivery. The timing of the introduction and removal of these gases is precisely controlled using predefined inspiratory flow and volume thresholds. These thresholds serve to ensure that dead space exhalation gas, at or near the patient WYE, is cleared by inspiratory gas flow prior to any gas removal by the metabolic system. Such a technique ensures that the gas being removed from the patient circuit is pure inspiratory gas (of known oxygen partial pressure) from the ventilator and not mixed gas entrained from backflow or exhalation flow from the test lung. Thus, this strategy ensures that the gas removed is of known concentration.
Metabolic Simulator Gas Flow. Gas addition and removal are regulated by mass flow controllers or MFCs (Model 201, Porter Instrument Co, Hatfield PA). The MFCs provide closed-loop flow control which is highly tolerant of temperature and line-pressure variations. One MFC is used for nitrogen, one for carbon dioxide and one for vacuum removal of ventilator inspiratory gas. The
Page 10 N = Check Valve 2 CO 2 Inspiratory Vacuum Valve
Expiratory Sensor Valve
Ventilator TTL
N = Check Valve 2 CO 2 Inspiratory Vacuum Valve
Expiratory Sensor Valve
Ventilator TTL
Figure 2.2. A complete respiratory cycle showing the addition of carbon dioxide and
nitrogen as well as the removal of breathing gas during inspiration (above), as well as
passive elimination of gas during exhalation (below).
Page 11
Figure 2.3. A complete respiratory cycle showing inspiratory and expiratory flow and volume. The timing of gas removal (vacuum) and gas introduction (of CO 2 and N 2) from
the metabolic simulator to the test lung during the inspiratory phase of breath delivery is
illustrated.
Page 12 MFC’s used are of appropriate flow ranges (0-5 SLPM and 0-10 SLPM), thus ensuring that simulation of VO 2 and VCO 2 can be simulated at levels typical of common physiologic ranges
(0-240 and 0-192 ml/min respectively 24 ). The MFC’s used have a 1% full scale accuracy with a temperature coefficient of +/- 0.1%/ oC of full scale. The upstream pressures of the nitrogen and carbon dioxide sources are controlled at 30 PSI by pneumatic pressure regulators (Model 310,
Humphrey, Kalamazoo MI). The vacuum source is a regulated wall vacuum at XXX PSI. Due to the limited dynamic flow response characteristics of the MFCs (T 10-90 of 1.2 seconds) coupled with the relatively short duration flow pulses (10 msec – 1000 msec) necessary for metabolic simulation, the MFCs are not configured to operate in a transient on/off modality. Instead, the
MFCs are configured to run in a steady-state mode wherein flow is not varied with time, but rather diverted into the test lung for short time durations. In this configuration, external flow diverter valves are used to direct gas flow into/out of the test lung (Figure 2.4.). The flow diverter valves (XM-400, Evolutionary Concept, CA) are fast acting (Tau ≈ 12 msec) 3-way electrically activated solenoid valves.
Valve Timer Board. The programmable valve timer board consists of three erasable programmable logic devices (EPLD’s, Altera, San Jose, CA) and associated support hardware.
The EPLD’s both communicate with the software program running on the IBM personal computer (Dell X86-21575) as well as direct the timing of valve activation. Each EPLD outputs valve activation time to a 7-segment display for real-time update during valve activation (similar to a stopwatch). The configuration of the valve timer board is shown in Figure 2.5 and a picture of the programmable valve timer board is shown in Figure 2.6.
Page 13
Pressure Mass Flow 3-Way 2 Regulator Controller Position Solenoid Valve
O2 Positive Pressure Training/ Back Test Pressure Lung System CO2 Positive Pressure
Back Pressure System Vacuum Ambient Negative Pressure
Back Pressure System
Figure 2.4 Pnuematic schematic of flow delivery system.
Page 14
DB25 Parallel Crystal and +5VDC Port Interface Frequency Power Divider Supply
MAX MAX MAX 7128 7128 7128
Resistor Resistor Resistor Bank Bank Bank
7-Segment 7-Segment 7-Segment Displays Displays Displays
Timer Timer Timer Activation Activation Activation LEDs LEDs LEDs
Valve Valve Valve Driver Driver Driver Amplifier Amplifier Amplifier
Figure 2.5. Functional Arrangement of Valve Timer Board
Page 15
Figure 2.6. Programmable valve timer board.
Page 16 Metabolic Simulator Software Program . A program which runs on an IBM personal computer has been developed to control the metabolic simulator. This program uses input received from the NICO Respiratory Profile Monitor as well as internal algorithms to command both valve activation and valve timing in order to achieve desired values of VO 2 and VCO 2. The software program was developed in the C++ programming language in the Borland C++ Builder 3 programming environment. Desired VCO 2, VO 2, flow and volume thresholds are required.
Figure 2.7 shows the user interface for this program in which settings changes can be made.
Accuracy Determination
In order to perform an error sensitivity analysis, a system transfer function was derived. This transfer function was used in turn as the basis for a Monte Carlo assessment of overall system accuracy. This parametric analysis technique assessed the effects on system output of input errors as they propagate through the system. Input variables are considered stochastic variables with distributions reflective of the known behavior of the variables.
Potential Error Sources. In order to achieve a reasonable assessment of overall system error, all potentially significant sources of system error were included in the analysis. Table 2.1. lists these potential system errors. Ventilator F IO2 delivery errors are a potentially significant system error source as F IO2 values are assumed (from gas bottle concentrations) and not measured (Praxair precision Nitrox mixture +/- 0.1%). Gas flow delivery errors in the form of vacuum flow, CO 2 flow and N 2 flow may present significant error sources
Page 17
Figure 2.7. User interface of metabolic simulator software
Page 18 TABLE 2.1. Potential sources of system error
Input Variable Potential System Error Contribution Vacuum Flow Large Carbon Dioxide Flow Large FiO2 Large Ventilator Minute Volume Small Nitrogen Flow Small Valve Timing Very Small Upstream Pressure Effects Very Small Backpressure Effects Very Small
System Calibration. In order to assess the accuracy of the system as a whole, the accuracy of the gas flow systems was measured. A calibration was performed on each of the gas flow systems on the metabolic simulator (N 2, CO 2 and vacuum flow). A primary standard mercury-sealed spirometer (Volu-meter, Brooks, Hatfield PA) was used to collect gas from each of the gas flow systems. Valve timing was externally mediated and valve on-time vs. delivered gas volume was plotted for each of the gas systems. This was performed by setting the valve on-time and recording the displaced volume in the spirometer following 20 on/off valve cycles. To determine system accuracy, Bland Altman plots were constructed using the same data sets.
VO 2 and VCO 2 Algorithms. VO2 and VCO 2 are the primary metabolic simulator system outputs.
Thus, it is necessary to derive algorithms that determine the relationship between system inputs and these system outputs. This deterministic relationship is essential for the error sensitivity analysis and Monte Carlo analysis to follow. As previously described, gas is removed from the
Page 19 test lung through a precision flow controller. Nitrogen and carbon dioxide are subsequently added to makeup the gas volume shortfall (Figure 2.8). Thus, VO2 and VCO 2 can be calculated by the following equations:
VO 2 = Volume O 2 in – Volume O 2 out (2.1)
VO 2 = V I*F IO2 – V E*F EO2 (2.2)
VCO 2 = Volume CO 2 in – Volume CO 2 out (2.3)
VCO 2 = V E*F ECO 2 (2.4)
Where
VO 2 = O 2 consumption (ml/min)
VCO 2 = CO 2 production (ml/min)
V I = Inspiratory tidal volume (ml)
V E = Expiratory minute volume (ml)
F IO2 = Inspiratory oxygen fraction
F EO2 = Expiratory oxygen fraction
F ECO 2 = Expiratory CO 2 fraction
Equation (2.1) can be expanded as follows:
VO 2 = V I*F IO2 – V E*(FEO 2) (2.5)
VO 2 = V I*F IO2 – V E*[(V I-∆VAC)*F IO2]/ (V I) (2.6)
Page 20 Before After After N and CO Simulator Vacuum 2 2 Activation Activation Addition
VENTILATOR VENTILATOR VENTILATOR GAS GAS GAS FIO2 FEO2
Vacuum Nitrogen Depletion Carbon Dioxide
VI VE
Figure 2.8. Test lung volumes before during and after vacuum, nitrogen and carbon dioxide valve activation.
Page 21 Where
∆VAC = Vacuum volume removed (ml).
However, when the assumption is made that no system leaks are present V I ≡VE. Thus, Equation
(2.6) can be further simplified as follows:
VO 2 = V I*( F IO2 – (V I - ∆VAC)*FIO 2/V I) ) (2.7)
Error Sensitivity Analysis. The algebraic description of a system can be written in general form as follows:
η η η z = z(y 1 + Є1, y 2 + Є2,…,y n + Єn ,a 1 + 1, a 2 + 2,…,a m + m) (2.8)
Where
z = The system output
yi = The system inputs necessary to determine z.
aj = System parameters which may or may not cause error (e.g. constants)
Єk = System input errors
ηk = System parameter errors
Page 22 The desired or nominal performance equation can be written as the error-free combination of system inputs and parameters:
zo = z o(y 1, y 2 ,…,y m ,a 1,a 2,…,a n) (2.9)
Thus, the error εz = z - z o can be determined by expansion of the Taylor series as follows:
εz = δz/ δy1(Є1) + δz/ δy2(Є2) + …. + δz/ δym(Єm)+ δz/ δa1(η1) + δz/ δa2(η2) + ….
2 2 2 2 + δz/ δan(ηn) + 1 /2! δ z/ δy 1(ε1 ) + 2 /2! δ z/ δy1δy2 ( ε1ε2) + …. (2.10)
The higher order terms are assumed to be small and are, for the sake of simplicity, neglected.
Since Є and η vary with each measurement, it will be necessary to replace εz with a statistic such as the standard deviation σεz. This leaves us with the following equation:
σ δ δ σ δ δ σ εz = ∑ z/ yi( Єi) + ∑ z/ aj( ηj) (2.11)
The derivatives in equation (2.11) are the coefficients of the error terms (often called sensitivity coefficients) and represent the sensitivity of the output to input errors.
Equation (2.11) is now used to determine the accuracy of the metabolic simulator system.
Equations (2.7) and (2.8) can be rewritten as follows to aid in the simplicity of the analysis:
Page 23 a = F IO2
b = ∆VAC
c = ∆CO 2
d = V I
y = VO 2
z = VCO 2
Thus, equations (2.6) and (2.7) become respectively:
y = d (a-(d-b)/d) ) (2.12)
z = dc (2.13)
Due to the simplicity of equation (2.13), we will work exclusively with equation (2.12) at the present time. Substitution of equation (2.12) into equation (2.11) leads to the following expression:
2 σεy = [d] σεa + [1] σεb + [a-(d-b)/d + d(-1/d + (d-b)/d )] σεd (2.14)
Dividing equation (2.14) by equation (2.12) and placing each error term over its respective variable to produce an expression for relative errors gives:
Page 24
σεy/y = ad/(d(a-(d-b)/d))) σεa/a + b/(d(a-(d-b)/d))) σεb/b
2 + (a-(d-b)/d + d(-1/d + (d-b)/d ))/(a-(d-b)/d)) σεd/d (2.15)
Typical values for the input variables for a 70 kg adult breathing room air are given in Table 2.2.
