WO2006119546A1

WO2006119546A1 - Pulmonary capnodynamic method for continuous non-invasive measurement of cardiac output

Info

Publication number: WO2006119546A1
Application number: PCT/AU2006/000593
Authority: WO
Inventors: Philip John Peyton
Original assignee: Philip John Peyton
Priority date: 2005-05-06
Filing date: 2006-05-05
Publication date: 2006-11-16

Abstract

This invention relates to a method and system for monitoring cardiac output of a subject. Described are a method and system for measuring effective pulmonary capillary blood flow (or non-shunt pulmonary blood flow) and total pulmonary blood flow (or cardiac output) on a continuous, breath-by-breath basis. Effective pulmonary capillary blood flow for a given breath is used to determine effective pulmonary capillary blood flow for a subsequent breath.

Description

PULMONARY CAPNOD YNAMIC METHOD FOR CONTINUOUS NONINVASIVE MEASUREMENT OF CARDIAC OUTPUT

Field The present invention relates to the measurement of cardiac output, in particular to a method and system for monitoring cardiac output of a subject, and a method and system for measuring effective pulmonary capillary blood flow (or non-shunt pulmonary blood flow), Qc , and total pulmonary blood flow (or cardiac output), Qt . The invention allows the measurement of these parameters in a non-invasive manner, and to be measured breath by breath in a substantially continuous manner.

Background

Cardiac output (total pulmonary blood flow) is the rate at which blood is pumped by the heart to the body. Along with the blood pressure, it fundamentally reflects the degree of cardiovascular stability and the adequacy of perfusion of vital organs. Knowledge of the cardiac output will not itself provide a diagnosis of a patient's condition, but can provide information useful in making a diagnosis. Monitoring cardiac output is most important where cardiovascular instability is threatened, such as during major surgery and in critically ill patients. In these situations "moment to moment" or continuous monitoring is most desirable, since sudden fluctuations and rapid deterioration can occur, for instance, where sudden blood loss complicates an operation.

In contrast to cardiac output monitoring, real time monitoring of arterial blood pressure is readily performed via an indwelling peripheral arterial line. Because of its availability, minimally invasive nature and relative safety, continuous blood pressure monitoring via an arterial line has become almost routine during major surgery. In contrast, continuous monitoring of cardiac output is still not performed routinely during anaesthesia and critical care in the absence of a safe, non-invasive and accurate method.

The established techniques for measurement of cardiac output, such as pulmonary thermodilution via a pulmonary artery catheter, are invasive and associated with occasional but serious complications, such as pulmonary artery rupture, or are time consuming and heavily operator dependent, as in the case of Doppler echocardiography. Improvements in this field are taking place, such as the development of pulse contour techniques, transpulmonary thermodilution and improved thoracic bioimpedance devices, but these all have limitations, such as poor accuracy under clinical conditions, the need for repeated calibration, invasive central or peripheral cannulation, or are simply unsuitable for patients during surgery and critical care who are intubated or ventilated.

Techniques based on pulmonary gas exchange measurement are among the oldest methods used for cardiac output measurement, and are attractive because of their potentially noninvasive nature. Recent refinements have produced systems or devices based on inert gas uptake (Innocor, Innovision, Denmark), partial CO₂ rebreathing (NICO, Novametrix, USA) and differential lung ventilation via a double lumen endobronchial tube (the throughflow method). (Gabrielsen et al 2002, Capek and Roy 1988, Robinson et al 2003). However, none of these alternatives allows truly continuous and non-invasive cardiac output monitoring. It follows that it would be useful to provide at least a useful alternative, or advantageous method and system for monitoring cardiac output of a subject, and in particular a non-invasive, continuous (breath by breath) measurement method and system suitable for routine use in patients undergoing general anaesthesia or in intensive care.

Summary

It has now been found that effective pulmonary capillary blood flow ( Q^c ) measured or otherwise determined for a given breath "i" (Q^ci ) can be used to determine Q^c of a subsequent breath "k" (Q^ck). This permits continuous, ongoing, breath-by-breath monitoring of Q^c , and of acute changes in Q^c . This represents a substantial departure from the prior art methods based upon pulmonary gas exchange measurement listed above, which make discrete measurements of δ^c at spaced points in time, based on the assumption that Q^c remains stable during each measurement. Accordingly, in one aspect the present invention provides a method for monitoring cardiac output of a subject, the method including: determining an effective pulmonary capillary blood flow of said subject at a first time on the basis of an effective pulmonary capillary blood flow of said patient at an earlier time, pulmonary uptake or elimination of a breathed gas species by said subject at said first time and said earlier time, partial pressures of said gas species in lungs of said subject at said first time and said earlier time, and a solubility of said gas species in blood of said subject.

Preferably, the method includes measuring said net rates of pulmonary uptake or elimination of said gas species G at respective breaths of said subject.

Preferably, the method includes measuring said partial pressures substantially at the end- tidal point of respective breaths of said subject.

Preferably, the method includes performing said step of determining at successive breaths of said subject to provide breath-by-breath monitoring of said effective pulmonary capillary blood flow of said subject.

Preferably, the method includes determining cardiac output of said subject at said first time by adding shunt blood flow of said subject to said effective pulmonary capillary blood flow.

Preferably, the method includes determining said shunt blood flow of said subject.

Preferably, said method includes measuring rates of change of alveolar partial pressures of said gas species, in lungs of said subject at each of said first time and said earlier time. Preferably, said step of determining includes determining (Qc _k) , the effective pulmonary capillary blood flow for a breath k, according to:

where F₀. and F_{0 k} are the net rates of pulmonary uptake or elimination of said gas species G at breaths i and k, respectively Qc₁ is the effective pulmonary capillary blood flow for an earlier breath /, Cv₀ and Cv_0. are the mixed venous gas contents at breaths k and ft '

/, PE' _Gk and PE' _G) are the alveolar (end-tidal) partial pressures of gas species G at breaths k and i, PB is barometric pressure, Veffa is an effective lung volume of gas species G, S_G is a partition coefficient for said gas species G in blood of said subject, and dPE'oj/dt and dPEOk/dt are the rates of change of said partial pressures between successive breaths at the times of breaths i and k, respectively.

Preferably, the method includes determining said effective pulmonary capillary blood flow of said patient at said earlier time on the basis of partial pressures of said gas species at respective breaths of said subject, rates of change of said partial pressures at said respective breaths, net uptakes or eliminations of said gas species in lungs of said subject at said respective breaths, a solubility of said gas species in blood of said subject, and an effective lung volume of said patient for said gas species; wherein an alveolar ventilation of said subject at an initial breath of said respective breaths is substantially different from an alveolar ventilation of said subject at a subsequent breath of said respective breaths.

Preferably, alveolar ventilation of said subject is repeatedly alternated between a first level of alveolar ventilation maintained for a plurality of breaths, and a second level of alveolar ventilation maintained for a plurality of breaths. Preferably, the method includes determining said effective lung volume of said subject for said gas species on the basis of an effective pulmonary capillary blood flow of said patient, a solubility of said gas species in blood of said subject, rates of changes in alveolar partial pressures of said gas species in lungs of said patient at respective times, and net uptakes or eliminations of said gas species in lungs of said subject at respective times.

Preferably, said rates of change and said net uptakes or eliminations are each determined at an initial time and a subsequent time, wherein alveolar ventilation of said subject at said initial time is substantially different from an alveolar ventilation of said subject at said subsequent step.

Preferably, said effective lung volume is determined at one or more first breaths of a plurality of breaths at a changed level of alveolar ventilation.

Preferably, the method includes repeatedly performing said step of determining said effective lung volume at a plurality of breaths of said subject.

Preferably, said first level of alveolar ventilation constitutes a first half-cycle of a cyclic alternation of alveolar ventilation, said second level of alveolar ventilation constituting a second half-cycle of said cyclic alternation of alveolar ventilation; and the method further includes:

(i) performing, for one or more last breaths of said first half-cycle of alveolar ventilation, said step of determining said effective pulmonary capillary blood flow of said patient at said earlier time to determine a first effective pulmonary capillary blood flow;

(ii) performing said step of determining said effective lung volume of said subject for one or more first breaths of one of said half-cycles of alveolar ventilation; and (iii) performing, at each remaining breath of said second half-cycles, said step of determining said effective pulmonary capillary blood flow on the basis of said first effective pulmonary capillary blood flow.

Preferably, the method includes repeating steps (i) to (iii) to provide breath-by-breath monitoring of said effective pulmonary capillary blood flow.

Preferably, the method includes determining a cardiac output of said subject on the basis of said effective pulmonary capillary blood flow to provide breath-by-breath monitoring of said cardiac output of said subject.

Advantageously, the method may be executed by a computer system having means for receiving gas species and gas flow data representing constituents, pressures and flow rates of gas inhaled and exhaled by said subject at said first time and said earlier time; and means for processing said gas species data to determine said effective pulmonary capillary blood flow of said subject at said first time.

The present invention also provides a system for monitoring cardiac output of a subject having components for executing the steps of any one of the above processes.

The present invention also provides a computer-readable storage medium having stored thereon program instructions for executing the steps of any one of the above processes.

The present invention also provides a system for monitoring cardiac output of a subject, including: means for receiving gas species and flow data representing constituents, pressures and flow rates of gas inhaled and exhaled by said subject at a first time and an earlier time; and means for processing said gas species and flow data and solubility data representing a solubility of said gas species in blood of said subject to determine an effective pulmonary capillary blood flow of said subject at said first time; wherein said effective pulmonary capillary blood flow of said subject at said first time is determined on the basis of an effective pulmonary capillary blood flow of said patient at said earlier time, pulmonary uptake or elimination of said breathed gas species by said subject at said first time and said earlier time, partial pressures of said gas species in lungs of said subject at said first time and said earlier time, and said solubility of said gas species in blood of said subject.

Preferably, the system includes means for cyclically alternating alveolar ventilation of said subject between a first level of alveolar ventilation maintained for a plurality of breaths, and a second level of alveolar ventilation maintained for a plurality of breaths.

Advantageously, the system may also include means for operating a valve to selectively introduce a serial deadspace for gas breathed by said subject.

Advantageously, the system may further include a gas analyser for analysing gas breathed by said subject; and a gas flow device for determining flow of said gas breathed by said subject.

Advantageously, said subject may be a human being.

Preferably, said gas species includes CO₂.

In another aspect, the present invention provides a method for measuring the effective pulmonary capillary blood flow in a subject including:

providing the subject with alveolar ventilation by ventilation of the lungs of the subject;

determining the effective pulmonary capillary blood flow, (Q^c), the pulmonary uptake or elimination of a gas species G, (VG ) , and the alveolar (end-tidal) partial pressure of gas G (PE'o) for a breath "/"; determining the pulmonary uptake or elimination of gas species G, the alveolar partial pressure of gas G for a subsequent breath "k"; and

determining the effective pulmonary blood flow for breath k (Qc _k) according to "continuity equation"

where PB is barometric pressure, Veffo is effective lung volume of gas G, and S_G is the solubility of gas G in blood.

This continuity equation assumes that the mixed venous gas content (Cv₀) at breath k has not changed significantly from that at breath / such that Cv₀ = Cv₀. . To allow for fluctuations in Cv₀ , the continuity equation can be modified as follows:

where

and

This modification assumes instead that the subject's body tissue absorption or metabolic production of G, V_Gbody_l , is not significantly changed between breaths "/" and "&".