These values can be plugged into equation (2.15) to produce the following equation:
σεy/y = [1] σεa/a + [1] σεb/b + [~ 0] σεd/d (2.16)
The values in brackets are the sensitivity coefficients and dictate the weighted effect of each input variable on the output. These coefficients are listed in Table 2.3.
Table 2.3 can be interpreted as indicating that at FIO2 of 0.21, a 1% change in F IO2 will produce a 1% change in VO 2 and a 1% change in vacuum volume will also produce a 1% change in VO 2.
Input Variable Typical Standard Variable Designator Operational Deviation Value/Breath (σ)
VO 2 Variables
F O a 0.21 % 0.100 % I 2 ∆ VAC b 64 ml 0.195 ml VI c 333 ml 8.62 ml VCO 2 Variables
∆CO 2 D 11.67 ml 0.067 ml
TABLE 2.2. Typical values of input variables for a V E of 4000 ml and a respiratory rate
of 12.
Page 25 Accuracies are taken from the Bland Altman plots (Figures 2.21-23) for the appropriate per breath gas volume. F IO2 accuracies are determined by the quoted accuracies of precision gas sources (Praxair, Salt Lake City, Utah) utilized in the metabolic simulator test bench. Inspiratory volume accuracies were determined based on a +/-3.0% σ2 (or +/- 2.59 σ) Siemens ventilator
specification at the operational value. The fourth entry in the table applies to the VCO 2 case. The same technique can be applied to equation (2.7.) which results in a sensitivity coefficient of 1 for
∆CO 2.
RESULTS:
Worst Case Errors. The sensitivity coefficients and relative errors for each variable are listed in
Table 2.3. A drift from a calibration baseline of 0.2% for the vacuum and carbon dioxide mass flow controllers was added to ensure a conservative worst case estimate of accuracy. This drift was based on the largest noted one day drift values over a ten day span. This table shows that worst case errors of one standard deviation are +/- 0.981% for VO 2 and +/-0.774% for VCO 2.
Since the respiratory quotient (RQ) is defined as the ratio of VCO 2 to VO 2, the worst case accuracy of RQ can be computed from the ratio of worst case errors for VO 2 and VCO 2. This results in a worst case RQ of +/- 1.77% (SD = 1).
Typical Errors. In order to determine system accuracies which might typically be encountered during operation, a Monte Carlo analysis was performed in which typical errors associated with each of the input variables are used to determined the output accuracy. In this analysis, the input
Page 26 parameters are assigned 1,000 random values selected from their respective distributions. The distributions used were gaussian with standard deviations as listed in Table 2.2.
Input Sensitivity Error (%) Variable Coefficients VO 2 Variables FIO2 1 0.476 ∆VAC 1 0.305 + 0.200 Drift
VI 0 2.59 Worst Case VO Error 0.981 2 VCO 2 Variables ∆CO 1 0.574 + 0.200 Drift 2 Worst Case VCO 2 Error 0.774
TABLE 2.3. Error sensitivity coefficients. The relative errors for ∆VAC and ∆CO 2 are
obtained from the calibration data and an additional worst case 0.2% flow delivery error due
to mass flow controller drift has been added.
System Accuracy Output (1 Standard Deviation)
VO 2 +/- 0.503 %
VCO 2 +/- 0.774 % RQ +/- 0.936 %
TABLE 2.4. Monte Carlo analysis results
The input values were plugged into equation 2.16 (VO 2 case). The VCO 2 output distribution is simply equal to the input distribution since the equation relating input to output is:
Page 27 σεz/z = [1] σεd/d
Thus the sensitivity coefficient is 1 and all input variation is transmitted directly to output variation. The standard deviation of the system output following 1000 iterations was recorded in
Table 2.4. The distribution of the ratio of outputs was also noted and recorded as RQ accuracy in
Table 2.4.
Page 28
N2 Valve On-Time vs. Volume/Breath (STPD)
120.00
100.00 y = 0.07458x - 1.16559 R2 = 0.99996 80.00
60.00
40.00 Volume/BreathSTPD (mL)
20.00
0.00 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 N2 Valve On-Time (msec)
Figure 2.9 Valve on-time vs. delivered gas volume for N 2. Note: the per breath values on the ordinate were determined by delivering breaths to the spirometer and dividing the total volume by 20.
Page 29 CO2 Valve On-Time vs. Volume/Breath (STPD)
25.00
20.00 y = 0.01530x - 0.94851 R2 = 0.99987
15.00
10.00 Volume/Breath STPD Volume/Breath (mL) 5.00
0.00 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 CO2 Valve On-Time (msec)
Figure 2.10. Valve on-time vs. delivered gas volume for CO 2. Note: the per breath values on the ordinate were determined by delivering breaths to the spirometer and dividing the total volume by 20.
Page 30 Vacuum Valve On-Time vs. Volume/Breath (STPD)
80.00
y = 0.04946x - 0.16340 R2 = 0.99990 60.00
40.00
Volume/BreathSTPD (mL) 20.00
0.00 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Vacuum Valve On-Time (msec)
Figure 2.11. Valve on-time vs. delivered gas volume for vacuum. Note: the per breath values on the ordinate were determined by delivering breaths to the spirometer and dividing the total volume decrease by 20.
Page 31
Bland-Altman Plot For Vacuum Gas Removal
0.80
0.40 +2 SD
0.00
-2 SD -0.40
40 Points Difference PREDICTEDDifference MEASURED and (mL) Bias = 0.00 +/- 0.195 -0.80 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 MEASURED (mL)
Figure 2.12. Bland-Altman plot of Valve on-time vs. delivered gas volume for vacuum.
Page 32
Bland-Altman Plot For Carbon Dioxide Delivery
0.20
+2 SD 0.10
0.00
-0.10 -2 SD
40 Points DifferencePREDICTED andMEASURED (mL) Bias = 0.00 +/- 0.067 -0.20 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 MEASURED (mL)
Figure 2.13 Bland-Altman plot of Valve on-time vs. delivered gas volume for CO 2. .
Page 33
Bland-Altman Plot For Nitrogen Delivery
0.60
+2 SD 0.40
0.20
0.00
-0.20 40 Points Bias = 0.00 +/- 0.246 -0.40 -2 SD Difference PREDICTEDDifference MEASURED and (mL)
-0.60 0.00 20.00 40.00 60.00 80.00 100.00 120.00 MEASURED (mL)
Figure 2.14 Bland-Altman plot of Valve on-time vs. delivered gas volume for N 2
Page 34
Discussion:
A metabolic simulator capable of simulating a wide range of lung physiologies and gas exchange values was described. The simulator represents an advancement to other simulators described in the literature due to both its ability to simulate a range of lung physiologies coupled with its high degree of accuracy. Previous metabolic simulation strategies described in the literature include a
19,20,21 technique based on alcohol burn (methanol or butanol) which produce CO 2 and H 2O and consume O 2 in known proportion. These burns are typically done in a bottle or combustion chamber and the simulated lung compliance is therefore fixed. Attempts at using flow controller techniques to produce gas flow into bottle 22,23 have also failed to address the need for variable lung mechanics. The system described herein addresses these shortcomings. The test lung
(Training/Test Lung, Michigan Instruments Inc. Grand Rapids MI) employed in this design is a well accepted industry standard for lung simulation and meets appropriate ISO and ANSI standards for mechanical ventilator testing. It is therefore considered to be acceptable for the metabolic simulator described herein from the standpoint of adequacy of lung mechanics simulation. The test lung consists of a spring-tensioned bellows to simulate lung compliance and precision orifice restrictors to simulate airway restrictance. The lung compliance can be set independently of airway restrictance and vice versa. The lung compliance modeled by the test lung is linear due to the linear force vs. displacement (volume) characteristic of the spring and bellows mechanism employed. The airway restrictance through the precision orifice restrictors produces a parabolic pressure vs. flow relationship representative of true physiologic airway restrictance. Finally, the bellows resting volume produces a typical adult functional residual capacity (FRC). Table 2.5. gives applicable specifications for the test lung.
Page 35 TABLE 2.5. Applicable Training/Test Lung Specifications
Test Lung Characteristic Specification
Compliance Range 10 –150 mL/cmH 2O
Compliance Accuracy +/- 5% at 150 mL/cmH 2O
Restrictors Rp5, Rp20, Rp50
Lung Capacity 0 – 2000 mL
Monitoring of ventilator delivered breath patterns is performed by a Respiratory Profile Monitor
(Novametrix Inc, Wallingford CT). The monitor is configured to communicate with the software program. The monitor is a non-invasive monitor generally used in a critical care setting for management of ventilator-dependent patients. Data obtained from the monitor, which are used here as a basis for control of the metabolic gas flows, include such real-time information as airway flow, breath volume, and breath timing. Applicable specifications for the monitor are listed in Table 2.6:
TABLE 2.6. Applicable Specifications
Characteristic Specification
Flow Range 0.25 - 180 L/Min
Flow Accuracy +/- 3% reading or
0.5 L/min
Volume Range 1-3000 mL
Breath Timing Resolution 0.01 sec
Page 36 Monte Carlo analysis was employed for the determination of overall system accuracy as this technique is useful for assessing the combinatorial effects of input errors which would be difficult or impossible to determine directly, as is the case here. The difficulty with direct measurement of system errors lies in the fact that small changes in pCO 2 and pO 2 content in the lung cannot be directly measured with sensors with acceptable accuracy. Thus, the Monte Carlo technique is employed to assess system accuracy with the principle drawback being the open- loop nature of the technique (i.e. VO 2 and VCO 2 error cannot be verified should it occur in the lung). All potential error sources were investigated for this analysis. Carbon dioxide, oxygen and vacuum flows were all determined to be potentially significant error sources. Ventilator volume delivery errors were determined to not present a large accuracy problem as changes in ventilator delivered tidal volumes have little bearing on the underlying gas removal and addition strategies used by the metabolic simulator module (i.e. tidal volume does not effect how much gas is removed by vacuum or how much carbon dioxide and nitrogen gas is added; these being the determinants of VO 2 and VCO 2). Timing variation in the flow delivery system could also present a source of error but this error is likely quite small due to the high precision of the timing mechanism of the simulator and therefore was not be considered in this analysis. Another potentially small source of system error is the variable backpressure seen downstream of the mass flow controllers due to pressure variations within the lung during breath delivery. However, the backpressure system serves to greatly minimize an otherwise relatively small source of error §§ . Finally, the effect of upstream pressure variation is a potential error source. However, the mass flow controllers are designed to minimize long term upstream pressure drift on flow output and, thus, this error source was considered to be quite small and was not considered in this analysis.
Page 37 Since direct measurement of simulator output was not utilized, the results show only indirect evidence of simulator accuracy based on mathematical formulations and calibration data. Worst case simulator accuracies obtained of +/- 0.503% for VO 2, +/- 0.774% for VCO 2, and +/- 0.936% for RQ are impressive relative to existing simulators.
§§ Over the course of a single breath delivery, the slow PID controlled mass flow controller (T10-
90 ≈ 1 second) acts like a simple flow restrictor. Typical flow delivery errors seen on a breath with a mean inspiratory pressure of 20 cmH 2O would therefore be equal to 20 parts in 3515 (50
PSI upstream pressure = 3515 cmH 2O) or 0.5%. Typical flow delivery errors seen with the backpressure system would be 1 part in 3515 or 0.025%.
Page 38
REFERENCES:
1. Damask, M.C, Weissman C, Askanazi J, Hyman I, Rosenbaum SH, Kinney JM: A
systematic method for validation of gas exchange measurements. Anesthesiology. 1982;
57: 213-218.
2. Weisman C, Sardar A, Kemper M: An in vitro evaluation of an instrument designed to
measure oxygen consumption and carbon dioxide production during mechanical
ventilation. Crit Care Med. 1994; 22:1995-2000.
3. Nunn, J.F., Makita K, Royston B: Validation of oxygen consumption measurements
during artificial ventilation. J Appl. Physiol. 67(5):2129-34:1989.
4. Shortland G.J.,Fleming P.J.,Walter J.H.: Validation of a portable indirect calorimetry
system for measurement of energy expenditure in sick preterm infants. Arch Dis Child.
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5. Braun U, Zundel J, Frieboth K, Weyland W, Turner E, Heidelmeyer CF, Hellige G.
Evaluation of methods for indirect calorimetry with a ventilated lung model. Intensive
Care Med. 15(3):196-202:1989.
6. Miodownik S, Melendez J, Carlon VA, Burda B. Quantitative methonol-burning lung
model for validating gas-exchange measurements over wide ranges of FIO2. J Appl
Physiol. Jan;84(6):2177-82:1998.
7. MacKay S. J., Loiseau A., Poivre R. Huot A., Calibration method for small animal
indirect calorimeters. Am J Physiol. Nov;261(5 Pt 1): E661-4:1991.
Page 39 8. Makita K., Nunn J.F., Royston B., Evaluation of metabolic measuring instruments for use
in critically ill patients. Crit Care Med. 18(6), 638-44:1990.
9. Mayfiield S.R.: Technical and clinical testing of a computerized indirect calorimeter for
use in mechanically ventilated neonates. Am J Clin Nutr; 54:30-4: 1991.
10. Takala J, Keinanen O., Vaisanen P, Kari A.: Measurement of gas exchange in intensive
care: Laboratory and clinical validation of a new device. Crit Care Med; 17:1041: 1989.
11. Phang P.T., Rich T., Ronco J.: A validation and comparison study of two metabolic
monitors. J Parenter Enteral Nutr. May-Jun;14(3):259-61: 1990.
12. Makita K., Nunn J.F.,Royston B.: Evaluation of metabolic measuring instruments for use
in critically ill patients. Crit Care Med. Jun; 18(6):638-44: 1990.
13. Weissman C., Sardar A., Kemper M., In vitro evaluation of a compact metabolic
measurement instrument. J Parenter Enteral Nutr. Mar-Apr;14(2):216-21:1990.
14. Gore C.J., Catcheside P.G.,French S.N., Bennett J.M., LaForgia J.: Automated VO2max
calibrator for open-circuit indirect calorimetry systems. Med Sci Sports Exerc.
Aug;29(8):1095-103: 1997.
15. Nicholson M.J., Holton J, Bradley A.P., Beatty P.C.: The performance of a variable-flow
indirect calorimeter. Physiol Meas. Feb;17(1):43-55:1996.
16. Garrow JS, Webster JD: A computer-controlled indirect calorimeter for the measurement
of energy expenditure in one or two subjects simultaneously. Hum. Nutr. Clin. Nutr.
1986; 40C: 315 – 321.
17. Henderson AM, Mosse CA, Forrester PC, Halsall D, Armstrong RF: A system for the
continuous measurement of oxygen uptake and carbon dioxide output in artificially
ventilated patients. Br. J. Anaesth. 1983; 55: 791 – 800.
Page 40 18. Levinson MR, Groeger JS, Miodownik S, Ray C, Brennan MF: Indirect calorimetry in
the mechanically ventilated patient. Crit. Care Med. 1987; 15: 144-147.
19. Bursztein S, Elwyn D, Askanazi J, Kinney J. Energy Metabolism, Indirect Calorimetery,
and Nutrition. Williams & Wilkins. Baltimore. 1989, 58.
20. Garrow JS, Webster JD: A computer-controlled indirect calorimeter for the measurement
of energy expenditure in one or two subjects simultaneously. Hum. Nutr. Clin. Nutr.
1986; 40C: 315 – 321.
21. Henderson AM, Mosse CA, Forrester PC, Halsall D, Armstrong RF: A system for the
continuous measurement of oxygen uptake and carbon dioxide output in artificially
ventilated patients. Br. J. Anaesth. 1983; 55: 791 – 800.
22. Levinson MR, Groeger JS, Miodownik S, Ray C, Brennan MF: Indirect calorimetry in
the mechanically ventilated patient. Crit. Care Med. 1987; 15: 144-147.
23. Damask, M.C, Weissman C, Askanazi J, Hyman I, Rosenbaum SH, Kinney JM: A
systematic method for validation of gas exchange measurements. Anesthesiology. 1982;
57: 213-218.
24. Weisman C, Sardar A, Kemper M: An in vitro evaluation of an instrument designed to
measure oxygen consumption and carbon dioxide production during mechanical
ventilation. Crit Care Med. 1994; 22:1995-2000.
Page 41 CHAPTER 3.
A NOVEL RESPIRATORY QUOTIENT ALGORITHM BASED ON PARTIAL PRESSURE
OXYGEN AND CARBON DIOXIDE SENSORS
ABSTRACT
A new and novel indirect algorithm for the determination of respiratory quotient (RQ) has been derived. The algorithm provides a basis for RQ determination through the use of real-time partial pressure oxygen and carbon dioxide sensors. The RQ value is defined clinically as the ratio of carbon dioxide volume production to oxygen volume consumption over time (VCO 2/VO 2). The algorithm is based on the slope of the pp CO 2 vs. pp O2 trace during exhalation and relies, only indirectly, on gas volume data which are a significant source of error in other existing algorithms. A mathematical transformation is provided to obtain the ratio VCO 2/VO 2 from the
∆pp CO 2/∆pp O2 trace. In addition, resting energy expenditure (REE) which is defined as the number of calories per day an individual consumes at rest can be determined from the VCO 2 and
2,3 VO 2 numbers using the well established Weir Equation . A bench validation was performed to assess the accuracy of the new algorithm using a metabolic simulator. This validation indicated that an algorithm known as Slope Algorithm #2 outperformed the industry standard Haldane
Transform at F IO2 values of 0.6 and below. A clinical validation was further undertaken to compare the Slope Algorithm #2 to an industry standard metabolic cart Deltatrac (Datex-
Ohmeda, Finland). This clinical validation indicated the difference between the Slope Algorithm
Page 42 #2 and the Deltatrac. Respiratory Quotient to be 4.02% (95% confidence level) while REE difference was found to be 5.7% (95% confidence level).
Keywords: RQ, REE, Slope Algorithm, Haldane Transform, VO 2, VCO 2,
Page 43 Introduction
The respiratory quotient (RQ = VCO 2/VO 2) is a useful clinical parameter for the determination of both the caloric and nutritional substrate balance requirements of patients undergoing life support therapy. It provides clinicians with information on the proportionate amounts of fat, carbohydrate and protein being consumed by the patient.
Currently, all RQ algorithms based on the VCO 2/VO 2 relationship rely on the use of volumetric data from ventilation. Unfortunately, the volume sensing devices typically used are only accurate in the ± 3-5% range. These volume sensing device accuracies become intrinsic to the overall accuracy of RQ algorithms which rely on these readings.
A new algorithm is described which improves the accuracy in calculated RQ by reducing the effect of volume sensor error on algorithm output. The goal in the derivation and test of this algorithm is to improve the accuracy of RQ readings thus, producing a concomitant improvement in the quality of clinical decisions based on more accurate numbers.
Methods:
Two primary gas laws were utilized in the development of this algorithm, Boyle’s Law and
Dalton’s Law.
Page 44 Boyle's Law. Robert Boyle investigated the relationship between the volume of a dry ideal gas and its pressure. Upon fixing the amount of gas and its temperature, Boyle found that when he manipulated the pressure, the volume responded in the opposite direction. This led to the following well-known equation:
P1V1 = P 2V2 (3.1)
where the variables with the “1” subscript mean initial values before a change of volume or pressure, and variables with the “2” subscript indicate final values following the change.
Dalton's Law. Dalton's Law applies to ideal gases in a mixture. Dalton observed that the total pressure (P total ) of a gas mixture was the sum of the partial pressures (P1,2…n ) of each gas.
Ptotal = P 1 + P 2 + P 3 + ...... P n (3.2)
Partial pressure is defined as the pressure that a single gas exerts on a container as if that gas alone occupied the container.
Algorithm Preliminaries. In order to derive the algorithm, let’s think of the process of a single breath delivery (inhalation to exhalation) for a typical 70 kg adult given a 0.5 Liter inspired tidal volume (TV I) with an F IO2 of 0.5. Let’s further say that the gas is humidified to a relative humidity of 100% (47 mm Hg) at 37 oC (during inspiration and expiration). Let’s also assume that the respiratory metabolic production of carbon dioxide (CO 2) is 20 mL/breath and the
Page 45 respiratory metabolic consumption of oxygen (O 2) is 25 mL/breath (RQ = ∆CO 2/∆O2 = 20/25 =
0.8). Next, let’s assume that the water vapor relative humidity (R h) and temperature of the
o inspired and expired gas are known to be 100% at 37 C and the barometric pressure (P b) is 760 mm Hg. For this case as described, Figure 3.1. indicates the progression of the breath with partial pressures of the gases before and after metabolic gas exchange.
Inhalation Exhalation
47 47 mmHg H2O mmHg H2O
+ 356.5 20 ml CO2 360.37 mmHg N2 mmHg N2 _ 25 ml O2 30.72 CO2 356.5 321.9 mmHg O2 mmHg O2
500 mL 495 mL
Figure 3.1. Gas partial pressures before and after the addition/removal of respiratory
gases due to metabolic gas exchange.
Page 46 Since the assumption has been made that the inspired gas has a relative humidity of 100% at body temperature (37 oC), we can say by Dalton's Law that the inspired gas water vapor pressure must have a partial pressure equivalent to that of the water vapor acting alone (i.e. 47 mmHg).
The remaining partial pressures must add to the barometric pressure of 760 mmHg. Since the remaining gas mixture is 50% O 2 and 50% N 2, we can say that the partial pressures of O 2 and N 2 are ((760-47)*0.5) or 356.5 mmHg. Thus, given an F IO2, one can determine the partial pressures of the inspired gas as follows:
PIO2 = (P b - R h-Insp(37oC) *47)*F IO2 (3.3)
PIH2O = (R h-Insp(37oC) )*(47) (3.4)
PIN2 = (P b - P IH2O - P IO2) (3.5)
PICO 2 ≅ 0 (3.6)
During exhalation, the gas loses 25 mL of O 2 and gains 20 mL of CO 2. Thus, in the expired gas there appears to be a volume change of -5 mL. However, since the partial pressure of water vapor in this volume remains unchanged, the amount of water vapor in this, now reduced volume, must be itself reduced. This can be expressed mathematically as follows:
VH2O = (P IH2O)*(V I/P b) - (P EH2O) * (V E/P b) (3.7)
Where the first term represents the water vapor volume during inhalation and the second term represents the water vapor valume during exhalation.