Preferably, Qc ,- is determined as follows.

The method may include a calibration step, made when the method makes a determination, that the cardiac output and lung gas exchange is sufficiently stable. Preferably, the calibration step is performed by solving the following "calibration equation" to obtain effective non-shunt pulmonary blood flow (Qc). For any two breaths / and j made at different levels of alveolar ventilation,

dPε

PB-V_G, -V_G]-Veff_G - '' ^G, dPE\ GJ dt dt

Qc =

]

Preferably, breaths / and j are sufficiently close in time to one another that CV_Q and Qc can be assumed to have not changed substantially.

Accordingly, in a further aspect the invention provides a method for measuring the effective pulmonary capillary blood flow in a subject including:

providing constant alveolar ventilation to the subject for a plurality of breaths; determining the pulmonary uptake or elimination of a gas species G ( ^a ), and the alveolar

(end-tidal) partial pressure of gas G (P ^E' G ) at a breath "z" during said period of constant alveolar ventilation;

inducing a change in the alveolar ventilation of the subject and providing constant alveolar ventilation to the subject for a plurality of breaths at the changed level of alveolar ventilation;

determining the pulmonary uptake or elimination of gas G and, the alveolar partial pressure of gas G, at a subsequent breath "j"

calculating the effective pulmonary blood flow Q^c by solving the calibration equation

dPε^< _Gι dPE^< _Gj

PB \V, G, V_oλ-Veff_G dt dt Qc = vhv^'J

where PB is barometric atmospheric pressure, Veffa is the effective lung volume of gas, G, and Sg is the solubility coefficient in blood of G;

determining the pulmonary uptake or elimination of gas species G and the alveolar partial pressure of gas G for a subsequent breath "k"; and

determining the effective pulmonary blood flow for breath k (Qc ^) according to a continuity equation

where Qc _j = Qc .

As before, the continuity equation can be modified to allow for differences in the mixed venous gas content between breaths / and k.

The changes in alveolar ventilation can be introduced at arbitrary or discrete intervals to permit determination of the calibration equation to obtain Qc where cardiac output and lung gas exchange is stable, Preferably these changes are induced in a continuous alternating cyclic manner, so that computation of the calibration equation to obtain Qc can be done at every opportunity where cardiac output and lung gas exchange is stable.

It will be convenient to further describe the invention with reference to such continuous alternating/cyclic alveolar ventilation of the subject, with each period of alveolar ventilation at a particular level constituting a half cycle. Preferably a cycle comprises from 6 to 20 breaths of the subject, typically 12 breaths; a half cycle being half of this number of breaths. However all that is required is that periods of alveolar ventilation at one level are followed by periods of alveolar ventilation at a different level, and for the purposes of measurement of pulmonary blood flow, any period of alveolar ventilation at a particular level can be considered to constitute a "half cycle" if it is followed and/or proceeded by a period of alveolar ventilation at a different level. Similarly, any two adjacent periods of alveolar ventilation at different levels can constitute a full cycle.

Preferably the method induces alternating cyclic changes in alveolar ventilation by the modulation of an automatic ventilator to alternate tidal volumes, overall rate, the inspiratory to expiratory ratio or the duration of end-expiratory pause, or by alternating the volume of serial deadspace in the breathing system using an automated valve or similar device.

Preferably, breaths / andy occur within a single cycle, with breath i occurring in the first half cycle and breathy occurring in the second half cycle. Preferably, breaths i andy occur at periods within the half cycle during which washin or washout of G in the lung is minimised, as this minimises error in the determination of Qc due to any inaccuracy in estimation of Veffij. This will not normally occur until at least two or three breaths following a change in alveolar ventilation. The number of breaths required for stabilisation will be greater when there is a larger change in the level of alveolar ventilation or lower cardiac output.

To alleviate this source of error, the method may also include the step of determining effective lung volume ( Veff_G) with each breath and using the determined value Veff_G when solving the calibration equation. Preferably Veffg is determined by solving the following equation, hereinafter referred to as the "capacitance equation":

Preferably Veffg is calculated from the capacitance equation on one or more breaths immediately following the calibration equation, using the same input variables and the value for Qc determined by the calibration equation.

Preferably, the continuity equation is used with each subsequent expired breath k, whenever the calibration equation is not used to determine effective non-shunt pulmonary blood flow (Qc _k) in terms of Qc ,- as described above. Preferably, once Qc (effective or "non-shunt" pulmonary capillary blood flow) has been determined for any given breath Jc, shunt pulmonary blood flow (Qs ) is determined as described below, and then cardiac output (Qt ) for that breath is determined, being the sum of Qc and Qs .

The gas species G can be an inert gas species administered to the patient by inhalation or otherwise. Alternatively, the gas species G can be a physiological respired gas species, preferably carbon dioxide (CO₂). For convenience, embodiments of the invention are hereinafter described with reference to the use of CO₂ as the gas G. However it is to be understood that other physiological gas species can also be used. Preferably, the value of S in blood for CO₂ ( S_QQ ) is determined by differentiating standard equations relating the content of CO₂ in blood to its partial pressure, as described below.

Preferably, the method includes the use of a data averaging or smoothing function to determine the Qc or Qt of the subject.

In another aspect of the invention, there is provided apparatus and a system for performing the method of the invention.

Accordingly the invention provides apparatus for measuring effective pulmonary capillary blood flow in a subject comprising:

one or more breathing systems for ventilating lungs of the subject;

ventilation adjustment means for rapidly adjusting alveolar ventilation between two or more levels;

a rapid gas analyser and gas flow measuring device to allow measurement of alveolar (end- tidal) partial pressure and pulmonary uptake or elimination of a gas species G; a data processor with inputs to receive data from the rapid gas analyser and gas flow measuring device, said processor being configured to determine Qc from gas species data received relating to a breath i taken at alveolar ventilation level / and a breath j taken at alveolar ventilation level/, levels / andy representing ventilation levels before and after an adjustment respectively, the determination being made according to the calibration equation:

where PB is barometric atmospheric pressure, Veffo is the effective lung volume of gas, G, and S_G is a solubility coefficient in blood of G;

and wherein the processor is further configured to use the value of Q^c determined from the calibration equation (Q^ci ) and data received relating to a breath k, to determine the effective pulmonary capillary blood flow for breath k according to the continuity equation:

where PB is barometric pressure, Veffo is effective lung volume of gas G, and S_G is the solubility of gas G in blood; and

means for communicating to an operator of the system at least an indication of at least one of effective pulmonary capillary blood flow and cardiac output for breath k. Advantageously, said means may include one or more visual or audio display device(s).

The apparatus may have other components and the processor may have other functions to assist in the breath by breath measurement of effective pulmonary capillary blood flow or cardiac output. For example, the processor may also be configured to determine the effective lung volume of gas species G according to the capacitance equation described herein. The apparatus may also have input means for inputting the haemoglobin content of the subject and the processor may also have an input for receiving data from a device for measuring arterial oxygen content, such as a pulse oximeter, and/or for measuring pH and/or arterial CO₂ partial pressure. These would be of assistance in allowing the processor to determine the shunt fraction of pulmonary blood flow using standard methods, thereby allowing the processor to determine the cardiac output of the subject, and to improve the accuracy of determination of Q^c and to allow concurrent monitoring of the patient's metabolic acid-base status and lung function.

The apparatus or system preferably automatically displays and records relevant data in real time.

Brief Description of the Drawings

Preferred embodiments of the invention are hereinafter described, by way of example only, with reference to the accompanying drawings, in which:

Figures 1 to 6 described below show typical measured input and determined output data for a subject where CO₂ is used as measurement gas G to continuously determine cardiac output Qt on a breath-by-breath basis in accordance with a preferred embodiment of the invention.

Figure 1 is a graph which depicts the measured expired tidal volume VE (in litres) with each breath of the measurement cycle, in accordance with a preferred embodiment of the invention in which cyclic variation in delivered tidal volume is used to produce cyclic changes in alveolar ventilation of the patient's lungs

Figure 2 is a graph which depicts the measured mean rate of elimination of CO₂ with each breath ( VE₀₀ in litres/min) over the same measurement cycle shown in Figure 1. Figure 3 is a graph which depicts the measured end-expired (end-tidal) partial pressure of CO₂ (PE₍J_Q in mmHg). over the same measurement cycle shown in Figure 1.

UPEQ¹ ₀ Figure 4 is a graph which depicts the determined rate of change of PE_C' _O ( ), over

the same measurement cycle shown in Figure 1 , on which is indicated the points at which effective lung volume for CO₂ ( Veff_cθ2 ) can be determined using the capacitance equation if Qc is stable.

Figure 5 is a graph which depicts the determined cardiac output Qt (in litres/min) over the same measurement cycle shown in Figure 1, following adjustment of Qc for pulmonary shunt. The points at which the calibration and continuity equations are used are indicated. Figure 6 depicts a capnography tracing (the expirogram for CO₂) over the same measurement cycle shown in Figure 1.

Figure 7 depicts a simulated measurement of cardiac output Qt over a 10 minute period in which a sudden drop in actual ("target") Qt takes place. The graph shows that the continuity equation closely follows the target Qt . In contrast, as expected, the calibration equation does not accurately compute the cardiac output for the first 2 minutes following the change in Qt . This because the assumptions inherent in application of the calibration equation, that cardiac output is stable within a measurement cycle, do not hold true during the acute change in Qt .

Figure 8 is a schematic diagram of a system for monitoring cardiac output in accordance with one preferred embodiment of the present invention, wherein the system controls a ventilator to produce changes in alveolar ventilation.

Figure 9 is a graph of cardiac output data generated by the system, representing the cardiac output of an anaesthetised and ventilated sheep, together with simultaneous measurements made with an ultrasonic aortic or pulmonary artery flow probe in the sheep. Figure 10 is a block diagram of a cardiac output monitor of the system. Figure 11 is a flow diagram of a preferred embodiment of a method for monitoring cardiac output executed by the system.

Figure 12 is a schematic diagram of an alternative preferred embodiment of a system for monitoring cardiac output, in which the system controls the operation of a partial rebreathing valve and rebreathing loop to produce changes in alveolar ventilation by altering the volume of serial deadspace in the breathing circuit.

Detailed Description of the Preferred Embodiments

The capnodynamic method is the name that has been given to a new technique for automated and continuous determination of cardiac output (total pulmonary blood flow) on a breath-by-breath basis. It is non-invasive and is suitable for use in patients during anaesthesia or in critical care, who are intubated with either an endotracheal tube, endobronchial tube, or laryngeal mask airway or similar airway management device.

The method is based on the uptake or elimination of carbon dioxide (CO₂) and/or other gases by the lungs. The prefix capno used in this specification refers to use of measurement of CO₂ to determine cardiac output. CO₂ is the preferred gas to measure since it is present under all physiological conditions. However, other expired gases, such as anaesthetic gases being administered to the patient, can be used instead, or at the same time. Consequently, the use of the prefix capno should not be understood as limiting the invention to the use of CO₂. More generally, the method is referred to as a method for monitoring cardiac output.

With every breath, the rate of elimination of CO₂ by the lungs, and consequently the partial pressure of CO₂ in gas expired from the lungs at the end of a breath, the end-expired partial pressure (referred to as end-tidal partial pressure), is measured in real time. These are the measured inputs used by the capnodynamic method. The method can achieve quasi- continuous measurement of cardiac output by application, with each of a plurality of successive breaths, of the "continuity equation" described below. This measures change in cardiac output relative to a baseline measurement of cardiac output with its accompanying inputs.

The baseline cardiac output measurement may be obtained by a number of methods, but the preferred means is by application of the "calibration equation". This uses the same inputs as the continuity equation, but these are measured while the level of alveolar ventilation of the lungs is changed. This can be done one or more times, or continuously, repeatedly alternating between higher and lower levels of alveolar ventilation in a cyclic manner. Making a sudden change in alveolar ventilation also allows lung volume to be determined from the same measured inputs, using the "capacitance equation" described below.

The underlying theory of the capnodynamic method is outlined below. The method has been developed with the assistance of theoretical computer modelling of lung gas exchange. An automated measurement system, which is suitable for use in patients, is also described below, together with the results of bench tests.

Background and Existing Techniques for Pulmonary Blood Flow Measurement using CO₂ Elimination by the Lungs Non-shunt ("effective") pulmonary capillary blood flow Qc is that part of the total pulmonary blood flow (cardiac output, Qt ) which engages in gas exchange with an inspired gas mixture in the lung. Qc can be related to measured CO₂ elimination by the lungs V₀₀ by a variation of the Fick equation:

where CC'_CQ2 and Cv_Co₂ ^are the fractional contents of CO₂ in pulmonary end-capillary and mixed venous blood, respectively. Since the pulmonary end-capillary blood and alveolar gas can be considered to be in equilibrium with one another, Cc¹Co₂ ^can ^^e related to the content of CO₂ in the alveolar gas mixture if the solubility of CO₂ in blood is known, so that

where PA_COI is the alveolar partial pressure of CO₂ and PB is the atmospheric pressure corrected for the presence of water vapour at body temperature (47mmHg at 37⁰C). S_co is the blood-gas partition coefficient of CO₂, a constant representing the solubility of CO₂ in blood under the conditions present in the patient at that time.

To permit non-invasive measurement, measured partial pressure of CO₂ in end-tidal gas ( PE_C' _O ) is used as an approximation of PA_CO :

Equation (3) is not directly solvable, because CV_QQ is a second unknown term. CVQQ can only be directly measured by invasive mixed venous blood sampling via a pulmonary artery catheter. However, it can be estimated from changes in expired alveolar gas induced by certain unusual respiratory manoeuvres such as breath holding or rebreathing of expired gas (Defares 1958; Kim, Rahn and Farhi 1966; Russell et al 1990). Moreover, CV_QQ can be eliminated from consideration under such conditions if two simultaneous equations of the form of (3) are generated, during which both Cv _QQ and Qc are assumed to remain unchanged. This is known as the differential Fick approach (Capek and Roy 1988). If separate sets of measurements are made at times ti and t_∑ under conditions that provide substantial changes in lung CO₂ elimination at these times, then it can be shown that

Qc = ^V∞*^{x Vco>}'² (4)

-J^ ^" \^PE'co₂n -^pE'co₂t2 )

In particular, this equation allows Qc to be determined by changing the alveolar minute ventilation, which alters both V_co and PE' _QQ acutely. This can be achieved a number of means. The first method used in the past was to make a stepwise change in the respiratory rate (Gedeon et al 1980). An alternative method, referred to as partial CO₂ rebreathing, is to introduce a change in the serial deadspace, while holding tidal volume constant, thereby effectively reducing the alveolar ventilation (Capek and Roy, 1988). This is the technique used by the NICO device (Novametrix, USA).

The acute change in V_co and PE_C' _O rapidly levels out as washin or washout of CO₂ from alveolar gas and lung tissue stores briefly approaches a new steady state level (Gedeon et al 1980, Capek and Roy, 1988). However, the change in alveolar ventilation begins to alter the content of CO₂ in the mixed venous blood, CV_QQ , which has been assumed constant in order to derive equation (4). This becomes evident from measured alveolar CO₂ partial pressure after one body recirculation time, typically within a minute or so (Gedeon et al 1980). Consequently, the measurements for equation (4) are made prior to this point to avoid inaccuracy.

An important limitation of methods based on equations of the basic form of equation (4) is that they assume steady state gas exchange and stable Qc . Consequently, non-steady state gas exchange would invalidate such methods. For example, a change in CV_QQ between the two measurements due to the change in alveolar ventilation would invalidate the method and it would be necessary to wait some minutes before repeating the measurement to allow Cv _QQ to achieve a steady state level again, otherwise the accuracy of equation

(4) would be impaired. This limitation precludes the use of existing methods, for frequent (breath to breath) determination of pulmonary blood flow. For this reason it has not been previously possible to provide quasi-continuous (breath to breath) monitoring of pulmonary blood flow.

The Capnodynamic Method

The following description applies to any gas species "G" present in the alveolar gas mixture. To explain the concepts, a simplified model of the lung is used, wherein the lung is considered to be a single compartment consisting of alveolar gas and lung tissue and pulmonary capillary blood in equilibrium with one another.

With each tidal breath, gas enters the compartment during inspiration and leaves during expiration, a process known as "alveolar ventilation". The volume of each breath is the

"tidal volume" (Vf). This volume of breath first passes through the length of the larger conducting airways of the lung, which do not contribute to gas exchange with the blood, and are collectively referred to as the "serial deadspace", with total volume VD. A proportion of the inspired gas mixture is distributed to, and expired from, a separate alveolar gas compartment which is not in contact with the pulmonary blood, known as

"alveolar deadspace", with volume VDA.

Mixed venous blood from the body tissues arrives at the lung compartment and, after achieving equilibrium with the alveolar gas mixture in the pulmonary capillaries, leaves as pulmonary end-capillary blood. This flow of blood, which engages in gas exchange with the inspired alveolar gas, is the "non-shunt" or "effective pulmonary capillary blood flow" Qc . In addition, mixed venous blood which bypasses the alveolar compartment ("shunt" Qs ) will mix with this pulmonary end-capillary blood to form arterial blood, which travels to the body tissues as the cardiac output (Qt ). A gas species G enters the lung compartment in inspired gas and mixed venous blood, and is removed from it in pulmonary end-capillary blood and expired alveolar gas.

At any time t, the volume of the gas G present in the lung ( V_Q ) is given by

where Veff_G is the effective lung volume, and PA_G is the alveolar partial pressure of G.

Veff_G is determined by the alveolar gas volume (VA) along with the volume of lung tissue (VL) and the solubility of the gas in lung tissue (SL₀ ), and therefore is different for gases of different solubilities. A method for estimating Veff_G is described below, or it can be determined from the capacitance equation (14) below.

Changes in V_G can only occur due to changes in the rate of arrival of the gas G at the alveolar compartment in inspired gas and mixed venous blood and/or its removal in pulmonary end-capillary blood or expired alveolar gas. Thus the rate of change of the dV_G volume of G in the lung ( '-) is given by at

^jt _ PA

= Qc - Cv_G + V_Gι - Qc - S_G - G₁

(6) dt PB

where V_G is the net rate by the patient of uptake of G from, or elimination of G to, an external breathing system ("gas exchange"), with each paired inspiration and expiration ("breath"). A positive value for V_G represents net uptake of G by the lung from the breathing system, and a negative value represents net elimination of G to the breathing system, with any given breath at time t. Cv _G is the fractional content of G in mixed venous blood. S_G is the blood gas partition coefficient of G (Ostwald coefficient, frequently designated by the symbol λ) which reflects the solubility of G in blood, and is known for most inert gases that can be administered to patients, including anaesthetic gases.

Since, from (5)

dV_{Gt =} dPA_{G{ VeffG} dt dt PB

then substituting in (6) and transposing gives:

^dPAo, Veff_G PA_Γ

- - VV₀₀ == QQcc -- CCvv₀₀ -- QQcc .- SS₆₀ --^- (8) dt PB PB

During periods of stability, the terms on the left hand side of equation (8) equal the mass balance of the gas G (net uptake or elimination) at the mouth, and represent uptake or elimination by the body of the gas G. For CO₂, this equals the metabolic production rate of carbon dioxide by the body (V_co t_ody)-

Equation (8) contains three unknowns, Veff_G Cv_G and Qc . The left hand terms are measurable non-invasively if, as stated above (in relation to CO₂), the end-tidal partial pressure ( PE₀ ) is used as a non-invasive approximation for PA₀ . In this case Veff_G includes alveolar deadspace in the lung. Thus:

dt PB ^{G Gbody G} ^ ^G PB

Transposing to solve for the unknown mixed venous term gives

The calibration equation

Equation (10) allows Qc to be determined as follows.

Successive measurements are taken of the relevant variables at two points in time, for example two separate breaths, before and after producing an acute change in V₀ and PE_G' .

This is done by inducing a sudden change in the level of alveolar ventilation of the lungs, where Cv _Q and Qc are assumed to have not changed. It is then possible to determine Qc from two simultaneous equations of the form of equation (10). The determination is simplified with little loss of accuracy if VeJf₀ is assumed to be constant throughout the measurement period.

Specifically, for two breaths i and/ which are sufficiently close in time to one another that CV_Q and Qc are assumed to have not changed,

Therefore

S_G . [PE^< _Gι-Pε^< _Gj]

(12)

Equation (12) is referred to herein as the calibration equation.

The capacitance equation

A number of available methods allow the estimation of Veff_a (as described below) in humans. In addition, Veff_G can be determined, if Qc is known, by transposing Equation (11) to solve for Veff_G :

Veff_G (13)

Equation (13) is referred to herein as the capacitance equation. Veffa is best determined using measured data from the first breath of each half cycle immediately after determining Qc from Equation (12) (i.e., on breaths i+1 anάj+1), at which point dPE_G/dt is greatest.

Note that VeJf₀ is largely independent of Qc when applied at the appropriate time, for the reasons described below, so that the dominant term in the numerator of equation (13) is the first term, representing the measured gas exchange. A mutual solution to equations (12) and (13) is obtained from an iterative method. As described in Sainsbury et al, A reconciliation of continuous and tidal ventilation gas exchange models, Resp Physiol 1997; 108: 89-99, the lung volume can be additionally corrected for deadspace (VD), as follows: ^VeJΪ_G = Veff_G + -(VD + VT) using an assumed VD, typically 1/3 of the VT.

The fractional mixed venous gas content (Cv₀ ) is then determined for breath ? (or/) from equation (10):

Cv a_s = S₀

The continuity equations

Accurate determination of rapidly changing cardiac output with each breath is not possible using equation (12), where the assumption that Qc is constant is not correct. Furthermore, because a change in Qc will induce a change in Cv _Q , Cv _Q cannot be assumed to be constant either. However, it is possible to describe the relationship between both Qc and Cv _Q and measured input parameters, using appropriate mass balance equations. Changes in Qc and Cv _Q from breath to breath can then be determined iteratively.

If measured inputs for a previous breath / have been recorded, and Qc at breath / ( Qc₁ ) has been previously determined, from the calibration equation (12) for example, Qc at a subsequent breath k ( Qc_k ) can be determined as follows.