Page 47
Now, given that we have the initial inspired volume V I and we know the volume change due to
O2 consumption, CO 2 production and addition/elimination of water vapor, we can deduce the volume of the expired gas (V E) as follows:
V E = V I + VO2 + VCO 2 + VH 2O (3.8)
It is clear that given unequal values for VO2 and VCO 2, and given R hInsp(37oC) = R hExp(37oC) , we will have a change in the total volume of the gas between inspiration and expiration. Since the partial pressure of the water vapor is assumed to remain the same during the entire breath, the partial pressures of the other gases in this volume, which must add to P b, must change. Thus, normalizing the remaining partial pressures to the new volume (Vol Exp ) gives the following exhalation partial pressures:
P ECO 2 = (VCO 2/V E)*P b (3.9)
∆PEO2 = (VO2/V E)*P b (3.10)
P EO2 = ((P IO2/P b)*V I) - VO2)*(P b/V I)) (3.11)
P EH2O = 47 mmHg (3.12)
Page 48
Volume of CO2
Produced RQ During Breath
Volume of O2 Consumed During Breath
Figure 3.2. RQ represented as the slope of the change in volumes of CO 2 and O 2.
Page 49 The values of P EO2 and P ECO 2 seen above are the same values as measured using the partial pressure O 2 and CO 2 sensors. The exhalation side of Figure 3.1. shows the results of equations
3.9-12. Of note is how the changed inspiratory to expiratory volume resulted in a change in the exhalation partial pressures of the gases. Specifically, the decrease in the volume of expired gas increased the partial pressures of the gases (as can be seen clearly with N 2). The partial pressure of the water vapor does not change as the expired gas is assumed to be held at 100% R h throughout the breath.
Respiratory Quotient From Gas Partial Pressures
The definition of the Respiratory Quotient is the ratio of the volume of CO 2 produced to volume of O 2 consumed during breathing. Plotting VO2 against VCO 2, as shown in Figure 3.2. produces a slope which is equivalent to RQ. Unfortunately, the information obtained by way of the CO 2 and O 2 sensors is not a volume of gas but a gas partial pressure. If gas partial pressures are used instead of volumes, the slope of the PCO 2/ PO 2 changes with the magnitude of F IO2. This phenomenon is illustrated in Figure 3.3. which shows the change in slope PCO 2/ PO 2 vs. F IO2.
Inspection of Figure 3.3. indicates that, as the partial pressure of oxygen in the inspired gas is increased, the slope of the PCO 2/ PO 2 trace tends towards a value of 1 even though the true
RQ value is 0.8. Thus, the slopes of partial pressure changes of CO 2 and O 2 over a range of
FIO2's are not equivalent to the slope of volume changes for CO 2 and O 2. Inspection of Figure
3.3. also indicates that the two curves intersect at the theoretical point of zero F IO2. In fact,
Page 50
Calculated RQ vs. FIO2 Using Single Breath Partial Gas Pressures
1.2
1
0.8
Insp: 47 mmH2o, Exp: 47 mmH2O 0.6
FIO2 Ideal Behavoir
0.4
0.2
0 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Calculated RQ
Figure 3.3. RQ as determined from partial pressure slope vs. F IO2. The actual RQ
is plotted (vertical line).
Page 51
Figure 3.3 can be interpreted as showing that the dependency of partial pressure RQ values on volume information increases with increasing F IO2. The tendency of the partial pressure based
RQ calculations towards a value of 1.0 given F IO2 values approaching 1.0 can be understood by observing the equation used to obtain the partial pressure RQ (RQ pp ) values:
PECO 2 - PICO 2 RQ pp = 13.3( ) PIO2 - PEO2
Note: This equation, as state above, only becomes accurate as F IO2 →0.
To illustrate this point further, let’s assume that the VO2 and VCO 2 are 25 mL and 20 mL respectively. Using an F IO2 of 1.0, a barometric pressure of 760 mmHg, and an R h of 100%,
Equation 3.13. would produce:
RQ pp = (30.4 mmHg - 0 mmHg) / (713 mmHg - 682.24 mmHg)
or RQ pp ≅ 1.0
The volume based RQ algorithm would produce a result of 0.8 (20/25 = 0.8). Thus, the two algorithms diverge with increasing F IO2. Unfortunately, as stated earlier, this paper seeks to use partial pressure oxygen and carbon dioxide sensors only to obtain RQ (thus theoretically reducing the effect of volume sensor based errors propagating though the algorithm). Given this
Page 52 objective, a mathematical determination of the reason for the divergence is derived in the following section.
Mathematical Derivation of Reason for Divergence. Using an RQ definition for partial pressures in a format similar to that used for volumes gives:
RQ = VCO 2/VO2 (For volumes)
RQ pp = (P ECO 2 - P ICO2)/(P IO2 - P EO2) (For partial pressures)
It is clear upon inspection that the two RQ strategies shown above are not equivalent as the numerators and denominators in the expressions are not equal as can be deduced from 3.9 and
3.11 which require volume information for the calculation of VCO 2 and VO 2:
VCO 2 ≠ P ECO 2 – P ICO 2 3.14)
VO 2 ≠ P ICO 2 – P ECO 2 3.15)
Thus, a determination of the true RQ without volume or flow based devices is not possible using this approach. However, a technique will be presented in the next section which provides for a determination of true RQ using the information from volume and flow based devices in an indirect fashion only.
Page 53
Derivation of the Slope Algorithm:
Let:
VI = Volume of moist inspired air in ml
VCO 2 = mls of moist CO 2 added to V I in lung
VO 2 = mls of moist O 2 removed from V I in lung
FE = Fraction of moist gas in alveolar air (by Volumes).
R = Respiratory Quotient = VCO 2/VO 2
PCO 2 and PO 2 = Partial pressures of CO 2 and O 2 in alveolar air in mmHg (STPD).
FI and P I = Refer to moist inspired air.
By mass balance:
VCO 2 = F ECO 2(V I + VCO 2 - VO 2) - F ICO 2*V I (3.16)
VO 2 = F IO2*V I - F EO2(V I + VCO 2 - VO 2) (3.17)
Now, lets substitute VCO 2/R for VO 2 in 3.16 to yield:
VCO 2 = F ECO 2(V I + VCO 2 - VCO 2/R) - F ICO 2*V I (3.18)
= VCO 2 = F ECO 2* VI + F ECO 2* VCO 2 - F ECO 2* VCO 2/R) - F ICO 2*V I (3.19)
= VCO 2 - F ECO 2* VCO 2 + F ECO 2* VCO 2/R = F ECO 2* VI - FICO 2*V I (3.20)
Page 54 = VCO 2 = (F ECO 2* VI - FICO 2*V I )/ (1 - F ECO 2 + F ECO 2/R) (3.21)
Now, lets substitute R*VO 2 for VCO 2 in 3.17 to yield:
VO 2 = F IO2*V I - F EO2(V I + R*VO 2 - VO 2) (3.22)
= VO 2 + F EO2 *R*VO 2 - F EO2 *VO 2 = F IO2*V I - F EO2*V I (3.23)
= VO 2 = (F IO2*V I - F EO2*V I)/(1 + F EO2 *R - F EO2) (3.24)
Now, taking equations 3.21 and 3.24 and substituting VCO 2 and VO 2 into the equation
VCO 2/VO 2 =R and solving for F EO2 yields:
(F EO2*R/(1- F ECO 2+ F ECO 2/R)) - (F EO2/(1- F ECO 2+ F ECO 2/R)) +
(F EO2*R*V I/( F ECO 2* VI – F ICO 2* VI )) = (-1/(1- F ECO 2+ F ECO 2/R)) +
(R* F IO2*V I)/( F ECO 2* VI – F ICO 2* VI )) (3.25)
Further manipulation of the above relation yields:
F EO2 (-R*F ICO 2*V I + F ICO 2*V I + R*V I)/(1- F ECO 2+ F ECO 2/R)* ( F ECO 2* VI – F ICO 2* VI ))
= (-FECO 2*V I + F ICO 2*V I+R*F IO2*V I- R* F IO2*V I*F ECO 2 + F ECO 2* F IO2*V I)/
(1- F ECO 2+ F ECO 2/R)* ( F ECO 2* VI – F ICO 2* VI )) (3.26)
This, in turn leads to the following expression in terms of F EO2:
FEO2 = (F IO2*R + F ECO 2* F IO2 – R* F ECO 2* F IO2 + F ICO 2 – FECO 2)/( F ICO 2 – R* F ICO 2 + R)
(3.27)
Page 55 The previous expression 3.27 is commonly referred to as the general alveolar air equation.
Multiplying both sides by the barometric pressure P B minus the partial pressure of water vapor at body temperature or (P B-47) to change F (fraction) to P (partial pressure) will produce the following expression noting that p IO2 is equivalent to F IO2* (P B-47), P ICO 2 is equivalent to
FICO 2* (P B-47), so we have the following:
P EO2 = (P IO2*R + P ECO 2*F IO2*(1-R) + P ICO 2 - P ECO 2) /
(F ICO 2(1-R) + R) (3.28)
Equation 3.28. is the complete alveolar air equation often cited in the literature. Further manipulation of this equation produces:
P EO2*(R + (1-R)*F ICO 2) = (P IO2*R + P ECO 2*F IO2*(1-R) + P ICO 2 – P ECO 2)
(3.29)
Now, P IO2 is equivalent to F IO2*(P B-47) and P ICO 2 is equivalent to F ICO 2*(P B-47), so we have
the following:
PEO2*(R + (1-R)*F ICO 2) = (F IO2*(P B-47)*R + P ECO 2*F IO2*(1-R) + F ICO 2*(P B-47) – P ECO 2)
(3.30)
Next, let’s solve for P ECO 2 vs. P EO2 as that is what we are interested in with this derivation:
Page 56 PECO 2*(1-(1-R)*F IO2) = (P B-47)*(R*F IO2 +F ICO 2)
- (R + (1-R)*(F ICO 2)*P EO2 ) (3.31)
When rearranged, Equation 3.31. becomes:
P ECO 2 = (P B-47)*(R*F IO2 + F ICO 2)/(1-(1-R)*F IO2) -
(R+(1-R)*(F ICO 2)*P EO2)/(1-(1-R)*F IO2) (3.32)
Further manipulation of Equation 3.32 to obtain an equation in terms of the slope of the P ECO 2 vs. P EO2 plot is:
S = (R + (1-R)*F ICO 2)/(1 - (1-R)*F IO2) (3.33)
Where S = P ECO 2/P EO2
Solving for R yields the expression for instantaneous R based on the tangent to the P ECO 2 vs.
PEO2 plot:
R = ((S - F IO2*S) - F ICO 2)/(1-(F IO2*S) - F ICO 2) (3.34)
Equation 3.34 is the equation originally derived by Kim et al 4. Now, we know what the instantaneous value of R (RQ) is based on the partial pressure slopes of CO 2 and O 2 (as well as from F IO2 and F ICO 2). In order to produce an effective algorithm, we must somehow weigh
Page 57 these instantaneous RQ values over the course of the exhalation period in order to obtain a value of overall RQ based on an assemblage of weighted instantaneous RQ values.
Two approaches to weighting are attempted in this paper, with the latter being more mathematically sound, and as will be seen, with the latter producing better results in practice.
The first approach involves weighting the individual instantaneous RQ values based solely on flow while the latter approach involves weighting the instantaneous RQ values based on both flow and O 2 (CO 2 can also be used) partial pressure values.
The weighting technique used is as follows:
i=N (Ins tan tan eousRQi (*) Weighti /) ∑(Weight i) (3.35) i=1
Where i = 1 represents the beginning of exhalation and i = N represents the end of exhalation. In the first (less desirable) approach, weights are simply the value of exhalation flow at the time i.
In the latter approach, weights are the multiplicative product of exhalation flow and (current partial pressure O 2 /Maximum partial pressure O 2). It should be noted that CO 2 can be used for this expression as well. The latter approach is preferred as the relative weight of the instantaneous RQ should be based on the actual amount of gas exchange taking place at that moment. Gas exchange can be thought of as the volume of gas moving out of the lungs at that moment in time which would be the partial pressure of the gas multiplied by the flow. Thus,
Page 58 using the latter weighting approach appears to be a more theoretically sound approach. In conclusion, we have derived the following two approaches to the so-called slope algorithm:
Slope Algorithm 1 (flow only weighting):
i= N OverallRQf orbreath = (Ins tan tan eousRQi (*) Weighti /) ∑(Weight i) (3.36) i =1
Where:
i = 1 is the beginning of exhalation
i = N is the end of exhalation
Weight i = Magnitude of exhalation flow at time i.
InstantaneousRQ i = ((S - F IO2*S) – F ICO 2)/(1-(F IO2*S) - F ICO 2) at time i.
Slope Algorithm 2 (flow*ppO 2 weighting):
i= N OverallRQf orbreath = (Ins tan tan eousRQi (*) Weighti /) ∑(Weight i) (3.37) i =1
Where:
i = 1 is the beginning of exhalation
i = N is the end of exhalation
Weight i = Magnitude of exhalation flow*(ppO2i/ppO2max) at time i.
InstantaneousRQ i = ((S - F IO2*S) –FICO 2)/(1-(F IO2*S) - F ICO 2) at time i.
Additional Algorithms: The Haldane Transform and an Integration Technique:
Page 59 In order to assess the performance of the slope algorithm derived in the previous section, the author compared this technique to two common techniques for determining the Respiratory
Quotient. The first technique to be employed for comparison is the well-known Haldane
Transform. The derivation of this transform is as follows:
Let:
VI = Volume of inspired air in ml (STPD).
VE = Volume of expired air in ml (STPD).
F = Fraction of gas in alveolar air by volumes (STPD).
VO 2 = mls of O 2 removed from V I in lung (STPD).
Then, we have:
VO 2 = V I*F IO2 - V E*F EO2 (3.38)
By Nitrogen balance we have:
VI*N 2 = V E*N 2 (3.39)
Next, plugging in Nitrogen volume equivalents yields:
VI*(1-FIO2) = V E*(1-FEO2 - F ECO 2) (3.40)
Page 60
This is equivalent to:
VI = VE*(1-FEO2 - F ECO 2)/(1-FIO2) (3.41)
Finally, Equation 3.31. can be plugged into Equation 3.30. to yield the Haldane Transform:
VO 2 = (F IO2*(1-FEO2 - F ECO 2)/(1-FIO2)-FEO2)*V E (3.42)
This technique is commonly used in many indirect calorimetry devices and can be considered the gold standard algorithm for comparison purposes.
Integration Technique
The so-called Integration Technique involves simply integrating the values of partial pressure of
CO 2 and O 2 multiplied by instantaneous flow over the course of inhalation and exhalation producing the inhalation and exhalation volumes of oxygen and carbon dioxide entering and exiting the patient’s lungs. The result is then the integrated volume of carbon dioxide over the course of a breath divided by the integrated volume of oxygen over the course of a breath.
Humidity Considerations:
The derivations of the previous sections did not take into account gas humidity considerations.
Specifically, the humidity of the inhaled gas may not be equivalent to the humidity of the
Page 61 exhaled gas. If ignored, the humidity changes over the course of a breath can lead to errors in the accuracy of the algorithms discussed. The current system is incapable of assessing the real time change in humidity over the course of the breath. Approximation techniques can be employed to estimate humidity over the course of the breath. However, in the bench validation efforts undertaken in this paper, changes in relative humidity were not simulated.
Bench Validation:
In order to determine the relative accuracies of the four algorithms discussed, a comprehensive bench validation effort was undertaken. The hardware used for this validation consisted of the accurate metabolic simulator described in Chapter 2. This simulator was used in combination with a software based development system for:
1. Implementation of the four algorithms.
2. Control of the simulator.
3. Implementation of front-end signal processing tasks.
4. Simultaneous display of the four algorithm outputs.
The software based development system was constructed on an IBM compatible PC using the
Borland C++ version 3.0 compiler. Input to the development system consisted of data accumulated in real-time by the Respiratory Profile (CO 2, flow and airway pressure) Monitor and the QUO photo-luminescent oxygen sensor. Output from the development system consisted of control sequences sent to the accurate metabolic simulator as well as algorithm results display.
Page 62 Front-end signal processing was performed on each of the sensors in order to balance the frequency responses of the sensors.
The simulator was used to determine the algorithms’ responses to varying metabolic demand, as well as varying lung mechanics and ventilator settings. Each data point obtained is the result of
50 breaths delivered to the simulator. The ensemble averages shown at the bottom of the table were taken for cases when F IO2 was at 0.60 or below and with the test runs at lower RQ’s normalized to an RQ of one.
Clinical Validation:
In order to assess the accuracy of the metabolic system developed in a clinically realistic setting, an in vivo comparison of the system with a clinically accepted standard, the Deltatrac (Datex-
Ohmeda, Finland), was performed. The Deltatrac validation is available in the literature 1. The
Deltatrac is a large system also known as a “metabolic cart” consisting of a mixing chamber arrangement in which exhaled gases are collected in a chamber for analysis of mixed exhaled gas partial pressures. The readings are typically slow to materialize however, empirically, stabilization after 3-5 minutes can be expected. The patient is required to breathe on the device for a period of time after which the calculated value of RQ and REE are displayed.
Page 63 The results of the algorithm are reported using both RQ and REE values. The Resting metabolic rate (REE) is determined in both systems by use of the Weir 2,3 equation. This clinically accepted standard for determination of REE uses VO 2 and VCO 2 as inputs as shown below:
REE (Kcal/day) = (3.941*VO 2(ml/min) + 1.11*VCO 2(ml/min) )*1.440 (3.43)
Page 64 Table 3.1 Algorithms Compared. Mean and Std. Dev. displayed at ventilator and lung settings.
Setting Expected Integration Slope #1 Slope #2 Haldane
RQ Algo RQ Algo RQ Algo RQ Algo RQ
RQ vs. FIO2 FIO2 = .21 1.0 0.959+/-.070 0.928 +/- .031 0.969 +/- .012 0.940 +/- .035
RQ vs. FIO2 FIO2 = .40 1.0 0.960 +/- .166 0.978 +/- .029 1.011 +/- .013 0.970 +/- .026
RQ vs. FIO2 FIO2 = .60 1.0 0.670 +/- .062 0.979 +/- .040 1.005 +/- .036 0.973 +/- .034
RQ vs. FIO2 FIO2 = .80 1.0 0.691 +/- .108 1.435 +/- .525 1.488 +/- .436 1.117+/ -.169
RQ vs. Pause, Pause = 0% 1.0 0.819 +/- .079 1.015+/- .027 1.035 +/- .010 1.038 +/- .035
RQ vs. Pause,Pause = 5% 1.0 0.829 +/- .118 0.999 +/- .016 1.016 +/- .009 0.982 +/- .025
RQ vs. Pause,Pause = 10% 1.0 0.959 +/- .070 0.948 +/- .031 0.989 +/- .012 0.960 /-.035
RQ vs. Pause, Pause = 20% 1.0 0.790 +/- .054 1.045 +/- .019 1.070 +/- .011 1.047 +/- .043
RQ vs. Pause, Pause = 30% 1.0 0.793 +/- .071 1.018 +/- .014 1.042 +/- .010 1.030 +/- .033
RQ vs. PEEP, PEEP = 0 cm 1.0 0.959 +/- .070 0.938 +/- .031 0.979 +/- .012 0.950 +/- .035
RQ vs. PEEP, PEEP = 2.5 cm 1.0 0.743 +/- .139 1.001 +/- .036 1.031 +/- .010 1.025 +/- .025
RQ vs. PEEP, PEEP = 5 cm 1.0 0.742 +/- .023 0.978 +/- .027 1.006 +/- .012 1.019 +/- .031
RQ vs. PEEP, PEEP = 7.5 cm 1.0 0.779 +/- .074 1.005 +/- .050 1.034 +/- .024 1.046 =/- .034
RQ vs. PEEP, PEEP = 10 cm 1.0 0.768 +/- .042 1.028 +/- .042 1.059 +/- .026 1.046 +/- .032
RQ v Del’d RQ,Del’d RQ = 0.2 0.2 0.178 +/- .008 0.196 +/- .019 0.206 +/- .007 0.222 +/- .013
RQ v Del’d RQ,Del’d RQ = 0.4 0.4 0.408 +/- .010 0.393 +/- .015 0.398 +/- .007 0.443 +/- .028
RQ v Del’d RQ,Del’d RQ = 06 0.6 0.426 +/- .016 0.589 +/- .021 0.601 +/- .007 0.622 +/- .021
RQ v Del’d RQ,Del’d RQ = 0.8 0.8 0.752 +/- .027 0.803 +/- .020 0.821 +/- .008 0.836 +/- .030
RQ v Del’d RQ,Del’d RQ = 1.0 1.0 0.932 +/- .047 0.968 +/- .041 1.007 +/- .019 1.031 +/- .039
RQ v Resp Rate, Resp Rate = 5 1.0 0.839 +/- .030 0.984 +/- .021 1.025 +/- .007 0.968 +/- .014
RQ v Resp Rate,Resp Rate = 10 1.0 0.959 +/- .070 0.928 +/- .031 0.969 +/- .012 0.940 +/- .035
RQ v Resp Rate,Resp Rate = 15 1.0 0.910 +/- .030 0.959 +/- .019 0.994 +/- .009 0.957 +/- .014
RQ v Resp Rate,Resp Rate = 20 1.0 0.962 +/- .030 0.958 +/- .018 1.001 +/- .010 0.972 +/- .018
Page 65 Setting Expected Integration Slope #1 Slope #2 Haldane
RQ Algo RQ Algo RQ Algo RQ Algo RQ
RQ vs. TV , TV = 200 ml 1.0 0.963 +/- .088 0.931 +/- .055 0.991 +/- .016 1.016 +/- .016
RQ vs. TV , TV = 350 ml 1.0 0.943 +/- .058 0.964 +/- .024 1.004 +/- .013 0.964 +/- .009
RQ vs. TV , TV = 500 ml 1.0 0.959 +/- .070 0.928 +/- .031 0.969 +/- .012 0.940 +/- .035
RQ vs. TV , TV = 650 ml 1.0 0.961 +/- .030 0.953 +/- .018 0.986 +/- .006 0.947 +/- .006
RQ vs. TV , TV = 800 ml 1.0 1.078 +/- .054 0.986 +/- .029 1.026 +/- .008 0.978+/- .015
RQ vs. I time, Itime = 0.2 sec 1.0 0.896 +/- .126 0.963 +/- .017 0.996 +/- .010 0.963 +/- .010
RQ vs. I time, Itime = 0.25 sec 1.0 1.031 +/- .043 0.985 +/- .018 1.022 +/- .008 0.967 +/- .010
RQ vs. I time, Itime = 0.33 sec 1.0 0.970 +/- .080 0.947 +/- .022 1.004 +/- .009 0.945 +/- .021
RQ vs. I time, Itime = 0.5 sec 1.0 1.203 +/- .106 0.965 +/- .021 1.003 +/- .008 0.945 +/- .015
RQ vs. I time, Itime = 0.67 sec 1.0 1.267 +/- .180 0.979 +/- .019 1.021 +/- .007 0.943 +/- .017
RQ vs. I time, Itime = 0.8 sec 1.0 1.212 +/- .267 0.979 +/- .013 1.024 +/- .007 0.928 +/-.008
RQ vs. RC, Rp5, C.03 1.0 1.152 +/- .214 1.002 +/- .04 1.034 +/- .014 0.983 +/- .025
RQ vs. RC, Rp5, C.07 1.0 1.148 +/- .144 0.985 +/- .035 0.997 +/- .014 0.944 +/- .027
RQ vs. RC, Rp5, C.11 1.0 1.007 +/- .081 0.966 +/- .025 0.997 +/- .008 0.967 +/- .035
RQ vs. RC, Rp5, C.15 1.0 0.937 +/- .032 0.967 +/- .033 1.000+/- .009 0.976 +/- .020
RQ vs. RC, Rp20, C.03 1.0 0.893 +/- .046 0.941 +/- .025 0.991 +/- .008 0.983 +/- .024
RQ vs. RC, Rp20, C.07 1.0 1.109 +/- .172 0.952 =/- .016 0.994 +/- .009 0.936 +/- .018
RQ vs. RC, Rp20, C.11 1.0 0.873 +/- .042 0.964 =/- .021 0.955 +/- .007 0.947 +/- .015
RQ vs. RC, Rp20, C.15 1.0 0.959 +/- .070 0.968 +/- .031 1.009 +/- .012 0.980 +/- .035
RQ vs. RC, Rp50, C.03 1.0 1.180 +/- .064 0.991 +/- .023 1.025 +/- .011 0.980 +/- .023
RQ vs. RC, Rp50, C.07 1.0 1.066 +/- .087 0.949 +/- .022 0.998 +/- .019 0.972 +/- .028
RQ vs. RC, Rp50, C.11 1.0 1.019 +/- .059 0.962 +/- .018 1.010 +/- .010 0.982 +/- .009
RQ vs. RC, Rp50, C.15 1.0 1.055 +/- .080 0.942 +/- .022 0.994 +/- .011 0.968 +/- .019
ENS AVE FIO2 < 0.8 1.0 0.953 +/- 0.079 0.973 +/- 0.029 1.008 +/- 0.013 0.985 +/- 0.026
Page 66 The REE (RMR) calculated using this technique accounts for between 70 and 80% of an individual’s daily caloric burn (the percentage is a function of the individual’s activity and stress level). Additionally, the respiratory quotient (RQ) or the volumetric ratio of carbon dioxide production to oxygen consumption at rest indicates the proportionate amount of carbohydrate to fat being metabolized in the individual (given a protein metabolism estimate from urea nitrogen concentration). Thus, with the RQ and RMR indices, clinicians are empowered to tailor nutritional support regimens suitable to the individual requirements of a patient.