From equation (10), for breath /:

and for breath k: PE' dPE' Veff_a V_n.

Cv _Gt = S₀ ^■ + ^■ (16)

PB dt Qc_k - PB Qc _k

Combining equations (15) and (16) and transposing to solve for Qc _k in terms of Qc _i gives:

Equation (17) is referred to herein as the continuity equation.

Assuming that uptake or elimination of the gas species G by body tissues is constant from breaths i to k, then Cv_G can be estimated from equations (9) and (10) as:

Equations (17) and (18) are interdependent functions of each other, and can be solved iteratively. The solution gives values for Qc_k and Cv_G, which represent the point of balance in the interdependent relationship between pulmonary blood flow and mixed venous gas content.

This system of equations allows for changes in Qc to be determined on a quasi-continuous breath by breath basis from a series of other terms, all of which can be readily measured non-invasively. VeJf₀ can initially be estimated using one of the alternatives described below. This allows estimation of Qc using the calibration equation (12). VeJf₀ can subsequently be determined using the capacitance equation.

It should be noted that equations (11) to (18) ignore the presence of a difference between PA₀ and PE₀ , which arises from the presence of alveolar deadspace. However, in common with equation (4), and previously described differential Fick methods (Gedeon et al 1980, Capek and Roy, 1988), the capnodynamic method described herein shares the advantage that this difference largely cancels out in the denominator, since

PE_0, - PE₀. * PA₀. - PA₀ .

Measurement of input parameters for equations (11) to (18)

For any given breath, V₀ is the difference in the volume of G inspired ( Vi₀ ) and that expired ( VE₀ ) with each breath, so that

V₀ = VI₀ - VE₀ (19)

Both Vi₀ and VE₀ can be measured in a number of ways. The ideal approach allows immediate measurement with each breath.

Total gas flow rate is measured using a pneumotachograph, or other device for the measurement of gas flow within a hollow tube (such as a differential pressure transducer, hot wire anemometer, turbine anemometer or other device). Gas concentration is measured by sidestream sampling or inline measurement by a rapid gas analyser. Suitable gas analysers include infrared absorption devices, photoacoustic devices, mass spectrometers, paramagnetic devices, Raman scatter analysers or other devices. The volume of the gas G inspired and expired with each breath is obtained by multiplying flow by concentration point by point in time, and integrating the resultant waveform with respect to time. Accuracy is improved by compensating for transport delay (with sidestream sampling) and response time of the gas analyser. For example, if inspiration takes place between times tj and t₂, and expiration between t_∑ and t₃

and

where Vl₁ and V_βt are the measured total gas flow rates at time t during inspiration and expiration respectively. P_Q is the measured partial pressure of G at the point of gas sampling at time t.

Total gas flow measurement can be determined by measuring the concentration of a marker gas M fed into the gas stream at a known flow rate. This is usually an insoluble gas such as nitrogen, argon or sulphur hexafluoride, which is not taken up by the lungs. For example, the expiratory total gas flow rate at time t can be measured from

VE_{I =} ?≡^L . PB (22)

PEM₁ where VE ^ is the known flow rate of the marker gas M, and PEM _t its measured partial pressure at time t. The inspiratory total gas flow rate can be determined from a similar equation.

Improved accuracy of measurement of total gas flow rates, and therefore of V_G , can be obtained if flow and gas concentration are measured at other locations in the breathing system, where tidal variations in gas concentration have been removed by thorough mixing of expired gas prior to sampling (such as by presence of a length of mixing tubing, mixing box, mechanical baffles or agitator, such as a fan, in the breathing circuit). Thus VE₁ can be determined by:

where PEM₁ is the mean partial pressure of M in mixed expired gas. This provides a mean expired flow measurement which may be more stable and accurate than the dynamic tidal flows determined by equations of the form of equation (20) to (22), because rapid signal sampling and more complex data processing can be dispensed with. However this can be expected to dampen the response of the gas exchange measurement to the breath by breath changes in gas exchange preferred for the capnodynamic method. A potentially useful approximation for the volume of expired CO₂ with each breath can be obtained from the delivered tidal volume, adjusted for deadspace, and multiplied by the measured fractional concentration of alveolar CO₂.

Other methods of measurement of gas exchange that are less ideal but possible to employ include volume displacement methods in which the change in volume of a calibrated device such as concertina bag or spirometer is measured over a known time span to obtain net gas uptake from a circuit. These and other methods can be used for the measurement of gas exchange by the lungs. S_G is known for most inert gases that can be administered to patients, including anaesthetic gases. S₀ is a constant but may be modified by patient temperature; however S₀ can be adjusted for this. Values for S₀ for commonly available inert gases suitable for use in patients are set out in Tables 1 and 2 below.

PE_Q' can be measured at the end of each expired breath from a standard expirograph tracing for G. A typical expirograph for CO₂ is shown in Figure 6. The value of PE₀ is taken from a defined point on the plateau of the expirograph waveform, reflecting the end- expired (end-tidal) partial pressure of G. For CO₂, this lies at or near the top of the curve for each breath.

Determination of Veff_Q

Veff_G is determined by the alveolar gas volume (VA) along with the volume of lung tissue ( VL ) and the solubility of the gas in lung tissue ( SL₀ ). It will therefore be different for gases of different solubilities. Determination of Veffa by the capacitance equation has been described above.

Alternative methods for the determination of Veff_G are described below. These may be used, for instance, to initially estimate Veffo prior to its first determination by the capacitance equation.

(i) Determination of Veff_G by estimation from published data

The method described below uses published data (McDonnell and Seal 1991, Brudin et al

1994). However a number of different methods are known and accepted for use to estimate lung volume and can be used with the capnodynamic method described herein. The method is derived from the simplified model of the lung referred to above, i.e., a single compartment consisting of alveolar gas and lung tissue and pulmonary capillary blood in equilibrium with one another. The volume of the alveolar gas is VA and the volume of lung tissue is VL. With each tidal breath, gas enters the compartment during inspiration, and leaves during expiration. The volume of each breath is the "tidal volume" (VT), Mixed venous blood from the body tissues arrives at the compartment, and after achieving equilibrium with the alveolar gas mixture in the pulmonary capillaries, leaves as pulmonary end-capillary blood. This flow of blood, which engages in gas exchange with the inspired alveolar gas, is the "non-shunt" or "effective pulmonary capillary blood flow" Qc . In addition, mixed venous blood that bypasses the alveolar gas compartment ("shunt" Qs ) will mix with this pulmonary end-capillary blood to form arterial blood, which travels to the body tissues as the cardiac output (Qt). A gas species G enters the compartment in inspired gas and mixed venous blood and is removed from it in pulmonary end-capillary blood or expired alveolar gas.

VeJf₀ , the effective volume of distribution of a gas in the lung, is determined by VA , VL and the solubility of the gas in lung tissue ( SL₀). These parameters can be estimated from body height, weight, sex and other patient demographic data and the known solubility of the gas in lung tissue.

SL_CQ , the solubility coefficient of CO₂ in lung tissue has been measured to be approximately 2.7 (Sackner, Khalil and DuBois 1964). The solubility coefficients of various other gases in lung tissue are listed in Tables 1 and 2 below. Where not specifically available, the blood/gas partition coefficient for the gas (S₀) provides a useful approximation of its lung tissue partition coefficient ( SL_G).

Table 1. Approximate values for S₀ (blood gas partition coefficient) and SL_G (lung tissue gas partition coefficient) for commonly available inert gases suitable for use in patients. Values given are at 37⁰C.

Table 2. Approximate values for Sg (the blood gas partition coefficient) and SL_G

(the lung tissue gas partition coefficient) for other inert gases which may be suitable for use in patients. Values given are at 37⁰C.

However, for a gas which is eliminated by the lung, Veff_G is modified by the presence of shunt, which can be significant in anaesthetised or critically ill patients. Those areas of lung that contain shunted blood do not contribute to gas exchange, and therefore do not contribute to the effective volume of distribution of gas, such as CO₂, which diffuses from blood into the alveolar gas compartment.

Veff_G can be estimated for adults as follows. VL, the volume of lung tissue, is typically 0.5 litres, and for simplicity can be assumed to be proportional to body surface area (BSA). However, once again, those areas of lung tissue contained in shunting regions of the lung will not contribute to effective lung volume. So that:

with

Wt - Ht

BSA = (A2) 36

where Wt is the body weight in kg, Ht is the height in metres, and the shunt fraction (Qs I Qt) can be determined as set out further below.

From the data of McDonnell and Seal (McDonnell and Seal 1991) for adults:

M

VA = 0.825 5.18- /ft+ 0.11- -^r -23 -6.24 (A3) 3.34 ^Ht

where M is a modifier for the patient's sex: M is 3.34 for males and 2.86 for females. The scaling factor 0.825 represents the decrease in lung volume that occurs in all patients when anaesthetised (Nunn 1993).

Equation (A3) provides a value for the patient's resting lung volume, but can be augmented further by an adjustment for the tidal volume (Vf). VA is the time weighted mean of the value obtained from equation (A3) and that value can be augmented by VT, as follows:

VA = VA + VT - (I-Έ) (A4)

where LE is the inspiratory to expiratory ratio of each breath, typically 1 :2 or 0.33. VA is further modified by an adjustment (AVA) representing the proportion of alveolar gas volume contained in shunting areas of the lung. This will generally be a small proportion, but can be estimated from the data of Brudin (Brudin et al 1994) which relates the distribution of gas volume to blood volume in the lung. For the sake of simplicity, the distribution of VL is assumed to parallel that of blood volume. Overall VL is roughly 5/6 of the blood volume, so that from Brudin:

AVA - 0.05 - AVA] (A5)

This equation is evaluated iteratively to solve for AVA given the value for VL and shunt fraction, which can be determined as described further below. Finally:

Veff_G = VA - AVA + VL ■ SL₀ (A6)

For CO₂:

Veffco₂ = VA - A VA ₊ VL . SL_COI (Al)

The concentration of gas in the alveolar deadspace is always the same as in the inspired gas mixture, and does not alter in response the changes in alveolar ventilation or gas exchange. However, because PE_G already reflects the volume weighted partial pressures of G from both alveolar and alveolar deadspace compartments, Veff_G is not further reduced in proportion to the alveolar deadspace volume.

Determination of Veff_G by inert gas dilution.

A standard method of measurement of Veff_G is by insoluble inert gas dilution ("washin"). This is used in established methods for measurement of Qc by inert soluble gas uptake, such as acetylene or nitrous oxide rebreathing techniques (Cander and Forster 1959, Petrini et al 1978, Hook et al 1982, Gabrielsen et al 2002). An insoluble gas, which is not absorbed significantly by the blood, is administered simultaneously with the soluble gas. The measured change in concentration of the insoluble gas reflects the dilution of the inspired gas mixture throughout the effective lung volume, enabling the determination of VA. Estimation of VL is also required and this is done by other methods, such as extrapolation of soluble gas concentration change to time zero for the manoeuvre, to indicate uptake by lung tissues, which is assumed to be rapid compared with uptake by the blood.

Such techniques can be applied to estimation of Veff_G , either as an initial "once off or as an intermittent manoeuvre, as part of a continuous cardiac output measurement system, such as the system described herein.

Determination of Shunt Fraction (Qs I Qt) and Mixed Venous Oxygen Saturation

Pulmonary shunt (Qs I Qt) can be determined according to the traditional shunt equation. This determines Qs as a proportion of total pulmonary blood flow Qt , i.e., the shunt

Qs fraction (-^-) , as follows:

where Cc¹^₂ , Ca _Q2 and Cv₀₂ are O₂ fractional contents in "ideal" pulmonary end capillary blood, systemic arterial blood and mixed venous blood, respectively. Cv₀ can be measured invasively from mixed venous blood sampling from a pulmonary artery catheter, which may be equipped with a photometric probe to measure mixed venous O₂ saturation Sv₀ . As a non-invasive alternative, Sv₀ or Cv₀ can be simply assumed or estimated.

Alternatively the shunt fraction can be determined as follows (Peyton et al 2004):

where V₀^ is the measured O₂ uptake by the lungs.

Cc'o and CQ_Q can be determined or measured using minimally invasive methods. Cd '_Q can be determined from "ideal" alveolar O₂ partial pressure ( PA_Q2 ), obtained from the alveolar air equation:

^PAθ₂ = ^Plo₂ -^jτ (AlO)

where PO^_Q2 *^{s tne art}erial CO₂ partial pressure, RQ is the respiratory quotient (the ratio of V_COi to V₀ ), and Pi₀ is the inspired O₂ partial pressure which is routinely measured during anaesthesia. P^₀₂ can also be obtained from other equations, such as the modification of the alveolar air equation of Filley, Macintosh and Wright (Nunn 1993) which allows for the volume effects of uptake of other gases (such as nitrous oxide) during anaesthesia.

Cc¹Q₂ is determined from PΛ₀₂ using one of a number of methods, such as that of Kelman

(Kelman 1966), which incorporate appropriate corrections for patient temperature, pH and CO₂ tension.

- _i nn -8532.2289- f + 2121.401- P² -67.073989 - P³ + P⁴

°^{2 ~ '} 935960.87- 31346.258 • P + 2396.1674 • P² - 67.104406• P³ +P⁴

(Al l) where SA₀ is the percentage saturation of haemoglobin with O₂ and 0.06^1Og₁₀ J-≥ fS±22L.,+0.024-(37-r)+0.4-(7.4-p/0

P= P^₀ 40

⁴O₂ - I ' O^Λ (A12)

Finally,

SA₁ O₂

CcW = - • 1.34 - Hb + 0.003 - PA₀ (A13)

100

Ca_Q can be estimated continuously and non-invasively from Sp₀ obtained from pulse oximetry, using the same equation:

SPo₂ Ca₀₂ = -^f- • 1.34 - Hb+ 0.003 - Pa₀, (A14) 100

As described below, a system for determining cardiac output as described herein can advantageously incorporate a pulse oximeter, with oximetry probe attached to the patient, and/or indwelling arterial oximetry or blood gas probe and processor, alongside a gas analyser, allowing continuous estimation of shunt fraction as described above. Greater accuracy may be obtained from arterial blood gas sampling to directly measure Cag₂ and/or Pa₀₂ .

V₀ can be measured directly by a similar method to that described above for V_G using equations (19) to (23), but is most simply approximated from the measured mean VE₀₀ divided by an assumed value for the respiratory quotient (typically 0.8).

Shunt can also be estimated with less accuracy by other methods (Nunn 1993).

Total pulmonary blood flow Qt (cardiac output) is the sum of Qc and Qs . Continuous measurement of Qt as described above allows continuous estimation of mixed venous O₂ saturation Sv₀ , a useful marker of tissue perfusion and the adequacy of O₂ delivery to the tissues. This is done by transposing the Fick equation for O₂:

Sp₀ ^J2 obtained from pulse oximetry, allows Sa₀ to be non-invasively measured for this purpose.

Use of CO ₂ as the measurement gas G

CO₂ is the preferred gas to measure, since it is present under all physiological conditions, and administration of the gas to the patient is not required. For this reason, the method is referred to as the "capnodynamic" method (the prefix capno refers to CO₂) in the described embodiment, although other expired gases can be used instead, or as well.

Inert gases have the advantage that they obey Henry's law i.e., that the relationship of partial pressure to content in solution in the blood is linear: that is, they have a linear dissociation curve, and the partition coefficient S for these gases is constant. This is not the case for CO₂ which has an alinear dissociation curve in blood which is influenced by a number of physiological factors, including the patient's haemoglobin, temperature, oxygenation and acid-base status. S_co is in fact the slope of the tangent to the solubility curve for CO₂ at the operative point, and obtainable by a number of different methods. The preferred method is described below.

The determination of Qc is simplified with little loss of accuracy if the slope of the CO₂ dissociation curve in blood is treated as uniform across the relatively narrow range of PE_Q ¹ ₀ involved in the measurement cycle, giving S_co a single value in the equation. Since CO₂ is not present in the inspired gas mixture under normal operating conditions, equation (19) is simplified, as Vi _G is zero. This substantially improves the accuracy and precision of gas flow measurement and therefore of the final determination of cardiac output. Therefore, for CO₂:

* CO₂ ~ ^ ^¹CO₂ (24)

equation (12) thus becomes

and equation (13) becomes

\ LPE'_C ^C _O°2₍₊, -PE' ^CO2_{7 +}) J I

Veffco, (26)

and equation (17) becomes

(27)

where ^PE'co_2l Veff_cθ2 . r* - 9 ^P£'∞₂, , ^v∞^j»dyt _ c ^PE'^C°>, _I dt PB ^c°^2>

∞U ^C°2 p_B p_B ^CO> p_B Q_Ck

(28) and

Determination of S_CQ2 :

A preferred method for determining S_COl is described below. However it will be understood that alternative methods can be used.

For the purposes of the method described herein for determining cardiac output, S_COl quantitates the relationship between partial pressure of CO₂ in alveolar gas and the content of CO₂ in end-capillary blood. This relationship is the dissociation curve of CO₂, and is affected by a number of physiological variables. These include the acid base status of the blood, reflected by the pH, Base excess and the plasma bicarbonate concentration (HCO₃ ^"), as well as the blood temperature (T), haemoglobin (Hb) concentration. In addition, the carriage of CO₂ on haemoglobin has an interdependent relationship to the degree of oxygenation of the haemoglobin as measured by the arterial haemoglobin O₂ saturation (SpO₂).

A number of different methods can be used. The one described herein characterizes the dissociation curve of CO₂ across a wide range of partial pressures and in the face of widely varying physiological circumstances.

The independent input variables are as follows:

P_Q0 this is the measured PE_C' _O for a given breath (in mmHg) Spθ₂ measured by routine pulse oximetry (as %) or from an arterial blood gas sample Base excess this reflects the patient's metabolic acid-base balance (in mmole/1) and is measured from an arterial blood gas sample; if this is unavailable it can be assumed to be zero with little loss of accuracy to the determination of cardiac output T measured patient temperature (⁰C), as is routine practice in anaesthesia; if this is unavailable, it can be assumed to be 37⁰C with little loss of accuracy to the determination of cardiac output Hb patient haemoglobin concentration in g/dl; an estimate from a recent blood sample is required.

The Hendersen-Hasselbalch equation

is used to determine arterial blood pH from these input variables in conjunction with the following equations of Siggaard-Andersen (Siggaard- Andersen 1974):

Base excess = [1-0 - 037 - Hb]I(HCO₃ ^' -24 - 41) + (3.71 - Hb + 7 - 7)(pH - 7 - 4)] (A2)

and

ABase excess = 0 • 306 • Hb(I - Sp_Ol ) (Al 6)

These equations are evaluated iteratively to provide a unique value for arterial blood pH for a given P_cc,₂ . The published methods of Kelman (Kelman 1966 & 1967) are then used to determine the fractional content of CO₂ in blood (C_CQ2). S_CU2 is the slope of the CO₂ dissociation curve

at a given point, and is obtained by differentiating Kelman' s equations, as

follows:

(A17)

where

0.0844 + 0.0094 - 7.4]²

(Al 8)

and

\pH

(A19)

and

where

dlO

= log_e10 - [l + 0.00139(38 -r)+ 0.042] - 10^/(p//>r) (A21) dpH

and

f(pH, T)= [l+0.00139(38-7>0.042]- 6.086 + 0.00472 ■ (38-T)- 7.4 • (0.00139(38-r)+0.042)

(A22)

and where

CP = B.0307 + 0.00057 • (37- T)+ 0.00002- (37 -T)²~l P_cθ2 • [l + 10^/(p//>r)]

(A23)

and

dCP dlO f(P^H>^T)

= 10.0307 + 0.00057 • (37 - f)+ 0.00002 • (37 - ff 1 1 + _{l Q}f(pH,T)

' + P₁ CO₇ dR dpH

CO₇

(A24)

Computer processing makes evaluation of these complex equations straightforward and immediate. Other or simpler approaches to the determination of the solubility of CO₂ in blood may be available, and could be alternatively used.

Correction for alveolar-arterial Pco₂ difference:

The use of PE_C' _O in the denominator of equations (24) and (28) ignores the effect of the presence of alveolar deadspace which gives rise to the difference between P^co₂ &ΏUPE_C' O₂ - Accordingly, the value of S_COϊ , ^as determined from Equations (Al 5) to

(A24), will be slightly different for these two variables. While the error this causes in the determined values for cardiac output can be expected to be small, some improvement in accuracy may be possible if PA_QQ2 is estimated. This can be done by measuring the arterial CO₂ partial pressure Pθco₂ which is ^a reasonable approximation of PA_CQ₂ . Pdco₂ can be measured by arterial blood gas sampling, and this can be performed as an initial "once off measurement (since the degree of alveolar deadspace tends to remain fairly constant in an anaesthetised patient), which effectively "calibrates" the method for that patient. This can be repeated intermittently with further sampling, or performed on a continuous basis using continuous arterial blood gas analysis via an indwelling arterial probe specifically designed for the purpose. Such devices and probes for continuous arterial blood gas analysis are currently available and can be integrated into a cardiac output measurement system based on the capnodynamic method described herein.

The use of other gases

Any gas which is administered to the patient other than via inhalation, such as by intravascular injection for example, will obey equations of the form of (24) to (29).

Improved accuracy in the determination of Qc can also result from simultaneous measurement of the parameters described above for two or more gases present in the inspired or expired gas mixtures, and these measured parameters used to evaluate equations (12) to (29). For example, Qc can be determined from uptake of one or more inert anaesthetic gases G and simultaneously determined from the elimination of CO₂. It is also possible to use oxygen (O₂) as the measurement gas G because O₂ uptake (V₀ ) can be measured as described above in a similar manner to any other inspired gas. However, it should be noted that the use of O₂ presents greater difficulties for the determination of Qc by these equations due to the possibility of significant variations in the value of S for O₂ under different physiological conditions. This arises from the fact that O₂ carriage in the blood is almost entirely via its attachment to haemoglobin, and also from the highly alinear shape of the O₂-haemoglobin dissociation curve. A system and method for monitoring cardiac output

As shown in Figure 8, a system for monitoring cardiac output includes a rapid gas analyser 804 (Datex Capnomac Ultima, Datex-Ohmeda, Finland), a gas flow transducer 806 (Validyne Corp, USA), a Fleisch pneumotachograph 808 (Hans Rudolf Corp, USA) (or other gas flow measurement device), including side stream gas concentration sampling port for the gas analyser 804, and a cardiac output monitor 810. As shown in Figure 8, the system is also interconnected with a typical anaesthesia delivery system, including an anaesthesia machine 812, a ventilator 802 (Bear AV, 500, USA), and breathing circuit 813, connected to a common mouthpiece or other gas pathway of the breathing circuit, which is attached to a patient in order to provide gas to lungs 814 of the patient, and to receive exhaled gas from those lungs 814.