Clinical validation testing was performed in the Anesthesia Laboratory at the University of Utah
Medical Center. All testing was performed under the approval of the hospital’s Institutional
Review Board. Twenty volunteers participated in the study, with each signing a consent and release form prior to testing.
The volunteers were asked to relax in a chair for a period of ten minutes prior to initiation of the test to allow their metabolic rates to stabilize. Each volunteer breathed simultaneously through a facemask attached to both the Deltatrac and or our system (Our system using Slope Algorithm
#2). Our system was set up to use only the most promising “Slope Algorithm #2” (see Page 58) as determined by the bench validation results. The dead space volume for each system was approximately equalized by using identical masks and heat and moisture exhangers (HME’s) for each test run. RQ values as well as REE numbers in Kcal/daywere recorded for both systems following a three-minute warm-up period for both systems. This warm-up period allowed for the volunteer to become accustomed to the devices and, by extension, allow the volunteer’s metabolic rate to stabilize.
Page 67
All results are reported in STPD (760 mmHg barometric pressure, 0 o C, 0% humidity), conditions. Results were analyzed using linear regression techniques and Bland-Altman analysis.
Bland-Altman analysis lends itself to intra-system comparisons.
Figure 3.4 shows a plot of the Slope Algorithm REE (energy expenditure) vs. the Deltatrac energy expenditure in Kcal/day. The least squares linear regression line indicates a good correlation with an R 2 value of 0.979. The ordinate intersect is –4.50 which is close to zero as expected.
Figure 3.5 is a plot of the Respiratory Quotient for the Slope Algorithm vs. the Respiratory
Quotient for the Deltatrac. The least squares linear regression line has a correlation with an R 2 value of 0.9317. The ordinate of the intersect is a respectable –0.012.
Figure 3.6 is a Bland-Altman plot of the Slope Algorithm energy expenditure minus the
Deltatrac energy expenditure vs. the average output of the Slope and Deltatrac. The plot indicates that two standard deviations or a 95% confidence interval is located at +109 and –105 Kcal/day with an intra-system bias of 3.6 Kcal/day.
Figure 3.7 is a Bland-Altman plot of the Slope Algorithm respiratory quotient minus the
Deltatrac respiratory quotient vs. the average output of the Slope Algorithm and Deltatrac respiratory quotients. This plot shows a 95% confidence interval between +0.045 and –0.035.
Page 68
Slope Algorithm vs. Deltatrac, Resting Energy Expenditure y = 1.0039x - 4.5042 R2 = 0.9795 2800
2600 y)
2400
2200
2000
1800
1600
1400 Slope Algorithm Resting Energy Expenditure (Kcal/Da 1200
1000 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800
Deltatrac Resting Energy Expenditure (Kcal/Day)
Figure 3.4. XY plot of comparison between Slope Algorithm and Deltatrac Resting Energy
Expenditure Results in Kcal/day.
Page 69 Slope Algorithm vs. Deltatrac, RQ y = 1.0079x - 0.012 R2 = 0.9317 1.1
1
0.9
0.8 Slope Algorithm RQ (unitless)
0.7
0.6 0.6 0.7 0.8 0.9 1 1.1 Deltatrac RQ (unitless)
Figure 3.5. XY plot of comparison between Slope Algorithm and Deltatrac RQ (unitless).
.
Page 70
Resting Energy Expenditure Difference (Bland-Altman) Plot
150
Bias + 2 S.D.
100
50
Bias 0 0 500 1000 1500 2000 2500 3000
-50
Slope Algorithm REE - Deltatrac REE (Kcals/Day) -100 Bias - 2 S.D.
-150
(Slope Algorithm REE + Deltatrac REE)/2
Figure 3.6. Bland-Altman plot of the Slope Algorithm REE vs. the (Slope REE +
Deltatrac REE)/2 output.
Page 71
RQ Difference (Bland-Altman) Plot
0.08
0.06
Bias + 2 S.D. 0.04
0.02
Bias 0 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
-0.02 Bias - 2 S.D.
Slope Algorithm RQ - Deltatrac - (unitless) RQ RQ Algorithm Slope -0.04
-0.06
-0.08 (Slope Algorithm RQ + Deltatrac RQ)/2
Figure 3.7. Bland-Altman plot of the Slope Algorithm RQ vs. the (Slope RQ+
Deltatrac RQ)/2 output.
Page 72
Slope Algorithm and Harris-Bennedict vs. Deltatrac, Energy Expenditure y = 1.0024x - 0.7853 R2 = 0.9787 2800
2600
Expenditure 2400
2200
2000
(Kcal/Day) 1800
1600
1400 Slope vs. Deltatrace Harris-Bennedict vs. Deltatrac 1200 Linear (Slope vs. Deltatrace) SlopeAlgorithm and Harris-Bennedict Resting Energy
1000 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Deltatrac Resting Energy Expenditure (Kcal/Day)
Figure 3.8. X-Y plot of Slope Algorithm #2 REE vs. Deltatrac REE with the addition of
data from Harris-Benedict REE vs. Deltatrac REE. Plot shows large variation in expected
energy expenditures as estimated by the Harris-Benedict formulation with measured
energy expenditures.
Page 73 Finally, Figure 3.8 repeats the X-Y plot of the Slope Algorithm REE vs. the Deltatrac shown in
Figure 3.4, however, this plot additionally shows the values predicted by the Harris-Benedict
REE population studies vs. the Deltatrac. This plot clearly shows that estimates of REE based on measurement are highly correlated with each other while estimates based on the Harris-Benedict population studies, commonly used clinically, show poor correlation with measured values.
Specifically, the SEE for the measurement REE in comparison to the Deltatrac is 54.7 kcal while the SEE for the Harris-Benedict formulation vs. the Deltatrac is 349.1 kcal.
DISCUSSION:
Analysis of the bench validation results shown in both in Table 3.1 indicate that the Slope
Algorithm #2 appears to be the best performer at F IO2 values less than 0.8. Specifically, at target
RQ values of 1.0 for F IO2 values below 0.8, RQ values of 0.863 +/- 0.167, 0.961 +/- 0.029, and
0.961 +/- 0.018 were reported for the Integration Algorithm, Slope Algorithm #1 and the
Haldane Transform respectively. However, more respectable RQ values of 0.995 +/- 0.022 were reported in this regime using Slope Algorithm #2. Further, ensemble averages at F IO2 values of
0.21 given a physiologically varied set of lung simulator conditions (see Table 3.1) show an average and standard deviation for RQ at 1.0 of 1.008 +/- 0.013 for Slope Algorithm #2.. This is superior to the ensemble averages and standard deviations of the Haldane Transform, Slope
Algorithm #1 and Integration Algorithms of 0.985 +/- 0.026, 0.973 +/- 0.029 and 0.953 +/- 0.079 respectively. This represents the first time that the author is aware of, that an algorithm has been proven to outperform the gold standard Haldane Transform in a controlled setting. It must be note however, that at F IO2 values of 0.8, the Haldane Transform appears to be the best performer
Page 74 with reported mean and standard deviation values of 0.691 +/- 0.108, 1.435 +/- 0.525, 1.488 +/-
0.436 and 1.117 +/- 0.169 for the Integration Algorithm, Slope Algorithm #1, Slope Algorithm
#2 and the Haldane Transform respectively. One might be led to the conclusion that an ideal indirect calorimetry algorithm from the standpoint of accuracy may involve a weighted transition from Slope Algorithm #2 to the Haldane Transform with increasing F IO2. Such an algorithm would be advantageous in settings in which the patient is exposed to high F IO2 values such as in an OR or ICU setting.
The results of the clinical validation data show that our system using Slope Algorithm #2 compares favorably with the Deltatrac. The linear regression of the comparisons showed an ordinate intersection of only –4.5 Kcal/day and an R 2 value of .97 indicative of a good linear fit without significant offset at the zero crossing. The comparison of RQ’s also indicate good fit.
Additionally, the Bland-Altman comparison of the Slope Algorithm with the Deltatrac indicated that the devices can be expected to be within approximately 100 Kcal/day of each other with a
95% confidence interval. This amounts to be 5.7% given a typical energy expenditure of 2000
Kcal/day. Finally, Bland-Altman analysis of the respiratory quotients indicates that the respiratory quotients can be expected to be within 4.02% of each other with a 95% confidence interval. These results indicate overall good performance of the Slope Algorithm #2 both in a controlled bench setting and in volunteers.
Page 75 REFERENCES:
1. Phang, Terry P; Rich, Tom; Ronco, Juan: A validation and comparison study of two
metabolic monitors; Journal of Parenteral and Enteral Nutrition 1990:3, pp 259-261
2. Mansel, P.I., Macdonald I.A.: Reappraisal of the Weir equation for calculation of
metabolic rate; American Journal of Physiology 1990:R1347-R1354
3. Weir, J.B. De V.; New Methods for calculating metabolic rate with special reference to
protein metabolism; Journal of Physiology, London . 109:1-9, 1949
4. Kim, T.S., J. Rahn, and L.E. Fahri. Estimation of true venous and arterial PCO 2 by gas analysis of a single breath. J. Appl. Physiol. 21:1338-1344, 1966.
Page 76 CHAPTER 4.
CONCLUSION
This dissertation covered techniques which can be employed to produce an accurate indirect calorimetry system using real-time oxygen and carbon dioxide sensors. Indirect calorimetry has found extensive use in the critical care arena with such maladies as cancer, sepsis and burn injury. Indirect calorimetry provides for an assessment of both patient daily caloric burn rate at rest (REE) as well as the proportionate amount of fat, carbohydrate and protein being consumed by the patient.
The technique presented in Chapter 2 represents a new and novel validation approach to assess the accuracy of such systems. This approach involves the introduction and removal of gases from a human breathing simulator to simulate carbon dioxide production and oxygen consumption during breathing. The system was designed to simulate a wide variety of human physiologies which might be encountered clinically in an adult patient population. Validation of the system was performed using a primary-standard mercury sealed spirometer to assess the accuracy and precision of gas flow to/from the simulator as affected by the gas delivery system.
Monte Carlo based sensitivity analysis of the resultant volumes delivered to the spirometer was then performed. The Monte Carlo analysis indicated a worse case VO 2 error of 0.981% (SD = 1), a worse case VCO 2 error of 0.774% (SD = 1) and a worse case respiratory quotient (RQ =
VCO 2/VO 2) of +/- 1.77% (SD = 1).
Page 77
Chapter 3 includes both a description of a new and novel respiratory quotient algorithm as well as bench and clinical validation of overall system accuracy employing this algorithm. The Bench validation was aimed at determining the relative accuracies of four different algorithmic approaches to the determination of the respiratory quotient. Ensemble averages of a number of different metabolic simulator settings indicated that the “Slope Algorithm #2” was the best performer at F IO2 values below 0.8. The commonly implemented Haldane Transform was superior at values of F IO2 of 0.8 and above. The “Slope Algorithm #2” was subsequently used in volunteers to compare the accuracy of our development system using this algorithm with the accuracy of a clinical indirect calorimetry system (The Deltatrac). This comparison was made using actual subjects with the approval of, and in compliance with the University of Utah
Hospital’s Institutional Review Board. Results of the clinical validation indicated that our system running Slope Algorithm #2 compared favorably with the Deltatrac system.
Future directions:
The system as presented may find its first commercial employment in the Respiratory Profile
Monitor (Novametrix. Wallingford Ct). The system will consist of an addition to the monitor of an oxygen sensing board as well as firmware to add indirect calorimetry to the systems’ current capabilities. Algorithmic approaches developed in this dissertation will likely be employed in such a system. Future directions for the system may include extension of the indirect calorimetry specifications into the pediatric and neonatal realm. This extension will require modifications or improvements to the current hardware platform. These modifications may include speeding up
Page 78 the step response of the oxygen, carbon dioxide and flow sensors in order that the sensors are able to accurately represent the oxygen, carbon dioxide and flow patterns of the more rapid breathing patterns typically associated with this patient population. Further, a mathematical determination of the reasons for the poor performance of Slope Algorithm #2 relative to the
Haldane Transform at high F IO2 values should be investigated. Finally, a common use of indirect calorimetry systems in recent years has been in the area of obesity and weight management programs. When used in this capacity, these systems allow users to both determine their REE as well as trend their REE over time during weight loss or exercise regimens. This provides valuable information to the user allowing for the tailoring of specific diets to the metabolic demand of the individual. The author seeks to design a handheld version of such an indirect calorimetry system affordable to the average person. Such a system may proliferate widely in the consumer realm making the technology described herein both common and easily accessible to consumers outside of the medical realm.
Page 79
APPENDIX A
Page 80 Introduction:
The following appendix provides a detailed description of the QUO oxygen sensor used in previous chapters of this dissertation. In addition, other commonly used oxygen sensing technologies, which might lend themselves to the construction of an indirect calorimetry system, are described in order to highlight both the comparative advantages and disadvantages of the QUO oxygen sensor.
Oxygen Luminescence Quenching
Phosphorescence (and fluorescence) results from photon emission of an excited-state lumiphore. Lumiphores, or aromatic molecules capable of photoexcitation, can be excited from a ground state to an excited state by photon absorption. The ground and excited energy states are illustrated graphically in the Joblinski Diagram (Fig. A.1.).
Photoexcitation (photon absorption) of a lumiphore in the ground state (S 0) will excite the molecule to a higher energy state (singlet state) such as S 1 or S 2. The excited molecule will then relax to the lowest energy state of S 1 by means of loss of thermal energy known as vibrational relaxation. Since the energies associated with the lower energy singlet states S 2 and higher energy states of S 1 are similar, a change of singlet state from S 2 to S 1 is possible. This process is known as internal conversion. The vibrational relaxation and possible internal conversion of an excited molecule from a higher energy level of the S 1 or S 2 states to the lowest energy level of the S 1 state typically occurs in approximately
10 –12 seconds 1.
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Singlet states Triplet states Second excited (S2) Vibrational Second excited (T2) relaxation First excited (S1) First excited (T1)
Internal Conversion
Excitation Intersystem Phosphorescence crossing Fluorescence
Ground state (S0) External and internal conversion (quenching)
Figure A.1. Joblinski diagram 2.
Page 82 From the lowest energy level of S 1, two events may transpire, first the molecule may relax to the S 0 ground state. This relaxation to the ground state can occur by internal conversion or by emission of a photon (fluorescence). The latter event is more likely as internal conversion is a relatively slow process owing to the large energy difference between the S 1 and S 0 states. The second event which may transpire from the lowest energy level of S 1 is intersystem crossing to the triplet state T 1. A molecule in the T 1 state may then return to the S 1 state by intersystem crossing, or return to the S 0 state by a low probability vibrational relaxation or, finally, by emission of a photon
(phosphorescence).
Phosphorescence
Photon emission from the T 1 state to the S 0 state involves a change in electron spin. This event has a low probability of occurrence and as a result, phosphorescence is a long lived
-5 1 phenomenon (10 to 10 seconds) . Further, the lowest energy level of the T 1 state is lower than that of the S 1 state and as a result, the wavelength of photons emitted from the triplet state during phosphorescence are longer than those emitted from the singlet state during fluorescence. The long lifetime of phosphorescence renders the molecule vulnerable to outside influences such as the presence of oxygen. Oxygen, which has two unpaired electrons in different orbitals is a triplet state molecule. This makes the oxygen molecule reactive with other molecules in the triplet state and, thus a good quencher of such molecules. Quenching is the deactivation of an excited state lumiphore from the S 1 or T 1 state to the S 0 ground state. The drawback of using phosphorescence, as opposed to fluorescence for detection of pO2 is that excited state triplet molecules are, in effect, di-
Page 83 radicals and therefore photolabile 3. As a consequence, a progressive photo-bleaching of excited state triplet molecules leads to a reduction in phosphorescence with time. The advantage of using excited state triplet molecules for pO2 measurement is the long lifetime of phosphorescent radiative decay which makes quenching phenomenon quantifiable with current low cost signal processing electronics.
The Modified Stern-Volmer Equation
The quenching of phosphorescence (and fluorescence) is described by a modified version of the Stern-Volmer equation as follows:
Io/I = τo/τ = 1 + k Qτo[O 2] (A.1)
where the ratio of I o/I represents the intensity in the presence and absence of oxygen, respectively, and τo/τ represents the lifetime of luminescence in the presence and absence of oxygen, respectively. The variable k Q specifies the quenching rate constant and O 2 the oxygen concentration. Thus, this equation describes both the intensity drop and the lifetime change resulting from the presence of oxygen on a lumiphore. Figure A. 3. shows a typical exitation pulse and an associated delayed phosphorescent profile. The delay is approximately 1 microsecond.
Phosphorescence Lifetime vs. Intensity
As described above, both lifetime and intensity changes of a phosphorescent molecule in
Page 84 the presence of oxygen are affected equally ratiometrically. However, for measurement of pO2, the use of phosphorescent lifetime is preferred as intensity measurements may be affected by variations in excitation light source intensity, photobleaching, leaching of the lumiphore from its immobilized point of reference, and external factors such as the presence of water or sputum.
Oxygen Luminescence Quenching Sensor
A sensor has been developed which measures the phosphorescent lifetime of an oxygen quenched lumiphore. This lifetime provides an accurate measurement of pO2. This sensor is a main-stream respiratory pO2 sensor. Main-stream pO2 sensors are sensors which can obtain oxygen measurements directly from the patient breathing circuit without the need to sample or remove gas to an external device.
The luminescence quenching pO2 sensor is comprised entirely of solid-state components.
The lumiphore is immobilized on a temperature controlled polymer film which is encapsulated in a disposable cuvette placed in the patient circuit. The lumiphore used is non-toxic to the patient and provides clinically acceptable operational and shelf life, however, calibration drift remains a manufacturing issue yet to be resolved. A non- disposable light emitter/detector module snaps onto the cuvette and provides for photoexcitation and phosphorescent lifetime detection. The detector is optically filtered to reduce external lighting effects on sensor performance. The light emitter/detector also
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e ts n c c io s n e t t t t re ff ra n h c e E e a g fe f r st i f r e p i e e E te t O s s w s a e n n t In e R o o h re W r p ti g P ia r tu n s i r s o io e ra /L e ra t R b t o h p e a li c p t a n e e a a s /V p i t il t m e k a g s C p n l m m u a o Te A u e ta r C le m B T n q F b o o o o w e t w a C N N o d o o t Oxygen Sensing Technology N Lo C A N L S Polarigraphic Cell X X X X X X X Fuel Cell X X X X X X X Zirconium Oxide Cell X X X X X X Paramagnetic Cell - Pauling X X X X X X X Paramagnetic Cell - Hummel X X X X X X Mass Spectrometer X X X X X X O2 Luminescence Quenching X X X X X X X X X
Table A.1. Qualitative comparison of oxygen sensing technologies.
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PhotoLuminescent Film Heater Block
Heater Ring
PhotoEmitter PhotoDetector
Gas Flow
Figure A.2. Construct of Phosphorescence Quenching Sensor.