The cardiac output monitor 810 executes a method for monitoring cardiac output that determines at least Qc _; the effective pulmonary capillary blood flow of the patient, and preferably also the total cardiac output of the patient, on a quasi-continuous, breath-by- breath basis. In the described embodiment, the cardiac output monitor 810 is a standard computer system such as an Apple 7200 personal computer manufactured by Apple Corporation, and the cardiac output monitoring method is implemented in software. As shown in Figure 10, the computer 810 includes at least one processor 1002, random access memory 1004, at least one input/output interface 1006 for interfacing with the ventilator 802, the gas analyser 804, and the flow transducer 806, a keyboard 1008, a pointing device such as a mouse 1010, and a display 1011. The cardiac output monitor 810 also includes the Labview 4.01 software development application 1012, available from National Instruments, USA, and the cardiac output monitoring method is implemented as one or more software modules developed using the Labview software application 1012, being the cardiac output modules 1014 stored on non-volatile (e.g., hard disk) storage 1016 associated with the computer system 810. However, it will be apparent to those skilled in the art that the various components of the cardiac output monitoring system can be distributed over a variety of locations and in various combinations, and that at least part of the cardiac output monitoring method could alternatively be implemented by one or more dedicated hardware components such as application-specific integrated circuits (ASICs). As shown in Figure 12, in an alternative embodiment, a system for monitoring cardiac output includes a length or loop of deadspace tubing opened to or closed from the breathing circuit by a partial rebreathing valve 1202 whose operation is controlled by the cardiac output monitor 810, via a valve controller 1204. Additionally, the gas analyser 804, gas flow transducer 806, and cardiac output monitor 810 are provided in a single housing or chassis 1206 to provide an integral, stand-alone cardiac output monitoring system that can be attached to any standard anaesthesia delivery system. Although the components 804, 806, and 810 are notionally the same as those in the previous embodiment shown in Figure 8, it will be apparent that when those components are combined within a single chassis 1208, it may alternatively be preferable to select alternative versions of these components to make the integrated stand-alone system more compact and to improve its ergonomics.

In the alternative embodiment shown in Figure 12, the pneumotachograph/gas sampling line 808 is positioned between the patient's lungs 814 and the partial rebreathing valve 1202, and consequently Equation (19) should be used to determine the uptake or elimination of CO₂ because the patient will rebreath a substantial amount of exhaled CO₂ with each inspired breath. However, if the partial rebreathing valve 1202 is alternatively located between the patient's lungs 814 and the pneumotachograph/gas sampling line 808, the simpler Equation (24) can be used because the amount of rebreathed CO₂ will be substantially reduced in this arrangement.

As shown in Figure 8, the cardiac monitor 810 receives gas analysis data from the rapid gas analyser 804, and gas flow data from the flow transducer 806. The cardiac monitor 810 also generates and outputs ventilator control data to control the ventilator 802 and thereby the alveolar ventilation of the patient's lungs 814. However, it will be apparent that alternatively the ventilator could be independently configured to adjust the alveolar ventilation in a predetermined manner, and to provide an output signal to the cardiac monitor 810 to indicate these changes. As shown in Figure 11, the cardiac output monitoring method begins at step 1102 by beginning the cyclic alternation of alveolar ventilation, and the periodic measurement of the partial pressure and volume of the gas species G of interest. Total flow rates are measured by the flow transducer 806, which generates gas flow data and sends that data to the cardiac monitor 810. The gas breathed by the patient is analysed by the rapid gas analyser 804, which generates gas analysis data, and sends that data to the cardiac monitor 810 for processing. The gas flow data and the gas analysis data are generated and sent to the cardiac monitor 810 in real-time on a breath by breath basis. At step 1104, the cardiac output monitor processes the gas analysis data to determine the partial pressure of the gas species G of interest (typically CO₂), and compares the partial pressure data for the current half cycle of ventilation with the previous half cycle. At step 1106, a test is performed to determine whether the pattern of cyclic change in partial pressure appears to be stable, which would indicate that the effective pulmonary capillary blood flow is also stable. If this is the case, then at the last breath of the current half-cycle, Qc is determined using the calibration equation at step 1108. Since the current half-cycle is now complete, at step 1110, the next half-cycle is commenced by changing the level of alveolar ventilation. At the first breath of the new half-cycle, the effective lung volume of gas species G is determined using the capacitance equation at step 1112. As described above, the determination of Veffn ^ιs performed at this point to produce the most accurate value.

Having determined a calibrated value for Qc and an updated value of Veffc ^^e continuity equation is now used at each breath in the current half-cycle to determine updated values for Qc for each breath at step 1114. Following the last breath of the half-cycle, the process returns to step 1104 to assess whether Qc is stable, as described above. A calibrated value of Qc is only determined when Qc is stable.

By executing the above steps, the system determines the effective pulmonary capillary blood flow of the patient on a quasi-continuous, breath-by-breath basis. Preferably, the system also determines the shunt blood flow as described above, and adds the two values together to obtain updated values for the total cardiac output of the patient. These values are continually updated and displayed on the system monitor 1011 to allow medical or nursing staff to non-invasively monitor the patient's cardiac output during surgery, critical care, and other related procedures.

The acute changes in V_G and PE₀ are produced by inducing sudden changes in the level of alveolar ventilation of the lungs on a continuous basis. This can be achieved in a number of ways. In patients who are undergoing controlled ventilation by an automated ventilator, such as patients under anaesthesia or in intensive care, a stepwise change can be made in the tidal volume, as shown in Figure 1. Alternative approaches are to alternate respiratory rate (either by alternating overall rate, I:E (inspiratory to expiratory) ratio or the duration of end-expiratory pause, or similar mechanism). These methods will generally require automated control of an electronic ventilator, as shown in the embodiment of Figure 8.

However, the alternative embodiment of the cardiac output monitoring system shown in Figure 12 produces changes in the level of the alveolar ventilation by intermittently introducing a volume of serial deadspace into the breathing system, by opening and closing a partial rebreathing valve 1202 attached to a length or loop of deadspace tubing. By altering VD, the level of alveolar ventilation is altered in the opposite direction. This method can be used in patients who are not undergoing controlled ventilation, but are breathing spontaneously. It is also possible, although less practical, to produce the acute change in V₀ and PE₀ by means other than altering alveolar ventilation, e.g., by intermittently adding a gas species G (CO₂ or other gas) to the inspired gas mixture to alter its inspired concentration, in which case equations of the form of (11) to (18) will apply instead.

Where cyclic changes in alveolar ventilation are carried out in a continuing fashion, the method inevitably introduces fluctuations in Cv _QQ produced by the fluctuations induced in alveolar ventilation, but seeks to minimise the effect of these fluctuations. This can be achieved by continuing alternation of alveolar ventilation at the highest frequency that nevertheless provides accurate results. While a persistent change in alveolar ventilation produces a persistent change in PE_C' _Q2 and Cv Co, _? brief changes produce smaller fluctuations. Furthermore, the amplitude of the fluctuation in Cv _Q0 is damped by the passage of blood through the various vascular beds of the body. It follows that Cv _QQ will remain more stable and there will be a reduction of the error in the determined value of Qc if frequent alternation of the level of alveolar ventilation is performed.

The cyclic alternation of alveolar minute ventilation between higher and lower levels is repeated on an ongoing basis for as long as cardiac output monitoring is required. This permits ongoing recalibration using the calibration equation as frequently as possible, provided that cardiac output and lung gas exchange are sufficiently stable (see timing considerations, below). The higher and lower levels of alveolar ventilation are each considered to constitute a half cycle of the cyclic ventilation.

By way of example, a stepwise change can be made in the alveolar ventilation level and maintained at that level for 6 breaths (half cycle), and then return to the previous level and maintained at that level for a further 6 breaths. The total cycle length is therefore 12 breaths, but this can be varied to more or less.

The duration of each half cycle is limited by the magnitude of the change in CV_Q induced by each change. A persistent change in CV_Q will produce progressively increasing errors in the values determined by both the calibration and continuity equations. In contrast, brief changes are expected to cause smaller fluctuations in Cv _Q , but if too brief (fewer than 3 breaths or so), are likely to degrade the accuracy of the calibration equation.

Magnitude of the change in alveolar ventilation

The change in the alveolar ventilation is typically of the order of 50% or so (e.g., cyclic changes in tidal volume, or in the volume of serial deadspace in the breathing system, of 20OmL or so, or changes in respiratory rate of 5 breaths/min) although smaller or larger relative changes can be used. The larger the change, the greater the acute change in the variables measured to determine cardiac output ( V_G and PE_G ). Improved accuracy and precision of the determined cardiac output are expected from this, although practical limitations apply to the size of the tidal volumes or breath to breath intervals that can be used safely in a patient.

Overall, the mean value of alveolar ventilation (midway between high and low levels) is preferably such that the overall minute ventilation remains at the desired level for the patient.

dPE_c'

Estimation of dt

The rate of change of P Ej₃ ) can be estimated from the measured change of PE_G'

over a series of 3 breaths whose duration is measured by a timer. The pattern of change over the 3 breaths can be analysed using an appropriate least squares analysis technique, and assuming that the change follows an exponential washin/washout pattern, to obtain the

approximate slope of the tangent to the exponential curve, which is — . The dt determination of Qc is necessarily delayed by 2 breaths if this is done. Simpler alternatives which avoid this delay may possibly be used with little loss of accuracy, such as taking a simple linear measurement of the change in PE_G between the current breath and the previous breath, with or without an appropriate modifier. Other alternatives include employment of system identification methods such as those described in standard texts (Ljung 1999).

The present invention will now be described further with reference to the following non- limiting examples. Example 1

Figures 1 to 5 show typical data for the time course of changes in CO₂ elimination by the lungs for one measurement cycle. The data was generated from a computer model of tidal gas exchange which incorporates realistic physiological distributions of ventilation and blood flow in the lung, giving typical values for pulmonary shunt and deadspace. Values for independent input variables were nominated which were typical for a ventilated patient. The resting alveolar lung volume VA was 2.0 L, and lung tissue volume VL was 0.6 L. From the data of Sackner (Sackner et al, 1964), the solubility coefficient of CO₂ in lung tissue ( SL_CQ2) was taken to be 2.7. Tidal volume alternated between 400 and 600 mL/min at a rate of 10 breaths/min. Cardiac output was 5.0 L/min. Mean CO₂ production by the body was approximately 140 mL/min. Shunt Qs was approximately 10% of the cardiac output. To represent realistic levels of measurement imprecision for measured parameters, a random noise function with specified standard deviation was superimposed on the output data.