Page 87 contains a proportional-integral-derivative (PID) controlled temperature control circuit to provide for thermostating of the cuvette’s lumiphore/polymer assembly thus reducing temperature induced measurement inaccuracies resulting from the temperature sensitive nature of oxygen diffusivity (Figure A.2). The sensor is lightweight and rugged and may combined with other mainstream respiratory gas analysis devices such as infrared based capnography systems. Finally, the sensor provides for response times adequate to allow for breath-to-breath analysis of respiration. Table A.1. outlines the advantages of this sensor over previously described pO2 technologies.
Electrochemical pO2 Sensors
Electrochemical sensors, in which a chemical reaction takes place between a cathode and an anode, are commonly used in both gas phase and blood-gas analysis. The two commonly used sensors are polarographic (Clark) cells and fuel (galvanic) cells.
Polarographic Cells
In 1954, Leland Clark conceived of and built the first oxygen sensing electrode which consisted of an anode and cathode behind an oxygen permeable polyethylene membrane.
The Clark or polarographic cell (Fig. A.4.) can be used in both gas phase and blood-gas analysis. The electrode consists of four components, a platinum cathode, a silver anode,
Page 88
Excitation Pulse 1 Luminescent Emission
Decay Time Normalized PL Intensity PL Normalized
1 2 3 4 5 6 7
Time X (10-6 seconds)
Figure A.3. Timing diagram for phosphorescence quenching sensor.
Page 89 an electrolyte solution (e.g. KCl) and an oxygen permeable membrane. A negative voltage is applied to the silver anode and a positive voltage applied to the platinum cathode. Electrical contact is maintained between the anode and cathode via the electrolyte solution. Oxygen molecules pass through the membrane where they are electrolyzed at the platinum surface in accordance with the following reactions:
- - Cathode O 2 + 2H 2O + 2e → H 2O2 + 2OH (A.2)
- - Anode H 2O2 + 2e → 2OH (A.3)
Oxygen reduction rate alters the conductivity of the electrolyte solution. The resulting current flow is proportional to the concentration of O 2 in the electrolyte solution.
Polarographic electrodes are typically slow with response times of 3 seconds and longer 4.
Rapid response time polarographic electrodes have been reported 5,6 , and are typically constructed by reducing the distance between the cathode and the membrane, thus reducing the diffusion path length for oxygen. Unfortunately, these electrodes suffer from a short lifespan (2-3 days 6) and are vulnerable to electrolyte evaporation, gas bubbles in
7 the electrolyte, pressure and temperature effects at the membrane , and possible errors due to interaction with anesthetic agents such as halothane8 and nitrous oxide 9.
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To measuring unit
Anode Cathode
Ag-Ag/Cl reference anode
Insulated c ontainer
Elec trolyte
Insulating glass
rod with platinum wire sealed in
Rubber “O” ring
Platinum Sample tip of cathode
Figure A.4. Details of Polarographic (Clark) cell. 10
Page 91 Fuel Cells
The fuel or galvanic cell (Fig. A.5.) is an electrochemical cell which consists of two electrodes: a gold cathode and a lead anode. The gold cathode is exposed to oxygen through a polymer membrane. The electrolyte is typically a solution of potassium hydroxide. Oxygen diffuses through the membrane and a thin electrolyte layer to the cathode where it is electrochemically reduced as follows:
- - Cathode O 2 + 2H 2O + 4e → 4OH (A.4)
Anode Pb → Pb 2+ + 2e - (A.5)
The electrical current from this reaction is proportional to pO2. This reaction proceeds spontaneously in the presence of oxygen, thus requiring no external power source.
Fuel cells are inexpensive and in wide clinical use, however they suffer from poor
11,12 response times (T 10 -T90 of 9 to 48 seconds for a 100-21% O 2 step change) and are subject to output errors in the presence of condensing water vapor 11,4,15 .
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O Thin electrolyte layer 2 Cathode Sensing membrane
Electrolyte
Anode
_ Circular contact plate + Out
Figure A.5. Details of fuel cell. Redrawn from Merilainen PT 16 .
Page 93 Zirconium Oxide Cells
Zirconium oxide cells are solid electrolyte fuel cells (Fig. A.6.). The cell consists of a zirconium oxide (ZrO 2) tube which is typically stabilized with yttria (Y 2O3). The internal and external surfaces of the ZrO 2 tube are coated with platinum film to form separate electrodes on either side of the tube. The cell is heated to approximately 700–1000 oC.
The sampled gas is drawn through the tube where it is ionized. The electrolyte acts as a semi-permeable membrane; permeable to the oxygen ions but impermeable to electrons.
The outside of the tube is exposed to a reference gas of known pO2. The platinum electrode which is exposed to the higher pO2 becomes the anode and the following reaction takes place:
- -- Cathode O 2 + 4e → 2O (A.6)
-- - Anode 2O → O 2 + 4e (A.7)
The voltage generated across the cell follows the Nernst equation:
E = RT/nF* log(P 1/P 2) (A.8)
Where R is the universal gas constant (R = 8.31x10 7 erg/mol oK), T is temperture in degrees Kelvin, z is the charge number of the electrode reaction (which is the charge number of moles of electrons), and F is the Faraday constant (96,500 C mole-1). P 1 and
P2 are the pressures on the inside and outside of the electrode. Since the output voltage is
Page 94 a logarithmic function of the ratio of pO2 on either side of the cell (approximately 50 mV per decade of oxygen concentration) the cell has a high dynamic range allowing determinations of a broad range of pO2 differences. The zirconium oxide cell will combust many operating room gases at the temperature at which it operates. This renders the cell unusable for analysis of respiratory pO2 in the OR. However, this cell may be used for metabolic monitoring in the absence of such combustible gases. Breath-to– breath analysis is possible due to the adequate response of the cell (T 10 -T90 of 0.030 seconds for a 12% to 21% concentration change - Servomex Model 728). Unfortunately, the cell suffers from fragility 16 and requires a warm-up period.
Paramagnetic Cell Background
In 1845, Faraday discovered that substances other than iron could be attracted by magnetic fields 17 . In one experiment, he found that a glass sphere filled with oxygen and supported by silk fibers was displaced in the presence of a strong, non-uniform magnetic field. Faraday called this phenomenon paramagnetism. The paramagnetic nature of oxygen was later determined to be due to the presence of two unpaired electrons in the outer shell of the oxygen molecule. These unpaired electrons produce a magnetic moment which gives rise to oxygen’s paramagnetism. The strength of interaction of a material with a magnetic field is known as magnetic susceptibility 16 . Materials with a positive susceptibility, such as oxygen, are termed paramagnetic and those with a negative susceptibility, such as nitrogen, are termed diamagnetic. The effects of oxygen
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Figure A.6. Details of zirconium oxide fuel cell 14 .
Page 96 paramagnetism can be described by a physical law which relates the force (F) on the molecule to susceptibility (K) and the magnitude and gradient of the magnetic field (H):
F = K*H*dH/dx (A.9)
The magnetic susceptibility of oxygen is greater than that of other operating room respiratory gases. Two types of technologies based on oxygen paramagnetism are commonly used for determination of pO2. The original technology developed in 1940 by
Linus Pauling 20 utilizes a mechanical device which takes advantage of the differential magnetic behavior of paramagnetic and diamagnetic gases in a static, non-uniform magnetic field. The second technology, originally presented by Heinz Hummel in 1968 uses a dynamic principle based on the differential behavior of paramagnetic and diamagnetic gases in an electrically switched magnetic field.
The Pauling Paramagnetic Cell
The paramagnetic cell developed by Pauling consisted of a sealed glass dumbbell containing a diamagnetic gas (usually nitrogen). The dumbbell is suspended between two wedge shaped permanent magnets (Figure A.7.), which by virtue of their shape provide a non-uniform magnetic field. When a paramagnetic gas such as oxygen enters the cell, it will be attracted to the area where the magnetic field is the strongest. By contrast, the diamagnetic gas in the glass spheres of the dumbbell will be attracted to the area in which
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Magnet Magnet
0% O 2 21% O in Chamber 2 100% N 2 in Chamber
Light Source Light Source 100% N 2
0 100 0 100 50 50 Metered Output Metered Output
Magnet Magnet
Figure A.7. Details of Pauling cell showing torsional force on dumbbell resulting
from oxygen in sampling chamber.
Page 98 the magnetic field is the weakest. This generates a torsional force on the dumbbell roughly proportional to the pO2 of the surrounding gas, thus rotating the dumbbell vertically about its horizontal axis. The degree of rotation is measured optically using a photosensor based on the reflection of a light beam off a mirror mounted to the dumbbell assembly. In the early cells, the degree of dumbbell rotation was taken as a measure of pO2. However, rotation of the dumbbell produced a non-linearity due to the movement of the dumbbell spheres into areas of differing magnetic gradients. This non-linearity problem was later solved by C.W. Munday of Servomex Controls Limited. Munday introduced a feedback system which prevented the dumbbell from rotating by introducing current to coils surrounding the spheres. The current required to maintain the dumbbell in position is linearly related to pO2.
The drawbacks of this pO2 technology include the inherent fragility of the mechanical device and its susceptibility to contamination by particulate matter. In addition, slow response times (T 10 -T90 of 0.5 seconds at 90 ml/min flow for the Servomex Model 1111) render the sensor useless for spirographic (breath-by-breath) recording.
The Hummel Paramagnetic Cell
Hummel constructed a paramagnetic cell based on an electromagnet. This cell mixed two gas streams (a reference gas stream and a sample gas stream) inside a homogenous magnetic field. By alternating this magnetic field it is possible to measure the pressure difference upstream of the sample inlets using a differential pressure transducer (Fig.
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Electromagnet
Mixture Outlet
Reference
Inlet Changiing Magnetic Field
Sample Inlet
Differential Pressure Transducer
Figure A.8. Details of Hummel cell showing pneumatic path of sample and
reference gases through the electromagnet gap and differential pressure
measurement technique.
Page 100 A.8.). The amplitude of the differential pressure signal is proportional to the difference in pO2 of the sample and reference gases.
The major advantage of this configuration is the improved response time of the system
(T 10 -T90 of 0.150 seconds at 100 ml/min flow for the Datex sensor) which allows for spirographic recording. In addition, the pO2 of the sample gas can be altered allowing for accurate differential analysis of the sample and reference gases which is advantageous for measurement of metabolic oxygen consumption. The primary disadvantage of this configuration is the need for continuous reference gas which, when ambient air is used as a reference gas, results in a slow accumulation of nitrogen in closed-circuit anesthesia systems. In addition, water vapor partial pressure differences between the reference and sample gases as well as background acoustic noise can produce inaccuracies 18 .
Mass Spectrometry
Mass spectrometry can be used for the analysis of respiratory gases such as oxygen. Mass spectrometry separates ionized gas molecules by their ionic mass/charge ratios. Gas is sampled by means of an inlet system through the use of a vacuum pump. A portion of this gas is drawn into a high-vacuum source where it is ionized via bombardment with an electron beam. The ions are then passed through a magnetic field oriented normal to the direction of ion travel. As a result, ion streams follow separate circular trajectories based on their aforementioned ionic mass/charge ratios. The ion streams are captured by collector electrodes and the resulting current is amplified and displayed.
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Mass spectrometry can be used for analysis of partial pressures of a variety of respiratory
7 gases including oxygen. Response times (T 10 -T90 of 0.100 seconds for oxygen) are adequate for breath-to-breath analysis. Unfortunately, the technology is bulky and expensive.
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