Figure 1 shows the measured expired tidal volume VE with each breath. The first 6 breaths of the half cycle (numbered 1 to 6) are at 400 mL tidal volume. The next 6 breaths are at 600 mL, completing one measurement cycle.

Figure 2 shows the corresponding VE₀₀ values, Figure 3 the corresponding PE_C' _O values, dPE_C' ₀ and Figure 4 the corresponding values. dt

dPεc' o It can be seen that is significant in the continuity equation in the first few breaths dt of each half cycle. The times at which the effective lung volume for CO₂ (Veff_co ) can be determined are indicated. Timing of the equations

The calibration equation (equation (12) for inspired gas G, or equation (25) for CO₂):

Because the calibration equation is only valid if Qc is unchanging, the calibration equation is only used to determine Qc if certain conditions are fulfilled, which indicate that Qc is stable. A first condition is that PE₀ for each breath remains stable within set limits (typically 0.5 mmHg for CO₂) for a given number of breaths or duration of time (typically over 10-12 breaths or approximately 1 minute). The second condition is that, where cyclic alteration in alveolar ventilation is carried out in a continuing fashion, which will produce cyclic fluctuations in PE₀ , as illustrated in Figure 3, the pattern of change in measured PE_Q' within each half cycle is similar to that of the preceding half cycle. This is determined by comparing the shape of the curve PE₀ versus breath (see Figure 3) for each half cycle. To facilitate this comparison, the curve for the current half cycle can be inverted and normalised at its first breath to match that from the preceding half cycle. Alternatively, the curve for the current half cycle can be compared to the corresponding half cycle of the previous cycle. Stability in other indirect indicators of in cardiac output, such as blood pressure and V₀ measurement, can also be evaluated as well.

If these conditions are fulfilled, the calibration equation is used, to determine Qc . Where cyclic alteration in alveolar ventilation is carried out in a continuing fashion, this is done at the end of the current half cycle. Where ventilation has been stable, a cycle of alteration in alveolar ventilation is initiated first. For the calibration equation, breath i is at the end of the previous half cycle, and breath j at the end of the current half cycle. To improve the dPε' reliability (precision) of the measurement, PE₀ , V_G and — can be averaged over the

(Al last 3 breaths of each half cycle, as indicated in Figures 2 and 3.

The use of the calibration equation as described above provides a measurement of Qc that

is less dependent on effective lung volume Veff_a because — approaches zero at this dPEr' point in the half cycle. If — is negligible, the calibration equation becomes largely dt independent of Veff_G . In this circumstance, it becomes similar to equation (4). However, washout of soluble gas from the lung is generally incomplete after only several breaths, dPε¹ and ignoring — may cause the resulting value of Qc to be significantly in error (Yem dt et al).

The capacitance equation (equation (13) for inspired gas G, or equation (26) for CO ₂): The capacitance equation is used to determine Veff_G at the start of each half cycle, on the breath immediately following of the last breath of the previous half cycle that was used to determine Qc from the calibration equation, assuming that Qc has not significantly changed between these successive breaths. For the capacitance equation, breath i+1 is the first breath of the previous half cycle, and breath 7+ 7 the first breath of the current half dPε' cycle, since washin or washout of G is fastest and therefore — [_s greatest at this point, dt as shown in Figure 4. Additionally, VeJf₀ is relatively insensitive to Qc at this point, since the difference between Pε_G at breaths /+/ and 7+ 7 tends to be relatively small, and the dominant term in the numerator of equation (12) is the term containing the measured V_co .

To improve the reliability (precision) of the value determined for VeJf₀ , the measured

parameters PE_G , V₀ and — can be averaged over the first one or two breaths of each dt half cycle. Since VeJf₀ is a relatively stable physiological variable, a moving average of individual determinations of VeJf₀ can be made to improve its accuracy and precision.

The continuity equation (equation (17) for inspired gas G, or equation (27) for CO 2): For each breath k within the current half cycle, the continuity equation is used to determine Qc for that breath (Qc _k). Qc_k is determined from the measured parameters for breath k and from Qc₁ and the measured parameters for breath i. Breath / can be any recent breath corresponding to when Qc was determined. Although the previous value of Qc is described herein as being determined by use of the calibration equation, it will be apparent that the value of Qc₁ could alternatively be determined using any method.

Smoothing functions:

To reduce the effects of random measurement imprecision on Qc_k , a moving average of Qc_k can be used. Firstly, Qc_k is averaged with the value from the identical point of the previous half cycle. Secondly, the last 3-6 such values are averaged. This process has the effect of delaying the responsiveness of the system to real-time changes in cardiac output, but provides substantially more stable results. Technical improvements in measurement of input parameters which reduce random measurement imprecision may allow shorter averaging or none at all, thereby improving the real-time responsiveness of the system.

Determination of Qt (cardiac output) from Qc : To determine total pulmonary blood flow Qt (cardiac output), the additional unmeasured pulmonary shunt blood flow (Qs) is estimated. Shunt blood flow is by definition that proportion of total pulmonary blood flow which does not engage in gas exchange with alveolar gas and so is not measured by techniques based upon lung gas exchange measurement. As described above, lung shunt flow can be estimated by any one of a number of methods. Total pulmonary blood flow Qt (cardiac output) is the sum of Qc and Qs .

Figure 5 shows the determined cardiac output Qt for the measurement period. The breaths at which the calibration equation was evaluated are indicated (the end of each half cycle). The continuity equation was evaluated at all other breaths.

Figure 6 shows the simulated patient's capnography tracing over the measurement period. This is the expirogram for CO₂ partial pressure ( P_cc,₂ ) measured at the level of the endotracheal tube in a ventilated patient. It shows the fluctuation in P_co in real-time within each breath and from breath to breath and is a standard monitoring method for anaesthetised patients. It can be seen that the fluctuations in the end-tidal point ( PE_C' _Q2 ) caused by the alternating tidal volume are only apparent upon close inspection. Any disturbance to the patient's normal cardio-respiratory function induced by the ventilatory manoeuvre will be negligible.

Example 2

Data was collected from the same computer model described above to monitor the accuracy of the continuity equation and the calibration equation in real-time following a simulated sudden change in actual cardiac output. The simulated Qt ("target Qt ") was halved over the space of 3 breaths from 5.0 L/min to 2.5 L/min. The results are shown in Figure 7.

The calibration equation was evaluated at the end of each half cycle and the resulting values are shown ("calibration eq"). The continuity equation was evaluated with each breath. Both the raw Qt determined from the continuity equation ("continuity eq") and with 6 breath averaging ("continuity eq averaged") are shown.

It can be seen from Figure 7 that, during the period of change in Qt , the calibration equation gives unpredictable and unrealistic results. In fact, negative values for Qt often result, a physiological impossibility. During this brief period of instability, the calibration equation should not be used. In contrast, the continuity equation follows the , Qt well in

real time. The averaging function and the method described above for determining — dt imposed a delay in its response of roughly half a minute in this example.

The advantages of using the continuity equation are clear, as it can provide immediate and accurate warning of a clinically important change in actual cardiac output. Exampϊe 3

Quasi-continuous determinations of cardiac output were made by the capnodynamic method using the cardiac output monitoring system described above. These values were compared breath by breath with simultaneous measurements by an indwelling ultrasonic flow probe in six ventilated sheep, ranging in weight from 35-45 kg, anaesthetised with isoflurane in oxygen-air.

An ascending aortic flow probe was used in four of the animals, while a pulmonary artery probe was used with the remaining two sheep. Cardiac output was manipulated using a dobutamine infusion alternating with esmolol boluses. Qc determined by the capnodynamic method was adjusted by estimation of shunt fraction by pulse oximetry to obtain systemic cardiac output (Qt). Mean difference and standard deviation [sd] of the difference between capnodynamic and aortic flow probe measurements were determined for (i) Qt with each breath; and (ii) changes in Qt between successive 60 sec periods.

Results: The Indwelling flow probe Qt varied between zero and 9.4 L/min (mean 3.5

L/min). Overall mean bias for Qt (capnodynamic - aortic flow probe) was + 0.24 L/min [95% confidence limits: + 0.04 L/min]. The standard deviation of the difference was 1.26 L/min, giving upper and lower limits of agreement of + 2.7 and — 2.2 L/min.

Mean bias for changes in Qt over 60 second intervals was + 0.01 L/min, with a standard deviation of the difference of 0.62 L/min. Two cardiac arrest events in one animal were clearly identifiable by the capnodynamic method within 30-60 seconds of occurrence, as shown in Figure 11.

From the results of the above experiments, it was concluded that the cardiac output monitoring system had successfully tracked sudden dramatic fluctuations in cardiac output in real time in an animal model. The mean bias found is probably explained by coronary blood flow not measured by the aortic flow probe.

Many modifications will be apparent to those skilled in the art without departing from the scope of the present invention as herein described with reference to the accompanying drawings.

References

Brudin LH, Rhodes CG, Valind SO, Jones T, Jonson B and Hughes JMB. Relationships between regional ventilation and vascular and extravascular volume in supine humans. J Appl Physiol. 76(3): 1195-1204, 1994

Brudin LH, Rhodes CG, Valind SO, Jones T, and Hughes JMB. Interrelationships between regional blood flow, blood volume and ventilation in supine humans. J Appl Physiol. 76(3): 1195-1204, 1994

Cander L, Forster RE. Determination of pulmonary parenchymal tissue volume and pulmonary capillary blood flow in man. J Appl Physiol. 1959; 14(4): 541-551.

Capek, J. M. and R.J. Roy. Noninvasive Measurement of Cardiac Output During Partial CO₂ Rebreathing. IEEE Transactions on Biomedical Engineering. 35: 653-61, 1988.

Capek, J. M. and RJ. Roy. Encyclopedia of Medical Devices and Instrumentation. J. G. Webster Ed. Wiley, N.Y. 1988. pp. 1309-10.

Defares JG. Determination of Pvco₂ From the exponential CO₂ Rise During Rebreathing. J. Appl. Physiol. 1958; 13(2): 159-64.

Gabrielsen A, Videbaek R, Schou M, Damgaard M, Kastrup J, Norsk P. Non-invasive measurement of cardiac output in heart failure patients using a new foreign gas rebreathing technique. Clinical Science. 2002; 102: 247-52.

Gedeon A, Forslund L, Hedenstierna G and Romano E. A new method for non-invasive bedside determination of pulmonary blood flow. Med Biol Eng Comput. 18: 411-8, 1980.

Hook C, Meyer M. Pulmonary blood flow, diffusing capacity and tissue volume by rebreathing: theory. Respir. Physiol. 1982; 48: 255-279. Kelman, G.R. Digital computer subroutine for the conversion of oxygen tension into saturation. J. Appl. Physiol 21(4): 1375-1376, 1966.

Kelman, G.R. Digital computer procedure for the conversion of PCO₂ into blood CO₂ content. Respir. Physiol. 3: 111-115, 1967.

Kim TS, Rahn H, Farhi LE. Estimation of true venous and arterial PCO₂ by gas analysis of a single breath. J. Appl. Physiol 21(4): 1338-44, 1966.

Ljung, L. System Identification - Theory For the User 2e, PTR Prentice Hall, Upper Saddle River, NJ. 1999.

McDonnell WF and Seal E. Relationships between lung function and physical characteristics in young adult black and white males and females. Eur respir J. 4: 279-89, 1991.

Nunn J. Nunn's Applied Respiratory Physiology, 4th Edition, Butterworth-Heinemann, 1993, pp 196-7.

Petrini MF, Peterson BT, Hyde RW. Lung tissue volume and blood flow by rebreathing: theory. J Appl Physiol 44: 795-802, 1978.

Peyton PJ, Robinson GJB, McCaIl PR and Thompson B. Non-invasive measurement of intrapulmonary shunting. J Cardiothoracic Vase Anesth. 2004

Robinson GJB, Peyton PJ, Vartuli GM, Burfoot RB, Junor PA. Continuous Measurement of Cardiac Output by Inert Gas Throughflow - Comparison with Thermodilution. J. Cardiothorac. Vase. Anesth. 2003; 17(2):204-10.

Russell AE, Smith SA, West MJ, Aylward PE, McRitchie RJ, Hassam RM, Minson RB, Wing LMH and Chalmers JP. Automated non-invasive measurement of cardiac output by the carbon dioxide rebreathing method: comparisons with dye dilution and thermodilution. Br. Heart J. 63:195-9, 1990.

Sackner MA, Khalil AF and DuBois AB. Determination of tissue volume and carbon ioxide dissociation slope of the lungs in man. JAppl Physiol. 19(3): 374-80, 1964.

Sainsbury MC, Lorenzi A, Williams EM, Hahn CEW. A reconciliation of continuous and tidal ventilation gas exchange models, Resp Physiol 1997; 108: 89-99.

Siggaard- Andersen, O. The Acid-Base Status of the Blood, 4th edition. Copenhagen, Munksgaard Publishers. 1974, pp 51, 63.

Yem JS, Tang Y, Turner MJ and Baker AB. Sources of Error in Noninvasive Pulmonary Blood Flow Measurements by Partial Rebreathing. Anesthesiology 2003; 98:881-7.

Claims

THE CLAIMS:

1. A method for monitoring cardiac output of a subject, the method including: determining an effective pulmonary capillary blood flow of said subject at a first time on the basis of an effective pulmonary capillary blood flow of said patient at an earlier time, pulmonary uptake or elimination of a breathed gas species by said subject at said first time and said earlier time, partial pressures of said gas species in lungs of said subject at said first time and said earlier time, and a solubility of said gas species in blood of said subject.

2. A method according to claim 1 including measuring said net rates of pulmonary uptake or elimination of said gas species Q of respective breaths of said subject and said partial pressures substantially at the end-tidal point of respective breaths of said subject.

3. A method according to any one of claims 1 to 2 including performing said step of determining at successive breaths of said subject to provide breath-by-breath monitoring of said effective pulmonary capillary blood flow of said subject.

4. A method according to any one of claims 1 to 3 including determining cardiac output of said subject at said first time by adding shunt blood flow of said subject to said effective pulmonary capillary blood flow.

5. A method according to any one of claims 1 to 4 including measuring rates of change of alveolar partial pressures of said gas species at each of said first time and said earlier time.

6. A method according to claim 1 wherein said step of determining includes determining (Qc _k ) , the effective pulmonary capillary blood flow for a breath k, according to:

where V₀. and V_{0 k} are the net rates of pulmonary uptake or elimination of said gas species

G at breaths i and k, respectively Qc₁ is the effective pulmonary capillary blood flow for an earlier breath /, Cv₀ and Cv_G, are the mixed venous gas contents at breaths k and

i, PE' _Gt and P£'_G are the alveolar (end-tidal) partial pressures of gas species G at breaths k and /, PB is barometric pressure, Veffa is an effective lung volume of gas species G, S_G is a partition coefficient for said gas species G in blood of said subject, and dPE'oj/dt and dPEO_k/dt are the rates of change of said partial pressures between successive breaths at the times of breaths / and k, respectively.

7. A method according to any one of claims 1 to 6, said method further including determining said effective pulmonary capillary blood flow of said patient at said earlier time on the basis of partial pressures of said gas species at respective breaths of said subject, rates of change of said partial pressures at said respective breaths, net uptakes or eliminations of said gas species in lungs of said subject at said respective breaths, a solubility of said gas species in blood of said subject, and an effective lung volume of said patient for said gas species; wherein an alveolar ventilation of said subject at an initial breath of said respective breaths is substantially different from an alveolar ventilation of said subject at a subsequent breath of said respective breaths.

8. A method according to any one of claims 1 to 7 wherein alveolar ventilation of said subject is repeatedly alternated between a first level of alveolar ventilation maintained for a plurality of breaths, and a second level of alveolar ventilation maintained for a plurality of breaths.

9. A method according to any one of claims 1 to 8, said method including determining said effective lung volume of said subject for said gas species on the basis of an effective pulmonary capillary blood flow of said patient, a solubility of said gas species in blood of said subject, rates of changes in alveolar partial pressures of said gas species in lungs of said patient at respective times, and net uptakes or eliminations of said gas species in lungs of said subject at respective times.

10. A method according to any one of claims 1 to 9 wherein said effective lung volume is determined at one or more first breaths of a plurality of breaths at a changed level of alveolar ventilation.

11. A method according to any one of claims 1 to 10 including repeatedly performing said step of determining said effective lung volume at a plurality of breaths of said subject.

12. A method according to any one of claims 1 to 11 wherein said first level of alveolar ventilation constitutes a first half-cycle of a cyclic alternation of alveolar ventilation, said second level of alveolar ventilation constituting a second half-cycle of said cyclic alternation of alveolar ventilation; and the method further includes:

(iv) performing, for one or more last breaths of said first half-cycle of alveolar ventilation, said step of determining said effective pulmonary capillary blood flow of said patient at said earlier time to determine a first effective pulmonary capillary blood flow;

(v) performing said step of determining said effective lung volume of said subject for one or more first breaths of one of said half-cycles of alveolar ventilation; and

(vi) performing, at each remaining breath of said second half-cycles, said step of determining said effective pulmonary capillary blood flow on the basis of said first effective pulmonary capillary blood flow.

13. A method according to claim 12 including repeating steps (i) to (iii) to provide breath-by-breath monitoring of said effective pulmonary capillary blood flow.

14. A method according to claims 1 to 13 including determining a cardiac output of said subject on the basis of said effective pulmonary capillary blood flow to provide breath-by-breath monitoring of said cardiac output of said subject.

15. A method according to any one of claims 1 to 14 wherein the method is executed by a computer system having means for receiving gas species and gas flow data representing constituents, pressures and flow rates of gas inhaled and exhaled by said subject at said first time and said earlier time; and means for processing said gas species data to determine said effective pulmonary capillary blood flow of said subject at said first time.

16. A method according to any one of claims 1 to 15 wherein the gas species is CO₂.

17. A method according to any one of claims 1 to 16 wherein the subject is human.

18. A system for monitoring cardiac output of a subject, the system having components for executing the steps of any one of the methods of claims 1 to 17.

19. A computer-readable storage medium having stored therein program instructions for executing the steps of any one of the methods of claims 1 to 17.

20. A system for monitoring cardiac output of a subject, including: means for receiving gas species and flow data representing constituents, pressures and flow rates of gas inhaled and exhaled by said subject at a first time and an earlier time; and means for processing said gas species and flow data and solubility data representing a solubility of said gas species in blood of said subject to determine an effective pulmonary capillary blood flow of said subject at said first time; wherein said effective pulmonary capillary blood flow of said subject at said first time is determined on the basis of an effective pulmonary capillary blood flow of said patient at said earlier time, pulmonary uptake or elimination of said breathed gas species by said subject at said first time and said earlier time, partial pressures of said gas species in lungs of said subject at said first time and said earlier time, and said solubility of said gas species in blood of said subject.

21. A system according to claim 18 or 20, including means for cyclically alternating alveolar ventilation of said subject between a first level of alveolar ventilation maintained for a plurality of breaths, and a second level of alveolar ventilation maintained for a plurality of breaths.

22. A system according to claim 18 or claim 19 further including a gas analyser for analysing gas breathed by said subject; and a flow device for determining flow of said gas breathed by said subject.

23. A method for determining the effective pulmonary capillary blood flow in a subject including:

determining the effective pulmonary capillary blood flow, (Q^c), the pulmonary uptake or elimination of a gas species G, (VG ) , and the alveolar (end-tidal) partial pressure of gas G (PE a) for a breath "/";

determining the pulmonary uptake or elimination of gas species G, the alveolar partial pressure of gas G for a subsequent breath "k"; and

determining the effective pulmonary blood flow for breath k (Qc _k) according to a "continuity equation"

where PB is barometric pressure, Veffa is effective lung volume of gas G, and So is the solubility of gas G in blood.

24. A method for determining the effective pulmonary capillary blood flow in a subject including:

determining the effective pulmonary capillary blood flow, ( Q^c ), the pulmonary uptake or elimination of a gas species G, (FG ) , and the alveolar (end-tidal) partial pressure of gas G (PE'a) for a breath "/";

determining the pulmonary uptake or elimination of gas species G, the alveolar partial pressure of gas G for a subsequent breath "&"; and

where pβ is barometric pressure, Veffa is effective lung volume of gas G, and SQ is the solubility of gas G in blood,

Cv ^" PB G₁

G_k = S_r G S_r. ^■ + - dt

and

25. A method for measuring the effective pulmonary capillary blood flow in a subject including:

providing constant alveolar ventilation to the subject for a plurality of breaths;

determining the pulmonary uptake or elimination of a gas species G (^G ), and the alveolar

(end-tidal) partial pressure of gas G (^^E'G ) at a breath "i" during said period of constant alveolar ventilation;

determining the pulmonary uptake or elimination of gas G and, the alveolar partial pressure of gas G, at a subsequent contemporaneous breath "j"

determining the effective pulmonary blood flow Q^c according to a calibration equation:

determining the pulmonary uptake or elimination of gas species G and the alveolar partial pressure of gas G for a subsequent breath "&"; and

determining the effective pulmonary blood flow for breath k (Qc^) according to a continuity equation

where Qc_t = Qc .

26. A method according to claim 24 or claim 25 including the step of determining effective lung volume (Veffo) according to a capacitance equation:

27. A system for measuring effective pulmonary capillary blood flow in a subject, including: one or more breathing systems for ventilating lungs of the subject;

a rapid gas analyser and gas flow measuring device to allow measurement of alveolar (end- tidal) partial pressure and pulmonary uptake or elimination of a gas species G;

a data processor with inputs to receive data from the rapid gas analyser and gas flow measuring device, said processor being configured to determine Qc from gas species data received relating to a breath i taken at alveolar ventilation level / and a breath j taken at alveolar ventilation level j, levels / andy representing ventilation levels before and after an adjustment respectively, the determination being made according to a calibration equation:

and wherein the processor is further configured to use the value of Q^c determined from the calibration equation (Q^ci) and data received relating to a breath k, to determine the effective pulmonary capillary blood flow for breath k according to a continuity equation:

where PB is barometric pressure, Veffo is effective lung volume of gas G, and S_G is a solubility of gas G in blood; and

means for communicating to an operator of the system at least an indication of at least one of effective pulmonary capillary blood flow and cardiac output for breath k.

28. A system according to claim 27 wherein the processor is configured to perform one or more data averaging or smoothing functions to determine the Qc or Qt of the subject.